Identification of the Plane Strain Yield Strength of Anisotropic Sheet Metals Using Inverse Analysis of Notch Tests 2022-01-0241

Plane strain tension is the critical stress state for sheet metal forming because it represents the extremum of the yield function and minima of the forming limit curve and fracture locus. Despite its important role, the stress response in plane strain deformation is routinely overlooked in the calibration of anisotropic plasticity models due to challenges and uncertainty in its characterization. Plane strain tension test specimens used for constitutive characterization typically employ large gage width-to-thickness ratios to promote a homogeneous plane strain stress state. Unfortunately, the specimens are limited to small strain levels due to fracture initiating at the edges in uniaxial tension. In contrast, notched plane strain tension coupons designed for fracture characterization have become common in the automotive industry to calibrate stress-state dependent fracture models. These coupons have significant stress and strain gradients across the gage width to avoid edge fracture. A single notch test can thus provide both constitutive and fracture information. However, an overlooked complication of using notch tensile tests is that non-trivial shear stresses develop within the gage region. Tensile loading occurs over a range of material directions, rendering the inverse analysis non-unique if additional constraints are not imposed. The present study proposes a simple inverse methodology to exploit the stress gradients in notch tension tests to calibrate the local arc of the anisotropic yield surface from uniaxial-to-plane strain tension. The influence of the shear stress is investigated with a two-step calibration procedure proposed to ensure agreement with the local strain path at the notch center and the global engineering stress response. Only the uniaxial tensile stress response to the uniform elongation and R-value are required as input data. The plane strain yield strengths for a variety of automotive metals were characterized including 5xxx and 6xxx-series aluminum, 3^rd Gen advanced high strength steels, mild and stainless steel. The notch data was then compared with plane strain cruciform test data in the literature. Simple correlations to estimate the plane strain yield strength based upon the tensile R-value are then developed for use in yield surface calibration when notch or cruciform data is unavailable.