Mechanisms and Modeling of Bake-Hardening Steels: Part II. Complex Loading Paths
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TRODUCTION
BAKE-HARDENABLE steels belong to a class of forming steels used in the automotive industry for outer panels. They are particularly interesting because they provide both good formability and high dent resistance. Indeed, they can offer high yield strength after forming and paint baking even though they initially have a low yield strength before forming. This hardening after paint-baking process is due to a strain-aging phenomenon, which is the interaction between solute carbon and dislocations (formation of Cottrell atmospheres[1]). This effect has been particularly investigated in a previous article.[2] Descriptions of bake hardenability are usually based on uniaxial tensile tests. First, a test piece is loaded to 2 pct strain, which is a typical amount of strain received by outer panels during stamping. Then, the specimen is baked at 170 °C for 20 minutes to simulate the industrial paint-baking process. Finally, the prestrained and baked specimen is uniaxially tested in the same direction as the prestrain. The bake hardening (BH) is defined as the difference between the lower yield stress after baking and the final flow stress after prestraining, as displayed in Figure 1. V. BALLARIN, Research Engineer, is with the Automotive Applications Research Center, Arcelor-Mittal Montataire, 60761 Montataire, France. A. PERLADE and X. LEMOINE, Research Engineers, and O. BOUAZIZ, are with the Automotive Products Research Center, Arcelor-Mittal Maizie`res, Voie Romaine, 57283 Maizie`res-le`s-Metz, France. Contact e-mail: xavier.lemoine@arcelor mittal.com S. FOREST, CNRS Research Director, is with Mines ParisTech, Centre des Mate´riaux, UMR CNRS 7633, 91003 Evry Cedex, France. Manuscript submitted October 29, 2007. Article published online April 15, 2009 METALLURGICAL AND MATERIALS TRANSACTIONS A
However, sheet forming process and dent tests lead to strain paths that are very different from pure tension. Actually, stamping and dent tests are close to plane strain or equibiaxial stretching. The effect of aging on tensile tests has been widely studied in literature. It particularly causes the return of a sharp yield point and formation of Lu¨ders bands.[2] On the other hand, the influence of the aging treatment when strain path is changed has been far less investigated. Wilson et al.[3] carried out torsional tests with prestraining, aging treatment, and reverse or forward restraining. They found that, for Bauschinger tests, the sharp yield point returns very slowly, if at all, and the Bauschinger effect is reduced by the aging treatment. Other particular tensile tests were performed[4,5] with prestrain in uniaxial tension, baking, and then tensile tests but with an angle from 0 to 90 deg between directions of prestrain and restrain. Except for continuous loading, experiments showed a disappearance of the sharp yield point. However, results are contradictory regarding the aging influence on yield strength: Jun et al.[4] found an increase of yield strength whatever the angle between directions of loading, whereas Hiwatashi et al.[
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