The objective of the current research is the investigation into possible non-linear influence of hydrostatic pressure on yielding of asymmetric (exhibiting the so-called ‘‘strength-differential effect’’) anisotropic sheet metals. To reach this aim, two yield functions are developed, called here ‘‘non-linear pressure sensitive criteria I and II,’’ (NPC-1 and NPC-2). In addition, the non-associated flow rules are employed for these new criteria. The yield functions are defined as nonlinearly dependent on hydrostatic pressure, while the plastic potential functions are introduced to be pressure insensitive. To calibrate these criteria, the yield functions need 10 directional experimental yield stresses and the plastic potential functions need eight Lankford coefficients data points. Four well-known anisotropic sheet metals with different structures, namely AA 2008-T4, a Face Centered Cubic material (FCC), AA 2090-T3, a Face Centered Cubic material (FCC), AZ31, a hexagonal closed packed material (HCP) and high-purity a-titanium (HCP) are considered as case studies. Finally, it is observed that NPC-1 and NPC-2 are more successful than previous criteria in anticipating directional strength and mechanical properties.

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