iMechanica - Comments for "Discussion of fracture paper #9 - Crack tip modelling"
https://imechanica.org/node/17471
Comments for "Discussion of fracture paper #9 - Crack tip modelling"enDear Otmar,
https://imechanica.org/comment/26814#comment-26814
<a id="comment-26814"></a>
<p><em>In reply to <a href="https://imechanica.org/node/17471">Discussion of fracture paper #9 - Crack tip modelling</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Otmar,</p>
<p>Thank you for the comment. You are right, there is also the interface. In the case of a penetrating crack it might have a width that has to be considered. So two simplifying circumstances arise. Either the fracture process zone is small compared to the width of the interface. Then I guess the crack tip can be treated as a point with a prescribed KIc-tip, critical J_tip or whatever that can quantify the critical state of the crack tip. Opposed to this, the width of the interface may be much less than the size of the fracture process zone. Then the details of that process zone needs to be resolved. Unfortunately there are also general cases when neither the crack tip or the interface can be treated as perfectly sharp.</p>
<p>About the yield stress inhomogeneity, I am a bit uncertain myself what I meant. Of course as you write there may be a jump in yield stress. Then if the fracture process is ductile with void nucleation, growth and coalescence, a sharp crack tip model attempt to summarise all stages with a single parameter. The tip will be in either material A or material B. On the other hand, if the real crack is penetrating the bi-material interface, first there has to be void growth and coalescence in material A and void nucleation in material B. Later, the void growth and coalescence occur in material B and finally the entire process zone is in material B. This intermediate state will perhaps give a variation of the fracture toughness that otherwise is identical in both materials.</p>
<p>One might imagine two ductile materials with same elastic-plastic properties and same fracture toughness. Say that the only difference between the materials is that one has many and fragile inclusions while the other material has few and strong inclusions. Then the first material has its toughness from the extensive energy that is required for void coalescence, and the second material requires much energy for void nucleation. As you suggest, a cohesive zone model might be the solution. A sharp crack tip model would not reveal any difference between the materials while a proper cohesive zone model would. The material model for the continuum that surrounds the cohesive zone can still be elastic-plastic. I guess that would not be too complicated since you already have a model developed for that part. That would have the reward that you would be able to distinguish between energy dissipating in the stable elastic-plastic continuum and the unstable material fracture process zone modelled by the cohesive zone.</p>
<p>I am looking forward to your coming publication and the next episode of this story.</p>
<p>Per</p>
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</ul>Thu, 29 Jan 2015 21:37:00 +0000ESIScomment 26814 at https://imechanica.orgDear Per
https://imechanica.org/comment/26615#comment-26615
<a id="comment-26615"></a>
<p><em>In reply to <a href="https://imechanica.org/node/17471">Discussion of fracture paper #9 - Crack tip modelling</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Per</p>
<p>I think, you raised very interesting questions in your comments to our paper. </p>
<p>Let us first consider a linear elastic material with inhomogeneity of the Young's modulus E, i.e. E exhibits a jump at the interface. Theory predicts that, for a crack ending directly at the interface, the crack driving force becomes infinite, if E decreases in the crack growth direction. The crack driving force becomes zero if E increases in the crack growth direction. <br />As you write, this is unrealistic, and one should introduce a non-linear region around the tip. How large should such a region be? A related question is, how sharp can a real bimaterial interface be?<br />A region not less than an atomic distance is maybe reasonable.</p>
<p>I am not sure whether I understand correctly your question in the case of yield stress inhomogeneity. If we take the length of the process zone l_proc as being proportional to the crack tip opening displacement (with the proportionality constant of the order of 2), then we have considered in the paper also cases where the distance L between crack tip and interface is smaller than l_proc. I do not see a big problem here. Do we overlook something?</p>
<p>Another problem is - and maybe that is also what you had in mind - that not only the crack driving force, measured in terms of J_tip, changes when the crack tip approaches the interface. Also, the crack growth resistance R will, in general, change. You know, the crack extends, if J_tip >= R. How can we model the change in R? Here we have had, as you also proposed, the idea of applying the cohesive zone model since this model allows us to with an intrinsic fracture resistance of the materials, prescribed by the cohesive energy. The materials left and right of the interface can then have different material properties and different characteristic cohesive zone parameters (c energy and cohesive stress). <br />We have started with the analyses, the first results are already available, but not yet published.</p>
<p>Best regards,</p>
<p>Otmar Kolednik</p>
<p>(<em>This comment was submitted by Professor Kolednik on November 10, 2014. Accidently it was removed for a while. I am sorry about that. PS</em>)</p>
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</ul>Sun, 09 Nov 2014 23:00:00 +0000O. Kolednikcomment 26615 at https://imechanica.orgError | iMechanica