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# A New Algorithm for the Thermo-Mechanical Coupled Frictional Contact Problem of Polycrystalline Aggregates Based on Plastic Slip Theory

Yun Chen1, Junzhi Cui2, Yufeng Nie1, Yiqiang Li1
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an 710129, China. E-mail: ychensate@163.com
LSEC, ICMSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, China.

Computer Modeling in Engineering & Sciences 2011, 76(3&4), 189-206. https://doi.org/10.3970/cmes.2011.076.189

### Abstract

This paper presents a new numerical algorithm for thermal-mechanical coupled analysis of polycrystalline aggregates based on the plastic slip theory inside crystals and the frictional contact on their interfaces. It involves the mechanics and heat conduction behaviors caused by both force loads and temperature changing within crystal and contact interfaces between crystals. Firstly, the constitutive relationship inside single crystal, and the moment equations and energy equations are derived by means of rate-dependent plastic deformation theory and the formulation of elastic-plastic tangent modulus depended on temperature. Secondly, the contact conditions with friction, including frictional heat generation and heat transfer across the contact interface, are discussed. And then based on the ABAQUS software, the subroutines to calculate thermo-mechanical behaviors of polycrystalline copper are coded, and a polycrystalline body composed by four grains within 16 contact interfaces is simulated under the torsion and bending loadings. The numerical results show that crack propagation path are associated with loading ways and temperature change through the contact interfaces in addition to the friction heat generation. The displacement jumps are related to the contact pressure. The modeling approach presented in this work can be extended to more complicated systems with the interaction of a number of grains.

### Keywords

Polycrystalline aggregates, Friction contact, Thermo-mechanical coupled, Crystal slip theory.

Chen, Y., Cui, J., Nie, Y., Li, Y. (2011). A New Algorithm for the Thermo-Mechanical Coupled Frictional Contact Problem of Polycrystalline Aggregates Based on Plastic Slip Theory. CMES-Computer Modeling in Engineering & Sciences, 76(3&4), 189–206.

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