Heat Effects of Welding : Temperature Field, Residual Stress, Distortion

Almost all welding technology depends upon the use of concentrated energy sources to fuse or soften the material locally at the joint, before such energy can be diffused or dispersed elsewhere. Although comprehensive treatments of transient heat flow as a controlling influence have been developed progressively and published over the past forty years, the task of uniting the results compactly within a textbook has become increasingly formidable. With the comparative scarcity of such works, welding engineers have been denied the full use of powerful design analysis tools. During the past decade Dr Radaj has prepared to fulfil this need, working from a rich experience as pioneer researcher and teacher, co-operator with Professor Argyris at Stuttgart University in developing the finite element method for stress analysis of aircraft and power plant structures, and more recently as expert consultant on these and automotive structures at Daimler­ Benz. His book appeared in 1988 in the German language, and this updated English language edition will significantly increase the availability of the work.

1 Introduction.- 1.1 Scope and structuring of contents.- 1.2 Weldability analysis.- 1.3 Residual stresses.- 1.4 Welding residual stresses.- 1.5 Welding residual stress fields.- 1.6 Type examples.- 1.7 Welding deformations.- 1.8 References to related books.- 1.9 Presentation aspects.- 2 Welding temperature fields.- 2.1 Fundamentals.- 2.1.1 Welding heat sources.- 2.1.1.1 Significance of welding temperature fields.- 2.1.1.2 Types of welding heat sources.- 2.1.1.3 Output of welding heat sources.- 2.1.2 Heat propagation laws.- 2.1.2.1 Law of heat conduction.- 2.1.2.2 Law of heat transfer by convection.- 2.1.2.3 Law of heat transfer by radiation.- 2.1.2.4 Field equation of heat conduction.- 2.1.2.5 Initial and boundary conditions.- 2.1.2.6 Thermal material characteristic values.- 2.1.3 Model simplifications relating to geometry and heat input.- 2.1.3.1 Necessity for simplifications.- 2.1.3.2 Simplifications of the geometry.- 2.1.3.3 Spatial simplifications of the heat source.- 2.1.3.4 Time simplifications of heat source.- 2.1.3.5 User questions addressing welding temperature fields.- 2.1.3.6 Numerical solution and comparison with experiments.- 2.2 Global temperature fields.- 2.2.1 Momentary stationary sources.- 2.2.1.1 Momentary point source on the semi-infinite solid.- 2.2.1.2 Momentary line source in the infinite plate.- 2.2.1.3 Momentary area source in the infinite rod.- 2.2.2 Continuous stationary and moving sources.- 2.2.2.1 Moving point source on the semi-infinite solid.- 2.2.2.2 Moving line source in the infinite plate.- 2.2.2.3 Moving area source in the infinite rod.- 2.2.3 Gaussian distribution sources.- 2.2.3.1 Stationary and moving circular source on the semi-infinite solid.- 2.2.3.2 Stationary and moving circular source in the infinite plate.- 2.2.3.3 Stationary strip source in the infinite plate.- 2.2.4 Rapidly moving high-power sources.- 2.2.4.1 Rapidly moving high-power source on the semi-infinite solid.- 2.2.4.2 Rapidly moving high-power source in the infinite plate.- 2.2.5 Heat saturation and temperature equalization.- 2.2.6 Effect of finite dimensions.- 2.2.7 Finite element solution.- 2.2.7.1 Fundamentals.- 2.2.7.2 Ring element model.- 2.2.7.3 Plate element models.- 2.3 Local heat effect on the fusion zone.- 2.3.1 Electric arc as a welding heat source.- 2.3.1.1 Physical-technical fundamentals.- 2.3.1.2 Heat balance and heat source density.- 2.3.1.3 Heat conduction modelling of fusion welding.- 2.3.1.3.1 Melting of the electrode.- 2.3.1.3.2 Fusion of the base metal.- 2.3.1.3.3 Interaction of melting-off and fusion.- 2.3.1.4 Weld pool modelling.- 2.3.1.4.1 Weld pool physics.- 2.3.1.4.2 Welding arc modelling.- 2.3.1.4.3 Hydrostatic surface tension modelling.- 2.3.1.4.4 Hydrodynamic weld pool modelling.- 2.3.1.4.5 Hydrostatic weld shape modelling.- 2.3.1.4.6 Keyhole modelling.- 2.3.2 Flame as a welding heat source.- 2.3.2.1 Physical-technical fundamentals.- 2.3.2.2 Heat balance and heat flow density.- 2.3.3 Resistance heating of weld spots.- 2.3.4 Heat generation in friction welding.- 2.4 Local heat effect on the base metal.- 2.4.1 Microstructural transformation in the heat-affected zone.- 2.4.1.1 Thermal cycle and microstructure.- 2.4.1.2 Time-temperature transformation diagrams.- 2.4.1.3 Evaluation of time-temperature transformation diagrams.- 2.4.2 Modelling of microstructural transformation.- 2.4.3 Cooling rate, cooling time and austenitizing time in single-pass welding.- 2.4.3.1 Cooling rate in solids and thin plates.- 2.4.3.2 Cooling rate in thick plates.- 2.4.3.3 Cooling time in solids and plates.- 2.4.3.4 Austenitizing time in solids and plates.- 2.4.4 Temperature cycles in multi-pass welding.- 2.5 Hydrogen diffusion.- 3 Welding residual stress and distortion.- 3.1 Fundamentals.- 3.1.1 Temperature field as the basis.- 3.1.2 Elastic thermal stress field.- 3.1.3 Elastic-plastic thermal stress field.- 3.1.4 Basic equations of thermomechanics.- 3.1.5 Thermomechanical material characteristic values.- 3.2 Finite element models.- 3.2.1 Intelligent solution.- 3.2.2 Rod element model.- 3.2.3 Ring element model.- 3.2.4 Membrane plate element model in the plate plane.- 3.2.5 Membrane plate element model in the cross-section.- 3.2.6 Solid element model.- 3.3 Shrinkage force and stress source models.- 3.3.1 Longitudinal shrinkage force model.- 3.3.2 Transverse shrinkage force model.- 3.3.3 Application to cylindrical and spherical shells.- 3.3.4 Residual stress source model.- 3.4 Overview of welding residual stresses.- 3.4.1 General statements.- 3.4.2 Weld-longitudinal residual stresses.- 3.4.3 Weld-transverse residual stresses.- 3.4.4 Residual stresses after spot-welding, cladding, and flame cutting.- 3.5 Welding distortion.- 3.5.1 Model simplifications.- 3.5.2 Transverse shrinkage and groove transverse off-set.- 3.5.3 Longitudinal and bending shrinkage.- 3.5.4 Angular shrinkage and twisting distortion.- 3.5.5 Warpage of thin-walled welded components.- 3.6 Measuring methods for residual stress and distortion.- 3.6.1 Significance of test and measurement.- 3.6.2 Strain and displacement measurement during welding.- 3.6.3 Destructive residual stress measurement.- 3.6.3.1 Measurement of uniaxial welding residual stresses.- 3.6.3.2 Measurement of biaxial welding residual stresses.- 3.6.3.3 Measurement of triaxial welding residual stresses.- 3.6.4 Non-destructive residual stress measurement.- 3.6.5 Distortion measurement after welding.- 3.6.6 Similarity relations.- 4 Reduction of welding residual stresses and distortion.- 4.1 Necessities and kinds of measures.- 4.2 Design measures.- 4.3 Material measures.- 4.3.1 Starting points.- 4.3.2 Material characteristic values in the field equations.- 4.3.3 Traditional consideration of the influence of the material.- 4.3.4 Derivation of novel welding suitability indices.- 4.4 Manufacturing measures.- 4.4.1 Starting points.- 4.4.2 Measures prior to and during welding.- 4.4.2.1 Overview.- 4.4.2.2 General measures.- 4.4.2.3 Weld-specific measures.- 4.4.2.4 Thermal measures.- 4.4.2.5 Mechanical measures.- 4.4.2.6 Typical applications.- 4.4.3 Post-weld measures.- 4.4.3.1 Overview.- 4.4.3.2 Hot stress relieving (annealing for stress relief).- 4.4.3.2.1 Hot stress relieving in practice and relevant codes.- 4.4.3.2.2 Stress relaxation tests.- 4.4.3.2.3 Microstructural change during hot stress relieving.- 4.4.3.2.4 Equivalence of annealing temperature and annealing time.- 4.4.3.2.5 Creep laws and creep theories relating to hot stress relieving.- 4.4.3.2.6 Analysis examples and experimental results relating to hot stress relieving.- 4.4.3.3 Cold stress relieving (cold stretching, flame and vibration stress relieving).- 4.4.3.3.1 Rod element model for cold stretching.- 4.4.3.3.2 Notch and crack mechanics of cold stretching.- 4.4.3.3.3 Cold stretching in practice.- 4.4.3.3.4 Flame and induction stress relieving.- 4.4.3.3.5 Vibration stress relieving.- 4.4.3.4 Hammering, rolling, spot compression and spot heating.- 4.4.3.5 Hot, cold and flame straightening.- 5 Survey of strength effects of welding.- 5.1 Methodical and systematical points of view.- 5.2 Hot and cold cracks.- 5.3 Ductile fracture.- 5.4 Brittle fracture.- 5.5 Lamellar tearing type fracture.- 5.6 Creep fracture.- 5.7 Fatigue fracture.- 5.8 Geometrical instability.- 5.9 Corrosion and wear.- 5.10 Strength reduction during welding.