The Constitutive Relationship between High Pressure-High Strain Rate and Low Pressure-High Strain Rate Experiment

It is indicated that the constitutive equations at high strain rates proposed by Johnson-Cook(J-C), Zerilli-Armstrong (Z-A) and Bodner-Parton (B-P) collapse the data of flow stress in compression, tension, torsion, and shear into simple curve with the scalar quatities 'effective' stress and 'effective' strain, however, the collapsed data of flow stress did not include the data in the planar shock wave tests. The SCG constitutive equation proposed by Steinberg et al for the planar shock wave tests is discussed, which describes the coupled high pressure and high strain rate effects on the plastic deformation of materials. Basing on the recent experiments at elevated temperatures and high strain rates and the shear strength measurements during shock loading, the flow stress for tungsten at high pressure and high strain rates is estimated with J-C and SCG constitutive equations, respectively. It is concluded that the J-C, Z-A and B-P constitutive equations may not be appropriate to describe the plastic behavior of materials at high pressure and high strain rates, comparing with SCG constitutive equation. It is emphasized that the physical background of the constitutive equation at high pressure and high strain rates is different from that at low pressure and high strain rates.