MATERIAL FAILURE MODELS
Why do materials actually fail? Is there a single definition of failure? Is there an approach to failure that will not fail itself from microscopic (atomic) level up to macroworld structures? In the last decade, large effort is dedicated to formulate material failure in terms of atomic dislocations, inclusions, microvoids, crack initiation and propagation, thermodynamics and macroscopic quantities such as stresses and strains. Unified approaches have emerged from these efforts, which compare well to experimental evidence. Lately, some of these approaches have been ported to the finite element method, particularly for crack propagation studies. In this chapter, a small excursion into material failure models is presented, the T failure criterion is incorporated in Abaqus/Explicit and numerical verification is conducted. Also, a novel method for calculating threshold values for the Tfailure criterion used for the simulations is presented.
In modern research and industrial applications, the estimation of an ultimate safety factor under extreme loading conditions, plays an important role in the overall safety assessment of a structure. In structural problems, where the response should be determined beyond the initiation of nonlinear material behaviour, fracture may be of profound importance for the determination of the integrity of the structure. Such problems include deep drawing, impact and crushing. Finite element methodologies, provide analysts with sophisticated tools for performing both material and geometry nonlinear calculations, which are yielding fairly accurate results. On the other hand, due to the lack of globally accepted fracture criteria, the determination of the structure’s damage, due to material failure using finite element methods, is still under intensive research. One could distinguish material failure in two broader categories depending on the scale in which the material is examined:

Failure is defined in terms of crack propagation and initiation. In this case, the microscopic behaviour of the material is examined, and respective theories are translated to finite element decoupling or even special element formulations that can reproduce crack propagation. In this case, fine meshes are required to capture the evolution of cracks. Such methodologies are useful for gaining insight in the cracking of specimens and simple structures under well defined global load distributions.

Failure is defined in terms of element removal. In this work, failure of an element is considered to occur when the element is no longer capable of carrying further loading, or equivalently, cannot store any further deformational energy. In this case, rather macroscopic failure criteria should be applied. When the conditions of such criteria are met, the element is deleted from the analysis. Such a failure mechanism is incorporated in most explicit time integration dynamic codes available today.
The second approach is most appealing for determining an upper limit to a particular loading on a structure. This work, provides a methodology for incorporating failure criteria in Abaqus/explicit, for metals following the von Mises yield conditions, as well as an application of the Tfailure criterion [2] to [5]. Abaqus/Explicit is chosen because it is the only available explicit finite element code at NTUA that allows the implementation of user subroutines that describe material failure, in the sense defined earlier. It also requires the user to fully describe plasticity calculations. This has the drawback of requiring extensive benchmarking of the user subroutine, but on the other hand provides the user with the full stress and strain tensors at each time step. This makes the implementation of any failure criterion that exists or will occur much easier.