A Sixth Order Inverse PotentialFunction for Incorporation ofCrystallographic Texture IntoPredictions of Properties ofAluminium Sheet

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Abstract
In order to simulate adequately the formability of sheet, it is necessary to generate a yield criterion that takes into account the anisotropy of the crystallographic texture. This yield function must be in a form that can be used easily in finite element analysis. In addition, the formulation should allow the possibility to update the yield surface during simulation to take into account the texture evolution. This work investigates the use of a sixth-order strain rate potential that, when differentiated with respect to the strain rate, gives the components of stress. A method is given to solve the non-convexity problems that can arise when the proposed analytical sixth-order function is used. Examples are given for one cold rolled and one annealed aluminium sheet.

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