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Development of A Generalized Isotropic Yield Surface for Pressure Insensitive Metal Plasticity Considering Yield Strength Differential Effect in Tension, Compression and Shear Stress States Open Access

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AbstractDevelopment of A Generalized Isotropic Yield Surface for Pressure Insensitive Metal Plasticity Considering Yield Strength Differential Effect in Tension, Compression and Shear Stress StatesDue to effects of twinning and texture evolution, the yield surface for hexagonal close packed (HCP) metals displays an asymmetry between the yield in tension and compression, and significantly changes its shape with accumulated plastic deformation. Traditional von Mises (J_2) plasticity yield criteria and hardening assumptions can not accurately model these phenomena due to lack of stress state dependent yield stress and hardening approach. In this dissertation, a generalized isotropic yield surface model that can describe both the yielding asymmetry and distortional hardening (stress state dependent hardening) on the pressure independent plastic response of metals is proposed. Yielding is described by a newly developed macroscopic phenomenological yield function that accounts for asymmetry between yielding in uni-axial tension and uni-axial compression states. This yield criteria also provides flexibility for the yield stress in pure-shear compared to von Mises (J_2) plasticity; therefore it could be used by face-centered cubic (FCC) and body-centered cubic (BCC) materials as well as HCP materials. The coefficients involved in this proposed yield criterion are considered to be functions of the accumulated plastic strain. The proposed model was implemented into the explicit finite element code LS-DYNA and used to simulate the uni-axial tension, uni-axial compression, and torsion tests of Al2024-T351 and Ti-6Al-4V materials in the rolling direction using smooth dogbone, solid cylinder, and thin walled tube specimens respectively. Comparisons between predicted and measured force-displacement curves and macroscopic strain fields show that the proposed model describes very well the yield strength differential effect and distortional hardening (stress state dependent hardening) based on the uni-axial tension, uni-axial compression and pure-shear stress states. On the other hand, the anisotropic nature of Ti-6Al-4V causes directionally dependent plastic flow in some cases, and this phenomenon cannot be treated by the current material model due to the isotropic plasticity assumption.The proposed model is then extended to include the effects of strain rate and temperature softening related with the temperate increase within the material due to adiabatic heating using tabulated input curves for yield-temperature and yield-strain rate dependency. Then a new, viscoplastic material model with generalized yield surface is implemented into a non-linear explicit dynamics finite element code, LS-DYNA. In this material model, a higher order (higher than quadratic order) generalized yield function with isotropic and isochoric plasticity is utilized, and stress state dependent isotropic hardening, strain-rate hardening and temperature softening is considered. It is shown that the new material model is capable of predicting yielding asymmetry between uni-axial tension and uni-axial compression and pure-shear stress states accurately within the limits of the convexity region. Stress state, strain rate, and temperature dependent plastic flow prediction capability of the model suggests that the new material model can be used as a promising tool for diverse applications of dynamic plastic deformation and subsequent ductile failure phenomenon. Therefore, the material model can be used in the numerical solution of the impact problems in industry such as fan blade-out containment events in turbofan engines, vehicle crashworthiness, and metal forming.

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