Heat Treating Distortion and Residual Stresses Explanation of their Generation Mechanism Using Computer Simulation Kyozo Arimoto Arimotech Ltd. Table of Contents Part 1 Chapter 1 Heat treating distortion and residual stresses and their generation mechanism 1.1 Overview 1.2 Basic researches on generation mechanism of heat treating distortion and residual stresses 1.2.1 Origin of researches on generation mechanism 1.2.2 Development of heat treatment simulation 1.3 Outline of heat treatment simulation system Chapter 2 Heat treatment and its phenomena 2.1 Overview 2.2 Classification of heat treatment processes and its phenomena 2.2.1 Classification of heat treatment processes 2.2.2 Phenomena during heat treatment processes Chapter 3 Phase transformation 3.1 Overview 3.2 Outline of phase transformation 3.2.1 Classification of phase transformations 3.2.2 Phase transformation phenomena described by TTT and CCT diagrams 3.2.3 Phase transformation and thermodynamics 3.2.4 Nucleation and growth 3.3 Diffusion type transformation 3.3.1 JMAK formula for diffusion type transformation 3.3.2 Model coupled JMAK equation with TTT diagram 3.3.3 Austenite transformation and TTA diagram 3.3.4 Tempering transformation and TTT diagram 3.3.5 Application of JMAK equation to any cooling conditions 1
3.3.6 Growth models for pearlite 3.3.7 Stress dependency on diffusion type transformation 3.4 Non-diffusion type transformation 3.4.1 Measurement and definition of M s 3.4.2 Empirical equations of M s 3.4.3 Kinetics of martensite transformation 3.4.4 Martensite transformation and thermodynamics 3.4.5 Nucleation and growth in martensite transformation 3.4.5 Stress dependency on martensite transformation 3.5 Bainite transformation 3.5.1 Early researches on Bainite transformation 3.5.2 Kinetics of Bainite transformation 3.5.3 Researches on Bainite transformation after 1970s 3.6 Integrated predictive model of phase transformation 3.6.1 Approach by Ito et al. 3.6.2 Approach by Kirkaldy et al. 3.6.3 Approach by Li et al. 3.6.4 Approach by Bhadeshia 3.6.5 Other approaches 3.7 Hardness prediction 3.7.1 Quenching 3.7.2 Tempering Chapter 4 Diffusion and mass transfer 4.1 Overview 4.2 Diffusion equation in solid 4.2.1 Relation between diffusion flux and concentration 4.2.2 Initial and boundary conditions 4.3 Reaction of carburizing gas and its equilibrium 4.3.1 Carburizing gas and its chemical reactions 4.3.2 Carbon activity in austenite 4.3.3 Equilibrium constant of carburizing gas reactions 4.3.4 Carbon potential and it measurement 4.4 Gas reactions in furnace and their mass transfer coefficient on surface 4.4.1 Chemical reactions and their kinetics 4.4.2 Lumped diffusion capacity method and mass transfer coefficient 2
4.4.3 Elementary reactions of carburizing and their reaction rate 4.4.4 Mass transfer coefficient in commercial furnaces 4.5 Carbon diffusivity 4.5.1 Measurements by Wells et al. 4.5.2 Measurements performed after Wells et al. 4.5.3 Mean coefficient by Harris 4.6 Effects of alloying elements in carburizing 4.6.1 Effects of alloying elements on carbon potential 4.6.2 Effects of alloying elements on diffusion 4.7 Precipitation of chemical compounds in carburizing processes Chapter 5 Heat conduction and heat transfer 5.1 Overview 5.2 Heat conduction equation in solid 5.2.1 Relation between heat flux and temperature 5.2.2 Initial and boundary conditions 5.3 Thermal properties of steels 5.3.1 Specific heat 5.3.2 Enthalpy of phase transformation 5.3.3 Thermal conductivity 5.4 Heat transfer during heat treating 5.4.1 Cooling curves and cooling rate curves 5.4.2 Severity of quench; H value 5.4.3 Measurement of HTC by platinum wire methods: boiling curves 5.4.4 Prediction of HTC based on lumped heat capacity method 5.4.5 Prediction of HTC based on analytical or numerical solutions 5.4.6 Prediction of HTC based on inverse analysis 5.4.7 Prediction of HTC based on CFD 5.4.8 Outlook on deriving HTC for heat treatment simulation 5.5 Temperature recovery and inverse hardening phenomena 5.5.1 Temperature recovery phenomenon 5.5.2 Inverse hardening phenomenon Chapter 6 Stress-strain and distortion 6.1 Overview 6.2 Relation between stress-strain and distortion 3
6.3 Elastic strain and stress 6.3.1 Relation between elastic strain and stress 6.3.2 Elastic moduli of steels 6.4 Thermal and transformation strains 6.4.1 Relation between thermal, diffusion and transformation strains, and density 6.4.2 Temperature dependency of density, and thermal, diffusion and transformation expansion coefficients 6.4.3 Prediction of temperature-dilatation diagram and quenching expansion in cylinder 6.5 Plastic strain 6.5.1 Formulation of plastic phenomenon 6.5.2 Stress-strain characteristics with plasticity 6.6 Creep strain 6.6.1 Formulation of creep phenomenon 6.6.2 Characteristics of creep phenomenon 6.6.3 Application to stress-relief annealing 6.7 Transformation plastic strain 6.7.1 Review of studies on transformation plasticity 6.7.2 Formulation of transformation plasticity phenomenon 6.7.3 Coefficient of transformation plasticity Chapter 7 Induction heating 7.1 Overview 7.2 Induction heating of cylinder 7.2.1 Maxwell s equation 7.2.2 Eddy current 7.2.3 Total magnetic flux 7.2.4 Electric power consumption 7.2.5 Examples of theoretical calculation 7.3 Electric conductivity and permeability 7.3.1 Electric conductivity 7.3.2 Permeability Chapter 8 Mixture law 8.1 Overview 8.2 Mixture law of thermal and electrical conductivity 8.2.1 General formulation 4
8.2.2 Mixture in random dispersion of spheres 8.2.3 Other mixed states and their comparisons 8.3 Mixture law of elastic-plastic characteristics 8.3.1 Elastic moduli 8.3.2 Plastic characteristics 8.4 Heat treatment simulation and mixture law Chapter 9 Finite element method and heat treatment simulation 9.1 Overview 9.2 Finite element method 9.3 Structure of heat treatment simulation system Part 2 Chapter 10 Quench distortion and residual stresses in cylinders 10.1 Overview 10.2 Review of studies using cylindrical specimens and characteristics of their shape 10.2.1 Review of studies using cylindrical specimens 10.2.2 Characteristics and models of cylindrical shape 10.3 Water quenched pure iron cylinders 10.3.1 Review of major studies 10.3.2 Model and data used for this simulation 10.3.3 Simulated results and explanation of phenomenon 10.3.4 Summary 10.4 Water quenched Fe-Ni alloy cylinders 10.4.1 Review of major studies 10.4.2 Model and data used for this simulation 10.4.3 Simulated results and explanation of phenomenon 10.4.4 Summary K. Arimoto and K. Funatani, Historical Review of Residual Stress in Quenched Fe-Ni Alloy Cylinders and Explanation of Its Origin Using Computer Simulation, Proc. 24th Heat Treating Conference, 17-19, Sep., 2007, Detroit, ASM International, pp. 163-172.] 10.5 Water quenched practical steel cylinders 10.5.1 Review of major studies 10.5.2 Model and data used for this simulation 10.5.3 Simulated results and explanation of phenomenon for low Cr steel cylinders 5
K. Arimoto, T. Horino, F. Ikuta, C. Jin and S. Tamura, Explanation of the Origin of Distortion and Stress Distribution Patterns in Water-Quenched Chromium Steel Cylinders Using Computer Simulation, ASM Heat Treating Society Conference, September 26-28, 2005, Pittsburgh, PA] 10.5.4 Simulated results and explanation of phenomenon for carbon steel cylinders K. Arimoto, T. Horino, F. Ikuta, C. Jin, S. Tamura and M. Narazaki, Verification of Distortion Characteristics in Water Quenched Cylinders by Computer Simulation, 1st International Conference on Distortion Engineering, Bremen, Germany, 14-16, September, 2005, pp. 425-435. K. Arimoto, T. Horino, F. Ikuta, C. Jin, S. Tamura and M. Narazaki, Explanation of the Origin of Distortion and Residual Stress in Water Quenched Cylinders Using Computer Simulation, Journal of ASTM International (JAI), Vol. 3, Issue 5 (May 2006), Paper ID: JAI14204. ] 10.5.5 Summary 10.6 Carburized-quenched steel cylinders 10.6.1 Review of major studies 10.7 Induction hardened steel cylinders 10.7.1 Review of major studies 10.8 Conclusions Chapter 11 Quench distortion and residual stresses in rings 11.1 Overview 11.2 Review of studies using disk and ring specimens and characteristics of their shapes 11.2.1 Review of studies using disk and ring specimens 11.2.2 Characteristics and models of disk and ring shapes 11.3 Oil quenched and carburized-quenched steel rings 11.3.1 Review of major studies 11.3.2 Explanation of quench distortion and residual stresses in rings 11.3.3 Summary K. Arimoto, S. Yamanaka and K. Funatani, Explanation of the Origin of Distortion and Residual Stress in Carburized Ring Using Computer Simulation, 15th Congress of IFHTSE, Vienna, 25-29, Sep., 2006. K. Arimoto, S. Yamanaka and K. Funatani, Explanation of the Origin of 6
Distortion and Residual Stress in Carburized Ring Using Computer Simulation, Journal of ASTM International, Vol. 5, No. 10, 2008, Paper ID: JAI101797.] 11.4 Induction hardened steel ring 11.4.1 Review of major studies 11.4.2 Model and data used for this simulation 11.4.3 Comparison between experimental and simulated results 11.4.4 Explanation of quench distortion and residual stresses in a ring 11.4.5 Summary T. Horino, F. Ikuta, K. Arimoto, C. Jin and S. Tamura, Explanation on Origin of Distortion in Induction Hardened Ring Specimens by Computer Simulation, 1st International Conference on Distortion Engineering, Bremen, Germany, 14-16, September, 2005, pp. 203-212. T. Horino, F. Ikuta, K. Arimoto, C. Jin and S. Tamura, Explanation on Origin of Distortion in Induction Hardened Ring Specimens by Computer Simulation, Journal of ASTM International, Vol. 6, April, 2009, Paper ID: JAI101809] 11.5 Conclusions Chapter 12 Quench Bending Distortion and Residual Stresses in long parts 12.1 Overview 12.2 Review of studies on quench bending distortion and its characteristics 12.2.1 Review of studies on quench bending distortion in long parts 12.2.2 Characteristics and models of bending in long parts 12.3 Quench bending distortion in long steel cylinder with keyway 12.3.1 Experimental conditions and simulation model of long cylinder 12.3.2 Simulated results and explanation of phenomenon 12.3.3 Summary K. Arimoto, H. Kim, M. Narazaki, D. Lambert and W. T. Wu, Mechanism of Quench Distortion on Steel Shaft with Keyway, 19th Heat Treating Conference, ASM International, 2001, pp.144-151.] 12.4 Conclusions Chapter 13 Quench Crack in steel parts 13.1 Overview 13.2 Review of studies on quench crack and classification of its test 7
13.2.1 Review of studies on quench crack 13.2.2 Classification of quench crack test 13.3 Quench crack simulation 13.3.1 Cylindrical specimens 13.3.2 Complex shape Specimens 13.4 Quench crack prevention by computer simulation 13.4.1 Quench crack tests for verifying the simulation 13.4.2 Criterion of Quench Crack Prevention 13.5 Summary [These sections are based on the following article; K. Arimoto, F. Ikuta, T. Horino, S. Tamura, M. Narazaki and Y. Mikita, Preliminary Study to Identify Criterion for Quench Crack Prevention by Computer Simulation, 14th Congress of International Federation for Heat Treatment and Surface Engineering, October 26-28, 2004, Shanghai, China. (Transactions of Materials and Heat Treatment, Vol. 25, No. 5, 2004, pp486-493).] Chapter 14 Perspective Postscript 8