Extraction of Equivalent Stress Versus Equivalent Plastic Strain Curve of Necking Material in Tensile Test Without Assuming Constitutive Model

Abstract

An algorithm for extracting the equivalent stress versus equivalent plastic strain curve of a necking material in tensile test is proposed (the curve is called here the equivalent-plastic (EP) stress–strain (SS) curve). The presented algorithm traces the force–elongation curve via iterative finite element (FE) simulations without assuming a constitutive model and is suitable for a general-purpose FE solver available to a general audience. In the FE simulation and experiment, a slightly tapered geometry was employed around the specimen center to stably initiate necking there. The proposed algorithm and mentioned necking initiation method have been applied to extracting the EP SS curve of a high-strength steel material using an axisymmetric specimen. Because necking was initiated stably in simulation at the specimen center for a range of mesh sizes, the convergence of the extracted EP SS curve with the mesh size could be successfully verified. The EP SS curve of the tested material was extracted up to an EP strain of 0.85 with average strain intervals of approximately 2.5 mili-strain. The error values were less than 0.2 and 0.1% after four and seven FE simulations, respectively. The presented algorithm and necking initiation method in simulation can also be used for simultaneously quantifying the fracture EP strain of a necking material in the tensile test.