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SUMMARYWe introduce the notion of time continuity for the analysis of cohesive zone interface ÿnite element models. We focus on 'initially rigid' models in which an interface is inactive until the traction across it reaches a critical level. We argue that methods in this class are time discontinuous, unless special provision is made for the opposite. Time discontinuity leads to pitfalls in numerical implementations: oscillatory behavior, non-convergence in time and dependence on nonphysical regularization parameters. These problems arise at least partly from the attempt to extend uniaxial traction-displacement relationships to multiaxial loading. We also argue that any formulation of a time-continuous functional traction-displacement cohesive model entails encoding the value of the traction components at incipient softening into the model. We exhibit an example of such a model. Most of our numerical experiments concern explicit dynamics. Copyright COHESIVE ZONE MODELINGCohesive zone modeling is one of the most widely used techniques for modeling fracture. It is predicated on the fact that a process zone forms ahead of the crack front, in which material softening takes place. In the spirit of Dugdale [1] and Barenblatt [2] cohesive zone modeling idealizes the process zone with a weak interface of thickness zero. A material point on this interface is initially undamaged, but when the traction across the interface reaches some critical level it starts losing cohesion and gradually softens until a stress-free surface is created. In one dimension, softening is manifested as a gradual drop in traction with increasing relative displacement. Decohesion is usually modeled by a pointwise relationship between the traction across the interface and the relative displacement between the two faces of the interface.We formulate the problem in the following setting. Let the initial conÿguration of the body be denoted B 0 , and let M(X; t) : B 0 × [0; T ] → R 3 be its deformation map. The ÿrst argument to M is a coordinate X in the undeformed body, and the second argument is time. This map is * Correspondence to:

a b s t r a c tA damage-based cohesive model is developed for simulating crack growth due to fatigue loading. The cohesive model follows a linear damage-dependent traction-separation relation coupled with a damage evolution equation. The rate of damage evolution is characterized by three material parameters corresponding to common features of fatigue behavior captured by the model, namely, damage accumulation, crack retardation and stress threshold. Good agreement is obtained between finite element solutions using the model and fatigue test results for an aluminum alloy under different load ratios and for the overload effect on ductile 316 L steel.

SUMMARYWe consider the use of initially rigid cohesive interface models in a two-dimensional dynamic finiteelement solution of a fracture process. Our focus is on convergence of finite-element solutions to a solution of the undiscretized medium as the mesh spacing x (and therefore time-step t) tends to zero. We propose the use of pinwheel meshes, which possess the 'isoperimetric property' that for any curve C in the computational domain, there is an approximation to C using mesh edges that tends to C including a correct representation of its length, as the grid size tends to zero. We suggest that the isoperimetric property is a necessary condition for any possible spatial convergence proof in the general case that the crack path is not known in advance. Conversely, we establish that if the pinwheel mesh is used, the discrete interface first activated in the finite-element model will converge to the initial crack in the undiscretized medium. Finally, we carry out a mesh refinement experiment to check convergence of both nucleation and propagation. Our results indicate that the crack path computed in the pinwheel mesh is more stable as the mesh is refined compared to other types of meshes.

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