Spherical cavity expansion method dependent on strain, strain rate, and temperature

This paper presents a spherical cavity expansion method based on the self-similar field considering dynamic hardening, which includes plastic strain, plastic strain rate, and temperature for an infinite compressible medium under J2 plasticity. This study proposes an approach based on the gradients of plastic strain and temperature under self-similarity transformation to deal with dynamic hardening models such as the Johnson-Cook (JC) and the modified Johnson-Cook (mJC) models. A theoretical model shows that the effective and radial stresses are reduced near the cavity surface and increased away from the cavity under the mutual influence of hardening and thermal softening. The JC hardening model is used to analyze the behavior of the cavity expansion for AISI 4340 steel. The proposed theoretical model was validated by comparing the result of the explicit finite element method (FEM). This study discusses the behavior of the expanding cavity problem for thermal softening and strain rate sensitivities. In addition, rigid penetration problems are simulated to analyze the application of the presented method. FEM and the proposed cavity expansion method were compared with the penetration depth of AA6061-T651 target using the mJC hardening model for a hemispherical-nosed penetrator. A comparison is made for the performance of the penetration depth with an ogive-nose projectile for AA7075-T651 and AA6061-T651 materials using the mJC hardening model. This study concludes that the proposed method can be applied without modifying the hardening models to spherical cavity expansion problems that involve dynamic hardening models dependent on strain, strain rate, and temperature under adiabatic heat.