High-Strength Alloyed Steel: Modelling Dynamic and Multiaxial Loading Conditions

This work reports on the modelling of failure behaviour in case of a high strength alloyed steel, experimentally subjected to a range of strain rates and states of stress triaxiality. This material combines high strength with exceptionally high ductility, which makes it difficult to describe material behaviour based on well-known constitutive models such as Johnson-Cook [1] [2]. To solve this challenge, extensive experimental investigations were performed to record stress-strain relations and, in particular, failure behaviour. Different states of triaxiality were attained based on the specimen geometry. Experiments with flat, unnotched and notched specimens yielded triaxial stress-states under uniaxial loading conditions. Stress-states due to shear stress and combinations of shear and tensile stresses were studied with biaxial tensile specimens. The triaxiality of the uniaxial tensile specimens was calculated based on the approximation suggested by Bridgman [3]. Based on the detected data, the material models suggested by Johnson-Cook [1] [2] was parameterized. Parameterization was carried out with the software LS-OPT [5]. The parameters of the constitutive models were found in an optimization procedure which minimized the difference between simulation prediction and experimental results. The discretization and element size was varied in order to study discretization effects. Smaller element sizes enabled a more constant triaxiality over the duration of the simulation. The parameter space of the Johnson-Cook model allowed for a satisfactory agreement in case of uniaxial experiments with a value of the stress triaxiality ≥ 1/3. However, the more complex problem of accurately modelling failure at other values of stress triaxiality between 0 (pure shear) and 1/3 (uniaxial tension) could not be solved. We discuss possible reasons for the apparent inability of the Johnson-Cook failure model to describe the effects induced by triaxiality at large failure strains and under shear stresses.