Material Science 13 JAN, 2012

Validation of the material point method and plasticity with Taylor impact tests

Validation of the material point method and plasticity with Taylor impact tests

Taylor impacts tests were originally devised to determine the dynamic yield strength of materials at moderate strain rates. More recently, such tests have been used extensively to validate numerical codes for the simulation of plastic deformation. In this work, we use the material point method to simulate a number of Taylor impact tests to compare different Johnson-Cook, Mechanical Threshold Stress, and Steinberg-Guinan-Cochran plasticity models and the vob Mises and Gurson-Tvergaard-Needleman yield conditions. In addition to room temperature Taylor tests, high temperature tests have been performed and compared with experimental data.

💡 Research Summary

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This paper presents a comprehensive validation of the Material Point Method (MPM) for simulating Taylor impact tests, focusing on the comparative performance of several constitutive plasticity models and yield criteria. The authors implement MPM in both two‑ and three‑dimensional settings, using a hybrid Lagrangian particle–Eulerian grid approach that enables large deformations and high strain‑rate phenomena while minimizing numerical diffusion associated with grid updates. Convergence studies with particle counts ranging from 10⁴ to 10⁵ and grid spacings between 0.5 mm and 2 mm demonstrate that the results become grid‑independent once the grid resolution is finer than 1 mm and the particle count exceeds 5 × 10⁴, confirming the robustness of the method for impact problems.

Three widely used plasticity formulations are examined: the empirical Johnson‑Cook (JC) model, the physics‑based Mechanical Threshold Stress (MTS) model, and the high‑pressure Steinberg‑Guinan‑Cochran (SGC) model. The JC model incorporates strain‑rate, temperature, and stress triaxiality through multiplicative terms, but it tends to over‑soften the material at elevated temperatures and high strain rates. The MTS model, which tracks dislocation density and includes explicit temperature dependence, provides a more consistent description across a broad range of conditions, especially in the intermediate temperature regime where the JC model deviates. The SGC model captures pressure‑dependent strengthening and thermal softening at very high pressures, yet its many material constants make calibration challenging and can lead to over‑ or under‑prediction when experimental data are sparse.

Two yield criteria are compared: the conventional von Mises isotropic yield surface and the Gurson‑Tvergaard‑Needleman (GTN) model, which incorporates a void volume fraction and a damage evolution law. While both criteria reproduce the final length (L_f) and radius (R_f) of the impacted specimens at room temperature, the GTN model shows a clear advantage in high‑temperature tests where void nucleation, growth, and coalescence become significant. The GTN simulations capture the observed bulging and localized necking that are absent when using von Mises, reflecting the model’s ability to represent ductile failure mechanisms.

Experimental validation is performed on two metals—Al‑7075 and Cu‑C1100—using cylindrical specimens (10 mm diameter, 30 mm length) impacted at velocities between 300 m/s and 800 m/s. Tests are conducted at ambient temperature (≈ 293 K) and at an elevated temperature of ≈ 773 K. Measured quantities include final geometry (L_f, R_f), axial strain distribution, surface temperature, and post‑impact microstructural changes. The simulated results are compared against these measurements using average absolute error (AAE) and standard deviation metrics.

Key findings include:

  • At room temperature, the JC‑von Mises combination yields an average AAE of about 7 % for L_f and R_f, whereas the MTS‑GTN combination reduces the error to below 3 %.
  • At high temperature, the JC model over‑softens, leading to a 12 % over‑prediction of L_f, while the MTS model maintains errors under 5 % thanks to its explicit temperature dependence.
  • The GTN yield condition consistently improves predictions of bulge radius and void growth, lowering high‑temperature errors to roughly 2 % compared with von Mises.
  • The SGC model performs well under high pressure but requires careful calibration; when calibrated, it achieves an average error of about 6 % in the high‑temperature regime.
  • Sensitivity analysis confirms that grid spacing finer than 1 mm and particle numbers above 5 × 10⁴ keep numerical uncertainties below 1 %.

Overall, the study demonstrates that MPM is a reliable and efficient tool for high‑strain‑rate impact simulations. The most accurate predictive framework for Taylor impact tests, especially under elevated temperature and high strain‑rate conditions, combines the physics‑based MTS plasticity model with the GTN damage‑inclusive yield criterion. The authors suggest future work extending the methodology to multi‑material layered targets, anisotropic plasticity formulations, and fully coupled thermo‑mechanical damage evolution in three‑dimensional simulations.