Based on a transient temperature distribution of a 45 steel cylinder workpiece during magnetic quenching, which was obtained by solving the governing equations with nonlinear boundary on the condition of coupling effects of heat-magnetism. According to the theory of thermal non-elasticity, computational mechanics, ferromagnetism and phase transformation, a new constitutive equation considering effects of phase transformation is proposed and solved by means of finite element method. The transient thermal stress and residual stress are obtained and the influencing factors on the thermal stress of magnetic field are analyzed and discussed.
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