ESIS's blog

Around 20 years ago, I gave a fracture mechanics lecture and talked about crack initiation that happens in the plane with the largest tensile stress. True, at least if the material has isotropic properties. The students already knew where an isotropic material would give the largest stress at bending and torsion. I planned to make a desktop experiment with an icicle and a carrot. This was during the autumn with an abundance of icicles everywhere. The carrot, I found at home.

Dynamic fracture is a never-ending story. In 1951, EH Yoffe obtained an analytical solution for a crack of constant length travelling at constant speed along a plane. She used a Galilean transformation to get a solution for arbitrary speeds. The situation seems strange with a crack tip where the material breaks and a lagging tip where the material heals. However, there are applications. One that I encountered was several mode II cracks that travel in the contact plane between a brake pad and a brake disc. The moving cracks were blamed for the causing squeaking noise when braking.

The Nobel laureate Andre Geim made graphene by playing with pencil leads and Scotch tape and coauthored a paper on how to get the Nobel prize the fun way. Before that, he co-authored with his hamster, Ter Tisha, a paper on diamagnetic levitation and demonstrated it on a frog. He was honoured with the Ig Nobel prize for the paper and later became the only person so far who got both the Harvard Ig version and the real Alfred version of the Nobel prize. Geim is one of my favourite scientists, which led me to read the paper 

The advantage of simplicity is that mechanics and physics can be understood and predicted just by using pen and paper. In the end, numerics may have to be used but then you should already have a pretty good idea of what happens. The other way around, starting with numerics and a limited toolbox of models will seldom lead to anything new. 

The fracture of concrete and other semi-brittle materials offers some simplifications that simplify the analytical analysis. The simple check that reveals if something broken requires an elastic or an elastic-plastic fracture mechanical analysis by just trying to fit the pieces together sometimes fails. The suggestion is that if they do not fit together, we have an elastic-plastic fracture and if they do we have an elastic fracture. We may jump to the false conclusion that linear elastic fracture mechanics can be applied.

The subject of this blog is a well-written and technically detailed study of thermal crack initiation where an adhesive joint between two dissimilar materials meets a free surface. The method that is used goes under the group designation finite fracture mechanics. The paper is:

"Predicting thermally induced edge-crack initiation using finite fracture mechanics" by S. Dölling, S. Bremm, A. Kohlstetter, J. Felger, and W. Becker. in Engineering Fracture Mechanics 252 (2021) 107808.

Hydrogen embrittlement causes problems that probably will become apparent to an increasing extent as hydrogen is taken into general use for energy storage and as a fuel for heating and electricity production. According to Wikipedia, the phenomenon has been known since at least 1875. The subject of this blog 

This blog concerns an interesting review of the interaction integral methodology. It deserves to be read by everyone dealing with analyses of cracks. If one's focus is on mathematical analysis or numerics is irrelevant. The review is for all of us. The review paper is, ”Interaction integral method for computation of crack parameters K–T – A review", by Hongjun Yu and Meinhard Kuna, Engineering Fracture Mechanics 249 (2021) 107722, p. 1-34.

The paper, "A machine-learning fatigue life prediction approach of additively manufactured metals" by Hongyixi Bao, Shengchuan Wu, Zhengkai Wu, Guozheng Kang, Xin Peng, Philip J. Withers in Engineering Fracture Mechanics 242 (2021) 107508, p. 1-10., adopts a very interesting view of the correlation between fault geometry and fatigue properties. A simplified statistical description of irregular faults in large numbers is used.

A most readworthy paper, "Static and dynamic mode I fracture toughness of rigid PUR foams under room and cryogenic temperatures" by E. Linul, L. Marşavina, C. Vălean, R. Bănică, Engineering Fracture Mechanics, 225, 15 February 2020, 106274, 1-10, is selected for this ESIS blog. It has received a lot of attention and was for an extended period of time one of the most read papers in EFM.

Weight functions are practical tools in linear elastic systems where several discrete or continuously distributed sources cause something, deformation, stress, or related stuff. In linear fracture mechanics, as also in the object of this blog, weight functions are used to calculate stress intensity factors. If the load is divided into discrete or continuous separate or overlapping parts which each gives a known contribution to the stress intensity factor, i.e. has a known weight, calculation for new loads may be reduced to simple algebra instead of extensive numerical calculations.

The outstanding and brilliantly written paper, "Modeling of Dynamic Mode I Crack Growth in Glass Fiber-reinforced Polymer Composites: Fracture Energy and Failure Mechanism" by Liu, Y, van der Meer, FP, Sluys, LJ and Ke, L, Engineering Fracture Mechanics, 243, 2021, applies a numerical model to study the dynamics of a crack propagating in a glass fiber reinforced polymer. The paper is a school example of how a paper should be written. Everything is well described and carefully arranged in logical order.

The paper "Estimating static/dynamic strength of notched unreinforced concrete under mixed-mode I/II loading" by N. Alanazi and L. Susmel in Engineering Fracture Mechanics 240 (2020) 107329, pp. 1-18, is a readworthy and very interesting paper. Extensive fracture mechanical testing of concrete is throughly described in the paper.

Landau and Ginzburg formulated a theory that includes the free energy of phases, with the purpose to derive coupled PDEs describing the dynamics of phase transformations. Their model with focus on the phase transition process itself also found many other applications, not the least because many exact solutions can be obtained. During the last few decades, with focus on the bulk material rather than the phase transition, the theory has been used as a convenient tool in numerical analyses to keep track of cracks and other moving boundaries.

All materials are anisotropic, that's a fact. Like the fact that all materials have a nonlinear response. This we can't deny. Still enormous progress has been made by assuming both isotropy and linear elasticity. The success, as we all know, is due to the fact that many construction materials are very close to being both isotropic and linear. By definition materials may be claimed to be isotropic and linear, provided that the deviations are held within specified limits. Very often or almost always in structural design nearly perfect linearity is expected.

The subject of this blog is a fracture mechanical study of soft polymers. It is well written and technically detailed which makes the reading a good investment. The paper is:

"Experimental and numerical assessment of the work of fracture in injection-moulded low-density polyethylene" by Martin Kroon, Eskil Andreasson, Viktor Petersson, Pär A.T. Olsson in Engineering Fracture Mechanics 192 (2018) 1–11.

Carbon fibre reinforced polymers combines desired features from different worlds. The fibres are stiff and hard, while the polymers are the opposite, weak, soft and with irrelevant fracture toughness. Irrelevant considering the small in-plane deformation that the fibres can handle before they break. It is not totally surprising that one can make composites that display the best properties from each material. Perhaps less obvious or even surprising is that materials and composition can be designed to make the composite properties go beyond what the constituent materials are even near.

I came across a very interesting paper in Engineering Fracture Mechanics about a year ago. It gives some new results of stochastic aspects of fatigue. The paper is:

”On the distribution and scatter of fatigue lives obtained by integration of crack growth curves: Does initial crack size distribution matter?” by M. Ciavarella, A. Papangelo, Engineering Fracture Mechanics, Vol 191 (2018) pp. 111–124.

The last ESIS blog about how surprisingly few scientists are willing/able to share their experimental data, received an unexpectedly large interest. Directly after the publication another iMechanica blogger took the same theme but he put the focus on results produced at numerical analyses that are presented with insufficient information. While reading, my spontaneous guess was that one obstacle to do right could be the widespread use of commercial non-open codes.

Experimental data availability is a cornerstone for reproducibility in experimental fracture mechanics. This is how the technical note begins, the recently published 

"Long term availability of raw experimental data in experimental fracture mechanics", by Patrick Diehl, Ilyass Tabiai, Felix W. Baumann, Daniel Therriault and Martin Levesque, in Engineering Fracture Mechanics, 197 (2018) 21–26.

It is common practice to obtain stress intensity factors in elastic materials by using Williams series expansions truncated at the r^(-1/2)-stress term. I ask myself, what if both evaluations of experimental and numerical data is improved by including lower order (stronger singularities) terms? The standard truncation is done in a readworthy paper 

Extreme thermal and electrical conductivity, blocks out almost all gases, stiff as diamond and stronger than anything else. The list of extreme properties seems never ending. The paper

Growth speed of single edge pre-crack in graphene sheet under tension, Jun Hua et al., Engineering Fracture Mechanics 182 (2017) 337–355, 

A T-stress is generally not expected to contribute to the stress intensity factor because its contribution to the free energy is the same before and after crack growth. Nothing lost, nothing gained. Some time ago I came across a situation when a T-stress, violates this statement. The scene is the atomic level. As the crack is producing new crack surfaces the elastic stiffness in the few atomic layers closest to the crack plane are modified. This changes the elastic energy which could provide, contribute to or at least modify the energy release rate.

No doubt the energy release rate comes first. What comes next is proposed in a recently published study that describes a method based on a new constraint parameter Ap. The paper is:

Fracture assessment based on unified constraint parameter for pressurized pipes with circumferential surface cracks, M.Y. Mu, G.Z. Wang, F.Z. Xuan, S.T. Tu, Engineering Fracture Mechanics 175 (2017), 201–218 

It is common practice when solving boundary value problems to split the solution into a symmetric and an antisymmetric part to temporarily reduce the number of variables and the mathematical administration. As soon as the symmetric problem is solved, the antisymmetric problem, or vice versa, is almost solving itself. Any problem can be split into a symmetric and an antisymmetric part which is a relief for anyone who analyses mixed cases.