An Improved Heat Equation to Model Ductile-to-Brittle Failure Mode Transition at High Strain Rates Using Fully Coupled Thermal-Structural Finite Element Analysis

Abstract

In this paper a universal heat equation for fully coupled thermal structural finite element analysis of deformable solids capable of predicting ductile-to-brittle failure mode transition at high strain rates is presented. In the problem mathematical formulation appropriate strain measures describing the onset and the growth of ductile and total damage and heat generation rate per unit volume to model dissipation-induced heating have been employed, which were extended with the heat equation. The model was implemented into a finite element code utilizing an improved weak form for updated Lagrangian formulation, an extended NoIHKH material model for cyclic plasticity of metals applicable in wide range of strain rates and the Jaumann rate in the form of the Green-Naghdi rate in the co-rotational Cauchy’s stress objective integration. The model verification showed excellent agreement with the modelled experiment at low strain rates. Plastic bending of a cantilever has been studied at higher strain rates. A few selected analysis results are presented and briefly discussed.