iMechanica - Comments for "Resistance Curve "
https://imechanica.org/node/7674
Comments for "Resistance Curve "enRe: Crack propagation under constant loading
https://imechanica.org/comment/25666#comment-25666
<a id="comment-25666"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/18963#comment-18963">Crack propagation under constant loading</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 Paul: Please take a look at the drawing in the section "stable extension of a crack". At load lambda_2, the crack has extended to a length a. If the load is fixed, the crack will not extend further, because the loading curve is below the resistance curve.
</p>
<p>
Also, not all loading curves are increasing functions of the length of the crack. Consider a double cantilever beam under the displacement-controlled conditon.
</p>
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</ul>Sun, 09 Mar 2014 05:11:32 +0000Zhigang Suocomment 25666 at https://imechanica.orgCrack propagation under constant loading
https://imechanica.org/comment/18963#comment-18963
<a id="comment-18963"></a>
<p><em>In reply to <a href="https://imechanica.org/node/7674">Resistance Curve </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 Zhigang,
</p>
<p>
Thanks for this helpful lecture
</p>
<p>
I have a question regarding the stability of an advancing crack. When<br />
G<sigma0, there is no propagation, the crack is stable, I can<br />
understand it. It means a crack of length a<a0 (where G(a0)=sigma0)<br />
won't grow.
</p>
<p>
But what I don't understand is how a crack could stop when it has<br />
started to propagate. Indeed, when the crack starts to propagate from a<br />
length a1, it reaches a new length a2. From this new length, the R-curve<br />
will show us there is a propagation again, to a new length a3 and so<br />
on.
</p>
<p>
And G(a) being an increasing function of a,as long as G(a) is greater<br />
than sigma0, I don't understand why an advancing crack should stop when<br />
under a constant load. To my mind, it will propagate inevitably until<br />
the critical length and then propagate brutally.
</p>
<p>
Would you mind to explain to me what is actually happening ? I think my reasoning is biased but I cannot fix it.
</p>
<p>
</p>
<p>
Thanks in advance, best regards.
</p>
<p>
Paul
</p>
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</ul>Fri, 27 Apr 2012 13:01:27 +0000P. F. C.comment 18963 at https://imechanica.orgRe: DCB testing for the determination of bridging laws
https://imechanica.org/comment/13751#comment-13751
<a id="comment-13751"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/13744#comment-13744">DCB testing for the determination of bridging laws</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 Sergej and Bent: Thank you so much for your comments. I have been reading the papers that you suggested, and found them very helpful. My notes posted here was for one lecture in the course on fracture mechanics. In this lecture, I elected to introduce R-curve, without specifying any miscrospcopic mechanism.
</p>
<p>
As listed on the <a href="http://imechanica.org/node/7448">website of the course</a>, I will later give lectures on crack bridging. Your input is helping me to prepare these lectures.
</p>
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</ul>Sat, 06 Mar 2010 10:03:55 +0000Zhigang Suocomment 13751 at https://imechanica.orgDCB testing for the determination of bridging laws
https://imechanica.org/comment/13744#comment-13744
<a id="comment-13744"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/13696#comment-13696">DCB data reduction</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>As pointed out by Sergej, the J integral evaluated along the external boundaries of the DCB loaded with wedge forces is (per beam) force per unit width multiplied by the rotation angle at the pint where the force is applied (Paris and Paris, 1988). It is then easy to understand why the LEFM equation for G overestimates J (see Fig. 10 in Suo, Bao, Fan, 1992): The bridging tractions reduce the deflection and the rotation of the beam, so that the rotation at the point where the wedge force applies is less than what is predicted using beam theory - the beam theory equation for the energy release rate G can be considered as being the J integral solution with the rotation angle of an unbridged beam.</p>
<p>This may also be the reason why equation (9) in Sergej paper works better that equation (7). Bridging tractions will reduce both the defection and rotation of the beams. Thus, if the deflection is measured (but not the rotation) the reduce deflection used in (9) will reflect the reduced rotation. </p>
<p>The J integral solution described above also explains why the so-called root rotation is important for the wedge loaded DCB; it gives an additional rotation also at the point where the forces apply and thus influences the J value.</p>
<p>Ulf Stighs group in Sweden has successfully used a shaft encoder to measure the beam-end rotation of DCB-specimen loaded with wedge forces for the measurement of J, see e.g. </p>
<p>Andersson T. and Stigh U., 2004, "The stress-elongation relation for and adhesive layer loaded in peel using equilibrium of energetic forces",<em> International Journal of Solids and Structures</em> <strong>41</strong>, 413-434.</p>
<p>I prefer testing DCB-specimens using pure bending moments. As discussed in Suo, Bao and Fan (1992), the J integral is determined by the applied moments. There are no effects of root rotation. No additional measurements (crack length, rotations or deflections) are needed for the J integral determination. However, a special loading device is needed for the creation of pure bending moments. But I think it is better to perform experiments that are difficult to perform (requiring special loading devices), but are easy to model and interpret than visa versa.<br />
<br />
The J integral approach can be generalized to mixed mode cracking. Assuming that the fracture resistance is due to a mixed mode bridging law that can be derived from a potential function, the bridging law can be determined by partial differentiation. We have used that approach for the determination of mixed mode bridging laws from DCB specimens loaded with uneven bending moments.</p>
<p>Sørensen, B. F., and Jacobsen, T. K., 2009, "Delamination of fibre composites: determination of mixed mode cohesive laws", <em>Composite Science and Technology</em> <strong>69</strong>, 445-56.</p>
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</ul>Fri, 05 Mar 2010 21:19:41 +0000Bent F. Sørensencomment 13744 at https://imechanica.orgDCB data reduction
https://imechanica.org/comment/13696#comment-13696
<a id="comment-13696"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/13694#comment-13694">Large-scale bridging in DCB</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 Zhigang,
</p>
<p>
I think that strictly speaking they all do not work, Eq. (9) just has much better accuracy than others. As it was shown in our <a href="http://dx.doi.org/10.1016/S0266-3538(03)00042-3" target="_blank" title="next paper">next paper</a><br />
(Fig. 6), Eq. 9 in general is very accurate even for short cracks. The<br />
reason for this - it does not contain crack length. Williams in 1989<br />
have shown that for short cracks one needs to correct crack length to<br />
get accurate results in DCB test. There is no crack length in Eq. 9, no<br />
corrections are needed.
</p>
<p>
But it is also possible to use angle<br />
method (Williams 1987, Paris & Paris 1988, Nilsson 2006), which<br />
should incorporate all bridging effects, since it is based on<br />
J-integral computation along exterior boundary of the specimen.
</p>
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</ul>Mon, 01 Mar 2010 16:30:51 +0000Sergej Tarasovcomment 13696 at https://imechanica.orgLarge-scale bridging in DCB
https://imechanica.org/comment/13694#comment-13694
<a id="comment-13694"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/13687#comment-13687">I1: While this is true in a</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 Sergej: Thank you very much for your comments. I've just read <a href="http://dx.doi.org/10.1016/S0013-7944(00)00131-4">your paper</a>. I really like it. In particular, I am intrigued by your Figure 7, which shows that Eq. (9) can be used to evaluate J.
</p>
<p>
As you pointed out, the result is significant in practice. It enables one to use DCB to determine the bridging law from experimental data.
</p>
<p>
Do you know why Eq. (9) works, while Eq. (7), (8) and (10) do not?
</p>
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</ul>Mon, 01 Mar 2010 14:51:41 +0000Zhigang Suocomment 13694 at https://imechanica.orgI1: While this is true in a
https://imechanica.org/comment/13687#comment-13687
<a id="comment-13687"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/13683#comment-13683">RE:RE: wedge force vs. moment</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>
<strong>I1:</strong> While this is true in a strict sense, in practice a lot<br />
depends on data reduction methods. We have performed similar<br />
simulations in one <a href="http://dx.doi.org/10.1016/S0013-7944(00)00131-4" target="_blank" title="paper">paper</a><br />
and compared two data reduction methods with FEM calculations. For one<br />
method the same results like in your paper were obtained, but other was<br />
very close to FE results (the error was within few percent). Applying<br />
this method to the experimental data, we got steady state value of G<br />
for two specimen's thicknesses (for third thickness the specimens were<br />
too short).
</p>
<p>
<strong>I2:</strong> <strong> </strong>If the specimen is sufficiently long, we will get translational symmetry for wedge force.
</p>
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</ul>Sun, 28 Feb 2010 01:29:05 +0000Sergej Tarasovcomment 13687 at https://imechanica.orgRE:RE: wedge force vs. moment
https://imechanica.org/comment/13683#comment-13683
<a id="comment-13683"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/13682#comment-13682">RE: wedge force vs. moment</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>
<strong>I1</strong>: The dificulty lies in the determination of G or K in terms of the applied load. Under the large-scale bridging condition, the bridging zone is so large that one may not neglect it in solving the boundary-value problem. However, the bridging law is typically unknown prior to the experiment, so one does not not know what to use to set up the boundary condition.
</p>
<p>
One may choose to neglect this inconvenience, neglect the bridging zone, and use the linear elastic elastic solution to relate G to the applied load. But this practice has no reason to be valid. Fig. 10 in <a href="http://www.seas.harvard.edu/suo/papers/015.pdf">the 1992 paper</a> illustrates this point.
</p>
<p>
<strong>I2</strong>: By translational symmetry I mean that when the bridging zone is translated along the beam, the field remains unchanged.
</p>
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</ul>Sat, 27 Feb 2010 23:04:00 +0000Zhigang Suocomment 13683 at https://imechanica.orgRE: wedge force vs. moment
https://imechanica.org/comment/13682#comment-13682
<a id="comment-13682"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/13681#comment-13681">wedge force vs. moment</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 align="justify">
<strong>I1</strong>: Under the large-scale bridging condition, it is difficult to convert the experiemntally determined relation between the load and the crack extension into a R-curve.<strong><br />
Q1</strong>: You mean crack length is hard to be experimentaly measured in the presense of large bridging?
</p>
<p align="justify">
<strong>I2</strong>: In the case of wedge force, the configuration does not have a<br />
translational symmetry. Steady state is impossible, regardless of the<br />
size of the bridging zone. By contrast, when a moment is applied, a steady state can be attained.<br /><strong>Q2</strong>: I guess you mean material response is <strong>translational symmetric</strong> under the case of <strong>pure moment</strong> and/or <strong>shear</strong> (in the direction of the interface) forces, i.e. it develops along the interface (in weak adhesives) while crack is extending and different pre-bonded points are assumed to provide same material response. But I am looking for the reason of the case under wedge forces. Is that because when the crack slightly extends, the moment at the tip of the crack increases while the wedge force at the load-point is constant, so that the rate of energy release gradually increases?
</p>
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</ul>Sat, 27 Feb 2010 21:32:00 +0000Mehrzadcomment 13682 at https://imechanica.orgwedge force vs. moment
https://imechanica.org/comment/13681#comment-13681
<a id="comment-13681"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/13680#comment-13680">Steady state under wedge force</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>
I'm sorry to miss your question. Under the large-scale bridging condition, the length of the bridging zone is comparable or even exceeds the size of the specimen (e.g., the thickness of the beam). Consequently, it is difficult to convert the experiemntally determined relation between the load and the crack extension into a R-curve.
</p>
<p>
In the case of wedge force, the configuration does not have a translational symmetry. Steady state is impossible, regardless of the size of the bridging zone.
</p>
<p>
By contrast, when a moment is applied, a steady state can be attained.
</p>
<p>
</p>
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</ul>Sat, 27 Feb 2010 19:39:00 +0000Zhigang Suocomment 13681 at https://imechanica.orgSteady state under wedge force
https://imechanica.org/comment/13680#comment-13680
<a id="comment-13680"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/13679#comment-13679">large-scale bridging and steady state</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>
In the page 13 of the same article, you mentioned it does not take a steady state under <strong>Wedge </strong>forces and my question was regarding that.
</p>
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</ul>Sat, 27 Feb 2010 19:00:00 +0000Mehrzadcomment 13680 at https://imechanica.orglarge-scale bridging and steady state
https://imechanica.org/comment/13679#comment-13679
<a id="comment-13679"></a>
<p><em>In reply to <a href="https://imechanica.org/comment/13675#comment-13675">Why the resistance curve does not take a steady state</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>
Here is a discussion on the large-scale bridging condition:
</p>
<p>
Z. Suo, G. Bao and B. Fan, <a href="http://www.seas.harvard.edu/suo/papers/015.pdf">Delamination R-curve phenomena due to damage</a>, <em>J. Mech. Phys. Solids</em>. <strong>40</strong>, 1-16 (1992).
</p>
<p>
As illustrated in Fig. 2, a staedy-state is still possible even under the large-scale bridging condition. To attain the steady state, you need to use a long and thin beam.
</p>
<p>
You may also take a look at the <a href="http://imechanica.org/node/3672#comment-8829">comments on experiemnts by Bent Sorensen</a>.
</p>
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</ul>Sat, 27 Feb 2010 18:49:11 +0000Zhigang Suocomment 13679 at https://imechanica.orgWhy the resistance curve does not take a steady state
https://imechanica.org/comment/13675#comment-13675
<a id="comment-13675"></a>
<p><em>In reply to <a href="https://imechanica.org/node/7674">Resistance Curve </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>
Why the resistance curve does not take a steady state under wedge loading in materials not pocessing small-scale yielding (like cohesive zones with long bridging length and under small loading rate)? If the bonding length is long enough, will it approach a steady state when crack propagates?
</p>
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</ul>Sat, 27 Feb 2010 15:04:00 +0000Mehrzadcomment 13675 at https://imechanica.org