Incorporation of Material Variability in the Johnson Cook Model

Abstract

The Johnson Cook (JC) material model is often used for modeling hypervelocity impacts (HVI) because it is capable of capturing high rate deformation and temperature effects. Within the JC model, material damage leading to fracture is aggregated using a path dependent damage parameter. Contributions to the damage parameter are calculated at each cycle as the quotient of incremental effective plastic strain over the effective failure strain. The effective failure strain is a function of the stress state, strain rate, and temperature which changes locally throughout the simulation.Solid bodies often demonstrate variability in resilience resulting from material inclusions and defects. Therefore, in addition to the deterministic, state-based variability in the effective failure strain inherent to the JC model, efforts are often made to capture the effect of general material non-uniformity. Although other approaches may be available, the Weibull probability distribution is often employed within failure analyses to allow simulations to diverge from a completely uniform solution.In this paper, we investigate several methods of augmenting the JC damage model with Weibull variability. The implementation of each method provides a means for measured material uncertainty to enter the calculation. We focus on a standard three-parameter Weibull probability density function (pdf) although the methods proposed can be used with any probability distribution. Characteristics of the pdf are preserved within a solid body at its initial state but differ in the effect the JC effective failure strain has on these characteristics as the material state changes. The Weibull pdf under various loading conditions is discussed, and simulation results incorporating these methods are compared with those employing only the JC damage model or Weibull variability.