Pressure Sensitive Nonassociative Plasticity Model for DRA Composites

Abstract

Discontinuously reinforced aluminum (DRA) is currently used where design considerations include specific stiffness, tailorable coefficient of thermal expansion, or wear resistance. Plastic deformation plays a role in failures due to low cycle fatigue or simple ductile overload. DRA is known to exhibit pressure dependent yielding. Plastic deformation in metals is widely regarded to be incompressible, or very nearly so. A continuum plasticity model is developed that includes a Drucker–Prager pressure dependent yield function, plastic incompressibility via a nonassociative Prandtl–Reuss flow rule, and a generalized Armstrong–Frederick kinematic hardening law. The model is implemented using a return mapping algorithm with backward Euler integration for stability and the Newton method to determine the plastic multiplier. Material parameters are characterized from uniaxial tension and uniaxial compression experimental results. Model predictions are compared to experimental results for a nonproportional compression–shear load path. The tangent stiffness tensor is nonsymmetric because the flow rule is not associated with the yield function, which means that the commonly used algorithms that require symmetric matrices cannot be used with this material model. Model correlations with tension and compression loadings are excellent. Model predictions of shear and nonproportional compression–shear loadings are reasonably good. The nonassociative flow rule could not be validated by comparison of the plastic strain rate direction with the yield function and the flow potential due to scatter in the experimental results. The model is capable of predicting the material response obtained in the experiments, but additional validation is necessary for the condition of high hydrostatic pressure.