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This chapter presents that one common problem associated with welding is the dimensional tolerance and stability of the finished products. The welding-induced residual stresses in the weldment are sometimes also a concern regarding their effect on the fracture and fatigue behaviors of the welded structures subject to dynamic loading or adverse service environment. Although the inherent shrinkage model has been demonstrated to be accurate, convenient, and cost effective in the prediction of weld residual stresses and distortion, several fundamental issues remain unsolved to date. The inherent shrinkage model needs calibration constants for different applications. Those calibration constants will depend on the thermal characteristics of the welding process and the geometric details of the joint, as well as the jigging constraints. To prescribe the inherent shrinkage strains in the weld joint, the equivalent thermal strains may be defined using the artificial temperature fields. A standard procedure to determine the effective shrinkage strain temperatures will be required. An inherent shrinkage strain database for various production situations, joint designs and welding procedures needs to be developed. The Finite Element Analysis (FEA) modeling, simulation, and analysis procedures can be useful in determining the inherent shrinkage strains.

1.1 Introduction

One common problem associated with welding, which has been realized and documented for many years, is the dimensional tolerance and stability of the finished products. The welding-induced residual stresses in the weldment are sometimes also a concern with respect to their effect on the fracture and fatigue behaviors of the welded structures subject to dynamic loading or adverse service environment.

In making a weld, the heating and cooling cycle always causes shrinkage in both base metal and weld metal, and the shrinkage forces tend to cause a degree of distortion. Machining of a welded product may cause dimensional changes of the product owing to relaxation of weld residual stresses. As a result of welding, the finished product may not be able to perform its intended purpose because of poor fit-up, vibration problems, high reaction stresses, reduced buckling strength, premature cracking or unacceptable appearance. Control of weld residual stresses and distortion is a vital task in welding manufacturing.

Attempts have been made by many researchers since 1930 to understand weld residual stresses and distortion using predictive methodology, parametric experiments or empirical formulations. Attempts have also been made in the last three decades to predict weld residual stresses and distortion through computer simulations of welding process using the finite-element analysis (FEA) method. One significant conclusion from these studies is that the weld residual stresses and distortion are not influenced much by the weld heating cycle but instead occur as a result of shrinkage in the weld metal and its adjacent base metal during cooling when the yield strength and modulus of elasticity of the material are restored to their higher values at lower temperatures. Therefore, analysis of the shrinkage phenomena of welds alone may be sufficiently accurate to predict the state of weld residual stresses and distortion. This conclusion has led to the development of a modeling scheme referred to as the ‘inherent shrinkage model’ by some researchers. The root cause for welding-induced residual stresses and distortion may be described using a plasticity-based hypothesis1.

This chapter will present the following.

1.2 Thermal and mechanical processes during welding

In a welded joint, the expansion and contraction forces act on the weld metal and its adjacent base metal. As the weld metal solidifies and fuses with the base metal, it is in its maximum expanded state. However, at this point, the weld metal and its adjacent base metal are at high temperatures and have little strength or rigidity. The volume expansion causes local thickening in the weld area but is incapable of causing a significant amount of plastic strains in the cooler joint neighborhoods. On cooling, it attempts to contract to the volume that it would normally occupy at the lower temperature, but it is restrained from doing so by the adjacent cooler base metal. Stresses develop within the weld, finally reaching the yield strength of the weld metal. At this point the weld stretches, or yields, and thins out, thus adjusting to the volume requirements of the lower temperature, but only those stresses that do not exceed the yield strength of the weld metal, or the elastic mechanical strains, are relieved by this accommodation. In 1960, Blodgett2 properly described this thermal and mechanical evolution process.

The plastic strains accumulated over the welding thermal cycles are primarily compressive and remain in the weldment. By the time that the weld reaches room temperature, the weld will contain locked-in tensile stresses (residual stresses) of yield magnitude and the base metal away from the weld is usually in compression with smaller magnitude. The internal tensile and compressive forces are in equilibrium with the joint deforming to comply with the strain compatibility. The residual stress distributions and the amount of weld distortion depend on the final state of the plastic strain distributions and their compatibility in the joint. Over three decades since 1930, the shrinkage distortion phenomena were studied by Spraragen and Ettinger3, Guyot4, Watanabe and Satoh5 and others.

The welding-induced incompatible inelastic strains in the weldment during the heating and cooling weld cycles include transient thermal strains, cumulative plastic strains and final inherent shrinkage strains. At any instant during welding, the incompatible thermal strains resulting from the nonlinear temperature distributions generate the mechanical strains, which lead to incremental plastic strains in the weldment if yielding occurs. The incremental plastic strains accumulate over the periods of heating and cooling. Upon completion of the welding cycles, the cumulative plastic strains interact with the weldment stiffness and the joint rigidity, resulting in the final state of residual stresses and distortion of the weldment. This final state of the inelastic strains, which are always compressive, is referred to as the ‘inherent shrinkage strains’. Ueda et al.6 first presented this inherent shrinkage concept to predict weld residual stresses and distortion in 1979, followed by many publications demonstrating the numerical procedures for weld residual stresses and distortion prediction using the inherent shrinkage concept7–10. In 1993–1995, Tsai and coworkers11, 12 used spring elements to describe the inherent shrinkage strains in the numerical simulation and analysis of angular weld distortion of tubular joints in automotive frames.

Welding-induced incompatible plastic strains (assuming a two-dimensional (2D) plane-strain condition for illustration purpose) at each heating or cooling time increment may be described mathematically as follows1:

2(σx+σy)=−E1−2∇2(αθ)−[g(x,y)+Δg(x,y)] [1.1]

where ∇2 is the Laplacian operator, σx and σy are thermal stress components in the respective x and y directions, E is Young’s modulus, V is Poisson’s ratio, α is the thermal expansion coefficient, θ is a temperature function, g(x, y) is a cumulative plastic strain function and Δg(x, y) is the plastic strain increment function over each thermal loading step. The plastic strain functions may be written as follows:

(x,y)=E1−v2(∂2εxpdy2+∂2εyp∂x2−2∂2εxyp∂x∂y)−vE1−v2∇2(εxp+εyp) [1.2]

g(x,y)=E1−v2(∂2(Δεxp)∂y2+∂2(Δεyp)∂x2−2∂2(Δεxyp)∂x∂y)−vE1−v2∇2(Δεxp+Δεyp) [1.3]

The Laplacian thermal strains are governed by the rate of enthalpy change...