Mathematics

Structural engineering

Ultimate tensile strength

Dynamic strain aging

Engineering

Strain hardening exponent

Mathematical analysis

Strain rate

Composite material

Flow stress

Materials science

Layer (electronics)

Hardening (computing)

Monotonic function

Plasticity

International Journal of Plasticity

Constitutive models dealing with the thermal and visco-plasticity of metals have seen wide applications in the automotive industry. A basic plasticity and fracture characterization of a 1.5 mm thick DP780 dual phase steel sheet based on uniaxial tensile (UT) experiments with seven distinct material orientations is complemented by low (∼0.001/s), intermediate (∼1/s) and high (∼150/s) strain rate experiments on notched tensile (NT) and shear (SH) specimens at temperatures ranging from 20 °C to 500 °C. At low strain rates, we observe a non-monotonic effect of the temperature on the force-displacement curves, with the highest curve obtained at 300 °C. Contrasting low speed tests, a monotonic effect of temperature is observed for intermediate and high strain rate experiments, with the highest curves obtained at 20 °C for both cases. Strain rate jump tests are performed proving the positive strain rate sensitivity of the steel. A machine-learning based plasticity model is developed to capture the observed complex strain rate- and temperature effect. The material is modeled as elasto-plastic, with a Hill'48 yield surface and a non-associated flow rule. The flow resistance is decoupled into a reference strain hardening term and a neural network term, which is a function of the plastic strain, strain rate, temperature, and an additional dynamic strain aging variable. The plasticity model is implemented into a material user subroutine and identified using a counterexample-guided hybrid experimental-numerical approach. The extracted loading paths reveal a complex rate and temperature effect on the ductility of DP780. A neural network based fracture initiation model is therefore adopted to describe the fracture onset across various stress states, strain rates and temperatures considered.

Counterexample-trained neural network model of rate and temperature dependent hardening with dynamic strain aging