Mathematical model of phase transformations and elastoplastic stress in the water spray quenching of steel bars
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INTRODUCTION
W A T E R spray quenching is practiced industrially because high quench-hardness and compressive residual stresses are obtained on the surface o f the heat-treated part. m At high pressures, w a t e r spray quenching has a superior cooling capability compared with conventional w a t e r or oil quenching processes, because film boiling can be minimized. However, as with most heat-treatment processes, the quenching conditions continue to b e established empirically by trial-and-error procedures. A quantitative prediction o f microstructure and hardness distribution, as well as distortion and residual stresses, a f t e r quenching, clearly is desirable from the standpoint o f both cost savings and enhanced product quality. The achievement o f a predictive capability f o r quenching has been the objective o f numerous studies, t2-~61 Capitalizing on improved computer cost, performance, and numerical techniques, like the finite-element method, predictions have been made o f temperature, phase transformations, and stresses. Internal stresses are induced by density changes resulting from cooling and phase transformations during quenching; and, in turn, the evolution o f the microstructure depends on the thermal history as well as stress development in the part. The phase transformation kinetics for the isothermal diffusional transformation o f austenite to ferrite, pearlite, and bainite have been characterized by Johnson and Mehlt171 and Avrami,I18,~9,~°~ while Koistinen and Marburger t2~ proposed a general equation for the kinetics o f martensite Y. NAGASAKA, formerly Visiting Research Engineer with the University of British Columbia, is Research Engineer, Manufacturing Engineering Research Department, Komatsu Ltd., Osaka 5 7 3 , Japan. J.K. BRIMACOMBE, ALCAN Chair in Materials Process Engineering, E.B. HAWBOLT, Professor, I.V. SAMARASEKERA, Professor, and B. HERNANDEZ-MORALES, Graduate Student, are with the Centre for Metallurgical Process Engineering, T h e University of British Columbia, Vancouver, B C V6T 1Z4, Canada. S.E. CHIDIAC, formerly Research Associate with the University of British Columbia, is Research Engineer, National Research Council of Canada, Institute for Research in Construction, Ottawa, ON K1A OR6, Canada. Manuscript submitted December 9 , 1991. METALLURGICAL TRANSACTIONS A
transformation in steels. An issue in the development o f the models is the application o f isothermal transformation data to continuous cooling conditions. Turning to specific modeling studies, Inoue et al.t31 calculated thermalstresses during quenching by adopting a thermal expansion coefficient that is a function o f both cooling rate and temperature. This technique allows easy handling o f the constitutive equations; but a function for the thermal expansion coefficient o f each material at each cooling rate must be established. Some authors [g'5'6] have used continuous-cooling-transformation (CCT) diagrams to estimate volume changes due to phase transformation for the calculation o f internal stresses; howe
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