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In-plane simple shear tests have become commonplace in the fracture characterization of automotive sheet metals but have received less attention for constitutive characterization. Unlike tensile tests, simple shear tests do not have any tensile instability and remain in a state of plane stress until fracture. From plastic work equivalence, an isotropic hardening model can be readily constructed from the tensile and shear test data without inverse finite-element analysis. The success of the methodology hinges upon the shear specimen geometry and how the local strains in the gage region are measured using digital image correlation (DIC). In this study, finite-element simulations of seven shear test geometries were evaluated for an isotropic material in a series of virtual experiments by varying the input hardening response. The data from the simulations was extracted from the surface as if DIC was employed and used to determine the hardening behavior in comparison with the exact solution. Shear geometries without a notch eccentricity in the gage region appear to be best suited for characterizing low hardening materials with an error of less than 1% in the stress response for an n-value of 0.02. Conversely, for higher hardening materials corresponding to an n-value of 0.20 or greater, the geometries with a notch eccentricity performed best.

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The yield strength of materials under plane strain deformation is often not characterized experimentally due to difficulties that arise in interpreting the results of plane strain tensile tests. The strain and stress fields in the gauge region of these tests are inhomogeneous, making it challenging to extract the constitutive response from experimental measurements. Consequently, the plane strain yield stress is instead predicted using phenomenological plasticity models calibrated using uniaxial and biaxial tension data. To remove this uncertainty, a simple finite-element based inverse technique is proposed to determine the arc of the associated yield locus from uniaxial-to-plane strain tension using a constrained form of Vegter’s anisotropic yield criterion to analyze a notch tensile test. The inverse problem is formulated under associated deviatoric plasticity and constrained such that only a single parameter, the major principal yield stress under plane strain deformation, needs to be identified from the finite-element simulations. The methodology was applied to two different automotive steel grades, an ultra-high strength DP1180 and a DC04 mild steel. The predictive accuracy of the constitutive models was then evaluated using an alternate notch geometry that provides an intermediate stress state between uniaxial and plane strain tension. By performing notch tensile tests in three sheet orientations, three arcs of the yield surface were obtained and employed to calibrate the widely used Yld2000 yield function. The study shows that for DP1180, the normalized plane strain yield stress was in the range of 1.10 to 1.14 whereas for DDQ steel, the normalized plane strain yield stress was notably stronger, with values ranging from 1.22 to 1.27, depending on the orientation. The proposed methodology allows for a wealth of anisotropic plasticity data to be obtained from simple notch tests while ensuring the plane strain state is accurately characterized, since it governs localization and fracture in many forming operations.