When we simulate impact dynamics problems using Abaqus, we often consider using the Johnson-Cook constitutive model. Correctly inputting the various parameters of the material constitutive model is crucial for the accuracy of our simulation results. Today, we will introduce the parameter identification issues of the Johnson-Cook model in Abaqus.
The Johnson-Cook plasticity model is an analytical form of the von Mises plasticity model that incorporates hardening behavior and rate dependence, making it suitable for simulating high strain rate deformation of many materials, including most metals.
It is typically used for adiabatic transient dynamic simulations and is combined with the Johnson-Cook dynamic failure model in Abaqus/Explicit. In Abaqus/Explicit, it can be paired with a tensile failure model to simulate tensile tearing or pressure fracture. It can also be integrated with progressive damage and failure models to specify different damage initiation criteria and evolution laws, allowing for progressive degradation of material stiffness and removal of mesh elements. It must be combined with linear elastic material models (linear elastic behavior) or state equation material models (equation of state).
Below is the general expression of the Johnson-Cook model, where the main parameters to be determined are A, B, n, C, and m. As can be seen, the core of the Johnson-Cook model consists of three parts, representing material strain hardening, strain rate hardening (strengthening), and temperature softening, which can be summarized as “two hard, one soft.”
A is the initial yield stress at the reference strain rate and reference temperature; B and n represent the material strain hardening modulus and hardening exponent, respectively; C is the strain rate strengthening parameter of the material; and m is the thermal softening exponent of the material.
According to the help documentation, the meanings of each parameter are as follows:
When we disregard the effects of strain rate and temperature, the expression simplifies to the following form:
If we have determined the parameters A, B, and n, we can input the corresponding Johnson-Cook parameters in Abaqus. The key point is that, given the elastic modulus, Poisson’s ratio, yield stress, and ultimate strength of a material, we can use the JC plugin to automatically calculate parameters A, B, and n. Below is the stress-strain curve for aluminum alloy AL2024 obtained using the JC plugin.
