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Discussion of fracture paper #12 – Crack paths and fracture process region autonomy

5 December 2024 / admin / 0 Comments

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.

The recently published

“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,

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.

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.

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.

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?

Per Ståhle

https://imechanica.org/node/18931

Discussion of fracture paper #11 – Fracture processes and phase-field modelling

5 December 2024 / admin / 0 Comments

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:

”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.

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.

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.

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.

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.

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.

Per Ståhle

Discussion of fracture paper #10 – Searching for the length scale of stress corrosion

5 December 2024 / admin / 0 Comments

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.

The paper for this discussion is:

”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 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.

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.

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.

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.

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.

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?

Per Ståhle

https://imechanica.org/node/17865

Discussion of fracture paper #9 – Crack tip modelling

5 December 2024 / admin / 0 Comments

Dear Reader,

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.

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.

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.

The selected paper is: 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.

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.

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.

The paper is a well written and a technically detailed study that makes the reading a good investment.

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.

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?

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.

Per Ståhle
Professor of Solid Mechanics
Lund University, Lund
Sweden

https://imechanica.org/node/17471

Discussion of fracture paper #8 – Elastic follow-up

5 December 2024 / admin / 0 Comments

This is the story of threefold failure, which doubtlessly is the subject of fracture mechanics, a story of failure in various regards, however. First, it comments on an article dealing with failure assessment, second it reports on the personal failure of the blogger to understand this article, and finally it bemoans the failure of a seminal idea.

Chasing for “prey”, I came upon a contribution on the assessment of “crack-like defects under combined primary and secondary loads”, namely

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,

and was intrigued by the expression “elastic follow-up”, of which I had never heard before. I started asking friends and colleagues who are engaged in fracture mechanics but they couldn’t help me. Collins Compact English Dictionary explains “follow-up” as “something done to reinforce an initial action” – which wasn’t really helpful, either. The author of the above contribution states that “elastic follow-up can be considered to occur in cases where the secondary load acting over a sufficiently large length scale such that localised relaxation (e.g. in the vicinity of a crack) does not diminish the influence of the remote stresses” – which left me stranded, still not knowing which “effect” is actually addressed, particularly because I do not have the slightest idea what “primary and secondary loads” are. Assuming (!) that the respective effect (which one?) “can be described by a single parameter” the author presents a quantitative measure, the “elastic follow-up factor”, Z, at least, which traces back to a preceding article of an internationally acknowledged expert of integrity assessment,

R.A. Ainsworth: Consideration of elastic follow-up in the treatment of combined primary and secondary stresses in fracture assessments. Engineering Fracture Mechanics, Vol. 96, 2012, pp. 558–569,

where I read: “when elastic follow-up is high this leads to secondary loads acting as primary”, which appeared as mystical as the explanation cited above, just inverting cause and effect. Obviously, nobody who has not internalised the concept of primary and secondary loads or stresses will ever be able to understand this “effect”.

In engineering mechanics, students are taught Cauchy’s stress principle of 1823, which was a breakthrough in the science of strength of materials enabling engineers to reduce various loading configurations to simple entities, viz. stresses, and to measure strength limits on simple test specimens. Actually, we measure deformations and relate them to stresses by constitutive laws. There is no room or need for primary and secondary stresses within in this framework, least of all for primary and secondary loads.

I scanned further literature on the problem finding numerous contributions. The whole world seemed to know what “elastic follow-up” is, except me. A contribution on “creep-fatigue tests including elastic follow-up“ in the International Journal of Pressure Vessels and Piping of 2000 presents some uninspiring “illustration of follow-up behavior”. The essential hint resulted from the title of an article, “generalization of elastic follow-up model”, in Nuclear Engineering and Design of 1995: what, if this “effect” was not a physical phenomenon, a “behaviour”, but a model used in assessment codes? Finally, ITER Structural Design Criteria for In-Vessel Components (Appendix C) gave the enlightening explanation: “Neuber’s rule is applicable if the remote stress field away from the notch is elastic. If the remote stress-strain field itself undergoes plastic deformation, then a further correction is necessary, because the remote strain is greater than the elastically calculated strain.” It simply says that “elastic follow-up” is a correction term in an elastic analysis incorporating plasticity.

The code also gives a comprehensible definition of “primary and secondary stresses”, which appear to be model artefacts rather than having physical significance: “Consider a cylindrical bar of length L, cross-sectional area A, which is subjected to an axial load such that the extension would be uel if it behaved elastically. … There are a number of ways of applying the specified load, the two simplest being a displacement u = εel.L and a force F = E A εel.. imposed. As long as the behaviour is linear elastic, a strain εel.. is effectively obtained for both loads. When the behaviour ceases to be linear elastic, the two loadings no longer cause the same strain. For the imposed displacement loading u, the real strain remains the same as the elastically calculated strain εel., which means that no correction is necessary and the elastically calculated stress = E u/L is a pure secondary stress. For the imposed force load, the real strain corresponds to the real stress = F/A on the stress-strain curve. This stress is a pure primary stress that can be seen to cause real strain which is much higher than the elastically calculated εel.”

This I can comprehend as it fits in my terminology and my view of the world of mechanics.

Now what is the conclusion resulting from this story?

· If terminology creates insurmountable barriers of understanding even among people having similar scientific interests and background, namely fracture mechanics and structural integrity, we have to be concerned about the language we use in our publications.

· If no distinction is made between models and physical phenomena, misunderstanding and misconception are programmed.

Finally, the present contribution marks the failure of the constitutive idea for the present blog. Its aim was to create a forum ofscientific exchange, realising that scientific achievements require time and chance for free, impartial and uncensored discussions among people. The European Structural Society (ESIS) and an international publisher of scientific journals appeared as an ideal combination for launching such a project. However, encouraging young scientists to frank discussions about their findings will work in a large-minded and democratic atmosphere, only, where they must not fear sanctions. Representatives of a society who themselves do not stand divergent opinions give a poor example. This is my last blog entry I shall be able to write.

W. Brocks’s blog

https://imechanica.org/node/16898

Discussion of fracture paper #7 – Configurational force approach

5 December 2024 / admin / 0 Comments

New paradigms may help understanding unsolved scientific problems by looking on them from a different perspective. Or they may lead to a new unification theory of so far separate phenomena. The concept of “material” or “configurational” forces tracing back to a seminal publication of Eshelby in 1970 and significantly extended and promoted by Maugin twenty years later provides a generalised theory on the character of singularities of various kinds in continua, among which the “driving force” at a crack tip is a special case. Whereas Eshelby’s energy momentum tensor resulting in the J-integral is a firm constituent of fracture mechanics, the concept of configurational forces has only hesitantly been applied to fracture problems, e.g. by Kolednik, Predan, and Fischer in Engineering Fracture Mechanics, Vol. 77, 2010. Whether this new “look” upon J helped discovering anything new about it remains disputable.

Now there is a revival of this concept

K. Özenç, M. Kaliske, G. Lin, and G. Bhashyam: Evaluation of energy contributions in elasto-plastic fracture: A review of the configurational force approach. Engineering Fracture Mechanics, Vol. 115, 2014, pp. 137–153.

It is admittedly difficult to contribute some novel aspect to more than forty years of research on J in elastoplastic fracture mechanics. Though a clear perception of the nature of “path dependence” of J is often enough still missing in some publications to the point of the user’s manual of a major commercial FE code, there is no lack of theoretical knowledge. Background, applicability and limitations of J are quite clear. Those looking for deeper insight will be disappointed: The present publication just answers questions and solves problems which arose with the chosen approach of material forces.

“The path dependency of the material force approach in elasto-plastic continua is found to be considerably depending on the so-called material body forces.” This is well-known and trivial as the derivation of path independence of J is, among others, based on the absence of body forces. It does not need “numerical examples … to clarify the concept of path dependence nature of the crack tip domain (?) and effect of the material body forces”. Correction terms re-establishing path independence have been introduced years ago, see e.g. Siegele, Comput. Struct., 1989.As many continuum mechanics people, the authors start with a display of fireworks introducing the general nonlinear kinematics of large deformations which can be found in every respective textbook. In the end, this impressing framework is simmered down again to “small strain elasto-plasticity and hyperelasto-plasticity”, whatever “hyperelasto-plasticity” is supposed to mean. This does not become much clearer by the statement “the Helmholtz free energy function of finite elasto-plasticity is introduced in order to obtain geometrically nonlinear von Mises plasticity”. Finite, i.e. Hencky-type plasticity and incremental plasticity, i.e. the von Mises, Prandtl, Reuss theory are alternative approaches, where the latter is more appropriate for describing irreversible, dissipative processes. What a “geometrically nonlinear” material behaviour is remains the secret of the authors. They presumably applied the so-called “deformation theory of plasticity” which actually describes hyperelastic behaviour based on the existence of a strain-energy density as stress potential. Thus “path dependence” should not be an issue at all as the requirements for deriving path-independence are met. The rest is numerics!

So where are the problem and its solution after all? Can “material forces” be calculated by the finite element method – who doubts? Is the implementation of this concept in a commercial FE code a major scientific achievement – who knows?

»W. Brocks’s blog

https://imechanica.org/node/16356

Applicable limit of the stress intensity factor for steep yield strength distribution

5 December 2024 / admin / 0 Comments

“The number of bad papers is multiplying. … a new, dramatic problem arises: how to select in the mud the papers conveying innovative ideas?” wrote Piero Villaggio in his Editorial “Crisis of mechanics literature?”, Meccanica, Vol. 48, pp. 765–767. He identified, among others, two factors, “the necessity of multiplying published papers in a large international competition” and “the abuse of self-quotations in order to remedy the perverse rule imposed by the impact-factor”. Disregarding “journals ready to publish everything“, the editors of top-ranking scientific journals have to face up to the question how to ensure a constantly high quality of the published manuscripts. A strict and carefully executed review process is a mandatory requirement. However, reading published articles, I sometimes wondered how a reviewer could let pass a manuscript like this?

One indispensable demand is a minimum standard of English expression. If the reader cannot discriminate what is inapt expression and what is lack of understanding of the problem, he or she will put the paper aside and stop reading. The author has scored on the publication list in any case, but the scientific benefit is null!

I shall outline some examples in the paper by

Tetsuo Yasuoka, Yoshihiro Mizutani, Akira Todoroki: Applicable limit of the stress intensity factor for steep yield strength distribution, Engineering Fracture Mechanics, Vol.110, 2013, pp. 1–11,

not to blame the authors but to ask the reviewer(s) of this manuscript whether they have actually understood cryptic sentences like “The crack was divided into discrete bar elements in this model. Each bar element involved the stress, yield strength and displacement. The remote tensile stress and the yield strength distribution were discretized using the principle of superposition”. What is “the SIF of the jth bar element subjected to the loading stress σj“? What shall I imagine by “this rectangle means (!?) CTOD” in Fig. 4, if it is an area under a stress distribution curve in the ligament?

That the substance of a submitted manuscript is correct to the best knowledge of the reviewer should be a matter of course. This actually may be a time-consuming task to check including literature research. There are some simple sanity checks, however. One would be: How can there be normal stresses acting on the free surface of a crack in Fig. 2? Newman’s respective Fig. 2 (ASTM STP 748 [1981]) which the authors quote shows compressive stresses due to crack closure, but this is not examined in the present manuscript.

Did the reviewers of the above-mentioned manuscript ask the authors any of these questions – or did they just wave the paper through?

A final delicate question a reviewer might ask is how substantial and significant the presented results are: what did he or she really learn from this contribution? A considerable number of submitted papers could be rejected with this argument. Taking a look on the references in the present manuscript raises doubts. Despite an own publication of 2012, the rest is mostly from the 60s and 70s of the last century. What did the scientific community miss over the last 40 to 50 years not having read this manuscript?

W. Brocks’s blog

https://imechanica.org/node/15504

A blog for discussing fracture papers

5 December 2024 / admin / 0 Comments

The aim of ESIS 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.
For these purposes, three Elsevier journals – Engineering Fracture Mechanics , Engineering Failure Analysis and International Journal of Fatigue – are published in affiliation with ESIS.

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 Engineering Fracture Mechanics. Its editors, Profs. Karl-Heinz Schwalbe and Tony Ingraffea,fully support this initiative.

ESIS hopes that this blog will achieve the following objectives:

To start a scientific discussion on relevant topics through comments by leading scientists (the chief ‘commenter’ will be Prof. Wolfgang Brocks);
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 make some of these books available on-line to ESIS members;
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);
To focus attention on new ideas that run the serious risk of not emerging from the noise of too much published “stuff”;
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.

The proposed rules of usage of this blog include:

A group of leading scientists headed by Prof. W. Brocks will post onto this iMechanica node comments and remarks to some of the papers published in EFM;
The authors of the papers will receive a notification of the remarks by ESIS Webmaster and they will be invited to reply through a detailed document that will appear on the ESIS website;
The replies will also be posted onto iMechanica by ESIS (so that the authors do not have to worry about technical details). Hopefully, we will receive further comments and questions by other scientists/practitioners.

To start, this blog will concentrate only on fracture papers; later other sections devoted to fatigue and other sectors of structural integrity will be added.

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’.

S. Beretta & W. Brocks ESIS Executive Committee

Discussion of fracture paper #5 – Yield ciriterion or failure criterion

5 December 2024 / admin / 0 Comments

What is the difference betwee a failure criterion and a yield condition?

You may meet natural and engineering scientists who blame their colleagues from social sciences or humanities for working unscholarly, not adhering to an explicit and unique terminology but substituting scientific cognition by adopting novel terms. Those sitting in a glasshouse should not throw stones, however. Imprecise terminology and hazy definitions are not at all a “privilege” of social scientists. When I started learning fracture mechanics, I discovered that nearly every anomaly in the real failure behaviour of components which did not fit into the common concept was attributed to “constraint” – but few people had a precise idea what constraint actually is and how to quantify it. The multifarious usage of “damage” in the current literature is an actual example, and “plasticity” is another.

Though von Mises, Drucker, Hill and many others established a precise foundation of phenomenological plasticity, it has become a bad habit to call any inelastic, nonlinear mechanical behaviour “plastic”. One will find applications of the Mises-Prandtl-Reuss equations to polymers, and the authors do not even query, much less justify this approach. In my previous blog, #4, I criticised Mäkelä and Östlund (Engineering Fracture Mechanics, Vol. 79, 2012) for modelling the deformation of paper by means of plasticity. One year later I find an “application” to wood.

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.

The authors’ misconception is a different one. The deformation behaviour of wood is considered as linear elastic and, of course, orthotropic. But they add a new facet to the term “plasticity”, namely the irreversible and unstable material softening in some process zone: “Initiation of softening, i.e. the formation of a fracture process zone, is determined by an initial yield function F according to the Tsai–Wu failure criterion”. This is a failure criterion, correct, and the respective limit surface in the stress space may be assumed as convex as the yield surface in the theory of plasticity. For the sake of a thermodynamically consistent theory, one may also define a corresponding damage potential, but this is not a plastic potential! Once again: The theory of plasticity deals with the stress-strain relationship of ductile materials, having metals in mind, where plastic flow occurs by sliding along crystallographic planes or by twinning. “A physical theory of plasticity starts with these microscopic details and attempts to explain why and how plastic flow occurs” (Khan & Huang: Continuum Theory of Plasticity, Wiley, 1995, p. 310). Following Drucker, classical phenomenological plasticity describes stable, i.e. strain-hardening, material behaviour.

The authors continue “The change in size of the yield surface f is described by the softening parameter K which is a function of an internal variable that memorizes the plastic loading and determines the softening behavior”, and they introduce a “dimensionless deformation δeff“, as internal variable, which is „related to the plastic straining of the material” (wood?), whatever this is supposed to mean. It is not just the “size” of the failure surface that changes, by the way, as Fig 2 shows. In the context of cohesive models, δ is commonly called “separation”, i.e. a jump in the discontinuous displacement field, and Fig 3 is a typical traction-separation law. So why introduce a terminology divergent from the established one?

Roberto Balarini stated in a blog node/7622 : “Cohesive models are linear elasticity”. In contrast, the present authors apparently assert that cohesive models “are” plasticity. What is so difficult in understanding the model of a cohesive zone? Cohesive models “are” neither elasticity nor plasticity. They describe the nonlinear decohesion process in a continuum that obeys any kind of constitutive equations, for instance plasticity, visco-plasticity or, as in the present case, orthotropic elasticity.

More generally: What is so complicated in applying a unique terminology which is established in the scientific community, and how about the reviewers of manuscripts like this: Are they not aware of the correct terminology themselves or do they just don’t care about it? Remember: The corruption of reasoning starts with a false handling of language!

W. Brocks’s blog

https://imechanica.org/node/14387

Discussion of fracture paper #4 – Is paper ductile?

5 December 2024 / admin / 0 Comments

In my previous blog, I complained about colleagues developing constitutive models without having any notion about the specific nature of deformation and damage and their micromechanical mechanisms. Unfortunately, this happens more often than one might (or would like to) believe, as a recent example testifies.

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.

Looking at the title and the Abstract:

“In this work, a cohesive crack model suitable for static fracture mechanics analysis of thin sheet materials exhibiting anisotropy, plasticity, and large-scale damage evolution was developed”,

the reader might think of “metal sheets”. But far wrong: the authors talk about paper! And the unbelieving reader starts realising this at the end of the Introduction:“The elastic–plastic model was calibrated by tensile testing and the cohesive zone model was calibrated by stable tensile testing for one grade of paper material”,and in section 2.4, where the tests are described.

The theory of plasticity deals with the stress-strain and load deflection relationships for ductile materials. Is paper “ductile”, and what means “ductile”, actually? Talking about ductility, people commonly think of the behaviour of metals, and it were metals for which phenomenological plasticity has been developed. Metals have a crystalline structure, so the plastic flow occurs by sliding along crystallographic planes or by twinning. “A physical theory of plasticity starts with these microscopic details and attempts to explain why and how plastic flow occurs” (A.S. Khan & S. Huang: Continuum Theory of Plasticity, Wiley, 1995, p. 310). What are the mechanisms of deformation and damage in paper? The authors do not tell us!

They just present a pretty conventional phenomenological model of orthotropic plasticity based on a transformation of the stress tensor and the von Mises yield criterion with an associated flow rule, and apply this to paper specimens. The “excellent prediction” of the test results by the model, which the authors claim with respect to Fig. 6, is not at all impressive, as it just shows that the uniaxial stress-strain curves can be described by an exponential function as in Eq. (6). Finally, they combine this with some exponential cohesive softening law to describe the tearing of the paper and as the respective cohesive parameters were fitted to the test results, there is no reason why this should not “predict” failure of centre-cracked sheets for varying crack lengths, a/W, satisfactorily.

What a “large-scale damage evolution” announced in the title is supposed to be, remains obscure, as a cohesive zone describes localised and no “large scale” damage.

That the authors try to surprise us with repeated statements like

“The accuracy of the cohesive crack model is largely dependent on accurate constitutive modelling.”
“The performance of the cohesive crack model is generally most dependent on the accurate formulation and calibration of the cohesive zone model.”
“The key to accurate cohesive crack modelling is constituted by the ability to accurately determine the cohesive material behaviour.”

underlines the lack of information about paper in the present manuscript.

Final remark: The present blogs intend to encourage discussion on fracture mechanics and related subjects. No reaction by the authors has yet come to any of them. Does this support the suspicion that publishing does not intend to contribute to science but just to increase the individual scoring of scientists?

W. Brocks’s blog

https://imechanica.org/node/11741