Cohesive Surface Models

We present the major results established in the description of crazing and the recent developments in this field. Crazing has been investigated within continuum or discrete approaches (e.g., spring networks or molecular dynamics calculations to model the craze fibrils), which have provided phenomenological or physically based descriptions. Both are included in the presentation of the crazing process, since they will provide the basis for the recent cohesive surface model used to represent crazing in a finite element analysis [20-22],... 

A description of crazing with a cohesive surface appears appropriate for the crazes observed in glassy polymers, since the trends reported experimentally are quite well captured. The cohesive surface model distinguishes the three steps of crazing (initiation, thickening, and breakdown) and is flexible enough to incorporate more sophisticated formulations of one of these stages when available. 

As the craze microstructure is intrinsically discrete rather than continuous, the connection between the variables in the cohesive surface model and molecular characteristics, such as molecular weight, entanglement density or, in more general terms, molecular mobility, is expected to emerge from discrete analyses like the spring network model in [52,53] or from molecular dynamics as in [49,50]. Such a connection is currently under development between the critical craze thickness and the characteristics of the fibril structure, and similar developments are expected for the description of the craze kinetics on the basis of molecular dynamics calculations. 

In section 12.3.4, we will discuss a wide class of constitutive models that are broadly known as cohesive surface models. These models postulate the existence of an elastic potential that can be used to describe sliding and opening of interfaces. 

A key point to be made in the present context is that such cohesive surface models can be used to describe the energetics of a number of different dissipative processes related to fracture as shown in fig. 12.8. The claim is that each of these different mechanisms is amenable to a treatment in which the interfacial normal tractions can be derived from a nonlinear interplanar potential according... 

We present recent results on the analysis of the interaction between plasticity and crazing at the tip of a preexisting crack under mode I loading conditions. Illustrations of the competition between these mechanisms are obtained from a finite element model in which a cohesive surface is laid out in front of the crack. 

The cohesive surface description presented here has some similarities to the thermal decohesion model of Leevers [56], which is based on a modified strip model to account for thermal effects, but a constant craze stress is assumed. Leevers focuses on dynamic fracture. The thermal decohesion model assumes that heat generated during the widening of the strip diffuses into the surrounding bulk and that decohesion happens when the melt temperature is reached over a critical length. This critical length is identified as the molecular chain contour. 

Because the events which it deals with are transient and relatively inaccessible, it is very difficult to estimate how realistic the adiabatic decohesion model is. Ultimately it can only be judged by how well it succeeds in predicting high-rate decohesion and fracture behaviour. The new numerical model offers a flexible method for predicting decohesion under a wide range of cohesive surface displacement vs. time histories — of which the present situation represents the simplest possible — and for a variety of thermo-mechanical material properties. 

Fig. 12.35. Schematic of the various crack tip geometries using the cohesive surface dislocation nucleation model (adapted from Xu et at. (1997)).

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