Simulating Knoop hardness anisotropy of aluminum and β-HMX with a crystal plasticity finite element model

Abstract

We report a crystal plasticity finite element model for simulating the variation of the Knoop hardness number with indenter orientation, i.e., the hardness anisotropy. We propose a modification to the Voce hardening law to include the effects of slip on multiple systems on the hardening rate. The model is validated using single crystal aluminum in a two-step procedure: (a) calibration of the material model with single crystal tension experiments, and (b) prediction of the hardness anisotropy of the {001}, {011} and {021} planes. The predicted hardness anisotropy follows experimental trends very well for the {001} and {021} planes, while for the {011} plane there is a deviation of the predictions from experiments at higher angles of the indenter. The model is then used to simulate the hardness anisotropy of the (010), (011) and (110) planes of β-HMX measured by Gallagher et al. (2015). Due to the lack of single crystal data, we were unable to calibrate the model prior to simulating the hardness anisotropy. Hence, we assumed unknown variables to make predictions for comparison to experiments, including the set of active slip systems and the hardening and twinning behavior. From simulations of the indentation of the (010) plane with the set of slip systems from Barton et al (2009) we found that the hardness anisotropy is inversely proportional to the activity of the slip system (101)[01¯0], and to a lesser extent the twin system. Suppressing the (101)[01¯0] slip system improved the predictions, suggesting that the viable set of slip systems for β-HMX need not include it. The predicted twinning activity did not match well with the observations from Gallagher et al. (2015). Suppressing the twinning resulted in a better prediction of the hardness anisotropy. Due to the simplicity of the twinning part of the model we do not make definite conclusions related to twinning. We report predictions for the hardness anisotropy of the (011) and (110) planes of β-HMX using parameters that maximized agreement between simulations and experimental indentation of (010) plane. These predictions are in reasonable agreement with experiments. In addition, we report the predictions of the hardness anisotropy using the sets of slip systems proposed by Pal and Picu (2018) and Zhou et al. (2012), which both gave inferior agreement with experiments.