iMechanica - J integral
https://imechanica.org/taxonomy/term/1545
enWhich theory Abaqus' Contour Integral for the determination of SIFs is based on?
https://imechanica.org/node/20633
<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/289">ABAQUS</a></div><div class="field-item odd"><a href="/taxonomy/term/11446">Contour integral</a></div><div class="field-item even"><a href="/taxonomy/term/1545">J integral</a></div><div class="field-item odd"><a href="/taxonomy/term/32">fracture mechanics</a></div><div class="field-item even"><a href="/taxonomy/term/256">Fatigue</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>I am actually using Abaqus' Contour Integral for the determination of stress intensity factors. But I do not know, which theory it is based on. Is it the same like the path-independent determination of J integral? Or is there a difference?</p>
</div></div></div>Tue, 29 Nov 2016 12:30:54 +0000havelmay20633 at https://imechanica.orghttps://imechanica.org/node/20633#commentshttps://imechanica.org/crss/node/20633A paper on fracture resistance enhancement of layered structures by multiple cracks
https://imechanica.org/node/19293
<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/1974">Paper</a></div><div class="field-item odd"><a href="/taxonomy/term/10921">toughnening</a></div><div class="field-item even"><a href="/taxonomy/term/5256">laminates</a></div><div class="field-item odd"><a href="/taxonomy/term/10607">fracture resistance</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><span>We have just published a new paper that presents a theoretical model to test if the fracture resistance of a layered structure can be increased by introducing weak layers changing the cracking mechanism. An analytical model, based on the J integral, predicts a linear dependency between the number of cracks and the steady state fracture resistance. A finite element cohesive zone model, containing two cracking planes for simplicity, is used to check the theoretical model and its predictions. It is shown that for a wide range of cohesive law parameters, the numerical predictions agree well quantitatively with the theoretical model. Thus, it is possible to enhance considerably the fracture resistance of a structure by adding weak layers.</span></p>
<p><span>The paper, which is called <strong>Fracture resistance enhancement of layered structures by multiple cracks</strong>, co-authored by Stergios Goutianos and Bent F. Sørensen, is published in <em>Engineering Fracture Mechanics</em> <strong>151</strong> (2016) 92–108.</span></p>
<p><span>You can use the following link, which will provide free access until January 30, 2016</span></p>
<p><span><a href="https://mail.win.dtu.dk/owa/redir.aspx?SURL=1kF7ZXa9Od6RgCReO0e1rbPjmhubByA6mI9eypGqhVWnKdMRLBXTCGgAdAB0AHAAOgAvAC8AYQB1AHQAaABvAHIAcwAuAGUAbABzAGUAdgBpAGUAcgAuAGMAbwBtAC8AYQAvADEAUwBCAFQAbwAzADgAbAAzAEQARAA4AHkA&URL=http%3a%2f%2fauthors.elsevier.com%2fa%2f1SBTo38l3DD8y" target="_blank">http://authors.elsevier.com/a/1SBTo38l3DD8y</a></span></p>
<p><span>I hope you enjoy reading the paper!</span></p>
<p><span>Best regards,</span></p>
<p><span>Bent</span></p>
</div></div></div>Mon, 04 Jan 2016 17:41:12 +0000Bent F. Sørensen19293 at https://imechanica.orghttps://imechanica.org/node/19293#commentshttps://imechanica.org/crss/node/19293Calculation of J integral of graphene using molecular dynamics simulations
https://imechanica.org/node/16081
<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/32">fracture mechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/93">molecular dynamics</a></div><div class="field-item even"><a href="/taxonomy/term/95">nanomechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/671">graphene</a></div><div class="field-item even"><a href="/taxonomy/term/694">crack propagation</a></div><div class="field-item odd"><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>
In our recent paper, <a href="http://rd.springer.com/article/10.1007/s10704-014-9931-y" target="_blank">atomistic and continuum modelling of temperature-dependent fracture of graphene</a>, we directly calculate J integral using the data obtained from molecular dynamics simulations. Fig. 1 outlines the calculation procedure of JIC. Fig. 1(a) shows the changes in potential energy with time (or applied strain) in an armchair graphene sheet with a size of 7.6 nm × 7.6 nm. A crack, length of ~0.7 nm, is placed in the centre of the sheet. Periodic boundary conditions are used along in plane directions. Simulation temperature is 1 K, and strain rate is 0.001 ps-1. Fig 1(b) shows the variation in potential energy during the crack propagation. It can be seen that the potential energy increases just after the crack starts to propagate (around point d). This is due to the chemical potential energy release from carbon-carbon bond breaking overcomes the strain energy release by crack propagation. As more bonds break, the strain energy release due to crack propagation starts to govern the total strain energy release. The crack propagation at various stages (marked as d to g in Fig. 1(b)) is shown in Fig. 1(d) to Fig. 1(g). The figures show that the crack propagates symmetrically. The out of plane deformation of the sheet, as shown in the video 1, prevails. </p>
<p><img src="files/J%20from%20MD.png" alt=" " width="562" height="742" /><br /><strong>Fig. 1</strong> Calculation of energy release rate of graphene. (a) Variation of potential energy with time. (b) and (c) variation of potential energy during the crack propagation. (d) to (g) show the crack propagation in graphene. The corresponding positions of Fig. (d) to (g) in the potential energy-time curve are marked in Fig. (b)
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The slope of the piece wise continuous curves in Fig 1(c) is proportional to the critical value of J integral (JIC). Figure 2 shows the variation of JIC with the propagated crack length (2ap), which has been normalized with respect to the width of the sheet (w). The value of 2ap/w is approximately 0.1 when a crack starts to propagate since w is kept around 10 times the initial crack length (2a) to avoid the effects of finiteness. When 2ap/w reaches 1, the periodic cracks start to interact with each other. Therefore Fig. 2 shows the value of JIC up to 0.8 of 2ap/w, where the periodic cracks do not interact with each other for the smallest sheet considered (i.e. w = 7.6 nm). <br /><img src="files/change%20in%20j%20with%20crack%20propagation.png" alt=" " width="300" height="300" /><br /><strong>Fig. 2</strong> Variation of JIC of armchair graphene with propagated crack length (2ap) for various initial crack lengths (2a). The solid symbols indicate the average value of JIC (JIC,avg) at various crack lengths. The left most solid symbol is the JIC,avg for 2a = 0.73 nm and other marks are in ascending order of initial crack lengths. The right most symbol is the JIC,avg for 2a = 3.63 nm.
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<object classid="d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" width="420" height="315">
<embed type="application/x-shockwave-flash" width="420" height="315" allowfullscreen="true" allowscriptaccess="always" src="//www.youtube.com/v/fczFNMXXWrI?hl=en_GB&version=3&rel=0"></embed></object><p>
<strong>Video 1</strong>: Crack induced ripples and fracture of an armchair graphene sheet with a central crack. The colour of atoms indicates the out of plane movement of atoms.</p>
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</div></div></div>Thu, 13 Feb 2014 06:53:26 +0000Nuwan Dewapriya16081 at https://imechanica.orghttps://imechanica.org/node/16081#commentshttps://imechanica.org/crss/node/16081J integral variation through thickness in tubes with through-wall circumferential crack, calculated with Abaqus/CAE
https://imechanica.org/node/11107
<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/1060">ABAQUS/CAE</a></div><div class="field-item odd"><a href="/taxonomy/term/1545">J integral</a></div><div class="field-item even"><a href="/taxonomy/term/4433">tube</a></div><div class="field-item odd"><a href="/taxonomy/term/6635">through-wall circumferential crack</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>Dear friends: </span><span>I am a PhD candidate studying fracture problems in tubes. I am doing J integral calculations in Abaqus, for tubes with through-wall circumferential cracks subjected to tensile and bending loads. I am using quadratic 20 nodes isoparametric elements with reduced integration (C3D20R), ranging from two to five elements through the wall thickness mesh. The singularity is modeled with midside node parameter t=0.3 (not 0.25 because the 3D elements planes are not perpendicular to the crack line) and collapsed element side, duplicate nodes, to create a combined square root and 1/r singularity for hardening materials (the material is modeled as elastic-plastic, with a stress-strain curve introduced with a data table). The results show that the J integral varies through the thickness of the tube. Up to now we have only one reference showing this kind of J integral behavior through thickness for tubes (see attachment 1). This reference shows a variation of J with the highest value at the mid-thickness of the wall, and depends on the number of elements through thickness: the question is if this is a numerical artifact or has some physical meaning. Our results also show J variation through thickness, but with the higher J values at the wall surfaces for high loads (see attachment 2). Obviously, the comparison between these results is not direct due to the fact that both problems have different geometry, material properties and loading conditions. </span><span>From the earlier, I have the following questions: </span><span><span>1)<span> </span></span></span><span>Are there more references regarding the J variation through thickness for tubes with through-wall circumferential cracks? </span><span><span>2)<span> </span></span></span><span>The high J variation through thickness, is it a physical or numerical result? </span><span><span>3)<span> </span></span></span><span><span> </span>The singularity modeling in our case (t=0.3 and collapsed duplicated nodes), is it adequate? </span><span><span>4)<span> </span></span></span><span>Abaqus calculates a J integral in each element face, where are located the nodes. In the case of quadratic elements, Abaqus also calculates the J integral in the middle of the element, using the midside nodes. Are the last J integral values comparable with the J integral values obtained in the element faces? I mean if the J values have the same “weight” in an averaging process, for instance, or if there is some difference in the accuracy depending if the nodes used to calculate J are in the faces or in the mid-face of the element. Is it better to calculate element averages than individual values in each face and mid-face?</span><span>Thank you very much for your comments!</span><span>Best regards, </span><span>Marcos</span> </p>
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</div></div></div>Tue, 20 Sep 2011 13:20:08 +0000Marcos Bergant11107 at https://imechanica.orghttps://imechanica.org/node/11107#commentshttps://imechanica.org/crss/node/11107use of CINT command for J integral calculation of 3d model with ansys
https://imechanica.org/node/10072
<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/1258">3D crack analysis using ansys</a></div><div class="field-item odd"><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>
I used for the first time the CINT command with ansys, and I get strange results:
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negative values
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very different values for 2 adjacent nodes on the crack front
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non converging values (values fluctuating from 1 contour to another, going up and down)
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Also, i don't know what are the units of the J integral (I am using SI units, dimensions in mm ). It's important to know so I can calculate the SIF
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How can I know what contour gives the best result? what are the units of the Jintegral in the SI.
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Anybody have some information for me?
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Thanks
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</div></div></div>Mon, 11 Apr 2011 01:13:13 +0000proussy10072 at https://imechanica.orghttps://imechanica.org/node/10072#commentshttps://imechanica.org/crss/node/10072Discussion 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/9793Fracture Mechanics
https://imechanica.org/node/6673
<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/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>
Hello...
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Can any one help me in how to solve J INTEGRAL for simple 2D geometries.Atleast can anyone help me where can i get PDF files on J integral... Plz its urgent its a part of Thesis... Plz post your conmments at <a href="mailto:ravikumar_04333@yahoo.com">ravikumar_04333@yahoo.com</a>
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</div></div></div>Sun, 23 Aug 2009 04:50:24 +0000ravimech043336673 at https://imechanica.orghttps://imechanica.org/node/6673#commentshttps://imechanica.org/crss/node/6673J-Integral Elliptical Hole (Plane Stress) Perfectly Plastic Material
https://imechanica.org/node/4032
<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 fracture mechanics community may be interested in a new evaluation of a J-Integral for a fundamental geometry: an elliptical hole in a perfectly plastic material under the Tresca yield condition for plane stress loading conditions. The analysis is exact and involves only elementary functions. This makes the problem suitable as a classroom example or as a homework problem for a graduate level course in fracture mechanics. See J. Elasticity (2008) 92:217-226. <a href="http://www.springerlink.com/content/102932/">http://www.springerlink.com/content/102932/</a>
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</div></div></div><div class="field field-name-taxonomy-forums field-type-taxonomy-term-reference field-label-above"><div class="field-label">Forums: </div><div class="field-items"><div class="field-item even"><a href="/forum/666">Fracture Mechanics Forum</a></div></div></div><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/128">education</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-above"><div class="field-label">Free Tags: </div><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/1545">J integral</a></div><div class="field-item odd"><a href="/taxonomy/term/2438">plane stress</a></div><div class="field-item even"><a href="/taxonomy/term/2906">elliptical hole</a></div><div class="field-item odd"><a href="/taxonomy/term/2907">mode I loading</a></div><div class="field-item even"><a href="/taxonomy/term/2908">perfectly plastic material</a></div><div class="field-item odd"><a href="/taxonomy/term/2909">Tresca yield condition</a></div></div></div>Sat, 11 Oct 2008 19:28:26 +0000David J Unger4032 at https://imechanica.orghttps://imechanica.org/node/4032#commentshttps://imechanica.org/crss/node/4032Jintegral and Umat subroutine
https://imechanica.org/node/2709
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Hello,
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I have implemented a new constitutive viscoelastic-mechanosorptive creep model for porous materials in the Umat subroutine. Plasticity is not included. I use the thermal-displacement Abaqus analysis, that is, a transient analysis. Now, I would like to calculate the J-integral for a cracked body and, since I am able to define the strain energy density of my constitutive model, I suppose that I should calculate the new expression of the energy in Umat and this energy could be used by Abaqus for calculating the J-integral at each time step of the transient analysis. Actually, into the Abaqus manual I found that for time-dependent problems I should use the C_t integral for creep but in this case I wonder if I have to use both the Umat and the CREEP subroutines. How?
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</div></div></div><div class="field field-name-taxonomy-forums field-type-taxonomy-term-reference field-label-above"><div class="field-label">Forums: </div><div class="field-items"><div class="field-item even"><a href="/forum/666">Fracture Mechanics Forum</a></div></div></div><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-above"><div class="field-label">Free Tags: </div><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/1545">J integral</a></div><div class="field-item odd"><a href="/taxonomy/term/1587">UMAT</a></div><div class="field-item even"><a href="/taxonomy/term/1859">creep</a></div></div></div>Thu, 14 Feb 2008 11:22:29 +0000Stefania Fortino2709 at https://imechanica.orghttps://imechanica.org/node/2709#commentshttps://imechanica.org/crss/node/2709cracking analyses in a bended sandwich beam
https://imechanica.org/node/2299
<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/1545">J integral</a></div><div class="field-item even"><a href="/taxonomy/term/1546">Energy release rate</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>
I'm studying cracking analyses in a three point loaded specimen of a composed beam.I'm using ANSYS and i want to create codes for estimation of J integral and energy release rate in the vicinity of crack tip.After that i'll calculate the stresses and strains fields,and then i can compare the equivalent fields i retrived using CTOD and K(I,II,III) factors (according to ANSYS algorithm).
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My problem is that I'd like to find a relationship between the above mentioned quantities(J,G) with K(I,II,III)factors.
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Another subject i'm thinking of ,is that i'm studying the pressed area of the beam (negative normal stresses -the cracking faces are parallel with the beam axis-),so i retrived KI nearly 0.It sounds logical but i am not sure that the method of K factors estimation using CTOD IS CORRECT.Actually i have negative desplacements between the crack faces and in some cases penetration to each other.
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I would appreciate any ideas for the above.
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</div></div></div>Thu, 15 Nov 2007 13:24:22 +0000Ilias I. Tourlomousis2299 at https://imechanica.orghttps://imechanica.org/node/2299#commentshttps://imechanica.org/crss/node/2299