Abstract
In this paper I will take a close look at a statistical crack model (SCM) as is used in engineering computer codes to simulate fracture at high strain rates. My general goal is to understand the macroscopic behavior effected by the microphysical processes incorporated into an SCM. More specifically, I will assess the importance of including local interactions between cracks into the growth laws of an SCM. My strategy will be to construct a numerical laboratory that represents a single computational cell containing a realization of a statistical distribution of cracks. The cracks will evolve by the microphysical models of the SCM, leading to quantifiable damage and failure of the computational cell. I will use the numerical data generated by randomly generated ensembles of the fracture process to establish scaling laws that will modify and simplify the implementation of the SCM into large scale engineering codes.
Highlights
In this paper I will consider the evolution of damage and failure as described by a statistical crack model (SCM) designed for use in an engineering scale simulation program
From the viewpoint of ensuring mesh independence, failure must depend on a dimensionless moment of the crack size distribution in Equation (7); any other moment would involve a length scale that would have to be compared to the computational cell size DX
A basic idea of this paper is to introduce a simple crack interaction model into the array code, accumulate statistics on damage and failure, and to formulate modifications to the basic growth laws from the numerical results
Summary
In this paper I will consider the evolution of damage and failure as described by a statistical crack model (SCM) designed for use in an engineering scale simulation program. The relationship between damage and failure is more complicated than the simple postulate that failure occurs at a constant percolation threshold, there are simple scaling relations that can be observed in the array code results. These relate the evolution of damage to time of crack growth and so obviate the need for keeping track of the crack size probability distribution. I will conclude the paper in Section 8 with a summary of results and some thoughts on future directions
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