The Effective Unloading Modulus for Automotive Sheet Steels

In stamping advanced high strength steels (AHSS), the deviations from desired part geometry caused by springback from a radius, curl, twist, and bow are major impediments to successfully producing AHSS parts. In general, the conventional elastic modulus is used to quantify the strain that occurs on unloading. This unloading strain causes deviations from desired part geometry. Considerable evidence in the literature indicates that for tensile testing, the conventional elastic modulus does not accurately describe the unloading strain. The present study uses new data and results from the literature to examine the average slope of tensile stress strain curves on unloading. This slope is termed the effective unloading modulus. The results from this study quantitatively describe how the effective unloading modulus decreases with increasing strength, prestrain, and unloading time. Calculations are also included that describe the relative contributions of: 1) dislocation related phenomena, 2) thermal contraction, and 3) conventional elasticity. The effective unloading modulus can be used as an engineering estimate to replace the conventional elastic modulus in mechanics equations that predict springback from a radius, curl, twist, and bow. The results from this study also indicate a need for evaluating the effective unloading modulus for other strain paths. Determination of the effective unloading modulus for other strain paths is needed before quantitative relationships suitable for finite element analysis codes can be precisely specified.