ESIS's blog
https://imechanica.org/blog/23810
enDiscussion of fracture paper #25 - The role of the fracture process region
https://imechanica.org/node/23886
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The subject of this blog is a fracture mechanical study of soft polymers. It is well written and technically detailed which makes the reading a good investment. The paper is:</p>
<p><a href="https://www.sciencedirect.com/science/article/pii/S0013794417310548" target="_blank" rel="noopener noreferrer">"Experimental and numerical assessment of the work of fracture in injection-moulded low-density polyethylene" by Martin Kroon, Eskil Andreasson, Viktor Petersson, Pär A.T. Olsson in Engineering Fracture Mechanics 192 (2018) 1–11.</a></p>
<p>As the title says, it is about the fracture mechanical properties of a group of polymers. The basic idea is to identify the energy release rate that is required to initiate crack growth. To distinguish between the energy required for creating crack and the energy dissipated in the surrounding continuum, the former is defined as the unstable material which has passed its largest load carrying capacity, and the remaining is the stable elastic plastic continuum. The energy required for creating crack surface is supposed to be independent of the scale of yielding.</p>
<p>The authors call it the essential work of fracture, as I believe was coined by Mai and Cotterell. If not the same, then this is very close to the energy dissipation in the fracture process region, as suggested by Barenblatt, and used by many others. Material instability could, of course also be the result of void or crack nucleation at irregularities of one kind or another outside the process region. How much should be included as essential work or not, could be discussed. I guess it depends on if it is a necessary requirement for fracture. The fact that it may both support and be an impediment to fracture does not make it less complicated. In the paper an FE model is successfully used to calculate the global energy release rate vis à vis the local unstable energy release in the fracture process region, modelled as a cohesive zone.</p>
<p>What captured my interest was the proposed two parameter cohesive zone model and its expected autonomy. With one parameter, whatever happens in the process region is determined by, e.g., K, J, G. The single parameter autonomy has its limits but more parameters can add more details and extend the autonomy and applicability. For the proposed cohesive zone, the most important parameter is the work of fracture. A second parameter is a critical stress that marks the onset of the fracture processes. In the model the critical stress is found at the tip of the cohesive zone. By using the model of the process region, the effect of different extents of plastic deformations is accounted for through the numerical calculation of the surrounding elastic plastic continuum.</p>
<p>The work of fracture is proportional to the product of the critical stress and the critical separation of the cohesive zone surfaces. The importance of the cohesive zone is that it provides a length scale. Without it, the process region would be represented by a point, the crack tip, with the consequence that the elastic plastic material during crack growth consumes all released energy. Nothing is let through to the crack tip.</p>
<p>Stationary cracks are surrounded by a crack tip field that releases energy to fracture process regions that may be small or even a singular point. If the crack is growing at steady-state very little is let through to a small fracture process region and to a singular point, nothing. In conventional thinking a large cohesive stress leads to a short cohesive zone, and by that, the available energy would be less. A variation of the critical stress is discussed in the paper. Presently, however, the two parameter model is more of a one parameter ditto, where the cohesive stress is selected just as sufficiently plausible. </p>
<p>What could be done to nail the most suitable critical cohesive stress? With the present range of crack length and initiation of crack growth nothing is needed. The obtained constant energy release rate fits the experimental result perfectly. Further, it is difficult to find any good reason for why the excellent result would not hold also for larger cracks. As opposed to that, small, very small or no crack at all should give crack initiation and growth at a remote stress that is close to the critical cohesive stress. As the limit result of a vanishing crack, the two stresses should be identical. I am not sure about the present polymer but in many metals the growing plastic wake requires significant increase of the remote load. Often several times rather than percentages. So letting the crack grow at least a few times the linear extent of the plastic zone, would add on requirements that may be used to optimise both cohesive parameters. </p>
<p>I really enjoyed reading this interesting paper. I understand that the paper is about initiation of crack growth which is excellent, but in view of the free critical cohesive stress, I wonder if the model can be extended to include very small cracks or the behaviour from initiation of crack growth to an approximate steady-state. It would be interesting if anyone would like to discuss or provide a comment or a thought, regarding the paper, the method, the autonomy, or anything related. The authors themselves perhaps.</p>
<p>Per Ståhle</p>
</div></div></div>Sun, 05 Jan 2020 17:25:11 +0000ESIS23886 at https://imechanica.orghttps://imechanica.org/node/23886#commentshttps://imechanica.org/crss/node/23886Discussion of fracture paper #24 - The sound of crack growth
https://imechanica.org/node/23731
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Carbon fibre reinforced polymers combines desired features from different worlds. The fibres are stiff and hard, while the polymers are the opposite, weak, soft and with irrelevant fracture toughness. Irrelevant considering the small in-plane deformation that the fibres can handle before they break. It is not totally surprising that one can make composites that display the best properties from each material. Perhaps less obvious or even surprising is that materials and composition can be designed to make the composite properties go beyond what the constituent materials are even near. A well-known example is the ordinary aluminium foil for household use that is laminated with a polymer film with similar thickness. The laminate gets a toughness that is several times that of the aluminium foil even though the over all strains are so small that the polymer hardly can carry any significant load. </p>
<p>In search of something recent on laminate composites, I came across a very interesting paper on material and fracture mechanical testing of carbon fibre laminates::</p>
<p><a href="https://www.sciencedirect.com/science/article/abs/pii/S001379441731250X?via%3Dihub" target="_blank" rel="noopener noreferrer">"Innovative mechanical characterization of CFRP using acoustic emission technology" by Claudia Barile published in Engineering Fracture Mechanics Vol. 210 (2019) pp. 414–421</a></p>
<p>What caught my eye first was that the paper got citations already during the in press period. It was not less interesting when I found that the paper describes how acoustic emissions can detect damage and initiation of crack growth. The author, Barile, cleverly uses the wavelet transform to analyse the response to acoustic emission. In a couple of likewise recent publications she has examined the ability of the method. There Barile et al. simulate the testing for varying material parameters and analyse the simulated acoustic response using wavelet transformation. This allow them to explore the dependencies of the properties of the involved materials. </p>
<p>They convincingly show that it is possible to both detect damage and damage mechanisms. In addition, a feature of the wavelet transform as opposed to its Fourier counterpart is the advantages at analyses of transients. By using the transform they were able to single out the initiation of crack growth. Very useful indeed. I get the feeling that their method may show even more benefits.</p>
<p>A detail that is unclear to me, if I should be fussy, is that there are more unstable phenomena than just crack growth that can appear as the load increases. Also regions of damage and in particular, fracture process regions may grow. When the stress intensity factor <em>K</em> alone is sufficient there is no need to consider neither size nor growth of the fracture process region. The need arises when <em>K</em>, <em>J</em>, or any other one-parameter description is insufficient, e.g. in situations when the physical size of the process region becomes important. Typical examples are when cracks cross bi-material interfaces or when they are small relative to the size of the process region. When the size seems to be the second most important feature, then the primary parameter may be complemented with a finite size model of the process region to get things right. There is a special twist of this in connection with process region size and rapid growth. In the mid 1980's cohesive zones came in use to model fracture process regions in FEM analyses of elastic and elastic-plastic materials. Generally, during increasing load, cohesive zones appear at crack tips and develop until the crack begins to grow. One thing that at first glance was surprising, at least to some of us, was that for small cracks the process region first grows stably and shifts to be fast and uncontrollable, while the crack tip remains stationary. Later, of course the criterion for crack growth becomes fulfilled and crack growth follows.</p>
<p>Is it possible to differentiate between the signals from a suddenly fast growing damage region or fracture process region vis à vis a fast growing crack?</p>
<p>It would be interesting to hear from the authors or anyone else who would like to discuss or provide a comment or a thought, regarding the paper, the method, or anything related.</p>
<p>Per Ståhle</p>
<p> </p>
</div></div></div>Tue, 05 Nov 2019 09:23:48 +0000ESIS23731 at https://imechanica.orghttps://imechanica.org/node/23731#commentshttps://imechanica.org/crss/node/23731Discussion of fracture paper #23 - Paris' exponent m<2 and behaviour of short cracks
https://imechanica.org/node/23169
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>I came across a very interesting paper in Engineering Fracture Mechanics about a year ago. It gives some new results of stochastic aspects of fatigue. The paper is:</p>
<p><a href="https://www.sciencedirect.com/science/article/pii/S0013794417310810" target="_self">”On the distribution and scatter of fatigue lives obtained by integration of crack growth curves: Does initial crack size distribution matter?” by M. Ciavarella, A. Papangelo, Engineering Fracture Mechanics, Vol 191 (2018) pp. 111–124.</a></p>
<p>The authors remind us of the turning point the a Paris' exponent m=2 is. Initial crack length always matters but if the initial crack is small, the initial crack is seemingly very important for the if m>2. For exponents less than 2, small initial cracks matters less or nothing at all. If all initial cracks are sufficiently small their size play no role and may be ignored at the calculation of the remaining life of the structure. Not so surprising this also applies to the stochastic approach by the authors. </p>
<p>What surprised me is the fuzz around small cracks. I am sure there is an obstacle that I have overlooked. I am thinking that by using a cohesive zone model and why not a Dugdale or a Barenblatt model for which the analytical solutions are just an inverse trigonometric resp. hyperbolic function. What is needed to adopt the model to small crack mechanics is the stress intensity factor and a length parameter such as the crack tip opening displacement or an estimate of the linear extent of the nonlinear crack tip region.</p>
<p>I really enjoyed reading this interesting paper and get introduced to extreme value distribution. I also liked that the Weibull distribution was used. The guy himself, Waloddi Weibull was born a few km's from my house in Scania, Sweden. Having said that I will take the opportunity to share a story that I got from one of Waloddi's students Bertram Broberg. The story tells that the US army was skeptic and didn't want to use a theory (Waloddi's) that couldn't even predict zero probability that object should brake. Not even at vanishing load. A year later they called him and told that they received a cannon barrel that was broken already when they pulled it out of its casing and now they fully embraced his theory. </p>
<p>Per Ståhle</p>
</div></div></div>Mon, 18 Mar 2019 17:05:16 +0000ESIS23169 at https://imechanica.orghttps://imechanica.org/node/23169#commentshttps://imechanica.org/crss/node/23169Discussion of fracture paper #22 - Open access puts scientists in control of their own results
https://imechanica.org/node/23157
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The last ESIS blog about how surprisingly few scientists are willing/able to share their experimental data, received an unexpectedly large interest. Directly after the publication another iMechanica blogger took the same theme but he put the focus on results produced at numerical analyses that are presented with insufficient information. While reading, my spontaneous guess was that one obstacle to do right could be the widespread use of commercial non-open codes. The least that then could be done is to demonstrate the ability of the code by comparing results with an exact solution of a simplified example. My fellow blogger also had an interesting reflection regarding differences between theoreticians and computational scientists and it suddenly occurs to me that everything is not black or white. Robert Hooke concealed his results and by writing an anagram, he made sure that he could still take the credit. He didn't stop at that. When he made his result known he added some ten years to how early he understood the context. And he got away with it.</p>
<p>To some consolation, the EU 8th Framework programme, also called Horizon 2020, finances the OpenAIRE-, and its successor the OpenAIREplus-project that is developed and managed by CERN. The intention is to increase general access to research results with EU support. As a part of this the Zenodo server system was launched. As the observant reader of the previous blog might have seen noted, Zenodo was used by the authors of the survey we discussed in the previous ESIS blog</p>
<p><a href="https://www.sciencedirect.com/science/article/pii/S0013794418303023" target="_blank" rel="noopener noreferrer">"Long term availability of raw experimental data in experimental fracture mechanics", by Patrick Diehl, Ilyass Tabiai, Felix W. Baumann, Daniel Therriault and Martin Levesque, in Engineering Fracture Mechanics, 197 (2018) 21–26</a>, with supplementary materials including all bibtex entries of the papers here <a href="https://zenodo.org/badge/latestdoi/110383353"><img src="https://zenodo.org/badge/110383353.svg" alt="DOI" /></a> </p>
<p>The purpose of Zenodo is to make sure that there will be enough storage capacity for open access data for everyone. Mandatory for all Horizon2020 financed projects and in first hand all EU financed projects.</p>
<p>I learn from the parallel blog that there are a DataVerse, an openKIM, a Jupyter project and probably much more, in the support of open-access. It seems to me that DataVerse covers the same functionality as Zenodo. In addition they offer an open-source server with the possibility to set up and run your own server and become integrated in a larger context, which seems very practical. OpenKIM is a systematic collection of atomistic potentials built by users. Jupyter Notebooks yet another open-source project supporting computing in any programming language. They have a written code of conduct. It is not as depressing as it first looks. In essence it summarises your rights and obligations.</p>
<p>It could possibly be better with one single repository or at least one unified system. But why not let a hundred flowers bloom. At the end the solution could be a search engine that covers all or a user's choice of the open-access repositories. </p>
<p>Per Ståhle</p>
</div></div></div>Mon, 11 Mar 2019 10:46:44 +0000ESIS23157 at https://imechanica.orghttps://imechanica.org/node/23157#commentshttps://imechanica.org/crss/node/23157Discussion of fracture paper #21 - Only 6% of experimentalists want to disclose raw-data
https://imechanica.org/node/22590
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>Experimental data availability is a cornerstone for reproducibility in experimental fracture mechanics. This is how the technical note begins, the recently published </span></p>
<p><a href="https://www.sciencedirect.com/science/article/pii/S0013794418303023" target="_blank"><span>"Long term availability of raw experimental data in experimental fracture mechanics", by Patrick Diehl, Ilyass Tabiai, Felix W. Baumann, Daniel Therriault and Martin Levesque, in Engineering Fracture Mechanics, 197 (2018) 21–26.</span></a></p>
<p><span>It is five pages that really deserves to be read and discussed. A theory may be interesting but of little value until it has been proven by experiments. All the proof of a theory is in the experiment. What is the point if there is no raw-data for quallity check?</span></p>
<p><span>The authors cite another survey that found that 70% of around 1500 researchers failed to reproduce other scientists experiments. As a surprise, the same study find that the common scientists are confident that peer reviewed published experiments are reproducible.</span></p>
<p><span>A few years back many research councils around the world demanded open access to all publications emanating from research finansed by them. Open access is fine, but it is much more important to allow examination of the data that is used. Publishers could make a difference by providing space for data from their authors. Those who do not want to disclose their data should be asked for an explanation.</span></p>
<p><span>The pragmatic result of the survey is that only 6% will provide data, and you have to ask for it. That is a really disappointing result. The remaining was outdated addresses 22%, no reply 58% and 14% replied but were not willing to share their data. </span><span>The result would probably still be deeply depressing, but possibly a bit better if I as a researcher only have a single experiment and a few authors to track down. It means more work than an email but on the other hand I don't have 187 publications that Diehl et al. had. Through friends and former co-authors and some work I think chances are good. The authors present some clever ideas of what could be better than simply email-addresses that are temporary for many researchers.</span></p>
<p><span>The authors of the technical note do not know what hindered those 60% who did receive the request and did not reply. What could be the reason for not replying to a message where a colleague asks you about your willingness to share the raw experimental data of a published paper with others? </span><span>If I present myself to a scientist as a colleague who plan to study his data and instead of studying his behaviour, then chances that he answers increase. I certainly hope that, and at least not the reversed but who knows, life never ceases to surprise. It would be interesting to know what happens. If anyone would like to have a go, I am sure that the author's of the paper are willing to share the list of papers that they used.</span></p>
<p><span>Again, could there be any good reason for not sharing your raw-data with your fellow creatures? What is your opinion? Anyone, the authors perhaps. </span></p>
<p><span>Per Ståhle</span></p>
</div></div></div>Tue, 21 Aug 2018 22:14:07 +0000ESIS22590 at https://imechanica.orghttps://imechanica.org/node/22590#commentshttps://imechanica.org/crss/node/22590Discussion of fracture paper #20 - Add stronger singularities to improve numerical accuracy
https://imechanica.org/node/22425
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>It is common practice to obtain stress intensity factors in elastic materials by using Williams series expansions truncated at the </span><em>r</em><span>^(-1/2)-stress term. I ask myself, what if both evaluations of experimental and numerical data is improved by including lower order (stronger singularities) terms? The standard truncation is done in a readworthy pape</span>r </p>
<p><a href="https://www.sciencedirect.com/science/article/pii/S0013794417304411" target="_blank"><span>"Evaluation of stress intensity factors under multiaxial and compressive conditions using low order displacement or stress field fitting", R. Andersson, F. Larsson and E. Kabo, in Engineering Fracture Mechanics, 189 (2018) 204–220,</span></a></p>
<p><span>where t</span><span>he authors propose a promising methodology for evaluation of stress intensity factors from asymptotic stress or displacement fields surrounding the crack tip. The focus is on cracks appearing beneath the contact between train wheel and rail and the difficulties that is caused by compression that only allow mode II and III fracture. The proposed methodology is surely applicable to a much larger collection of cases of fracture under high hydrostatic pressure such as at commonplace crushing or on a different length scale at continental transform faults driven by tectonic motion. In the paper they obtain excellent results and I cannot complain about the obtained accuracy. The basis of the analysis is XFEM finit element calculations of which the results are least square fitted to a series of power functions </span><em>r^n</em><span>/2. The series is truncated </span><span>at </span><em>n</em><span>=-1 for stresses and 0 for displacements. Lower order terms are excluded.</span><span> </span></p>
<p><span>We know that the complete series, converges within an annular region between the largest circle that is entirely in the elastic body and the smallest circle that encircles the non-linear region at the crack tip. In the annular ring the complete series is required for convergence with arbitrary accuracy. </span><span>Outside the annular ring the series diverges and on its boundaries anything can happen. A single term autonomy is established if the stress terms for </span><em>n</em><span><-1 are insignificant on the outer boundary and those for </span><em>n</em><span>>-1 are insignificant on the inner boundary. Then only the square root singular term connects the outer boundary to the inner boundary and the crack tip region. Closer to the inner boundary the </span><em>n</em><span>≤-1 give the most important contributions and at the outer the </span><em>n</em><span>≥-1 are the most important.</span></p>
<p><span>I admit that in purely elastic cases the non-linear region at the crack tip is practically a point and all terms <em>n</em><-1 become insignificant, but here comes my point: Both at evaluation of experiments and numerics the accuracy is often not very good close to the crack tip which often force investigators to exclude data that seem less accurate. This was done in the reviewed paper, where the result from the elements closes to the crack tip was excluded. This is may be the right thing to do but what if <em>n</em>=-2, a <em>r</em>^-1 singularity is included? After all the numerical inaccuracies at the crack tip or the inaccurate measurements or non-linear behaviour at experiments are fading away at larger distances from the crack tip. In the series expansion of stresses in the elastic environment this do appear as finite stress terms for <em>n</em>≤-1.</span></p>
<p><span>It would be interesting to hear if there are any thoughts regarding this. The authors of the paper or anyone who wishes express an opinion is encouraged to do so.</span></p>
<p><span><span>Per Ståhle</span><br /></span></p>
</div></div></div>Sun, 10 Jun 2018 22:04:39 +0000ESIS22425 at https://imechanica.orghttps://imechanica.org/node/22425#commentshttps://imechanica.org/crss/node/22425Discussion of fracture paper #19 - Fracture mechanical properties of graphene
https://imechanica.org/node/21985
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Extreme thermal and electrical conductivity, blocks out almost all gases, stiff as diamond and stronger than anything else. The list of extreme properties seems never ending. The paper</p>
<p><a href="http://www.sciencedirect.com/science/article/pii/S0013794416304246" target="_blank">Growth speed of single edge pre-crack in graphene sheet under tension, Jun Hua et al., Engineering Fracture Mechanics 182 (2017) 337–355</a>, </p>
<p>deals with the fracture mechanical properties of graphene. A sheet of armchair graphene can be stretched up to 15 percent which is much for a crystalline material but not so much when compared with many polymers. The ultimate load, on the other hand, becomes huge almost 100 GPa or more. Under the circumstances, it is problematic to say the least, that the fracture toughness is that of a ceramic, only a few MPam^(1/2). Obviously cracks must be avoided if the high ultimate strength should be useful. Already a few microns deep scratches will bring the strength down to a a few hundred MPa. </p>
<p>The research group consisting of Jun Hua, Qinlong Liu, Yan Hou, Xiaxia Wu and Yuhui Zhang from the dept. of engineering mechanics, school of science, Xi’an University of Architecture and Technology, Xi’an, China, has studied fast crack growth in a single atomic layer graphene sheet with a pre-crack. They are able to use molecular dynamics simulations to study the kinetics of a quasi-static process. They pair the result with continuum mechanical relations to find crack growth rates. A result that provide confidence is that the fracture toughness obtained from molecular primitives agrees well with what is obtained at experiments. The highlighted results are that the crack growth rate increases with increasing loading rate and decreasing crack length. The tendencies are expected and should be obtained also by continuum mechanical simulations, however then not be first principle and requiring a fracture criterion.</p>
<p>Another major loss would be the possibility to directly observe the details of the fracture process. According to the simulation results the crack runs nicely between two rows of atoms without branching or much disturbances of the ordered lattice. The fracture process itself would not be too exciting if it was not for some occasional minor disorder that is trapped along the crack surfaces. The event does not seem to occur periodically but around one of ten atoms suffers from what the authors call abnormal failure. Remaining at the crack surface are dislocated atoms with increased bond orders. All dislocated atoms are located at the crack surface. The distorted regions surrounding solitary dislocated carbon atoms are small. </p>
<p>A motivated question would be if the dissipated energy is of the same order of magnitude as the energy required to break the bonds that connects the upper and lower half planes before fracture. Can this be made larger by forcing the crack to grow not along a symmetry plane as in the present study. Without knowing much about the technical possibilities I assume that if two graphene sheets connected to each other rotated so that the symmetry planes do not coincide, the crack would be forced to select a less comfortable path in at least one of the sheets. </p>
<p><span>Everyone with comments or questions is cordially invited raise their voice.</span></p>
<p><span>Per Ståhle</span></p>
</div></div></div>Sun, 31 Dec 2017 15:45:54 +0000ESIS21985 at https://imechanica.orghttps://imechanica.org/node/21985#commentshttps://imechanica.org/crss/node/21985Discussion of fracture paper #18 - A crack tip energy release rate caused by T-stress
https://imechanica.org/node/21796
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>A T-stress is generally not expected to contribute to the stress intensity factor because its contribution to the free energy is the same before and after crack growth. Nothing lost, nothing gained. Some time ago I came across a situation when a T-stress, violates this statement. The scene is the atomic level. As the crack is producing new crack surfaces the elastic stiffness in the few atomic layers closest to the crack plane are modified. This changes the elastic energy which could provide, contribute to or at least modify the energy release rate. If the energy is sufficient depends on the magnitude of the T-stress, the change of the elastic modulus and how many atomic layers that are involved. </span></p>
<p><span>If I should make an estimate it would be that the energy release rate is the change of the T-stress times the fraction of change of the elastic modulus times the square root of the thickness on the affected layer. Assuming that the T-stress is a couple of GPa, the change of the fraction of change of the elastic modulus is 10% and the affected layer is around ten atomic layers one ends up with 100kPa m^(1/2). Fairly small and the stress and its change are taken at its upper limits but still it is there. The only crystalline material I could find is ice with a toughness of the same level. Other materials are affected but require some additional remote load.</span></p>
<p><span>Interestingly enough I came across a paper describing a different mechanism leading to a T-stress contribution to the energy release rate. The paper is:</span></p>
<p><a href="http://www.sciencedirect.com/science/article/pii/S001379441500613X" target="_blank"><span>Zi-Cheng Jiang, Guo-Jin Tang, Xian-Fang Li, Effect of initial T-stress on stress intensity factor for a crack in a thin pre-stressed layer, Engineering Fracture Mechanics, pp. 19-27.</span></a></p>
<p><span>This is a really read worthy paper. The reasons for the coupling between the T-stress and the stress intensity factor is made clear by their analysis. The authors have an admirable taste for simple but accurate solutions. The paper describes a crack with a layer of residual stress, that gives a T-stress in the crack tip vicinity. As the crack advances increasing more material end up behind the crack tip rather than in front of it. The elastic energy density caused by the T-stress is larger in front of the tip than it is behind it. The energy released on the way and can only disappear at the singular crack tip, not anywhere else in the elastic material. The reason for the energy release is the assumed buckling in the direction perpendicular to the crack plane. An Euler-Bernoulli beam theory is used to calculate the contribution to the energy release rate.</span></p>
<p><span>Having read the paper I realise that in a thin sheet buckling out of its own plane in the presence of a crack and a compressive T-stress there will be energy released that should contribute to crack growth. The buckling will give a more seriously distorted stress state around the crack tip, but never the less. In this case the buckling area would be proportional to the squared crack length in stead of crack length times the height of the layer as in the Jiang et al. paper. The consequence is that the contribution to the stress intensity factor should scale with the T-stress times square root of the crack length.</span></p>
<p><span>Suddenly I feel that it would be very interesting to hear if anyone, maybe the authors themselves, know of other mechanisms that could lead to this kind of surprising addition to the energy release rate caused by T-stresses. It would be great if we could add more to the picture. Anyone with information is cordially invited to contribute.</span></p>
<p><span>Per Ståhle</span></p>
</div></div></div>Wed, 01 Nov 2017 20:12:19 +0000ESIS21796 at https://imechanica.orghttps://imechanica.org/node/21796#commentshttps://imechanica.org/crss/node/21796Discussion of fracture paper #17 - What is the second most important quantity at fracture?
https://imechanica.org/node/21722
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>No doubt the energy release rate comes first. What comes next is proposed in a recently published study that describes a method based on a new constraint parameter <em>Ap</em>. The paper is:</span></p>
<p><span><a href="http://www.sciencedirect.com/science/article/pii/S0013794417301583" target="_blank">Fracture assessment based on unified constraint parameter for pressurized pipes with circumferential surface cracks, M.Y. Mu, G.Z. Wang, F.Z. Xuan, S.T. Tu, Engineering Fracture Mechanics 175 (2017), 201–218</a> </span></p>
<p><span>The parameter <em>Ap</em> is compared with established parameters like <em><span>T</span></em>, <em>Q</em> etc. The application is to pipes with edge cracks. I would guess that it should also apply to other large structures with low crack tip constraint.</span></p>
<p><span>As everyone knows, linear fracture mechanics works safely only at small scales of yielding. Despite this, the approach to predict fracture by studying the energy loss at crack growth, using the stress intensity factor</span> <em>K</em>I and its critical limit, the fracture toughness, has been an engineering success story. <em>K</em>I captures the energy release rate at crack growth. This is a well-founded concept that works for technical applications that meet the necessary requirements. The problem is that many or possibly most technical applications hardly do that. The autonomy concept in combination with <em>J</em>-integral calculations, which gives a measure of the potential energy release rate of a stationary crack, widens the range of applications. However, it is an ironin that the <em>J</em>-integral predicts the initiation of crack growth which is an event that is very difficult to observe, while global instability, which is the major concern and surely easy to detect, lacks a basic single parameter theory.</p>
<p><span>For a working concept, geometry and load case must be classified with a second parameter in addition to <em>K</em>I or <em>J</em>. The most important quantity is no doubt the energy release rate, but what is the second most important. Several successful parameters have been proposed. Most of them describe some type of crack tip constraint, such as the <em>T</em>-stress, <em>Q</em>, the stress triaxiality factor <em>h</em>, etc. A recent suggestion that, as it seems to me, have great potential is a measure of the volume exposed to high effective stress, <em>Ap</em>. It was earlier proposed by the present group GZ Wang and co-authors. <em>Ap</em> is defined as the relative size of the region in which the effective stress exceeds a certain level. As pointed out by the authors, defects in large engineering structures such as pressure pipes and vessels are often subjected to a significantly lower level of crack tip constraint than what is obtained in laboratory test specimens. The load and geometry belong to an autonomy class to speak the language of KB Broberg in his book "Fracture and Cracks". The lack of a suitable classifying parameter is covered by <em>Ap</em>.</span></p>
<p><span>The supporting idea is that <em>K</em>I or <em>J</em> describe the same series of events that lead to fracture both in the lab and in the application if the situations meet the same class requirements, i.e. in this case have the same <em>Ap</em>. The geometry and external loads are of course not the same, while a simpler and usually smaller geometry is the very idea of the lab test. The study goes a step further and proposes a one-parameter criterion that combines the <em>K</em>I or <em>J</em> with <em>Ap</em> by correlation with data.</span></p>
<p><span>The method is reinforced by several experiments that show that the method remains conservative, while still avoiding too conservative predictions. The latter of course makes it possible to avoid unnecessary disposal and replacement or repair of components. The authors' conclusions are based on experience of a particular type of application. I like the use of the parameter. I guess more needs to be done extensively map of the autonomy classes that is covered by the method. I am sure the story does not end here.</span></p>
<p><span>A few questions could be sent along: Like "Is it possible to describe or give name to the second most important quantity after the energy release rate?" The paper mentions that statistical size effects and loss of constraint could affect <em>Ap</em>. Would it be possible to do experiments that separates the statistical effect from the loss of constraint? Is it required or even interesting? </span></p>
<p><span>It would be interesting to hear from the authors or anyone else who would like to discuss or comment the paper, the proposed method, the parameter or anything related. </span></p>
<p><span>Per Ståhle</span></p>
</div></div></div>Wed, 18 Oct 2017 17:08:09 +0000ESIS21722 at https://imechanica.orghttps://imechanica.org/node/21722#commentshttps://imechanica.org/crss/node/21722Discussion of fracture paper #16 - What is wrong with pure mode I and II? A lot it seems.
https://imechanica.org/node/21428
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>It is common practice when solving boundary value problems to split the solution into a symmetric and an antisymmetric part to temporarily reduce the number of variables and the mathematical administration. As soon as the symmetric problem is solved, the antisymmetric problem, or vice versa, is almost solving itself. Any problem can be split into a symmetric and an antisymmetric part which is a relief for anyone who analyses mixed cases.</p>
<p>It gives a clearer view but it is an academic exercise while nature usually doesn't have any comprehension of symmetry and antisymmetry. Fracture is no exception. The fracture processes will be activated when sufficient conditions are fulfilled. Even the smallest deviation from the pure mode I or II caused by geometry or load will not affect the conditions at the crack tip in any decisive way. Everything is almost pure mode I or II and it may be convenient ignore the small deviation and still treat the problem as a pure case. This seems simple enough but the paper reviewed tells that it has been a tripwire for many. The selected paper is the recently published:</p>
<p><a href="http://www.sciencedirect.com/science/article/pii/S0013794417301303">"An improved definition for mode I and mode II crack problems" by M.R. Ayatollahi, M. Zakeri in Engineering Fracture Mechanics 175 (2017) 235–246.</a></p>
<p>The authors examine a power series expansion for an Airy stress function about the crack tip. The series give stress as a sum of powers r-1/2, 1, r1/2, r, etc. of the distance to the crack tip. Each term has an known angular dependence. The application is to a plane crack with any in-plane load. The series starts with a square root singular term while it is assumed that the crack tip is sharp and the material is linear elastic. The assumption requires that the geometrical features of the crack tip and the nonlinear region is not visible from where the expansion with some accuracy describes the stress field. The problem that the authors emphasise is that the splitting in symmetric and antisymmetric modes that leads to two similar expansions of the radial power functions with symmetric and antisymmetric angular functions. The representations so far has been called pure if the solution is strictly symmetric or strictly antisymmetric, i.e. the notation has been pure mode I and pure mode II. The problem is that not only seldom, has a vanishing mode I stress intensity factor misled investigators to drop all symmetric terms of the series expansion. Also mode II has been unfairly treated in the same way. The most striking problem is of course when the constant stress acting along the crack plane, the T-stress, by mistake is neglected. The authors are doing a nice work sorting this out. They describe a range of cases where one stress intensity factor vanishes but for sure the crack tip stress state is neither strictly symmetric nor strictly antisymmetric. They also provide quite many examples to demonstrate the necessity to consider the T-stress even if the mode I singular stress term is absent. I commend the authors for doing a conscientious work. </p>
<p><span>I</span><span>f I should bring up something where different positions may be assumed it would be the selection of the series. The powers of r-1, r-3/2, r-2 etc are never mentioned and I agree that it is not always necessary. It should be commonly known that a sharp crack, a linear elastic material and traction free crack surfaces says it. There cannot be any stronger singularities than r-1/2. However, isn't one consequence that close enough to the crack tip any constant stress should be insignificant as compared to the singular stress terms. If so, it should not have any significant effect on the stresses closest to the crack tip and neither affect the fracture processes nor the selection of crack path. On the other hand, if the constant term has a real influence on the course of events, that would as far as I understand mean that the nonlinear region has to have a substantial extent so that its state is given by both singular terms and the T-stress. The contradiction is then that the stronger singular terms r-1, r-3/2, etc. cannot be neglected. These terms are there. Already the r-1 term seems obvious if the crack has grown because of the residual stress caused by plastic strain along the crack surface that in the wake region behind the crack tip. </span></p>
<p>Also, the region of convergence, which is at most the length of the crack, is another pothole. Outside the convergence region a different series or an analytical continuation, may be used. For the series expansions the symmetric and antisymmetric solutions have to be treated as well, with the difference that there are constant stresses in both symmetric and antisymmetric modes that have to be included. </p>
<p>It would be interesting to hear if there are any thoughts regarding this.</p>
<p>Per Ståhle</p>
<p>P.S. On the courtesy of Elsevier there is a <span>3 month promotional access to the latest article in the blog, meaning the articles are freely available to everyone. </span>Now everyone who wishes to comment or discuss the paper here can do so. (Dr. Kumar, I hope you are reading this).</p>
</div></div></div>Thu, 20 Jul 2017 17:18:07 +0000ESIS21428 at https://imechanica.orghttps://imechanica.org/node/21428#commentshttps://imechanica.org/crss/node/21428Discussion of fracture paper #15 - Designing for crack arrest
https://imechanica.org/node/20605
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>Everyone loves an elegant engineering solution. It is particularly true when the alternatives are terrifying. In the paper:</span></p>
<p><span><a href="http://www.sciencedirect.com/science/article/pii/S0013794416301333">”Brittle crack propagation/arrest behaviour in steel plate – Part I: Model formulation” by Kazuki Shibanuma, Fuminori Yanagimoto, Tetsuya Namegawa, Katsuyuki Suzuki, Shuji Aihara in Engineering Fracture Mechanics, 162 (2016) 324-340</a><a href="http://www.sciencedirect.com/science/article/pii/S0013794415000958">.</a></span></p>
<p><span>a team from University of Tokyo proposes a model for prediction of the arrest of propagating brittle cracks in steel plates. The approach, in spite of its simplicity, captures the physics of the fracture process. The model formulates the energy release rate in simple and comprehensible terms and gives accurate predictions. The theory is validated on several experiments described in a subsequent paper, a <a href="http://www.sciencedirect.com/science/article/pii/S0013794416301321">”Part II: Experiments and model validation”</a> also</span><span> in Engineering Fracture Mechanics. The characteristics are those of a pilot study with the goal to provide a design tool for predicting crack arrest in steel plates.</span></p>
<p><span>In the model, the energy to complete the fracture process is at most what is left of the released energy when the work of plastic deformation and the part of the kinetic energy that is reflected away from crack tip region have been covered. The energy dissipation at plastic deformation is reduced at increasing crack tip velocity while the opposite applies to the dissipated kinetic energy. The energy required for the fracture processes is supposed to be constant. If it at some velocity is more than required then the energy is in balance only at a single stable higher crack tip velocity. If crack growth is initiated then the crack accelerates until the energy balance is obtained. When the crack subsequently loose driving force or require additional work, caused, e.g., by elevated temperature which decreases the material viscosity or by whatever, the crack decelerates until zero velocity or until the minimum energy release rate is obtained and the crack arrest comes abruptly.</span></p>
<p><span>Surface-ligaments are assumed to consume a serious part of the available energy. The slower the crack grows the wider these ligaments become which rapidly increases the plastic dissipation. Finally the energy balance and the stability of the crack tip velocity cannot be maintained and the crack will come to a stop.</span></p>
<p><span>Considering that one has to keep trac</span><span>k of the complicated </span><span>sequence of processes</span><span> that keep the crack growing, it </span><span>seemed obvious to me that this would end up in a horrible and time consuming analysis. Then,</span><span> to my surprise, the investigators present an </span><span>ingenious </span><span>solution that simplifies the analysis a lot. It is based on three assumptions: 1) that the crack front is assumed to be straight through the plate, 2) that the unbroken side-ligaments are regarded as integrated parts of the crack front, and 3) that the evaluation of the state of the crack front in done at the plate mid-plane.</span></p>
<p><span>In the subsequent part II the functionality of the model is verified. The validation is performed on different grades of steel that are exposed to different load levels. The authors believe that this model can be used to establish a design strategy for steel plates. I too believe that, even if more possibly needs to be done to qualify the method as a design standard.</span></p>
<p><span>I understand that the authors are familiar with the series of wide plate experiments on crack arrest in very large specimens (around 11x1x0.1 m3) reported by Naus et al., NUREG/CR-4930 ORNL-6388, Oakridge Laboratories, USA, 1987. </span></p>
<p><span>In the aftermath of the experiments a variety of models where proposed. An interesting observation made by D. Alexander and I.B. Johansson at Oakridge Labs when they examined the crack surfaces was that remains of plastic deformation framed the cloven grains. The guess was that this was remaining parts of broken ligaments between the crack surfaces and that these ligaments were ripped apart during the fracture process. The area covered by these remains was clearly increasing with decreasing crack tip velocity. Just before crack arrest they could cover as much as 10 to 20 % of the ”brittle” part of the crack surface. I have a feeling that this may mean something. The plastic ligaments per se consume large amounts of energy and with increasing fractions they might influence the crack tip velocity at arrest. Only 10% may seem as small or even insignificant, but considering that the plastic ligaments that bridge a crack may consume many times more energy than the pure cleavage of the remaining 90%, even 10% must be important. It would be interesting to know if the authors observed any remains of plastic ligaments. If so, did the fraction of them change in any systematic way during crack growth? </span></p>
<p><span>Any contribution to this blog is gratefully acknowledged.</span></p>
<p><span>Per Ståhle</span></p>
</div></div></div>Sun, 20 Nov 2016 21:23:48 +0000ESIS20605 at https://imechanica.orghttps://imechanica.org/node/20605#commentshttps://imechanica.org/crss/node/20605Discussion of fracture paper #14 - How to understand the J-integral when multiple cracks are growing at different rates
https://imechanica.org/node/20004
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>A nice demonstration of toughening by introducing multiple secondary cracking of planes parallel with the primary crack is found in the paper:</p>
<p><span><a href="http://www.sciencedirect.com/science/article/pii/S0013794415006268">”Fracture resistance enhancement of layered structures by multiple cracks” by Stergios Goutianos and Bent F. Sørensen in Engineering Fracture Mechanics, 151 (2016) 92-108.</a></span></p>
<p><span>The 14th paper belong to the category innovative ideas leading to improved composites. We already know of combinations of hard/soft, stiff/weak or brittle/ductile materials that are used to obtain some desired properties. The results are not at all limited to what is set by the pure materials themselves. It has been shown that cracks intersecting soft material layers are exposed to elevated fracture resistances (see eg. the paper 9 blog). Differences in stiffness can be used to improve fatigue and fracture mechanical properties as found in studies by Surresh, Sou, Cominou, He, Hutchinson, and others. Weak interfaces can be used to diverge or split a crack on an intersecting path. A retardation is caused by the additional energy consumed for the extended crack surface area or caused by smaller crack tip driving forces of diverging crack branches. </span></p>
<p>A primary crack is confined to grow in a weak layer. The crack tip that is modelled with a cohesive zone remains stationary until the full load carrying capacity of the cohesive forces is reached. Meanwhile the increasing stress across an even weaker adjacent layer also develops a cohesive zone that takes its share of the energy released from the surrounding elastic material. At some point the cohesive capacity is exhausted also here and a secondary crack is initiated. Both cracks are confined to different crack planes and will never coalesce. The continuation may follow different scenarios depending on the distance between the two planes, the relative cohesive properties like cohesive stress, critical crack tip opening, the behaviour at closure etc. of the second layer. All these aspects are studied and discussed in the paper.</p>
<p>The investigators have successfully found a model for how to design the cohesive properties to obtain structures with optimal fracture resistance. Parameters that are manageable in a production process are the ratio of the cohesive properties of the different crack planes and the distance between the them. A theoretical model is formulated. With it they are able to predict whether or not the toughness of a layered structure can be increased by introducing weak layers as described. </p>
<p>Their results coincide well with the experimental results by Rask and Sørensen (2012) and they have found a model for how to design the cohesive properties to obtain a structure with optimal fracture resistance. Parameters that are manageable in a production process are the ratio of the cohesive properties of the different crack planes and the distance between the them. </p>
<p>The part that I would like to discuss concerns an estimation of an upper bound of the enhancement of the fracture toughness. The derived theoretical model is based on the J integral taken along a path that ensures path independence. Two different paths are evaluated and compared. Along a remote path the J-value is given as a function of external load and deformation. The structural stiffness is reduced as the crack advances in the direction of the primary crack. In the linear elastic case the J-value is half of the work done by the external load during a unit of crack growth. In an evaluation taken along a local path, J receive contributions from the primary crack tip and the two crack tips of the secondary crack. All three tips are supposed to move a unit of length in the direction of the extending primary crack. </p>
<p>As observed by the authors the secondary crack does not contribute to the energy release rate while what is dissipated at the propagating foremost crack tip is to the same amount produced at the healing trailing crack tip. Both crack tips propagate in the same direction so that the crack length does not change. </p>
<p>An observation from the experimental study was that all crack tips have different growth rates and especially the trailing tip of the secondary crack was found to be stationary. Therefore the contribution from that crack tip to the local energy release rate is annulated which leaves less available to the primary crack. To me this seems right. However, when the two remaining advancing crack tips grow does not the respective contributions to J have to be reassessed to reflect their different growth rates? If we assume that the secondary crack grow faster than the primary crack then the enhancing effect is underestimated by the J-integral. Upper bound or lower bound - I can't decide. I would say that it is a fair estimate of where the fracture resistance will end up. </p>
<p>In conjunction with the evaluation of the work done by the external load during a ”unit of crack growth” it seems to be an intricate problem to correlate the unit of crack growth with the different crack tip speeds. Some kind of average perhaps.</p>
<p>Any contribution to the blog is gratefully acknowledged.</p>
<p>Per Ståhle</p>
</div></div></div>Fri, 17 Jun 2016 08:05:22 +0000ESIS20004 at https://imechanica.orghttps://imechanica.org/node/20004#commentshttps://imechanica.org/crss/node/20004Discussion of fracture paper #13 - Cohesive properties at ductile tearing
https://imechanica.org/node/19424
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/6647">ductile</a></div><div class="field-item odd"><a href="/taxonomy/term/834">crack growth</a></div><div class="field-item even"><a href="/taxonomy/term/7475">tearing</a></div><div class="field-item odd"><a href="/taxonomy/term/5169">thin plates</a></div><div class="field-item even"><a href="/taxonomy/term/10457">fracture processes</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>In this review of particularly readworthy papers in EFM, I have selected a paper about the tearing of large ductile plates, namely:</p>
<p><a href="http://www.sciencedirect.com/science/article/pii/S0013794415000958">”Cohesive zone modeling and calibration for mode I tearing of large ductile plates” by P.B. Woelke, M.D. Shields, J.W. Hutchinson, Engineering Fracture Mechanics, 147 (2015) 293-305.</a></p>
<p>The paper begins with a very nice review of the failure processes for plates with thicknesses from thick to thin, from plane strain fracture, via increasing amounts of strain localisation and failure along shear planes, to the thinnest foils that fail by pure strain localisation.</p>
<p>The plates in the title have in common that they contain a blunt notch and are subjected to monotonically increasing load. They are too thin to exclusively fracture and too thick to fail through pure plastic yielding. Instead the failure process is necking, followed by fracture along a worn-out slip plane in the necking region. Macroscopically it is mode I but on a microscale the final failure along a slip plane have the kinetics of mixed mode I and III and, I guess, also mode II. </p>
<p>A numerical solution of the problem resolving the details of the fracture process, should perhaps be conceivable but highly unpractical for engineering purposes. Instead, the necking region, which includes the strain localisation process and subsequent shear failure is a region of macroscopically unstable material and is modelled by a cohesive zone. The remaining plate is modelled as a power-law hardening continuum based on true stress and logarithmic strains.</p>
<p>The analysis is divided into two parts. First a cross-section perpendicular to the stretching of the cohesive zone is treated as a plane strain section. This is the cross section with a shape in which the parable with a neck becomes obvious. Here the relation between the contributions to the cohesive energy from strain localisation and from shear failure is obtained. A Gurson material model is used. Second, the structural scale model reveals the division of the tearing energy into the cohesive energy and the plastic dissipation outside the cohesive zone. The cohesive zone model accounts for a position dependent cohesive tearing energy and experimental results of B.C. Simonsen, R. Törnqvist, Marine Structures, vol. 17, pp. 1-27, 2004 are used to calibrate the cohesive energy.</p>
<p>It is found that the calibrated cohesive energy is low directly after initiation of crack growth, and later assumes a considerably higher steady state value. The latter is attained when the crack has propagated a distance of a few plate thicknesses away from the initial crack tip position. Calculations are continued until the crack has transversed around a third of the plate width.</p>
<p>I can understand that the situation during the initial crack growth is complex, as remarked by the investigators. I guess they would also agree that it would be better if the lower initial cohesive energy could be correlated to a property of the mechanical state instead of position. As the situation is, the position dependence seems to be the correct choise until it is figured out what happens in a real necking region</p>
<p>I wonder if the investigators continued computing the cohesive energy until the crack completely transversed the plate. That would provide an opportunity to test hypothesises both at initiation of crack growth and at the completed breaking of the plate. The situations that have some similarities but are still different would put the consistency of any hypothesis regarding dependencies of mechanical state to the test. </p>
<p>I am here taking the liberty to suggest other characteristics that may vary with the distance to the original crack tip position.</p>
<p>The strains across the cohesive zone are supposed to be large compared to the strains along it. This is the motivation for doing the plane strain calculations of the necking process. Could it be different in the region close to the original blunt crack tip where the situation is closer to plane stress than plane strain? The question is of course, if that influences the cohesive energy a distance of several plate thicknesses ahead of the initial crack position.</p>
<p>Another hypothesis could be that the compressive residual stress along the crack surface that develops as the crack propagate, influence the mechanical behaviour ahead of the crack tip. For very short necking regions the stress may even reach the yield limit in a thin region along the crack surface. Possibly that can have an effect on the stresses and strains in the necking region that affects the failure processes.</p>
<p>My final candidate for a hypothesis is the rotation that is very large at the crack tip before initiation of crack growth. In a linear elastic model and a small strain theory, rotation becomes unbounded before crack growth is initiated. A similar phenomenon has been reported by Lau, Kinloch, Williams and coworkers. The observation is that the severe rotation of the material adjacent to a bi-material adhesive lead to erroneous calibration of the cohesive energy. Could this be related to the lower cohesion energy? I guess that would mean that the resolution is insufficient in the area around the original crack tip position.</p>
<p>Are there any other ideas, or, even better, does anyone already have the answer to why the cohesive energy is very small immediately after initiation of crack growth?</p>
<p>Per Ståhle</p>
</div></div></div>Tue, 02 Feb 2016 20:12:29 +0000ESIS19424 at https://imechanica.orghttps://imechanica.org/node/19424#commentshttps://imechanica.org/crss/node/19424Discussion of fracture paper #12 - Crack paths and fracture process region autonomy
https://imechanica.org/node/18931
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Cracks typically follow paths that locally give a mode I crack tip load. At mixed modes crack are extended via a kink in a direction that locally restores mode I. In isotropic materials this is known to more or less, true for static and dynamic loads. Exceptions are cracks that are subjected to high compressive load, e.g., at contact between train wheels and rails or at cracks caused by seismic movements. Other exceptions are cracks growing in anisotropic materials, at grain boundaries or other weak, or by deformation weakened, interfaces. </p>
<p>The recently published </p>
<p><span><a href="http://www.sciencedirect.com/science/article/pii/S0013794415001216">"Method for calculating G, GI, and GII to simulate crack growth in 2D, multiple-material structures" by E.K. Oneida, M.C.H. van der Meulen, A.R. Ingraffea, Engineering Fracture Mechanics, Vol 140 (2015) pp. 106–126,</a> </span></p>
<p>is an interesting paper about the calculation of mixed mode loads and crack paths by use of a combination of several concepts for crack tip modelling. The developed method has general applicability in that it includes cracks that pass, join or deflect from interfaces, cracks at bifurcation points where three materials meet, and of course the crack paths embedded in homogeneous materials. A scheme is presented that uses two slightly altered local meshes to obtain the variation of the energy release rate due to a small variation of the crack path. The M-integral by Yau, Wang and Corten, J. Appl. Mech., 1980 for separation of mode I and mode II is used. The paper is nicely completed with a demonstration of a crack propagation framework, which combines the developed methods. The result is a convincing simulation of crack growth through a composite material. The path that maximises the strain energy release rate relative to the toughness, is followed.</p>
<p>When the fracture processes are confined to a small region it may be safe to use a sharp crack tip. However, occasionally it leads to an unreasonable behaviour, such as when the energy release rate disappears as the crack tip passes through a bimaterial interface from a weaker to a stiffer material (cf. discussion of paper 9 in this series). Similarly, let's say that a crack meets a conceivable branching point with two branches or paths to chose between and both paths are having equal loading and equal toughness. This seems to be a dead heat. However, say that initiation of the fracture processes need sufficient hydrostatic stress and sufficient subsequent deformation to complete the fracture and that the relation between these quantities are different along the two paths. Then even though the toughnesses are equal, the growing crack is likely to follow the path that first allow initiation of the fracture processes and the other path will never be activated. Perhaps there are exceptions but in general it seems to me that a crack tip model with more details is needed for these cases. </p>
<p>Cases when cracks deflect from a weak interface are, I believe, similarly problematic. Whether a crack will follow a weak plane under a mixed mode load or kink out of that plane should to a large extent depend on the affinity to initiate a fracture process outside the interface.</p>
<p>I understand that the paper is concerned with indivisible fracture toughness which is excellent, but in view of the sketched scenarios above, I wonder if the model can be extended to include modelling of the process region with a finite physical extent, e.g. by using a cohesive zone model, that provides a two parameter model for the process region. One difficulty that I immediately come to think of is that the strain energy singularity is annulated by the cohesive stresses so that the M-integral possibly will fail. Still, if the foremost part of the process region, i.e. the tip of the cohesive zone rather than the crack tip, is the path finder then maybe a stress criterion could be a suitable candidate. Are there other possibilities? Could the point shaped crack tip be kept while using a stress criterium at some fixed distance ahead of the crack tip? Or would "fixed distance" per se require process region autonomy?</p>
<p> </p>
<p>Per Ståhle</p>
</div></div></div>Thu, 01 Oct 2015 13:07:32 +0000ESIS18931 at https://imechanica.orghttps://imechanica.org/node/18931#commentshttps://imechanica.org/crss/node/18931Discussion of fracture paper #11 - Fracture processes and phase field modelling
https://imechanica.org/node/18255
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10457">fracture processes</a></div><div class="field-item odd"><a href="/taxonomy/term/5722">phase field model</a></div><div class="field-item even"><a href="/taxonomy/term/10458">crack path</a></div><div class="field-item odd"><a href="/taxonomy/term/2213">composite</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>In the latest volume of Engineering Fracture Mechanics there is an interesting paper about the calculation of crack growth paths by use of a phase field model. The considered material is inhomogeneous and that causes the crack to follow a winding path through the material. The material structure is from a CT scanned micro-structure of a cement-based porous material. The paper is:</p>
<p><a href="http://www.sciencedirect.com/science/article/pii/S0013794415001332">”A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure” by T.T. Nguyen, J. Yvonnet, Q.-Z. Zhu, M. Bornert, C. Chateau, Engineering Fracture Mechanics, Vol 139 (2015) pp. 18–39.</a></p>
<p>The phase field method used, is adopted to fracture analyses. It is according to the authors the first time the method is used in the present context with a modified algorithm to handle the damage due to traction.</p>
<p>The phase field model, suggested by Landau and Lifshitz in E. Phys Zeit Sowjetunion 8:153 (1935) is based on the principles of statistical physics and continuous variation of the structure. The original usage was for thermodynamical studies of solidification, coherent interfaces and other problems where the specific physics of surfaces and interfaces are important. Later the models came to be used to keep track of surfaces and interfaces with less interest in the particular physics of the interfaces. The model was successfully used in mechanics and not the least by many for analyses of growing cracks.</p>
<p>In conventional fracture analyses a known or a postulated crack is required, which is not needed in phase field modelling, as is pointed out by Ngueyen et al. This is a serious drawback in studies of fatigue or stress corrosion whereas a large part of the lifetime of cracks and surface flaws is spent during an initiation phase. Further, crack growth and crack path criteria are obsolete in phase field modelling, since the continuous disintegration of the body is an inherent part of the general structural model. In the work by Ngueyen et al., much of the interest concerns the numerical efficiency of the method, which obviously is paying off as the increased efficiency is demonstrated for crack nucleation and propagation in 2D and 3D geometries taken from images of porous cement-based materials.</p>
<p>A couple of perplexing questions got stuck with me after having read the article. One question is: Did it work with the crack path predictions? Of course the crack grew through the inhomogeneous material following a path that would pass as visually acceptable, but so would a variety of alternative paths. To be more specific, the path is controlled by the fracture processes which in the present case would be the evolving damage in the way that it is governed by the phase-field model. It would be interesting to know what the expected physics are behind the path selected by the proposed model? Is it a path closely following maximum energy release rate as is suggested by the basic principles of the phase-field model, or is it perhaps closer to a pure mode I path since the model is restricted to consider damage solely initiated by tractions? In conventional material modelling these paths become different. I think that similarities between conventional models and the phase field model would give increased confidence to both models and the differences would be interesting to discuss.</p>
<p>Another property of the phase-field model that captured my curiosity is its ability to penetrate bi-material interfaces between materials with different stiffnesses as is observed in the compression cases in the paper. The paradoxical result of brittle materials and sharp cracks is that the crack can only grow from a stiffer to a weaker material whereas the interface is impenetrable in the opposite direction. This was the subject of the ESIS review no. 9. The authors comment that it is desirable to investigate the influence of the length scale, that control the sharpness including the width of the crack tip and the stress level ahead of the crack tip which I agree would be very interesting as regards the described paradoxical behaviour.</p>
<p>Per Ståhle</p>
</div></div></div>Sat, 02 May 2015 15:13:46 +0000ESIS18255 at https://imechanica.orghttps://imechanica.org/node/18255#commentshttps://imechanica.org/crss/node/18255Discussion of fracture paper #10 - Searching for the length scale of stress corrosion
https://imechanica.org/node/17865
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>According to the Swedish Plant Inspectorate the major part of all reported fracture related failures in Sweden are due to stress corrosion. I guess it is more or less a reality everywhere. The association with accidents is probably because it comes without warning and usually at surprisingly low loads. Just a mm sized spot of decomposing grease is enough to create a locally extremely acid environment. In an otherwise friendly environment this often not even considered as a possibility by the designer.</p>
<p>The paper for this discussion is:</p>
<p><a href="http://www.sciencedirect.com/science/article/pii/S0013794414002665">”Further study on crack growth model of buried pipelines exposed to concentrated carbonate-bicarbonate solution”, B.T. Lu, Engineering Fracture Mechanics vol. 131 (2014) pp. 296-314.</a> </p>
<p>A stress corrosion cracking model is developed. The main character of the fracture processes is a repeated breaking and healing of a passivating oxide film. When it is intact it prevents the metal from being dissolved by an aggressive environment, and when it is broken, metal ions escape from the surface and the crack thereby advances. The bare metal surface quickly becomes covered by a new thin oxide film when it is exposed to air and moist. To keep up with the oxidisation rate a sufficient strain rate has to be maintained in the crack tip region.</p>
<p>The authors study the combined effect of cyclic loading leading to stress corrosion cracking and mechanical fatigue with good results. The model is used successfully in describing the behaviour of several experimental results reported by different groups. </p>
<p>In ESIS review no. 3 the importance of knowing the length scales of fracture processes was emphasized. In the present paper this is fully understood. The crack tip is confined to a point that is under KI control. To deal with the problem of assigning a strain rate to the singular stress field, the strain rate a short distance (a few microns) ahead of the crack tip is selected. It seems to be an accepted practice by more than the present author and the precise distance is regarded to be a material parameter. However, I feel a bit uncertain about the physical reasons for the actual choice. </p>
<p>Is it possible that there is no length scale that is simultaneously relevant to both the mechanical and the chemical processes. Assume that the width of the blunted tip is a few microns as it is given by KI. We also have an oxide film of a few nm that covers the blunted surface. A distance of a few nm is not likely to be exposed to any gradients of the strain field where the meaningful distances are of the order of microns. In this case the film thickness seems irrelevant. The dissolution of the metal takes place around the crack tip and keeps the growing crack blunt. With the only length scale relevant to the mechanical state being provided by the stress intensity factor the result would be a self-similar shape and a constant stress and strain field in the crack tip region.</p>
<p>A consequence would be that the crack growth rate would be independent of the remote load. Something like that can be seen in the paper "Q.J. Peng et al. Journal of Nuclear Materials 324 (2004) 52–61" that is cited in the present paper. Fig. 2 test 3 shows almost constant growth rate in spite of an almost doubled remote load. </p>
<p>A length scale of a few microns is introduced in the discussed paper. What could be the relevance of the choice? Is a length scale always necessary?</p>
<p>Per Ståhle</p>
</div></div></div>Fri, 30 Jan 2015 15:28:29 +0000ESIS17865 at https://imechanica.orghttps://imechanica.org/node/17865#commentshttps://imechanica.org/crss/node/17865Discussion of fracture paper #9 - Crack tip modelling
https://imechanica.org/node/17471
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/31">fracture</a></div><div class="field-item odd"><a href="/taxonomy/term/91">interface</a></div><div class="field-item even"><a href="/taxonomy/term/10185">Process region</a></div><div class="field-item odd"><a href="/taxonomy/term/6016">ESIS</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span><span>Dear Reader, </span></span></p>
<p>I recently took over as the ESIS blog editor. Being the second in this baton relay, I will do my best to live up to the good reader expectations that has been established by my precursor, who is also one of the instigators of the blog, Wolfgang Brock. </p>
<p>I did not follow the blog in the past. That I regret now that I go through the previous blogs. Here I discover many sharp observations of new methods and concepts paired with a great ability to extract both the essential merits and to spot weaknesses. Much deserve additional studies to bring things to a common view. We are reminded that common views, often rightfully, but not always, are perishable items.</p>
<p>Paper 9 in this series of reviews concerns phenomena that occur when a crack penetrates an interface between two materials with dissimilar material properties. In the purely elastic case it is known that a variation of Young’s modulus along the intended path of a crack may improve the fracture resistance of inherently brittle materials. If the variation is discontinuous and the crack is about to enter a stiffer material the stress intensity factor becomes unlimited with the result that fracture will never happen. At least if the non-linear region at the crack tip is treated as a point. To resolve the problem the extent of the non-linear region has to be considered.</p>
<p>The selected paper is: <a href="http://www.sciencedirect.com/science/article/pii/S0013794414000605">Effect of a single soft interlayer on the crack driving force, M. Sistaninia and O. Kolednik, Engineering Fracture Mechanics Vol. 130, 2014, pp. 21–41</a>. </p>
<p>The authors show that spatial variations also of the yield stress alone can improve the fracture resistance. They find that the crack tip driving force of a crack that crosses a soft interlayer experiences a strong dip. The study is justified and the motivation is that the crack should be trapped in the interlayer. The concept of configurational forces (a paper on configurational forces was the subject of ESIS review no. 7) is employed to derive design rules for an optimal interlayer configuration. For a given matrix material and load, the thickness and the yield stress of a softer interlayer are determined so that the crack tip driving force is minimised. Such an optimum configuration can be used for a sophisticated design of fracture resistant components. </p>
<p>The authors discuss the most important limitations of the analysis of which one is that a series of stationary cracks are considered instead of a growing crack. The discussion of growing versus stationary cracks is supported by an earlier publication from the group. Further the analysis is limited to elastic-ideally plastic materials. A warning is promulgated by them for directly using the results for hardening materials.</p>
<p>The paper is a well written and a technically detailed study that makes the reading a good investment.</p>
<p>The object of my discussion is the role of the fracture process region in analogy with the discussion above of the elastic case. The process region is the region where the stresses decay with increasing straining. When the process region is sufficiently small it may be treated as a point but this may not be the case when a crack penetrates an interface. The process region cannot be small compared to the distance to the interface during the entire process. In the elastic case the simplification leads to a paradoxical result. The main difference as compared with the elastic case is that the ideally plastic fields surrounding a crack tip at some short distance from the interface have the same characteristics as the crack that has the tip at the interface, i.e. in the vicinity of the crack tip the stress is constant and the strain is inversely proportional to the distance to the crack tip. This means that the distance between the crack tip and the interface do not play the same role as in the elastic case. A couple of questions arise that perhaps could be objects of future studies. One is: What happens when the extent of the process region is larger than or of the order of the distance to the interface? If the crack is growing, obviously that has to happen and at some point the fracture processes will probably be active simultaneously in both materials. The way to extend the model could be to introduce a cohesive zone of Barenblatt type, that covers the fracture process region. The surrounding continuum may still be an elastic plastic material as in the present paper.</p>
<p>A problem with growing cracks is that the weaker crack tip fields does not provide any energy release rate at a point shaped crack tip. Would that limitation also be removed if the finite extent of the process region is considered?</p>
<p>With these open questions I hope to trigger those who are interested in the subject to comment or contribute with personal reflections regarding the paper under consideration.</p>
<p> </p>
<p>Per Ståhle<br />Professor of Solid Mechanics<br />Lund University, Lund<br />Sweden</p>
</div></div></div>Fri, 07 Nov 2014 21:59:46 +0000ESIS17471 at https://imechanica.orghttps://imechanica.org/node/17471#commentshttps://imechanica.org/crss/node/17471Discussion of fracture paper #8 - Elastic follow-up
https://imechanica.org/node/17810
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>P.M. James: Re-derivation of plasticity interaction for combined loading under significant levels of elastic follow-up. Engineering Fracture Mechanics, Vol. 126, 2014, pp. 12–26.</p>
<p><a href="http://imechanica.org/node/16898">To the discussion</a></p>
</div></div></div>Tue, 15 Jul 2014 22:00:00 +0000ESIS17810 at https://imechanica.orghttps://imechanica.org/node/17810#commentshttps://imechanica.org/crss/node/17810Discussion of fracture paper #7 - Configurational force approach
https://imechanica.org/node/17809
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/9650">Elasto-Plastic Fracture</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span><span>K. Özenç, M. Kaliske, G. Lin, G. Bhashyam: Evaluation of energy contributions in elasto-plastic fracture: A review of the configurational force approach, Engineering Fracture Mechanics, 2014, Vol. 115, pp. 137-153.</span></span></p>
<p><a href="http://imechanica.org/node/16356" target="_self">To the discussion</a></p>
</div></div></div>Thu, 03 Apr 2014 22:00:00 +0000ESIS17809 at https://imechanica.orghttps://imechanica.org/node/17809#commentshttps://imechanica.org/crss/node/17809Discussion of fracture paper #6 - Stress intensity factor for steep yield distribution
https://imechanica.org/node/17808
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/327">stress intensity factor</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span><span>T. Yasuoka, Y. Mizutani, A. Todoroki: Applicable limit of the stress intensity factor for steep yield strength distribution, Engineering Fracture Mechanics, 2013, Vol. 110, pp. 1-11.</span></span></p>
<p><a href="http://imechanica.org/node/15504" target="_self">To the discussion</a></p>
</div></div></div>Sun, 20 Oct 2013 22:00:00 +0000ESIS17808 at https://imechanica.orghttps://imechanica.org/node/17808#commentshttps://imechanica.org/crss/node/17808Discussion of fracture paper #5 - Yield ciriterion or failure criterion?
https://imechanica.org/node/17807
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10300">Plasticity; cohesive zone model; Failure Criteria</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Henrik Danielsson and Per Johan Gustafsson: A three dimensional plasticity model for perpendicular to grain cohesive fracture in wood, Engineering Fracture Mechanics Vol. 98 2013, pp.137–152.</p>
<p><a href="http://imechanica.org/node/14387" target="_self">To the discussion</a></p>
</div></div></div>Wed, 20 Mar 2013 23:00:00 +0000ESIS17807 at https://imechanica.orghttps://imechanica.org/node/17807#commentshttps://imechanica.org/crss/node/17807Discussion of fracture paper #4 - Is paper ductile?
https://imechanica.org/node/17806
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/7020">cohesive modelling</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span><span>P. Mäkelä and S. Östlund: Cohesive crack modelling of thin sheet material exhibiting anisotropy, plasticity and large-scale damage evolution. Engineering Fracture Mechanics,Vol. 79, 2012 pp. 50-60.</span></span></p>
<p><a href="http://imechanica.org/node/11741" target="_self">To the discussion</a></p>
</div></div></div>Tue, 17 Jan 2012 23:00:00 +0000ESIS17806 at https://imechanica.orghttps://imechanica.org/node/17806#commentshttps://imechanica.org/crss/node/17806Discussion of fracture paper #3 - Length scales in fracture
https://imechanica.org/node/17805
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/1288">Ductile fracture; Aluminum alloy; Damage plasticity theory; Crack propagation</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>H. Krull and H. Yuan: Suggestions to the cohesive traction–separation law from atomistic simulations. Engineering Fracture Mechanics, Vol. 78, 2011, pp. 525-533.</p>
<p><a href="http://imechanica.org/node/10945" target="_self">To the discussion</a></p>
<p> </p>
</div></div></div>Fri, 19 Aug 2011 22:00:00 +0000ESIS17805 at https://imechanica.orghttps://imechanica.org/node/17805#commentshttps://imechanica.org/crss/node/17805Discussion of fracture paper #2 - The role of the T-stress
https://imechanica.org/node/17804
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/6159">crack extension</a></div><div class="field-item odd"><a href="/taxonomy/term/6160">T-stress</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>J.C. Sobotka, R.H. Dodds: Steady crack growth in a thin, ductile plate under small-scale yielding conditions: Three-dimensional modelling., Engineering Fracture Mechanics, Vol. 78, 2011, pp. 343-363; J.C. Sobotka, R.H. Dodds: T-stress effects on steady crack growth in a thin, ductile plate under small-scale yielding conditions: Three-dimensional modelling., Engineering Fracture Mechanics, Vol. 78, 2011, pp. 1182-1200. </p>
<p><a href="http://imechanica.org/node/10096" target="_self">To the discussion</a></p>
</div></div></div>Wed, 13 Apr 2011 22:00:00 +0000ESIS17804 at https://imechanica.orghttps://imechanica.org/node/17804#commentshttps://imechanica.org/crss/node/17804Discussion of fracture paper #1 - A contol volume model
https://imechanica.org/node/9793
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/77">opinion</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/65">opinion</a></div><div class="field-item odd"><a href="/taxonomy/term/238">journals</a></div><div class="field-item even"><a href="/taxonomy/term/1545">J integral</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>This is a premiere: my first contribution to the new ESIS' blog announced in January. Why comment on papers in a scientific journal after they have passed the review process already? Not to question their quality, of course, but animating a vital virtue of science again, namely discussion. The pressure to publish has increased so much that one may doubt whether there is enough time left to read scientific papers. This impression is substantiated by my experience as a referee. Some submitted manuscripts have to be rejected just because they treat a subject, which conclusively has been dealt years before - and the authors just don’t realise. So much to my and Stefano’s intention and motivation to start this project.</p>
<p>Here is my first “object of preference”:</p>
<p><a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V2R-50X2NK6-1&_user=2620285&_coverDate=11%2F30%2F2010&_rdoc=19&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info%28%23toc%235709%232010%23999229983%232491749%23FLA%23display%23Volume%29&_cdi=5709&_sort=d&_docanchor=&_ct=21&_acct=C000058180&_version=1&_urlVersion=0&_userid=2620285&md5=5e7b8a48834462161d0af2be381dcec1&searchtype=a" target="_blank">Ehsan Barati, Younes Alizadeh, Jamshid Aghazadeh Mohandesi, "J-integral evaluation of austenitic-martensitic functionally graded steel in plates weakened by U-notches", <em>Engineering Fracture Mechanics</em>, Vol. 77, Issue 16, 2010, pp. 3341-3358. </a></p>
<p><strong>The comment</strong></p>
<p>It is the concept of a finite <span>“control”</span> or <span>“elementary volume”</span> which puzzles me. It is introduced to establish “a link between the elastic strain energy E(e) and the J-integral” as the authors state. Rice’s integral introduced for homogeneous hyperelastic materials is path-independent and hence does not need anything like a characteristic volume. This is basically its favourable feature qualifying it as a fracture mechanics parameter relating the work done by external forces to the intensity of the near-tip stress and strain fields.</p>
<p>Fig. 2 (a) schematically presents this control volume in a homogeneous material, and the authors find that “the control volume boundary in homogeneous steel is semi-circular”. But how is it determined and what is the gain of it?</p>
<p><span><span>Introducing a characteristic volume for homogeneous materials undermines 40 years of fracture mechanics in my eyes.</span>. </span></p>
<p>One might argue that the introduction of this volume is necessary or beneficial for functionally graded materials (FGM). The authors state however that “comparison of the J-integral evaluated by two integration paths has shown that the path-independent property of the J-integral is valid also for FGMs”. Whether or not this is true (there are numerous publications on “correction terms” to be introduced for multi-phase materials), it questions the necessity of introducing a “control volume”. There is another point confusing me. The J-integral is a quantity of continuum mechanics knowing nothing about the microstructure of a material. The austenite and martensite phases of the FGM differ by their ultimate tensile strength and their fracture toughness. Neither of the two material parameters affects the (applied) J, only Young’s modulus does in elasticity. Hence it does not surprise that J emerged as path-independent! The authors compare J-integral values of homogeneous and FG materials for some defined stress level at the notch root in Fig. 10. The differences appear as minor. Should we seriously expect, that a comparison of the critical fracture load predicted by Jcr and the experimental results (Fig. 16) will provide more than a validation of the classical J concept for homogeneous brittle materials?</p>
<p><span>Not to forget</span>: The authors deserve thanks that they actually present experimental data for a validation of their concept, which positively distinguishes their paper from many others!</p>
<p><em>W. Brocks</em></p>
</div></div></div>Sat, 12 Feb 2011 14:59:55 +0000ESIS9793 at https://imechanica.orghttps://imechanica.org/node/9793#commentshttps://imechanica.org/crss/node/9793A blog for discussing fracture papers
https://imechanica.org/node/9631
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/77">opinion</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/31">fracture</a></div><div class="field-item odd"><a href="/taxonomy/term/65">opinion</a></div><div class="field-item even"><a href="/taxonomy/term/78">papers</a></div><div class="field-item odd"><a href="/taxonomy/term/238">journals</a></div><div class="field-item even"><a href="/taxonomy/term/2004">discussion forums</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>The aim of <a href="http://www.structuralintegrity.eu" target="_blank">ESIS</a> is not only to develop and extend knowledge in all aspects of structural integrity, but also to disseminate this knowledge world-wide by means of scientific publications and to educate young engineers and scientists. <br /> For these purposes, three Elsevier journals - <a href="http://www.elsevier.com/wps/find/journaldescription.cws_home/322/description#description" target="_blank"><em>Engineering Fracture Mechanics</em></a> , <em>Engineering Failure Analysis</em> and <em>International Journal of Fatigue</em> - are published in affiliation with ESIS.</span></p>
<p><span>Promoting and intensifying this aim is what we want to achieve through a new blog that ESIS will manage here for discussing some of the papers which appear in <em>Engineering Fracture Mechanics</em>. Its editors, Profs. Karl-Heinz Schwalbe and Tony Ingraffea,fully support this initiative.</span></p>
<p><span> ESIS hopes that this blog will achieve the following objectives:</span></p>
<ul><li>To start a scientific discussion on relevant topics through comments by leading scientists (the chief ‘commenter’ will be Prof. Wolfgang Brocks);</li>
<li>To remind the authors of papers in EFM (and all the fracture community) that perhaps they have forgotten something important which was published in the past (perhaps in old books): the policy of ESIS is to <a href="http://www.structuralintegrity.eu/documents/770.html" target="_blank">make some of these books available on-line</a> to ESIS members;</li>
<li>To promote a real cross-citation of the papers and a substantive discussion of ideas in a scenario where, in spite of the easy on-line access to most journals, there is a serious tendency to restrict the number of ‘external references’ and a snobbish tendency to promote ‘auto-citations’ (to the same group, the same journal, the same country);</li>
<li>To focus attention on new ideas that run the serious risk of not emerging from the noise of too much published “stuff”;</li>
<li>To induce bloggers to communicate their opinions on a paper, in particular their interpretation of the research results, thus adding new thoughts to that paper. In addition, to promote excellence in publication in a scenario where deficiencies of a paper may not have been detected by the reviewers, simply due to the pressure of time the reviewers have to do their work.</li>
</ul><p><span>The proposed rules of usage of this blog include:</span></p>
<ol><li>A group of leading scientists headed by Prof. W. Brocks will post onto this iMechanica node comments and remarks to some of the papers<span> </span>published in EFM;</li>
<li>The authors of the papers will receive a notification of the remarks by <a href="/user/23526" target="_blank">ESIS Webmaster</a> and they will be invited to reply through a detailed document that will appear on the ESIS website;</li>
<li>The replies will also be posted onto iMechanica by <a href="/user/23810">ESIS</a> (so that the authors do not have to worry about technical details). Hopefully, we will receive further comments and questions by other scientists/practitioners.</li>
</ol><p><span></span></p>
<p> <span>To start, this blog will concentrate only <span> </span>on <strong>fracture papers</strong>; later other sections devoted to fatigue and other sectors of structural integrity will be added.</span> </p>
<p><span>If you like the idea, then post a comment and bookmark this iMechanica node. Shortly, as soon as we will have prepared all the technical details, we will be ‘on the air’.</span> </p>
<p> </p>
<p class="MsoNormal"><em><span>S. Beretta & W. Brocks</span></em> <em><span>ESIS Executive Committee </span></em></p>
</div></div></div>Sat, 15 Jan 2011 11:03:11 +0000ESIS9631 at https://imechanica.orghttps://imechanica.org/node/9631#commentshttps://imechanica.org/crss/node/9631Index of all discussions
https://imechanica.org/node/9794
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/77">opinion</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/12420">#fracture</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span><strong><span>D</span></strong><strong><span>is</span><span>cussion of fracture paper #25 - The role of the fracture process region</span></strong></span></p>
<p><a href="https://imechanica.org/node/23886" target="_blank" rel="noopener noreferrer">The subject of this blog is a fracture mechanical study of soft polymers. It is well written and technically detailed which makes the reading a good investment. The paper: Experimental and numerical assessment of the work of fracture in injection-moulded low-density polyethylene, M. Kroon et al.</a></p>
<p><span><strong><span>D</span></strong><strong><span>is</span><span>cussion of fracture paper #24 - The sound of crack growth</span></strong></span></p>
<p><span><span><a href="https://imechanica.org/node/23731">Carbon fibre reinforced polymers combines desired features from different worlds. The fibres are stiff and hard, while the polymers are the opposite, weak, soft and with irrelevant fracture toughness. Irrelevant considering the small in-plane deformation that the fibres can handle before they break.</a></span></span></p>
<p><span><strong><span>D</span></strong><strong><span>is</span><span>cussion of fracture paper #2</span></strong><strong><span>3 - Paris' exponent m<2 and behaviour of short crack</span></strong><strong><span>s</span></strong></span><a href="https://imechanica.org/node/23157" target="_blank" rel="noopener noreferrer"><strong><span> </span></strong></a></p>
<p><a href="https://imechanica.org/node/23169">I came across a very interesting paper in Engineering Fracture Mechanics about a year ago. It gives some new results of stochastic aspects of fatigue. The paper is: <span><span>”On the distribution and scatter of fatigue lives obtained </span></span></a></p>
<p><span><strong><span>D</span></strong><strong><span>is</span><span>cussion of fracture paper #22</span><span> - Open access puts scientists in control of their own results</span></strong></span><a href="https://imechanica.org/node/23157" target="_blank" rel="noopener noreferrer"><strong><span> </span></strong></a></p>
<p><span><a href="https://imechanica.org/node/23157" target="_blank" rel="noopener noreferrer">The last ESIS blog about how surprisingly few scientists are willing/able to share their experimental data, received an unexpectedly large interest. Directly after the publication another iMechanica blogger took the same theme but he put the focus on results produced at numerical analyses that are presented with insufficient</a><br /></span></p>
<p><span><strong><span>D</span></strong><strong><span>is</span><span>cussion of fracture paper #21</span><span> - Only 6% of experimentalists want to disclose raw-data</span></strong><strong><span> </span></strong></span>
</p><p><a href="https://imechanica.org/node/22590" target="_blank" rel="noopener noreferrer">Long term availability of raw experimental data in experimental fracture mechanics, by Patrick Diehl, Ilyass Tabiai, Felix W. Baumann, Daniel Therriault and Martin Levesque, in Engineering Fracture Mechanics, 197 (2018) 21–26</a>.</p>
<p><span><strong><span>D</span></strong><strong><span>is</span><span>cussion of fracture paper #20</span><span> - Add stronger singluarities to improve numerical accuracy</span></strong></span><strong><span> </span></strong>
</p><p><a href="https://imechanica.org/node/22425" target="_blank" rel="noopener noreferrer">Evaluation of stress intensity factors under multiaxial and compressive conditions using low order displacement or stress field fitting, R. Andersson et al., in Engineering Fracture Mechanics, 189 (2018) 204–220</a>.</p>
<p><span><strong><span>D</span></strong><strong><span>is</span><span>cussion of fracture paper #19</span><span> - Fracture mechanical properties of graphene</span></strong></span><strong><span> </span></strong>
</p><p><a href="https://imechanica.org/node/21985" target="_blank" rel="noopener noreferrer">Growth speed of single edge pre-crack in graphene sheet under tension, Jun Hua et al., Engineering Fracture Mechanics 182 (2017) 337–355</a>.</p>
<p><strong><span>D</span></strong><strong><span>is</span><span>cussion of fracture paper #18</span><span> - A crack tip energy release rate caused by T-stress</span></strong><strong><span> </span></strong>
</p><p><a href="https://imechanica.org/node/21796" target="_blank" rel="noopener noreferrer">Zi-Cheng Jiang, Guo-Jin Tang, Xian-Fang Li, Effect of initial T-stress on stress intensity factor for a crack in a thin pre-stressed layer, Engineering Fracture Mechanics, pp. 19-27.</a></p>
<p><span><strong><span>D</span></strong><strong><span>is</span><span>cussion of fracture paper #1</span><span>7 - </span></strong></span><strong><span>What is the second most important quantity at fracture?</span></strong>
</p><p><a href="https://imechanica.org/node/21722">Fracture assessment based on unified constraint parameter for pressurized pipes with circumferential surface cracks, M.Y. Mu, G.Z. Wang, F.Z. Xuan, S.T. Tu, Engineering Fracture Mechanics 175 (2017), 201–218<span><br /></span></a></p>
<p><strong><span>D</span></strong><strong><span>iscussion of fracture paper #16 - What is wrong with pure mode I and II? A lot it seems</span></strong>
</p><p><a href="https://imechanica.org/node/21428">An improved definition for mode I and mode II crack problems" by M.R. Ayatollahi, M. Zakeri in Engineering Fracture Mechanics 175 (2017) 235–246.</a></p>
<p><span><strong><span>Discussion of fracture paper #15 - Design for crack arrest</span></strong></span><a href="http://imechanica.org/node/21428"><strong><span><span><br /></span></span></strong></a></p>
<p><a href="https://imechanica.org/node/20605">Brittle crack propagation/arrest behaviour in steel plate – Part I: Model formulation” by Kazuki Shibanuma, Fuminori Yanagimoto, Tetsuya Namegawa, Katsuyuki Suzuki, Shuji Aihara in Engineering Fracture Mechanics, 162 (2016) 324-340</a>.</p>
<p><span><strong><span>Discussion of fracture paper #14</span></strong></span><strong><span><span> - How to <span class="first">understand</span> the J-integral when multiple cracks are growing at different rates</span></span></strong>
</p><p><a href="https://imechanica.org/node/20004">Fracture resistance enhancement of layered structures by multiple cracks, S. Goutianos and B.F. Sørensen, Engineering Fracture Mechanics, 151 (2016) 92-108.</a></p>
<p><strong><span><span>Discussion of fracture paper #13 - </span>Cohesive properties at ductile tearing</span></strong></p>
<p><a href="https://imechanica.org/node/19424">Cohesive zone modeling and calibration for mode I tearing of large ductile plates, P.B. Woelke, M.D. Shields, J.W. Hutchinson, Engineering Fracture Mechanics, Vol 147 (2015) pp. 293-305.</a></p>
<p><span><strong><span>Discussion of fracture paper #12</span></strong></span><span><strong><span> - </span></strong><strong>Crack paths and fracture process region autonomy</strong></span></p>
<p><a href="https://imechanica.org/node/18931">Method for calculating G, G_I, and G_II to simulate crack growth in 2D, multiple-material structures, E.K. Oneida, M.C.H. van der Meulen, A.R. Ingraffea, Engineering Fracture Mechanics, Vol 140 (2015) pp. 106–126</a>. </p>
<p><span><strong><span>Discussion of fracture paper </span></strong></span><strong><span><span>#11 - </span>Fracture processes and phase field modelling</span></strong></p>
<p><a href="https://imechanica.org/node/18255">A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure, T.T. Nguyen, J. Yvonnet, Q.-Z. Zhu, M. Bornert, C. Chateau, Engineering Fracture Mechanics, Vol 139 (2015) pp. 18–39.</a></p>
<p><span><strong><span>Discussion of fracture paper #10 </span></strong></span><span><strong><span>- </span></strong><strong>Searching for the length scale of stress corrosion</strong></span></p>
<p><a href="https://imechanica.org/node/17865">Further study on crack growth model of buried pipelines exposed to concentrated carbonate-bicarbonate solution, B.T. Lu, Engineering Fracture Mechanics vol. 131 (2014) pp. 296-314.</a><span> </span></p>
<p><span><strong><span>Discussion of fracture paper #9 - Crack tip modelling</span></strong></span></p>
<p><a href="https://imechanica.org/node/17471" target="_blank" rel="noopener noreferrer">Effect of a single soft interlayer on the crack driving force, M. Sistaninia and O. Kolednik, Engineering Fracture Mechanics, Vol. 130, 2014, pp. 21–41.</a> </p>
<p><span><strong><span>Discussion of fracture paper #8 - Elastic follow-up</span></strong></span></p>
<p><a href="16898" target="_blank" rel="noopener noreferrer">P.M. James: Re-derivation of plasticity interaction for combined loading under significant levels of elastic follow-up. Engineering Fracture Mechanics, Vol. 126, 2014, pp. 12–26.</a></p>
<p><strong><span>Discussion of fracture paper #7 - Configurational force approach</span></strong>
</p><p><a href="16356" target="_blank" rel="noopener noreferrer">K. Özenç, M. Kaliske, G. Lin, G. Bhashyam: Evaluation of energy contributions in elasto-plastic fracture: A review of the configurational force approach, Engineering Fracture Mechanics, 2014, Vol. 115, pp. 137-153.</a></p>
<p><span><strong><span>Discussion of fracture paper #6 - Stress intensity factor for steep yield distribution</span></strong></span></p>
<p><a href="15504" target="_blank" rel="noopener noreferrer">T. Yasuoka, Y. Mizutani, A. Todoroki: Applicable limit of the stress intensity factor for steep yield strength distribution, Engineering Fracture Mechanics, 2013, Vol. 110, pp. 1-11.</a></p>
<p><span><strong><span>Discussion of fracture paper #5 - Yield ciriterion or failure criterion</span></strong></span></p>
<p><a href="14387" target="_blank" rel="noopener noreferrer">Henrik Danielsson and Per Johan Gustafsson: A three dimensional plasticity model for perpendicular to grain cohesive fracture in wood, Engineering Fracture Mechanics Vol. 98 2013, pp.137–152.</a></p>
<p><span><strong><span>Discussion of fracture paper #4 - Is paper ductile?</span></strong></span></p>
<p><a href="11741" target="_blank" rel="noopener noreferrer">P. Mäkelä and S. Östlund: Cohesive crack modelling of thin sheet material exhibiting anisotropy, plasticity and large-scale damage evolution. Engineering Fracture Mechanics,Vol. 79, 2012 pp. 50-60.</a></p>
<p><span><strong><span>Discussion of fracture paper #3 - Length scales in fracture</span></strong></span></p>
<p><a href="10945" target="_blank" rel="noopener noreferrer">H. Krull and H. Yuan: Suggestions to the cohesive traction–separation law from atomistic simulations. Engineering Fracture Mechanics, Vol. 78, 2011, pp. 525-533.</a></p>
<p><span><strong><span>Discussion of fracture paper #2 - The role of the T-stress</span></strong></span></p>
<p><a href="10096" target="_blank" rel="noopener noreferrer">J.C. Sobotka, R.H. Dodds: Steady crack growth in a thin, ductile plate under small-scale yielding conditions: Three-dimensional modelling., Engineering Fracture Mechanics, Vol. 78, 2011, pp. 343-363; J.C. Sobotka, R.H. Dodds: T-stress effects on steady crack growth in a thin, ductile plate under small-scale yielding conditions: Three-dimensional modelling., Engineering Fracture Mechanics, Vol. 78, 2011, pp. 1182-1200.</a> </p>
<p><span><strong><span>Discussion of fracture paper #1 - A contol volume model</span></strong></span></p>
<p><a href="9793" target="_blank" rel="noopener noreferrer">Ehsan Barati, Younes Alizadeh, Jamshid Aghazadeh Mohandesi: J-integral evaluation of austenitic-martensitic functionally graded steel in plates weakened by U-notches, Engineering Fracture Mechanics, Vol. 77, Issue 16, 2010, pp. 3341-3358. </a></p>
<p><span><strong><span>A blog for discussing fracture papers</span></strong></span></p>
<p><span>The aim of </span><a href="http://www.structuralintegrity.eu/" target="_blank" rel="noopener noreferrer">ESIS</a><span> is not only to develop and </span><span>extend knowledge in all</span><span> </span><span>aspects of structural </span><span>integrity,</span><span> </span></p>
<p><span>but also to disseminate this knowledge world-wide by means of scientific publications and to educate young engineers and scientists. </span><span>For these purposes, three Elsevier journals - </span><a href="http://www.elsevier.com/wps/find/journaldescription.cws_home/322/description#description" target="_blank" rel="noopener noreferrer"><em>Engineering Fracture Mechanics</em></a><span> , </span><em>Engineering Failure Analysis</em><span> and >> <a href="9631" target="_blank" rel="noopener noreferrer">Read more</a></span></p>
</div></div></div>Sat, 01 Jan 2011 15:04:29 +0000ESIS9794 at https://imechanica.orghttps://imechanica.org/node/9794#commentshttps://imechanica.org/crss/node/9794