Development of Plasticity and Ductile Fracture Models Involving Three Stress Invariants

by Tingting Zhang

Institution: University of Akron
Department: Mechanical Engineering
Degree: PhD
Year: 2012
Keywords: Plasticity modeling; Stress invariants; Lode angle; Consistent tangent moduli; Non-associated flow rule
Record ID: 1955720
Full text PDF: http://rave.ohiolink.edu/etdc/view?acc_num=akron1334113425


It has been shown that the plastic response of many materials, including some metallic alloys, depends on the stress state. Based on plasticity analysis of three metal alloys, a series of new plasticity models with stress state effect is proposed. The effect of stress state on plasticity and the general forms of the yield function and flow potential for isotropic materials are assumed to be functions of the first invariant of the stress tensor (I1) and the second and third invariants of the deviatoric stress tensor (J2 and J3). Finite element implementation, including integration of the constitutive equations using the backward Euler method and formulation of the consistent tangent moduli, are presented in this thesis. A 5083 aluminum alloy, Nitronic 40 (a stainless steel), and Zircaloy-4 (a zirconium alloy) were tested under tension, compression, torsion, combined torsion-tension and combined torsion-compression at room temperature to demonstrate the applicability of proposed I1-J2-J3 dependent models. It has shown that the output produced by the proposed model have better agreement with experimental data than those produced by the classical J2 plasticity theory for the tested loading conditions and materials. Furthermore, the Gurson-Tvergaard-Needleman porous plasticity model, which is widely used to simulate the void growth process of ductile fracture, is extended to include the effects of hydrostatic stress and the third invariant of stress deviator on the matrix material. The experimental and numerical work presented in this thesis reveals that the stress state also has strong effects on the ductile fracture behavior of an aluminum 5083 alloy. For the ductile fracture analysis, The Goluganu-Leblond-Devaux (GLD) model is employed to describe the porous plasticity behavior of aluminum 5083. The effect of stress triaxiality and Lode angle is analyzed and fracture locus is calibrated as a criterion for void coalescence. The GLD model combined with the fracture locus can be applied to predict the failure of aluminum 5083 specimens with experiencing a large range of stress triaxiality and Lode angle. The numerical analyses agree with the experimental data very well.