Light-weight and high-strength sheet metals, such as advance high-strength steel, aluminum alloys and titanium alloys, etc., are widely used in the aerospace and automotive industries, and the rolled sheet metals often exhibit significant anisotropic properties. Using a macroscopic plasticity mechanics model, like yield criterion, to describe the plastic flow of materials can provide theoretical guarantees for high-precision numerical simulations. However, with the development of new materials and processes, new challenges have emerged in describing macroscopic mechanical properties of materials with different microstructures using conventional yield criteria.
In order to solve the problem of complex interpolation and extrapolation methods to describe the evolution of yield surface under proportional loading, corresponding analytical yield criteria have been constructed by Prof. Jun Chen's team at the Department of Plasticity Technology, School of Materials Science and Engineering, Shanghai Jiao Tong University, under the funding of the National Natural Science Foundation of China (92160206, 52175347). These criteria were proposed for materials with incongruent plane strain and shear stress, and materials with asymmetric tensile and compressive yield stress, respectively, which revealed the mechanical evolution laws and rheological mechanisms of materials during plastic deformation.
Parameters in conventional yield criteria are mostly obtained by uniaxial tension and equi-biaxial tension experiments, which cannot accurately predict the yield surface of certain materials near shear stress. Therefore, it is an urgent need to conduct research on yield criterion for materials with incongruent plane strain and shear stress.
Prof. Jun Chen's team, in collaboration with Prof. Jeong Whan Yoon from Korea Advanced Institute of Science and Technology and Dr. Qi Hu from Technical University of Munich, investigated the yield locus envelope necessary for the composition of a complete yield surface. Analyzing the construction form of the Poly6 and Poly8 yield criterion, they proposed the Poly6-18p yield criterion with parameters expressed analytically by the experimental data, which realized the accurate prediction of yield surface for aluminum alloys with incongruent plane strain and shear stress, as well as the accurate finite element simulation in tube hydroforming. The research results were published in International Journal of Plasticity titled as “Analytically described polynomial yield criterion by considering both plane strain and pure shear states”.
Link: https://doi.org/10.1016/j.ijplas.2022.103514
Figure 1. Mechanical properties predicted by different yield criteria of AA6061-O with incongruent plane strain and shear stress and engineering applications.
In recent years, some new asymmetric yield criteria have been proposed for materials with significant asymmetry of tensile and compressive yield stress, such as magnesium alloys and titanium alloys with HCP structure, but there are still some problems such as complex mathematical structure, difficult parameter calibration and insufficient prediction accuracy.
Based on the idea of shape function, Prof. Jun Chen's team, in collaboration with Dr. Qi Hu from Technical University of Munich, have constructed a new asymmetry factor to describe the asymmetric yield stress and anisotropy coefficients in tension and compression of materials, breaking through the difficulty that the conventional asymmetric yield criteria cannot describe the asymmetry in the direction of 45° to rolling direction.
Since the curvature of yield surface affects yielding behavior of materials under plane strain, a curvature control factor was introduced to control of the yield surface curvature effectively. With the same mathematical form of the proposed yield function, an analytical asymmetric plastic potential function has been established for the first time to describe the anisotropy coefficients of asymmetric materials under tension and compression, which solved the problem that the current analytical plastic potential function cannot predict the anisotropy coefficients under tension and compression simultaneously. This research provided a theoretical basis for the evolution of the yield surface and rheological behavior of asymmetric materials in tension and compression. The research results were published in International Journal of Plasticity, titled as “A concise analytical framework for describing asymmetric yield behavior based on the concept of shape functions”.
Link: https://doi.org/10.1016/j.ijplas.2023.103593
Figure 2. Evolution of mechanical properties predicted by different analytical yield criteria for Ti6Al4V with asymmetry in tension and compression.