From Taylor to Sachs: An intermediate constraint based on a single microstructural parameter

Abstract

In this study, we propose lightweight and accurate method for predicting plastic anisotropy through macroscopic yield surfaces directly derived from crystallographic texture. By introducing an intermediate variable ϕ, the model bridges the classical isostrain (Taylor) and isostress (Sachs) assumptions, offering a continuous interpolation that captures the inhomogeneous mechanical behavior of real polycrystal aggregates or representative volume elements. Built upon a rate-independent single crystal yield function, the model enables efficient construction of anisotropic yield surfaces using only grain orientations and a single calibrated parameter ϕ. Validation is conducted through two complementary approaches: (1) for isotropic textures of FCC and BCC aggregates, the model reproduces classical yield surface shapes and converges to the Mises and Hershey criteria in the respective limiting cases; and (2) for textured materials including STS304, STS430, AA1050, and oxygen-free high-conductivity (OHFC) copper, the model accurately predicts directional plastic anisotropy in terms of yield stresses and r -values, demonstrating its broad applicability across materials with different crystal structures. Additionally, the predicted yield surfaces in the plane-stress regime show excellent agreement with crystal plasticity finite element (CPFE) simulations, with a mean absolute error of 0.44 %, calibrated using the same input. The proposed intermediate constraint model provides a computationally efficient yet physically robust mesoscale framework, making it particularly suitable for practical applications that require accurate prediction of anisotropic plasticity, even with limited experimental data.