New Constitutive Model for the Size Effect on Flow Stress Based on the Energy Conservation Law

Abstract

In this study, a new model involving energy is established to characterize the size effect on flow stress. The new model treats the experimental machine and the specimen as an isolated system, and this isolated system satisfies the Energy Conservation Law. The total work performed on the specimen by the experimental machine is nearly equal to the energy consumed by the specimen plastic deformation and the energy consumed by friction (which can be ignored when working without friction). The new model predicts the energy consumption of the specimen deformation by quantifying the total energy input to the specimen by the experimental machine and then obtaining the relevant parameters of the constitutive model. Through uniaxial tensile tests of pure nickel thin sheets with various thickness/average grain sizes (t/d), the new model was used to optimize the parameters of the existing constitutive model that predicts the flow stress of specimens with different t/d. The prediction accuracy of the optimized constitutive model is improved, especially for specimens with a t/d < 1. The new model is established from the perspective of energy input to avoid the analysis of the material deformation mechanism and improve the prediction accuracy.

A microscale constitutive model for thin stainless steel sheets considering size effect

“…Accordingly, they defined the strength coefficient in the Swift equation as a function of t / d considering the Hall–Patch equation and the surface layer model. Moreover, Wang et al 30 improved the prediction accuracy of the model by utilizing the energy method to optimize the hardening exponent in the Swift equation. Wang et al 31 modified the Hollomon equation to describe the strain-hardening behavior of titanium foils in the microscale.…”