A Novel Stress Relaxation Modeling for Predicting the Change of Residual Stress During Annealing Heat Treatment
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TRODUCTION
RESIDUAL stress has drawn remarkable attention in the metal-forming and machining fields by affecting the integrity of workpieces.[1] During a cold working process, tensile residual stress is commonly induced into workpieces, which can undermine its fatigue life, machinability, and geometric accuracy.[2] Stress-relief annealing is widely applied to reduce this kind of residual stress by heating the workpiece below its recrystallization temperature, keeping at a suitable temperature, and then cooling, which converts residual elastic strain to permanent inelastic deformation. Currently, many researches on characterizing and predicting the residual stress relaxation in stress-relief annealing have been conducted via empirical models[3–7] and classical creep models.[8–11] The empirical models are capable of describing the reduction of residual stresses when the workpieces are subjected to elevated additive temperatures after shot peening,[12] QIAN BAI, HENG FENG, LI-KUN SI, and YI-QI WANG are with the Key Laboratory for Precision and Non-traditional Machining Technology of Ministry of Education, Dalian University of Technology, Dalian 116024, P.R. China. Contact e-mail: [email protected] RAN PAN is with the Beijing Aeronautical Manufacturing Technology Research Institute, Beijing 100024, P.R. China. Manuscript submitted Feburary 11, 2019.
METALLURGICAL AND MATERIALS TRANSACTIONS A
manufacturing,[5] and machining.[6,13] Most of the empirical models are based on the thermodynamic behaviors of the workpieces, such as Zener–Wert– Avrami equation,[6,7] in which heating temperature and activation energy play the most important roles. Some other empirical models are proposed in the forms of exponential functions and calibrated by experimental data.[5] These empirical models could efficiently predict the residual stresses after annealing but failed to explain the physical mechanism of the residual stress relaxation. In addition to the empirical models, classic creep models have also been extensively studied for residual stress relaxation. It is believed that the internal stress-induced creep deformation prompts the residual stress relaxation.[11] Therefore, steady-state creep models have been applied for the annealing process with workpieces of shot peening,[8] welding,[9] and casting.[10] In these models, the initial work hardening of the workpieces is neglected. However, the extent of initial work hardening influences the stress relaxation curves,[14] which is difficult to be implemented in classic creep models. Moreover, physically based models describe the plastic flow of the material considering the interaction of dislocations, the recovery etc.[15] Some researchers have used elastic–viscoplastic self-consistent model,[16] creep plasticity model,[17] and Orowan equation[11] to describe the thermal relaxation of residual stresses. Nevertheless, in these approaches, the dislocation density evolution was considered as an internal state variable, and the
dislocation density was not measured or calculated explicitly.
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