A Novel Built-Up Constitutive Model of 40Cr Alloy Steel Considering the Geometric Effect with Simulation Verification

An accurate constitutive model is essential for modeling and simulation of metal processing. It is usually built by the Split Hopkinson Pressure Bar (SHPB) test. However, the previous studies have rarely considered the influence of specimen geometric effect on the dynamic mechanical behavior, which reduced the accuracy of the model. Hence, a novel built-up constitutive model considering the geometric effect was developed to accurately describe the constitutive relationship of 40Cr alloy steel. First of all, to quantize the geometric effect, the ratio of height to cross sectional area (length x width) of the specimen was defined as the size coefficient and the SHPB tests with various geometric size specimens and loading strain rates were designed to obtain the true stress-strain curves. The experimental results show that the mechanical properties of 40Cr alloy steel are influenced by the specimen's geometric size. The true stress decreases and the strain increases with the increase in the size coefficient. Secondly, a new constitutive model was established by supplementing the size coefficient. It consists of 2 parts: One describes the dynamic mechanical behavior before the peak stress-strain, and the other describes the dynamic mechanical behavior after the peak stress-strain. Accordingly, a finite element simulation model was established. The results show that the new model has better accuracy than the traditional J-C constitutive model. The constitutive model proposed in this paper can be applied to the finite element simulation models of impact, machining, and residual stress.