A micro-mechanically motivated phenomenological yield function for cubic crystal aggregates

A micro-mechanically motivated phenomenological yield function, for polycrystalline cubic metals is presented. In the suggested yield function microstructure is taken into account by the crystallographic orientation distribution function in terms of tensorial Fourier coefficients. The yield function is presented in a polynomial form in powers of the stress state. Known group-theoretic results are used to identify isotropic and anisotropic parts in the yield function, whereby anisotropic parts are characterized by tensorial Fourier coefficients. The form of the presented yield function is inspired by the classic, phenomenological von Mises - Hill yield function first published in 1913. For a specific choice of material parameters, both functions coincide, thus a micro-mechanically motivated generalization of the von Mises - Hill yield function is presented. For the given yield function, two dimensional experimental results are sufficient, to identify a three dimensional anisotropic yield behavior. The work concludes with a treatment of the isotropic special case, i.e. a tension-compression split in yield behavior as well as parameter ranges for convexity and shapes of the yield surface.