(A) ductile fracture criterion of sheet metals at a wide range of strain rates

Abstract

This dissertation introduces a ductile fracture criterion considering strain rate based on the Lou-Huh ductile fracture criterion. Fracture tests at various strain rates are conducted with tensile specimens of three sheet metals for the three different crystalline structures

4130 steel for BCC

Oxygen-free high thermal conductivity(OFHC) copper for FCC

and Ti6Al4V for HCP. The tensile tests are conducted at various tensile speeds to consider a wide range of strain rates ranging from $0.001 s^{-1}$ to $1000 s^{-1}$ with three different shapes of specimens: the diagonally notched specimen for the in-plane shear test

the dog bone specimen for the uniaxial tension test

and grooved specimen for the plane strain tension test. The fractography of the fractured specimens are carefully examined through scanning electron microscopy (SEM) experiments in order to discern the strain rate effect on the fracture mechanism. The transition of the fracture mechanism is observed with increasing strain rate. As the strain rate increases, the fracture mechanism changes from plastic rupture to ductile fracture and ductile fracture to void sheeting fracture. At quasi-static strain rates ranging from $0.001 s^{-1}$ to $0.1 s^{-1}$ , the void size decreases as the strain rate increases, however, the void size in-creases with increasing strain rate at intermediate strain rates ( $0.1 s^{-1}$ ~ $1 s^{-1}$ ) due to the thermal softening effect on the matrix surrounding the void. On the other hand, the generation of the shear band at high strain rate significantly induces the decrease of the equivalent strain to fracture on the in-plane shear condition. Those phenomena are empirically implemented to develop a strain rate dependent model based on the Lou-Huh ductile fracture criterion. The equivalent strain to fracture is locally traced by 2D digital image correlation (DIC) method on the surface of the specimen before the onset of the localized necking. The stress triaxiality and Lode parameter are also calculated with assumptions of the plane stress and the proportional loading conditions incorporated with $J_2$ plasticity. The damage function of the strain rate dependent Lou-Huh criterion is calibrated to obtain the fracture coefficients. The fracture loci are depicted with respect to the strain rate. As the strain rate increases, the equivalent strain to fracture decreases, which corresponds to the experimental results at low strain rate ranging from $0.001 s^{-1}$ to $0.1 s^{-1}$ . The transition of thermal condition from isothermal to adiabatic comes into play to increase the equivalent strain to fracture at the intermediate strain rate from $0.1 s^{-1}$ to $1 s^{-1}$ . The equivalent strain to fracture dramatically decreases with increasing strain rate on the in-plane shear condition due to the generation of the shear band. The strain rate dependent model empirically proposed in this dissertation shows acceptable agreement with the experimental data in the wide regime of triaxiality and strain rate.