THEORY OF THERMO MECHANICAL PROCESSES IN WELDING

Transcription

1 THEORY OF THERMO MECHANICAL PROCESSES IN WELDING

2 Theory of Thermomechanical Processes in Welding by Andrzej Sluzalec Technical University of Czestochowa. Poland ~ Springer

3 A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN DOl / ISBN (ebook) Published by Springer, P.O. Box 17,3300 AA Dordrecht, The Netherlands. Printed on acid-free paper springeronline.com All Rights Reserved 2005 Springer Softcover reprint of the hardcover 1st edition 2005 No part of this work may be reproduced. stored in a retrieval system, or transmitted in any form or by any means. electronic. mechanical. photocopying. microfilming. recording or otherwise. without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system. for exclusive use by the purchaser of the work.

4 Contents Preface... ix Part I FUNDAMENTALS OF WELDING THERMOMECHANICS Chapter 1. Description of Welding Deformations Introduction The Referential and Spatial Description The Deformation Gradient Strain Tensors Particulate and Material Derivatives Mass Conservation Chapter 2. Stress Tensor Momentum The Stress Vector Momentum Balance Properties ofthe Stress Tensor The Virtual Work Rate The Piola-Kirchhoff Stress Tensor The Kinetic Energy Theorem Chapter 3. Thermodynamical Background of Welding Processes Introduction The First Law of Thermodynamics The Energy Equation The Second Law of Thermodynamics... 35

5 vi Theory of Thermomechanical Processes in Welding 3.5 Dissipations Equations of State for an Elementary System The Heat Conduction Law Thermal Behaviour Heat Transfer in Cartesian Coordinates Heat Convection Heat Radiation Initial and Boundary Conditions Chapter 4. Motion of Fluids Viscous Fluids Navier-Stokes Equation Chapter 5. Thermomechanical Behaviour Thermoelasticity Plastic Strain State Equations Plasticity Criterion The Plastic Flow Rule Thermal Hardening The Hypothesis of Maximal Plastic Work The Associated Flow Rule Incremental Formulation for Thermal Hardening Models of Plasticity Part II NUMERICAL ANALYSIS OF WELDING PROBLEMS Chapter 6. Numerical Methods in Thermomechanics Introduction Finite-Element Solution of Heat Flow Equations Weighted Residual Method Variational Formulation Finite-Element Solution ofnavier-stokes Equations Time Discretization Time Integration Schemes for Nonlinear Heat Conduction Solution Procedure for Navier-Stokes Equation Modeling of the Phase Change Process The Theorem of Virtual Work in Finite Increments The Thermo-Elasto-Plastic Finite Element Model Solution Procedure for Thermo-Elasto-Plastic Problems

6 Contents VB Part III HEAT FLOW IN WELDING Chapter 7. Analytical Solutions of Thermal Problems in Welding Introduction Heat Flow in Spot Welding Temperature Distribution in a Thin Plate Temperature Distributions in an Infinitely Thick Plate Heat Flow in Friction Welding l Thermal Effects in Friction Welding Analytical Solutions Chapter 8. Numerical Solutions of Thermal Problems in Welding Introduction Temperature Distributions in Laser Microwelding Temperature Distribution in Electroslag Welding Part IV WELDING STRESSES AND DEFORMATIONS Chapter 9 Thermal Stresses in Welding Changes of Stresses During Welding Residual Stresses Two-Dimensional Case Plug Weld Circular Patch Weld Welded Structures Chapter 10 Welding Deformations Distortion Deformations in Friction Welding References and Further Reading Subject Index

7 Preface The main purpose of this book is to provide a unified and systematic continuum approach to engineers and applied physicists working on models of deformable welding material. The key concept is to consider the welding material as an thennodynamic system. Significant achievements include thermodynamics, plasticity, fluid flow and numerical methods. Having chosen point of view, this work does not intend to reunite all the information on the welding thermomechanics. The attention is focused on the deformation of welding material and its coupling with thermal effects. Welding is the process where the interrelation of temperature and deformation appears throughout the influence of thermal field on material properties and modification of the extent of plastic zones. Thermal effects can be studied with coupled or uncoupled theories of thermomechanical response. A majority of welding problems can be satisfactorily studied within an uncoupled theory. In such an approach the temperature enters the stress-strain relation through the thennal dilatation and influences the material constants. The heat conduction equation and the relations governing the stress field are considered separately. In welding a material is either in solid or in solid and liquid states. The flow of metal and solidification phenomena make the welding process very complex. The automobile, aircraft, nuclear and ship industries are experiencing a rapidly-growing need for tools to handle welding problems. The effective solutions of complex problems in welding became possible in the last two decades, because of the vigorous development of numerical methods for thermal and mechanical analysis. The book has been divided into four parts. Part I Fundamentals of Welding Thermomechanics is devoted to the description of the defonnation of the welding material. Both the Lagrangian and the Eulerian standpoints

8 x Theory of Thermo mechanical Processes in Welding are considered. The concept of stress is introduced. The derivations of the theorem of virtual work rate and the kinetic energy theorem are provided. A general thermodynamic framework for the formulation of all constitutive equations is given. In this framework the laws governing the heat flow are formulated. The background of plasticity in welding is introduced. Hardening and softening phenomena are refined in the global context of thermodynamics and the modeling of thermal hardening in welding is discussed. In Part II Numerical Solutions of Welding Problems all the constitutive models of the previous chapters are discussed extending wellestablished standard procedures for solid and liquid media. The numerical approach to thermo-elastic-plastic material model is discussed. The phasechange problems are analyzed. The numerical solution of fluid flow in welding is presented. Part III Heat Flow in Welding presents in details the solution of heat transfer equations under conditions of interest in welding. The restrictive assumptions will however limit the practical utility of the results. Nevertheless the results are useful in that they emphasize the variables involved and approximate the way in which they are related. In addition, such solutions provide the background for understanding more complicated solutions obtained numerically and provide guidance in making judgements. The numerical solutions of welding problems are focused on laser and electroslag welding. In Part IV Welding Stresses and Deformations coupled thermomechanical phenomena are discussed. First of all thermal stresses being the result of complex temperature changes and plastic strains in regions near the weld are analyzed. Deformations and residual stresses in welding structures are considered for chosen welding processes and geometry of elements. Cz~stochowa May 2004 Andrzej Sluzalec