State of the Art Review - Weld Simulation Using Finite ... · Report Title: State of the Art Review...

School of Mechanical, Materials & Manufacturing Engineering

Project: FENET EU Thematic Network (Contract G1RT-CT-2001-05034) Report Title: State of the Art Review - Weld Simulation

Using Finite Element Methods Authors: Dr Anas Yaghi and Professor Adib Becker University of Nottingham, UK FENET RTD (Durability & Life Extension) Date: 12 November 2004 Report No: FENET-UNOTT-DLE-08

Report FENET-UNOTT-DLE-08 by A. Yaghi and A.A. Becker of 27


ABSTRACT Welds are often an essential part of engineering structures. Residual stresses introduced in the welded regions, due to the nonlinear thermal processes during welding, can have detrimental effects, such as stress corrosion cracking, hydrogen-induced cracking and reduced fatigue strength. It is therefore pertinent to simulate the process of welding to predict the behaviour of welded structures from finite element residual stress and deformation results. This report introduces finite element volume methods for the modelling of welds and it depicts a brief history of the simulation of welds. A description of the heat flow processes and solid phase transformations is given in the theoretical background section. The procedure of thermal and mechanical finite element analyses is explained in the third section, titled Finite Element Weld Simulation, which also presents other examples of finite element analyses and describes the effects of solid phase transformations incorporated in the simulation of welds. In the fourth section of the report, related research published in literature is discussed, proposing many modelling considerations which are relevant to weld simulation. This includes parametric studies and characterisation of residual stresses, the effect of material properties on residual stresses, three-dimensional geometric influences, an outline of the adaptive mesh technique and the shrinkage volume approach, and the combination of welding simulation with other heat transfer engineering processes. Friction stir welding is described in the penultimate section of the report, which is followed by a description of the process of inertia friction welding. The finite element simulation of the two types of friction welding is discussed.


CONTENTS ABSTRACT CONTENTS

1. Introduction 1.1 Finite Volume Methods for the Modelling of Welds 1.2 Brief History of Weld Simulation

2. Theoretical Background

2.1 Heat Flow and Phase Transformation

3. Finite Element Weld Simulation 3.1 Thermal and Mechanical Finite Element Analyses 3.2 Further Finite Element Analyses 3.3 Solid Phase Transformations

4. Related Research

4.1 Influence of Welding Speed and Wall Thickness on Residual Stresses 4.2 Parametric Study on Residual Stresses in Welded Pipes 4.3 Simulation of Residual Stresses in a Bimaterial Joint 4.4 Characterisation of Axial Residual Stress 4.5 Effects of Material Properties on Stresses and the Inclusion of Phase

Transformation 4.6 Simulation of Combined Welding and Stress Relief Heat Treatment 4.7 Effect of Residual Stresses and Geometric Parameters on Fatigue Crack Initiation

Life of Welded Plates 4.8 Effect of Aluminium Material Properties on Temperature, Stress and Distortion 4.9 Adaptive Mesh Technique 4.10 Three-Dimensional Geometric Effects on Residual Stresses 4.11 Effect of Manufacturing Residual Stress and Strain, Prior to Welding, on

Distortion 4.12 Modelling of Thin Pipe Wall Cooling 4.13 Shrinkage Volume Approach

5. Friction Stir Welding

6. Inertia Friction Welding

REFERENCES


1. Introduction The process of welding is an integral manufacturing procedure in many engineering and structural components, having a direct influence on the integrity of the components and their thermal and mechanical behaviour during service. Due to the high temperatures introduced during welding and the subsequent cooling of the welded metal, welding can produce undesirable residual stresses and deformations. It is of important interest to simulate the process of welding to delineate the ensuing residual stresses and deformations and predict the behaviour of welded structures. Teng and Chang [1998] describe how welded structures are an essential part of many buildings, bridges, ships, pressure vessels and other engineering structures. Circumferentially welded pipes are often used in boiling water reactor piping systems, oil pipe transport systems and steam piping systems. Residual stresses are important in the consideration of cracking and fracture problems in welded structures. Their accurate evaluation can help resolve problems such as intergranular stress corrosion cracking, which has been observed in the weld fusion lines or nearby, on the inside surfaces of the pipes of boiling water reactors. Sahin et al [2003] explain that nuclear reactors, ships, pipes and pressure vessels are examples of engineering applications, considered to be shell-like structures made with weldments. Residual stresses developed from the process of welding significantly affect stress corrosion cracking, hydrogen-induced cracking and, to some extent, fatigue strength. 1.1 Finite Volume Methods for the Modelling of Welds Taylor et al [2002] explain that the numerical simulation of the process of welding can take place in two alternative ways. Firstly, the complex fluid and thermo-dynamics local to the weld pool are modelled by looking at the weld pool and the HAZ. The conservation of mass, momentum and heat together with the latent heat and surface tension boundary conditions are equated to represent the physical phenomena of the molten weld pool and thermal behaviour of the HAZ. Secondly, the solid mechanics approach is adopted by modelling the global thermo-mechanical behaviour of the weld structure, paying special attention to the heat source. A variety of simplified heat source models can be used in the simulation of welding, the accuracy of which relying on the theoretical and empirical parameters describing the weld pool size and shape. Taylor et al aim at drawing agreement between the two simulation methods, ultimately verifying the modelling parameters of the most appropriate heat source. PHYSICA is the software package used for either the thermo-fluid dynamics or thermo-mechanical approach, and it is applied to a girth welding of a thin pipe, to obtain distortion and residual stresses, without any metallurgical phase transition effects. The convective heat transfer in the weld pool is accounted for by modifying the conductivity of the molten metal. In their introduction, Taylor et al refer to a set of publications forming the basis of the two investigated general methods of weld simulations.


1.2 Brief History of Weld Simulation Teng and Chang [1998] explain that a thermomechanical model was developed by Friedman [1975] using the FE method to calculate temperatures, stresses and distortions during welding; that elastoplastic FE computer programs were developed by Muraki et al [1975] to monitor welding thermal stresses and metal movement; that residual stresses were estimated by Josefson [1993] in a multi-pass weld and in a spot-welded box beam with SOLVIA and ABAQUS, which are commercially available FE codes for non-linear analyses; and that temperatures and stresses were analysed by Karlsson [1989] and Karlsson and Josefson [1990] in single-pass girth butt welding of carbon-manganese pipe using the FE codes ADINAT and ADINA. Murthy et al [1996] propose a detailed methodology for the analysis of residual stresses due to welding and quenching processes. Temperature and stress distributions obtained numerically are validated against published data for butt welding of plates, circumferential welding of pipes, multi-pass welding of plates and quenching. Their thermal and thermo-elasto-plastic formulations take into consideration non-linearities due to the variation of material properties and heat transfer coefficients with temperature as well as the inclusion of a radiation boundary condition and solid phase transformation effects. They also highlight certain limitations on the usability of some commercial FE codes, in particular thermal effect concerns due to phase transformation and transformation plasticity, the latter being the microscopic plastic flow that occurs during phase transformations. A variety of FE software packages used for the simulation of welding have been documented in literature, typical examples of which are mentioned throughout this report, such as the FE software employed by Vincent et al [1999]. They consider a carbon dioxide laser beam delivering thermal loading to a thin disc of French vessel steel to simulate welding and compare ensuing residual stresses obtained either experimentally or using finite element codes referred to as Sysweld (Framatome) and Code_Aster (EDF). The metallurgical transformations have been taken into account and the FE results agree with the experimental ones, including temperatures, size of transformed zones, displacements and residual stresses. Mackerle [2001] has written a bibliography of the finite element and boundary element methods published in 1998, 1999 and the first quarter of 2000. The bibliography provides a list of 207 references on the analysis and modelling of residual stresses; general solution techniques as well as problem-specific applications are included.


2. Theoretical Background 2.1 Heat Flow and Phase Transformation In their introduction, Murthy et al [1996] point out that Goldak et al [1986] demonstrated the application of an elliptical power density distribution of heat flux input in cases of two and three-dimensional geometric configurations. Alternatively, they mention a simplified trapezoidal model of the heat input, referring to its publications in literature. They continue to explain that solid phase transformations during cooling produce material dilatations and induce microscopic plastic flow even though the stress state is elastic. The effect of the material dilatations of reducing the peak longitudinal tensile stresses is limited to the weld region and a part of the HAZ. Usually, with commercial software, the dilatations are evaluated by reducing the thermal expansion coefficient over the transformation temperature range, and the transformation plasticity is represented by reducing the yield stress of the material over the temperature range where transformation occurs. For more accurate simulation, especially in user oriented programs, the dilatations are computed in proportion to the quantities of various phases formed, and the transformation plasticity is modelled by including an additional plastic strain which is related to the progress of transformation and to the instantaneous deviatoric stress state. Murthy et al suggest that, with the exception for quenching, the phase transformation effects are negligible unless the transformation occurs at very low temperatures, the dilatations are comparable to thermal contraction strains or there is a rapid cooling of the weld pool. In their paper, Murthy et al propose thermal and thermo-elasto-plastic formulations relevant to the processes of welding and quenching. Their eight-noded isoparametric-element FE study includes latent heat effects due to phase changes and phase transformations by having additional enthalpy in the thermal equilibrium equation. They use empirical relationships on transformation kinetics and time-temperature-transformation curves of the material involved to compute the volume fractions of various phases transformed during the solid phase transformations in the cooling process. They refer to a published combined strain hardening rule to compute transient stresses incrementally. They include additional strains, at various time steps, to represent material dilatations due to solid phase transformations, in proportion to the volume fractions of the various phases formed. During solid phase transformation, Murthy et al derive the quantities of various phases formed at a time step from the time-temperature-transformation curves of the material and use them in proportion to compute the latent heat emitted. The fractions of non-martensitic phases are obtained from derived equations by Avrami [1939, 1940], and the martensitic fraction is calculated from Koistinen-Marburger empirical equations [1959]. Murthy et al explain that the quantities of various phases transformed at a node and the current nodal temperature are mutually dependent, and therefore the simultaneous temperatures and fractions of phases transformed are obtained from an iterative solution proposed by Agarwal and Brimacombe [1981].

Murthy et al equate the total strain increment, for small strains, to the sum of the elastic, plastic, thermal and phase transformation strains, during their stress analysis. Strains are induced when solid phase transformations from austenite to ferrite, pearlite, bainite and martensite take place during cooling, caused by local material dilatations assumed to be proportional to the material phases transformed which in turn are iteratively obtained for each time step in the thermal analysis. Murthy et al suggest that a volumetric strain of 0.044 or 0.007 is assumed to occur where pure austenite is transformed to either pure martensite or pure ferrite/pearlite respectively. They also describe isotropic and kinematic hardening, and they notice that, due to Bauschinger effect, the cyclic loading of the material during load variations is best represented by a combination of the two mentioned types of hardening. Teng and Chang provide analytical equations describing the temperature field in the thermal part of the FE simulation, which are then inserted in the mechanical model. They base their thermal elastoplastic material model on the von Mises yield criterion and the isotropic strain hardening rule. They also present analytical equations for the evaluation of displacements and stresses in the mechanical part of the FE analysis. Tsirkas, Papanikos, Kermanidis [2003] have carried out a three-dimensional FE analysis of laser-welded butt-joint thick AH36 shipbuilding steel plates using SYSWELD. Their work takes into account metallurgical transformations using the temperature dependent material properties and the continuous cooling transformation (CCT) diagram. The heat input to the welded plates is represented by a keyhole formation model, generated by a Gaussian distribution of heat flux with the aid of a moving heat source with a conical shape. The welded panel distortions obtained from the FE analysis agree with experimental measurements. They begin with the recommendation of laser welding over other types of welding, for its characteristic low heat transfusion into the welded component, leading to a relatively small HAZ and low panel distortion. Their thermal solution is derived from the quasi-steady-state technique. A non-linear thermo-mechanical FE analysis is performed and enhanced with user subroutines. The governing partial differential equation for the transient heat conduction is given by

k(T) (∂2T/∂x2) + (∂2T/∂y2) + (∂2T/∂z2) + Q = ρ(T) Cp(T) ) ∂T/∂t) (2.1) where x, y, z are the Cartesian coordinates and Q, the internal heat generation, ρ, the density, k, the thermal conductivity, and Cp, the specific heat, are functions of temperature, T. The mechanical analysis is performed using a thermo-elasto-plastic material formulation with von Mises yield criterion coupled to a kinematic hardening rule. The absorbed energy from the laser source is considered to be 70% of the laser power. It is stated that a keyhole heat input is best simulated with a cone following a Gaussian distribution of heat flux, computed according to the formula Q = (2P / (π r0

2 H)) e (1 – z/H) (2.2) 2

0 )/(1 rr−



Where P is the absorbed laser beam power, r0 is the initial radius (at the top of the keyhole), H is the depth, r is the current radius (the distance from the cone axis) and z is the current length. The heat flux is implemented into the FE calculation with the help of a FORTRAN subroutine. For the simulation of phase transformations involving diffusion for steels (austenitic, ferritic-pearlitic and bainitic transformations), under isothermal conditions, the Johnson-Mehl-Avrami law is used, and it is given by p(T, t) = p(T) (1 – exp(-(t/τR(T))n(T))) (2.3) where p represents the phase proportion obtained after an infinite time at temperature T, τR is the delay time and n is the exponent associated with the reaction speed. The martensitic transformations are described by the Koistinen-Marburger law: pm(T) = pm (1 – exp(-b(MS – T))) with T ≤ MS (2.4) where pm represents the phase proportion obtained at an infinitely low temperature (pm is frequently assimilated to 1), and MS and b characterise initial transformation temperature and evolution of the transformation process according to temperature, respectively. The parameters of the Johnson-Mehl-Avrami model are extracted from the continuous cooling transformation (CCT) diagram, according to the cooling speed, and are then inserted in the FE analysis. Part of the heat supplied to the weld pool by the laser beam is lost by free convection and radiation, the implementation of which needs a FORTRAN user subroutine. The heat loss by free convection follows Newton’s law, where the coefficient of convective heat transfer is assumed to vary with both temperature and orientation of the boundary, and is given by

qc = (k Nu / L) (T – Ta) (2.5) where k is the thermal conductivity of the material, L is the characteristic length of the plate (or surface), Ta is the ambient temperature and Nu is the Nusselt number defined by Nu = 5.67 Pr1/3 Gr1/3 (2.6) Where Pr is the Prandtl number and Gr is the Grashof number, both being functions of ambient air properties and temperature differences between the surface and the environment. The heat loss due to radiation is significant when the temperature difference between the weldments and environment is large; it is given by the standard Stefan-Boltzman relation: qr = ε σ (T4 - Tα

4) (2.7) where ε is the heat emissivity and σ is the Stephan-Boltzman constant.


3. Finite Element Weld Simulation 3.1 Thermal and Mechanical Finite Element Analyses Brickstad and Josefson [1998] simulate the residual stresses due to welding using ABAQUS to perform the finite element analysis. Their analysis consists of two main parts, the thermal and the structural. They assume rotational symmetry of the modelled multi-pass butt-welded stainless steel pipes. Hence the analysis is two-dimensional and axisymmetric. The thermal analysis models the heat input from the welding torch into the weld elements causing the weld to melt. Heat losses allow the weld region to solidify. The temperature contours obtained from this part of the analysis are used in the sequential, structural analysis to derive the stresses generated as the material heats up and cools down again. The behaviour of the material involves non-linearity and therefore residual stresses remain in the welded pipe after cooling. The thermal analysis is based on using distributed heat flux, DFLUX, to represent the heat input. The DFLUX is given by DFLUX = U I η / Vp (3.1) where U is the voltage of the welding torch, I is the current, η is the efficiency and Vp is the weld pass volume, which is the hypothetical volume of weld pass molten at the time of welding torch application, since the model is two dimensional. Also, since the model is axisymmetric it is assumed that the torch application delivers heat to a weld volume during a time period ∆t while the torch goes round a circumferential angle ranging between 1/16 and 1/2 of a radian, which is the same angle used to quantify Vp. The linear speed at which the torch travels around the circumference, v, is related to the net line energy, Q, in the following equation: Q = U I η / v (3.2) Three types of welding have been considered: TIG, SMAW and SAW refer to tungsten inert gas, shielded metal arc weld and submerged arc weld, respectively. For each type of weld, Brickstad and Josefson provide a value for Q, v and η. For a realistic analysis, the heat input energy per unit volume is kept constant for all the passes of the same weld. The magnitude of DFLUX is checked by referring to the temperature contours in the weld region and the heat affected zone, HAZ, making sure that, at peak temperatures, the weld region has all melted (1340-1390oC) and the HAZ temperature has ranged between 800 and 900oC. The modelled material is typical of welded stainless steel Swedish BWR-pipes and it is severely overmatched in yield stress: the yield stress of the weld material is twice the value of that for the base material. The latent heat is given as 260 kJ/kg between the solidus temperature of 1340oC and the liquidus temperature of 1390oC. The heat losses through convection and radiation are accounted for in the combined boundary condition represented by the following equations for the temperature-dependent heat transfer coefficient, αh:


αh = 0.0668 T in W/m2, oC when 0 < T < 500oC (3.3) αh = 0.231 T - 82.1 in W/m2, oC when T > 500oC (3.4) The thermal analysis has been conducted using the heat transfer element DCAX8, which is an 8-node quadratic axisymmetric diffusive heat transfer quadrilateral. The accuracy of the solution is controlled by specifying a maximum change in temperature of 40oC per time step in the finite element input file. For the FE technique used, all the weld elements exist from the beginning to avoid any displacement or strain mismatch at the nodes connecting the weld elements to those of the base material. For a weld pass, the relevant material thermal properties and simulated behaviour, such as conductivity, are changed in the weld elements before the actual time of laying the pass welds to effectively simulate having elements of air before the weld pass has been laid and then having stainless steel elements once the weld pass has been laid. This technique is referred to as ‘element birth’. The structural analysis relies on the thermal part to acquire the temperature contours throughout the modelling process, by employing the temperature contour file as an input file. The weld elements are kept at 1200oC, which is called the softening temperature (TSOFT), until they have been laid. At TSOFT the stiffness and yield stress are so low that the elements are effectively inactive. This is achieved through an ABAQUS user subroutine which manipulates the temperature contours delivered by the thermal analysis preparing them for the structural part. When a weld pass has been laid, the corresponding weld elements are allowed to assume their temperature values provided by the thermal analysis, i.e., the user subroutine no longer plays an active role and the elements reach their ‘birth time’. The subroutine is not only responsible for adjusting the relevant temperatures before element birth, it also truncates any temperatures above TSOFT throughout the program to save computing time. Brickstad and Josefson assume the von Mises yield criterion and associated flow rule together with kinematic hardening. The coefficient of thermal expansion is given a constant value corresponding to the mean temperature between 20 and 600oC. All the other material properties are temperature dependent and they are tabulated against temperature ranging between 20 and 2000oC. The element type used in the structural analysis is CAX8, which is an 8-node biquadratic axisymmetric stress/displacement quadrilateral. Large deformations have been assumed in the structural analysis although it is reported that, in comparison, small deformations only give a small difference in residual stress results. 3.2 Further Finite Element Analyses Fanous et al [2002] have introduced a new technique for metal deposition using element movement, which takes less time during simulation in comparison with previous techniques such


as “element birth”. In their analysis, they accounted for change of phase and variation of properties with temperature. Wen and Ferrugia [2001] have modelled residual stresses in steel pipes and pipe joints using ABAQUS. Both pipe seam and pipe girth weldings are considered and the temperature dependency of material properties is taken into account. Teng and Chang [1998] examine a three-dimensional FE model, analysing the temperature and stresses in circumferential single-pass welded pipes and discussing the influences of pipe wall thickness on the welding residual stresses. Murthy et al [1996] have carried out a numerical analysis, using their FE software, of the welding of two 25mm-thick butt welded plates of material IS 2062. The heat flux is modelled with a trapezoidal variation representing the approach of the welding torch, followed by a constant heat input and then the gradual withdrawal of the heat source. The material properties in the analysis are temperature dependent. The transient thermo-elasto-plastic analysis is conducted for the second pass only, since it is assumed that the overlapping of the weld passes relieves stresses at temperatures higher than the transformation temperature. The temperature contours and residual stresses have been verified against experimental data obtained from MIG welding in two passes. Murthy et al have also numerically analysed a butt welding of two 13.2mm-thick stainless steel 316L plates subject to submerged arc welding. The heat input is simulated with a simple trapezoidal model, and the ensuing temperatures and stresses agree with published results for a double ellipsoidal heat input model. Also included in the FE study are a single-pass butt-welded cylindrical pipe and a multi-pass welded thick plates. The pipe is made up of carbon-manganese steel and analysed axisymmetrically. Material dilatations are calculated in proportion to the time-temperature-transformation-diagram fractions of various material phases formed during cooling from austenitizing temperature. The results are compared to published residual hoop stress values. The multi-pass 50mm-thick welded plates have been analysed with the use of simplified models, reducing the CPU time and indicating that the maximum tensile residual stress appears near the finishing bead, leading to the conclusion that it is sufficient to consider the last few welding passes to obtain the same results. Murthy et al have gone further by verifying the accuracy of their computer program with the transient thermal and residual stress axisymmetric analyses of the quenching of a 1035 steel cylinder from a uniform temperature of 880oC into cold water at 20oC. The resulting temperature distributions and the order of tensile residual hoop stresses are in agreement with published data. Pasquale et al [2001] employ SYSWELD to simulate dissimilar girth welds made of an austenitic steel, a ferritic steel and a nickel weld metal. Their work includes three-dimensional and axisymmetric FE analyses which are in agreement with their X-ray diffraction measurement of residual stresses. FE transient temperature distributions and axial and circumferential residual


stresses are discussed for a variable weld fabrication conditions and different boundary conditions. Lindgren et al [2002] present a thermo-mechanical analysis in butt-welding of a copper canister for spent nuclear fuel. Their study looks at a plane copper end during electron beam welding to a copper canister. The FE method gives the transient and residual temperature, stress and strain field for the weldment. The authors acknowledge that perhaps the most important entity is the accumulated plastic strain, as high values of this entity would indicate an increased risk for creep fracture. From their FE analysis, the maximum plastic strain (plastic+creep) accumulated in the (possibly brittle) heat affected zone is approximately 7%, which is well below the reported ductility for the type of copper under investigation. 3.3 Solid Phase Transformations Cho and Kim [2002] take solid phase transformations into account during the simulation of gas tungsten arc welding for the prediction of residual stresses in welded carbon steel plates. ABAQUS is used in the FE analysis of medium carbon steel, AISI 1045, and low carbon steel, AISI 1020. Their numerical residual stress results are validated by a comparison with experimental data. The FE study is two-dimensional, consisting of a thermal analysis, followed by an uncoupled stress analysis, performed using the temperature results from the thermal analysis. The heat source from the modelled electric arc is assumed to have a Gaussian distribution, represented by:

q (r) = {3Q / {πrb}}exp{-3r2/rb2} (3.5)

where q(r) is the heat flux, rb is the effective arc radius, r is the distance from the arc centre, and Q is the arc power derived from the arc efficiency and the welding voltage and current. During the thermal cycle of welding and the ensuing metallurgical transformations, both the density and yield stress of steel change in addition to the volume change of the material, owing to the austenite and martensite transformations. Temperature-dependent material properties have been taken into consideration. On rapid cooling of the steel, once the arc has passed, the austenite face centred cubic (fcc) structure transforms to a martensite body centred tetragonal (bct) structure, thereby increasing the metal volume. Lattice parameters, a and c, determine the volume change due to martensite transformation according to the carbon content of the type of carbon steel, Cwt, according to the following equations: afcc = 3.548 + 0.044Cwt (3.6) abct = 2.861 − 0.013Cwt (3.7)


c = 2.861 + 0.116Cwt (3.8) Cho and Kim explain that the actual volume change due to martensite transformation is less than predicted due to residual austenite and cementite, and accordingly a value for the strain due to martensite transformation volume change is assigned for each type of carbon steel. The calculated martensite fractions, which are dependent on the cooling rate, show that 100% martensite is formed when the cooling time from 800 to 500oC is less than 1.17s for AISI 1045 and less than 0.93s for AISI 1020. The martensite fraction as a function of temperature at each instant of martensite transformation is given by:

m = 1 − exp{−k{Ms−T}} (3.9) where m is the martensite fraction, Ms is the start temperature for the martensite transformation, T is the temperature, and k is a constant. The applied dilatation during martensite transformation is given by: α = ∆m f εtr (3.10) where α is the total applied strain over the martensite transformation range, ∆m is the increment of martensite fraction as a function of temperature, f is the martensite fraction as a function of cooling rate, and εtr is the transformation strain. Cho and Kim explain that if a significant martensite volume increase takes place due to rapid cooling, resulting high compressive stresses can occur in the vicinity of the weld centreline. Since the increase in martensite volume is carbon-content dependent, it has been observed that AISI 1045 exhibits large longitudinal compressive stresses due to a rapid cooling rate, whereas AISI 1020 retains its longitudinal tensile stress. Cho and Kim conclude that metallurgical phase transformation must be considered in welding residual stress analysis for medium and high carbon steel, and it can be ignored for low carbon steel. They also conclude that most martensite is generated in the melted zone and the HAZ.


4. Related Research 4.1 Influence of Welding Speed and Wall Thickness on Residual Stresses Teng and Chang [1998] analyse a circumferential butt weld joining two sections of an SAE 1020 steel pipe. Their three-dimensional FE models are symmetric and the FE meshes are made from shell elements. Four FE models have been analysed, having a pipe diameter of 219.1 mm and two corresponding wall thicknesses of 2.8 and 3.8 mm, and a pipe diameter of 324 mm with two wall thicknesses of 3.96 and 4.6 mm. Teng and Chang conclude that the thicker walled pipes have higher tensile residual stresses compared to the thinner walled pipes. They justify this by stating that a higher welding speed not only reduces the amount of adjacent material affected by the heat of the welding arc, but also progressively decreases the residual stresses; higher speed welding yields a slightly narrower isotherm, influencing the shrinkage of butt welds and generally reducing residual stresses. Teng and Chang describe the residual stresses in their FE models by clarifying that along the weld centreline a high tensile axial stress occurs on the inner surface and a compressive residual stress appears on the outer surface. Away from the weld centreline, compressive residual axial stresses exist at the inner surface and tensile residual axial stresses at the outer surface. In the vicinity of the weld centreline, large tensile hoop stresses occur on the inner surface and compressive hoop stresses on the outer surface. 4.2 Parametric Study on Residual Stresses in Welded Pipes Brickstad and Josefson [1998] have modelled a set of butt welds, in stainless steel pipes, with a varying number of weld passes, ranging from 4 to 36. They have conducted a parametric investigation considering the effects of pipe size (pipe thickness and number of weld passes), net line energy, ratio of inner radius to thickness, weld yield stress and interpass temperature. The resulting axial and hoop stresses at the weld centreline and HAZ are plotted in groups to indicate the effects of each of the investigated parameters on the two types of stress. Based on this, Brickstad and Josefson have proposed recommendations on how to use residual stresses in assessing the growth of surface flaws at circumferential butt welds in nuclear piping systems. 4.3 Simulation of Residual Stresses in a Bimaterial Joint Sahin et al [2003] have conducted an FE analysis to obtain residual stresses in a bimaterial joint. In their work, a FORTRAN 77 program has been developed to calculate temperature contours and thermal and residual stresses using four-noded isoparametric elements. The results of the FE analysis agree with their experimental data from the hole-drilling strain-gauge method. The FE study consider the bimaterial welding of AISI 1020 steel and yellow brass (65%Cu, 35%Zn) thin plates using a very thin high-strength silver-solder film. The two-dimensional FE simulation of


the bimaterial joint uses von-Mises yield criterion with linear isotropic-hardening and the initial stress method, in addition to the kinematic Bauschinger effect being taken into consideration. 4.4 Characterisation of Axial Residual Stress Dong [2003] has performed finite element analyses on stainless steel and carbon steel welded pipes with different geometries, obtaining a range of through-thickness residual stresses. He has conducted a careful parametric investigation using his research results and other data published in literature to find characteristic trends for through-thickness residual stresses due to welding. His investigation has led him to a characteristic equation describing the axial component of residual stress:

σaxial(ξ) = A + B ξ + C sin [ (n π / 2) ( ξ - ξ0) ] (4.1) The equation breaks down the axial stress into three discrete components: a membrane component, A, which is negligible in most practical cases, except when the restraining axial forces are extremely large, such as in the case of a final assembly weld, where A, B and C are constants; a bending component, Bξ, which is dominated by restraint conditions of the joint, where ξ is a parametric coordinate system ranging linearly through the wall thickness from -1 at the bore to +1 at the outer surface; and a self-equilibrating component which is mainly influenced by welding procedures such as the number of passes in the weld and the heat input during welding, where n is the number of quarter wave which is dominated by the number of weld passes in the through-thickness direction and ξ0 is the value of ξ at the peak of the sine wave. In his paper, Dong considers the effect of pipe radius, r, pipe wall thickness, t, weld pass sequence and weld strength mismatch on the residual stresses. In pipes and cylindrical vessels, the joint restraints in the radial direction at the girth weld can be approximately measured by the joint radial stiffness per unit weld length: kr = E t / r2 (4.2) where E is Young’s modulus. It can be seen from the radial stiffness equation that the radius is the most significant parameter. According to Dong, in addition to stiffness, a sufficient radial shrinkage force per unit distance along the circumference due to welding will trigger the reaction of the radial bending stiffness, which is approximated as: Fr = Sy ti / r (4.3) Where Sy is the yield strength of the deposited weld metal and ti represents the depth of the weld pass layer in concern. From the above two equations, the important effect of the radius, on the bending content of the axial residual stress can be seen. Dong has demonstrated how the bending component is negligible and the self-equilibrating component is prevalent when t is


15mm and r/t is as large as 1000 by plotting the axial residual stress at the weld centreline and nearby. Although the effect of the wall thickness is important, it plays a secondary role compared to the radius, as indicated by the preceding equations. The weld pass sequence effects are even smaller in comparison to those of the radius and thickness; Dong describes them as being local, keeping the overall stress distribution hardly affected. Although the weld strength mismatch is important for the magnitude of the axial residual stresses, it does not significantly change the overall distribution of these stresses. 4.5 Effects of Material Properties on Stresses and the Inclusion of Phase

Transformation Mochizuki et al [2002] investigate the effects of material properties on residual stresses and those of phase transformation on thermal stresses. Two materials of high-tensile strength steels have been considered. Thermal stress history is consistent when FE and experimental results are compared. The FE study takes into account material properties for each microstructural phase by referring to CCT-diagrams. 4.6 Simulation of Combined Welding and Stress Relief Heat Treatment Berglund et al [2003] consider residual stresses and deformations in aero engine components during manufacture due to welding and stress relief heat treatment. Their FE analysis combines the operations of welding and stress relief heat treatment of martensitic stainless steel components. Heat input in their work is represented by a moving heat source having a double-ellipsoid energy input distribution, a method first proposed by Goldak et al [1984]. Berglund et al provide a historic account of FE research on the simulation of welding and post weld heat treatment. They obtain an approximation of the heat transfer coefficient of the modelled component’s surface during the heat treatment process by using computational fluid dynamics. 4.7 Effect of Residual Stresses and Geometric Parameters on Fatigue Crack

Initiation Life of Welded Plates Teng et al [2002] combine FE structural analysis with strain-life equations to develop a procedure for forecasting the fatigue crack initiation of weldments and verified their results against experimental data. They also consider the effects of residual stresses and weld geometry parameters on the fatigue crack initiation life of ASTM A36 carbon steel butt-welded plates. The geometric parameters include weld toe radius, weld bead flank angle, preparation angle and plate thickness, leading to specific geometric conclusions on how to prolong fatigue crack initiation life.


4.8 Effect of Aluminium Material Properties on Temperature, Stress and

Distortion In their introduction, Zhu and Chao [2002] present a concise literature review of the effects of material properties on transient temperature, thermal and residual stresses and distortion. They explain how their detailed and systematic investigation of the influence of each material property in a three-dimensional FE simulation of welded 5052-H32 aluminium alloy is based on three sets of material properties: those at room temperature; those averaged over the temperature history in the welding process; and those assumed to be functions of temperature. The in-house FE package WELDSIM is used for a comparison of the results for the three cases, drawing conclusions on the effect of each temperature-dependent material property on transient temperature, residual stress and distortion. The results are validated by comparing them to experimental data. Zhu and Chao conclude that the thermal conductivity has some effect on the distribution of transient temperature field during welding. The material density and specific heat have a negligible effect on the temperature field. Therefore, adopting room temperature values of all thermal properties can predict reasonable results for the transient temperature distribution, although using average values over the temperature history would yield more accurate results. Zhu and Chao recognise that the yield stress is the key mechanical property in weld simulation. They explain the reason why the yield stress value has a significant effect on the residual stress and distortion, suggesting that the temperature dependency of the yield stress must be considered in a welding process simulation to obtain correct results. Zhu and Chao demonstrate that Young’s modulus and the thermal expansion coefficient have small effects on the residual stress and distortion in welding simulation. They state that the numerical results obtained by using the room temperature value of Young’s modulus are significantly more accurate than those obtained using its average value over the welding temperature history. In conclusion, Zhu and Chao propose a validated welding simulation approach for aluminium constituted by a piece-wise linear function with temperature of the yield stress and the constant room temperature values of all other properties. They also postulate that a similar approach can be extended to welding simulations for steels. 4.9 Adaptive Mesh Technique Qingyu et al [2002] have developed an adaptive mesh technique applied in the three-dimensional numerical simulation of the welding process on the basis of the commercial software MARC. The adaptive mesh technique generates a dense mesh and makes it move simultaneously with the heat source. Any part of the mesh away from the heat source is much coarser, significantly saving CPU time. The calculation time comparison shows that the adaptive mesh technique can


reduce the CPU time by almost one-third. The adaptive mesh technique function is accomplished with a special user subroutine. A comparison between the adaptive mesh technique and the FE method without adaptation of the mesh shows that the temperature fields and the displacement distributions correspond accurately, whereas the stress distributions correspond qualitatively, with some quantitative difference. Runnemalm and Hyun [2000] have developed an in-house code, SIMPLE, for the creation of an adaptive FE mesh, increasing accuracy of results with reduced computational time. They describe a generic and a posteriori error formulation that evaluates the thermal and mechanical error distributions, which is used, together with the known movement of the local heat source, to designate areas of refinement in a mesh of graded hexahedral elements. The definition of an optimal mesh is based on equal distribution of the global error between all elements in the mesh. Alternatively, a uniform distribution of the error density in the mesh could have provided the basis of the definition. Two geometries have been investigated using the adaptive mesh scheme: a circumferential butt welding of a thin tube and a butt weld of a thin plate, both being made of AISI 304L, which is an austenitic stainless steel. The material properties are all temperature dependent. The error-driven adaptive mesh technique is extremely useful when complex three-dimensional weld geometries are being modelled, since efficient meshing is difficult even for an experienced user in this case. Lindgren et al [1997] have proven the validity and effectiveness of their technique of using an automatic remeshing algorithm in the three-dimensional FE simulation of electron beam welding of a large copper canister. They based the automatic remeshing algorithm on a graded hexahedral element. They explain that the strongly nonlinear thermomechanical effects in the vicinity of the moving heat source can more accurately be modelled with a dense element mesh that follows the heat source. 4.10 Three-Dimensional Geometric Effects on Residual Stresses Fricke et al [2001] have conducted a three-dimensional FE analysis of a circumferential weld in a thin austenitic steel pipe using the computer program FERESA based on the commercially available ABAQUS code. Instead of resorting to the more accurate 20 node FE elements in their analysis, 8 node elements form the FE mesh to allow the three-dimensional simulation to be completed within the computer time limit available. The calculated residual stresses are tensile at the weld root and compressive at the outer surface of the weld, the stress profile across the wall thickness being approximately linear. The peak residual stresses occur at the weld starting point but this could be avoided in practice by offsetting the starting point for every subsequent weld bead. The final pass also has a considerable effect on total residual stresses. Fricke et al have also considered the effect of interpass cooling on the HAZ, the effect of gap width on residual stresses and the effect of the ‘last pass heat sink welding’ (welding of the final passes while simultaneously cooling the inner surface with water) producing compressive residual stresses in the root area of their austenitic pipe.


4.11 Effect of Manufacturing Residual Stress and Strain, Prior to Welding, on Distortion

Wen et al [2001] have simulated the process of multi-wire submerged arc welding using ABAQUS. The welding process and its application in thick wall pipeline manufacturing have been briefly explained. Two and three-dimensional models of an X56 steel pipe have been generated. Through the two-dimensional FE model, detailed residual stress and strain distributions around the weld bead have been investigated, as well as the transverse distortion of the pipe. The main purpose of the three-dimensional model is to study the global distortion in the longitudinal direction of the pipe. The same material properties are used for the parent and weld metal and the HAZ. The mechanical properties are temperature dependent, whereas the thermal properties are assumed to be constant. Latent heat of fusion and solid state phase transformation have been ignored. The residual stress and strain developed from the pipe upstream forming operations prior to welding have been included in some of the two-dimensional analyses. It is concluded that such residual stresses and strains are important for an accurate prediction of geometrical distortion of the pipe. 4.12 Modelling of Thin Pipe Wall Cooling Sabapathy et al [2001] investigate the safe and effective welding of thin-walled high-strength X70 and X80 steel ‘live gas pipelines’ using three-dimensional FE simulation of the welding process. A modified ‘double ellipsoidal’ heat source has been developed to model the low-hydrogen manual arc welding process. The cooling times of the weldments show an agreement between the FE and experimental results. The reduced wall thickness of the pipe is more sensitive to strength loss and increases the possibility of burn-through during welding. Also, thin walls are more easily cooled by the flowing gas and high-strength steels can be more susceptible to the generation of excessive hardness for a given cooling rate. The FE study considers the common industrial hot-tap welding process of manual metal arc welding (MMAW) using low-hydrogen electrodes and a vertical-down welding technique, together with the cooling effect of the flowing pressurised gas. Any effects due to arc-initiation have been ignored. The weld pool convective heat transfer has been compensated for with an artificially high conductivity for the molten metal. Eight-noded linear brick elements in the three-dimensional FE analysis maintain balance between solution speed and accuracy of the FE results. 4.13 Shrinkage Volume Approach Bachorski et al [1999] are concerned with distortion during gas metal arc welding in their shrinkage volume approach. They define the Shrinkage Volume Method as a linear elastic FE modelling technique for predicting post weld distortion. By assuming that the linear thermal contraction of a nominal shrinkage volume, as it cools from elevated to ambient temperature, is the main cause for distortion, there is no longer a need to determine the transient temperature field and microstructural changes, thus substantially reducing the time for FE distortion analysis. The thermal contraction of the shrinkage volume is resisted by the surrounding parent metal,


resulting in the formation of internal forces, leading to distortion by the parent metal to accommodate the shrinkage forces until equilibrium is achieved. The method is applied to the distortion of plain carbon steel plates having butt-welded joints with different vee-angles. Bachorski et al explain that although significant progress have been in FE weld modelling, in actual structures many FE techniques are short of being successful at the control of residual stress and distortion. For simplicity, they describe the use of linear spring elements to model the thermal contraction of the weld metal in a welded joint. This crude method can predict distortion reasonably in a fraction of the time needed for the more sophisticated fully transient thermal elastic-plastic modelling regimes. The Shrinkage Volume Method assumes that a constant linear thermal strain is responsible for post weld distortion. Linear thermal strains are imposed as the weld metal elements cool from the assigned temperature, elastically distorting the weldment. Thermal strains produced in the temperature range 800-1500oC are hence ignored. The heating-up thermal cycle of the welding process is also ignored, neglecting the stress history and rendering the produced stress field invalid. For the FE distortion analysis, eight-noded brick elements allow for a parabolic distribution along the element edge and are used for all the models. Bachorski et al explain that Goldak et al [1984] has developed a heat source designed to compensate for the absence of flow in conduction models by distributing the heat source within an ellipsoidal volume below the welding arc and enhancing the conductivity for any molten material. They propose the more recent heat source representation by Smailes et al [1995] who have shown that a more effective heat definition for vee-joint butt welds for a plate is the ‘split’ heat source comprised of the heat content of the welding arc, applied to the weld surface with a Gaussian distribution, and a cylindrical volume heat source for the molten material. Any discrepancy between the shrinkage volume distortion results and experimental data is attributed to the difference between the assumed shrinkage (fusion) volume and the actual fusion zone determined from macro-graphs.


5. Friction Stir Welding Chen and Kovacevic [2003] have studied the thermal history and thermomechanical process in the butt-welding of aluminium alloy 6061 – T6 through three-dimensional FE analysis, using the software ANSYS. They consider friction stir welding (FSW) which is a relatively new welding process achieved due to friction and involving the pure solid-state joining of metals. FSW may lead to the reduced distortion and improved mechanical properties of welded alloys due to the peak temperatures remaining below the melting point of the welded metals. FSW can also join conventionally non-fusion weldable alloys. The FE model of Chen and Kovacevic base the heat source on the friction between the material of the welded metal and the welding tool, consisting of the probe and shoulder, although the frictional effect of the prone is ignored here. From the thermal history of the FE model, the stresses in the friction stirred weld are numerically simulated. The validity of the FE model is supported by the measured residual stresses using the X-ray diffraction technique. FSW process parameters such as tool traverse speed have been investigated for their effect on the calculated residual stresses. Friction between the welded material and the welding tool causes the former to soften at a temperature lower than the melting point. The rotational and transverse movements of the tool subject softened material underneath the shoulder to extrusion. Since the material does not reach its melting point, Chen and Kovacevic expect the weld to have smaller residual stresses and distortion compared to what is produced from fusion welding. Chen and Kovacevic simulate the friction stir welding of two thin rectangular plates. The tool is considered to be a rigid solid and the workpiece a ductile material having elasticity, plasticity and a kinetic hardening effect. The temperature calculation is based on Fourier’s equation. The rate of heat generation due to friction over the entire interface has been derived, and the thermal and mechanical solutions have been coupled. The microstructure of the weldment is described in four zones: stirred weld zone (or weld nugget) where the refined grains are equiaxed and are attributed to the dynamic recrystallization due to heat and mechanical work; thermomechanically affected zone (TMAZ); heat affected zone (HAZ) which usually contains a large amount of coarsened grains with relatively lower yield strengths than that in the TMAZ and the nugget; and finally base metal. Chen and Kovacevic conclude that the maximum temperature gradients in the longitudinal and lateral directions exist just beyond the shoulder edge and that a higher traverse speed induces a larger high longitudinal stress zone and a narrower lateral stress in the weld. Song and Kovacevic [2003] consider a three-dimensional friction stir welding FE model. A moving coordinate system reduces the difficulty of modelling the moving tool. In order to solve the controlled equations, the finite difference method is applied. The calculated results agree with those obtained from FSW experiments. In conclusion, Song and Kovacevic propose that preheat to the workpiece is beneficial to FSW.


Lockwood and Reynolds [2003] have studied the local and global mechanical responses of friction stir welding experimentally and numerically. Two-dimensional FE modelling of welded thin plates of aluminium alloy 2024-T351 agree with experimental results, revealing nearly plane stress conditions in the plates. The results have been corroborated by a three-dimensional FE model. Lawrjaniec et al [2003] have used SYSWELD and MARC to conduct a three-dimensional numerical simulation of Friction Stir Welding. Two different heat sources (two and three dimensional) are represented in the thermal stage. The FE residual stresses are compared to experimental measurements made by neutrons diffraction. Ulysse [2002] attempts to simulate the friction stir welding process of aluminium thick-plate butt joints using three-dimensional visco-plastic modelling. After a parametric survey and validation against available measurements, the FE study reveals that pin forces increase with welding speeds and reduce with rotational speeds. The pins forms the end parts of the welding tool, which digs into the work piece, sitting concentrically below the shoulder of the tool, which prevents material from being expelled from the workpiece. The numerical model can be considered a designing welding tool improving on the thermal gradients and avoiding tool breakage.


6. Inertia Friction Welding D’Alvise et al [2002] simulate the process inertia friction welding (IFW) between two metal rods with circular cross section and of dissimilar materials using the FE software FORGE2. Their mechanical equations incorporate physics terms of inertia, forces and friction. Rheological and tribological parameters are influenced by the thermal calculation, which is coupled to the mechanical analysis. The flash formation at the joint interface is modelled with a contact algorithm and an automatic remeshing procedure. In the thermal analysis the temperature is computed from Fourier’s equation, and the thermal and mechanical solutions are coupled. In the mechanical analysis the equilibrium equation is given as: div(s) = ρ.γ + grad(p) (6.1) where s is the stress tensor, ρ the equivalent density, γ the acceleration, p the hydrostatic pressure, and the body forces are neglected. At the start of heating, the shear stress is written as a classical Coulomb’s friction law: τf = -αp {{∆Vs}/{|∆Vs|}} (6.2) where the shear stress is proportional to the pressure applied. When the interface reaches a critical temperature, the friction law becomes temperature dependent and the shear stress decreases when the temperature increases: τf = -αK(T) {{∆Vs}/{|∆Vs|}} (6.3) where K(T) is the thermo-dependent material consistency, and ∆Vs the sliding rotational velocity. D’Alvise et al conclude that when the solidus temperature is approached, the friction regime changes from a Coulomb friction law to a viscous one. The friction parameters have been deduced from the experimental data for a first approximation, followed by a manual inverse analysis to fit the numerical predictions to the experimental date. The FE model can predict the shape of the flash with accuracy. Fu et al [2003] simulate inertia friction welding of 36CrNiMo4 steel in tubular form under given boundary conditions. The transient temperature, stress, strain, strain rate and deformation are investigated numerically and experimentally, using the FE software DEFORM and inferred detection respectively, taking the change in material properties into consideration. The thermal and mechanical analyses are coupled. The inferred images agree with numerically calculated temperature distributions. The numerically predicted shape of the tubular welded joint is also in agreement with empirical observation.


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