Generalisation of Hill’s Yield Function for Planar Plastic Anisotropy

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Abstract
In this paper we present a new generalised quadratic yield function for plane stress analysis [7] for the description of the plastic anisotropy of metals and also for the study of the asymmetric behaviour in tension-compression typical of the Hexagonal Closed-Pack (HCP) materials. The new yield function has a quadratic form in the stress tensor and it simultaneously predicts accurately the r-values and directional flow stresses. It also describes very well the biaxial symmetric stress state which is fundamental for the accurate modelling of aluminium alloys. The new quadratic yield function represents the non-symmetric biaxial stress state by performing a linear interpolation from pure uni-axial loading to a biaxial symmetric stress state. The most advanced yield functions for plastic planar anisotropy characterise very well the biaxial symmetric stress region by using experimental flow stresses for the symmetric bi-axial stress state. However, the behaviour of the alloy between the uni-axial stress state and the symmetric bi-axial stress state is still not very well characterised. In this new yield function that behaviour can be assessed from interpolation from the uni-axial stress state into the symmetric bi-axial stress state until experimental yield locus fitting is achieved within a reasonable tolerance in that region. The main advantages of this new yield function is that it can be used for the modelling of metals with any crystallographic structure (BCC, FCC or HCP), it only has five anisotropic coefficients and also that it is a simple quadratic yield criterion that is able to accurately reproduce the plastic anisotropy of metals whilst using an associated flow rule. In the results and discussion we validate the yield locus for FCC and HCP alloys and we apply the new yield function in a cup drawing simulation for the assessment of the cup earing profile.

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