Deformation and Fracture ; Modelling Techniques to Take Account of Strain-Rate Behaviour and Stress State

Abstract

Numerical simulations of the dynamic deformation and ductile fracture of notched tensile specimens have been carried out using the finite element hydrocode DYNA2D and advanced constitutive relations for both pure copper and Remko iron. The predictions of plastic flow were in good agreement with the observed shape at fracture of specimens tested dynamically in a unique impact test facility known as the 'flying wedge' which is capable of applying strain-rates in the range 1O2-lo4 s-'. The DYNA2D results were used to give accurate predictions of the triaxial state-of-stress (defined as the ratio of mean stress P to effective stress Y) at the fracture initiation site as a function of initial geometry, mean strain and strain-rate. Experimentally-measured failure strains were then plotted against predicted values of P/Y for each material. For copper, failure strains decreased with increasing stress triaxiality P/Y but no significant strain-rate effect was apparent. In the case of iron, the same trend of reducing fracture strain with increase in PIY was observed, but here increased strain-rate produced a marked effect. In fact, a ductile-brittle transition (confirmed by metallurgical examination) was seen to occur at the highest speed of testing and above a certain value of Ply. Parameters for simple empirical fracture models were estimated from the plots of failure strain versus Ply. When combined with the standard damage accumulation fracture criterion in DYNA2D, these models gave reasonable predictions of both the site of fracture initiation (ie the centre of the specimen) and the time-to-fracture when compared with fracture times measured on certain specimens using strain-gauges or high-speed photography. More fundamental ductile fracture models which allow for the statistical nature of void initiation and growth and the effect of voids on the yield surface are currently under investigation.

Necking phenomenon based on the Aramis system

“…16–18 However, in the stress triaxiality equation proposed by Bridgman, the influence of material was not taken into account, which resulted in some researchers to find that their numerical simulation results were not consistent with Bridgman formula, while others found that the results were in good agreement. 19,20…”