Development of the Johnson-Cook Flow Stress and Damage Parameters for the Impact Response of Polycarbonate: Experimental and Numerical Approach

Abstract

The Johnson and Cook (JC) flow stress and damage model parameters of a polycarbonate (PC) plate were determined by the mechanical tests and numerical simulations of the tests. The experimental tests included quasi-static and high strain rate tension and compression, quasi-static notched-specimen tension, quasi-static indentation (QSI), low velocity impact (LVI) and projectile impact (PI). Initially, five different quasi-static flow stress-strain equations were extracted from the experimental and numerical tests. The flow stress equa-tion determined from the experimental average true stress-true strain curve well agreed with the effective stress -strain obtained from the quasi-static numerical tension test. The numerical QSI force-displacement curve based on the experimental average true stress-true strain equation was further shown to be very similar to that of the experiment. The LVI and PI test simulations were then continued with the experimental average true stress-true strain equation using five different flow stress-strain rate relations: JC, Huh and Kang (HK), Allen-Rule and Jones (ARJ), Cowper-Symonds (CS) and the nonlinear rate approach (NLA). The rate sensitivity parameters of these relations were extracted from the quasi-static and high strain rate tests. The LVI test simulations using the stress -strain rate relations exhibited force-displacement curves higher than those of the experiments. The detected almost no strain rate sensitivity in the LVI tests was ascribed to low strain rate dependency of the flow stress at these intermediate strain rates and large strains involved. On the other side, all the stress-strain rate relations investigated nearly predicted the experimental damage types: dishing at 100 and 140 m s-1 and petalling at 160 m s- 1, except the CS relation which predicted the fracture of the plate at 140 m s-1. The experimental average projectile exit velocity at 160 m s- 1 was further well predicted by the used stress-strain rate relations while the experimental average petal thicknesses were under estimated by the models. The absorbed energy at 160 m s-1 PI test was determined 1.6 times that of the QSI test, which proved an increased energy absorption capability of the tested PC at the investigated impact velocities.