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Discussion of fracture paper #29 - Fast Crack Growth in Fibre Reinforced Composites

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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. Reading is recommended and especially to young scientists. 

During recent reviewing of several manuscripts submitted to reputable journals I think I see a trend of increased shallowing of the scientific style. Often the reader is referred to other articles for definitions of variables, assumptions made, background, etc. and not seldom with references to the authors' own previous works. The reading becomes a true pain in the ... whatever. The present paper is free of all such obstacles. With the excitement of the distinct technical writing, the reading became enjoyable and with it the interest of the subject grew. 

The adopted theory includes fracture of the polymer matrix, debonding of the interface between reinforcements and matrix, and the energy dissipation due to viscoelastic-plastic material behaviour. A process region is defined as the region that includes sites with tensile stresses that initiates decohesion. It is interesting that many of the initiated cohesive sites never contribute to the global crack meaning that the definition of the process region also includes shielding of the crack tip. Perhaps unorthodox, but absolutely okay. As I said, it is a well written paper.

A series of numerical simulations with different specimen sizes and various load speeds are analysed. Instead of an explicit dynamic analysis a smart implicit dynamic solution scheme is established. A dynamic version of the J-integral is used as a measure of the energy release rate. 

The polymer matrix with its visco-plastic material behaviour given by a Perzyna inspired model has and exponent mp that is slightly larger than 7 should leave a dominating plastic strain field surrounding a sharp crack tip. The singular solutions for materials with mp > 1 have an asymptotic behaviour that does not permit any energy flux to point shaped crack tips. This is in contrast to many metals that have an mp < 1 which forms an asymptotic elastic crack tip stress field and simplifies the analyses. 

The authors eliminate the inconvenient singularities by introducing a cohesive zone to model initiation and growth of cracks. This provides a length scale that allow a flow of energy to feed decohesive processes and crack growth.  Camacho and Ortiz' (1996) method for implementing cohesive zones is used.  The finite energy release rate required to maintain a steady state crack growth is observed to increase monotonically with increasing crack tip speed. The absence of a local minimum implies that sudden crack arrest, such as obtained by Freund and Hutchinson (1985) for an mp < 1 and a point shaped crack tip, cannot happen. For the present polymer the crack tip speed is always stable and uniquely given by the energy flux. Sudden crack arrest requires a finite minimum energy below which the crack cannot grow. 

Having said this I cannot help thinking that a material with the same toughness but represented by a large cohesive stress and small crack tip opening making the cohesive zone short, might like the point shaped crack tip receive visco-plastic shielding that decreases with increasing crack growth rate. This makes the crack accelerate and jump to a speed that is high enough to be be balanced by inertia. This probably means crack growth rates that are a considerable fractions of the Rayleigh wave speed.

I am not aware of any such studies. It would be interesting to know if there is. It would also be interesting to know if this, or a trend in this direction, has been observed. Perhaps the authors in their studies. I think that crack arrest could be of interest also for design of fibre reinforced polymer structures that are used in light weight pressure vessels, e.g., for hydrogen fuel in cars.

A comment regarding the J-integral that gives the energy dissipation of an infinitesimal translation in a given direction of the objects in the geometry enclosed by the integration path. Technically it means that the micro-cracks are climbing in the x1 direction. Could it be that it evens out if the micro-cracking appears as repeated? With the many micro-cracks that are modelled, I would like to think so.

Does anyone know or have suggestions that could lead forward? Perhaps the authors of the paper or anyone wishes to comment. Please, don't hesitate to ask a question or provide other thoughts regarding the paper, the method, the blog, or anything related,

Per Ståhle

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