Abstract
AbstractA 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.
Highlights
INTRODUCTIONA yield criterion is a function used to distinguish, whether the response of a material to a given stress state is reversible (elastic) or irreversible (e.g. plastic or viscoplastic) and can be viewed as equivalent stress hypotheses [1]
A yield criterion is a function used to distinguish, whether the response of a material to a given stress state is reversible or irreversible and can be viewed as equivalent stress hypotheses [1]
Hill is generally viewed as having introduced the first fully anisotropic quadratic yield criterion for orthotropic materials [7], but his function can be viewed as a special case of the quadratic von Mises yield function specified for
Summary
A yield criterion is a function used to distinguish, whether the response of a material to a given stress state is reversible (elastic) or irreversible (e.g. plastic or viscoplastic) and can be viewed as equivalent stress hypotheses [1]. Hill is generally viewed as having introduced the first fully anisotropic quadratic yield criterion for orthotropic materials [7], but his function can be viewed as a special case of the quadratic von Mises yield function specified for. On we will refer to the quadratic von Mises - Hill yield function This function can be used to describe plastically anisotropic material with an orthotropic symmetry by using six parameters for plastically incompressible behavior. A map Q → Q⊗r defines a r times dyadic product of the tensor Q with itself
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