Moving toward a more realistic material model of a ductile material with failure mode transition

Abstract

In this paper a universal mathematical model using fully coupled thermal-structural finite element analysis capable of predicting ductile-to-brittle failure mode transition at high strain rates is presented. Appropriate equivalent strain measures describing the onset and the growth of ductile and total damage and heat generation rate per unit volume for dissipation-induced heating have been proposed. The model was implemented into a finite element code using the updated Lagrangian formulation for finite strains, the von Mises material model with isotropic hardening and the Jaumann rate, in the form of the Green-Naghdi rate, in the co-rotational Cauchy's stress update calculation. Plastic bending of a cantilever was studied, applying constant pressure as stepped load to 1/3 of the upper surface of the beam. The analysis result shows that at higher strain rates the ductile damage value is significantly lower than the value of the total damage, while at low strain rates their values are approximately identical, thus the model is likely to open new perspectives in the study and numerical simulation of the behaviour of ductile materials.

An Alternative Material Model Using a Generalized <i>J2</i> Finite-Strain Flow Plasticity Theory with Isotropic Hardening

“…In this research, we have modified our former material model capable of imitating ductile-to-brittle failure mode transition of a ductile material at high strain rates [29]. In agreement with the above, the rate form of the constitutive equation of the material can take any of the following forms   [29].…”

“…The idea of the ratio of ductile and total damage increment xx was first introduced by Écsi and Élesztős in order to take into account the internal damping of the material properly during plastic deformations, where xx allowed for the redistribution of the plastic flow proportionally between the spring and the damper of a 1D frictional device representing the rheological model of the material [29]. The ratio is determined in an elastic corrector phase during return mapping and its value is then kept constant.…”

Analysis of Failures of Fixed Plate on Closing Mechanism of High Pressure Press

“…The stress analysis of fixed plate was realized by using numerical modelling by the finite element method [5,6,7]. Two cases of force transmission by leading columns has been modelled.…”

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

“…( 1)-( 6), the analytical solution is replaced with an optimization problem, in which stationary points of appropriate functionals are sought where the sought physical fields represent the solution of the original system of partial differential equations (PDE) [42]. After applying the Galerkin method to the governing PDE (2) and (3), the weak form for updated Lagrangian formulation, can be expressed as follows [39,40] : , dv dv dv ds…”

“…The aim of this paper is to propose a universal heat equation for a wide range of strain rates that considers thermoelastic heating, inelastic heating [36], internal damping induced heating [38][39][40] and is capable of imitating ductile-to-brittle failure mode transition at high strain rates [39], while using as few as possible easily identifiable material parameters. In the presented study we used an improved weak form of conservation of energy for fully coupled thermal-structural finite element analysis, which considers the strong coupling between the temperature field and the deformation field via the Cauchy's stress theorem on the boundary when convective or/and radiative heat transfer takes place [39,40].…”