COMPUTATIONAL MODELING OF RESIDUAL STRESS IN WELDS

S. Yushanov and K. C. Koppenhoefer*

ABSTRACT

Accurate prediction of stresses, strains, and residual stresses that are generated as a result of welding is important for a number of practical issues. Hydrogen-induced cracking, stresscorrosion cracking, distortion, as well as fatigue strength of welded structures can all be affected significantly by the residual stresses that are generated around welds. Due to the complexity involved in the experimental measurement of residual stresses, numerical simulation procedures are increasingly used for estimating the residual stresses that arise from welding. Commercially available simulation software readily allows one to account for the non-linearities due to variation of material properties and heat transfer coefficients with temperature. However, the material constitutive models available in most commercial packages do not account for some of the unique features associated with the welding process, e.g., material melting/remelting as different weld passes are deposited, solid phase transformation effects, etc.

These features of the welding process influence the prediction of residual stress and distortion. However, the open literature does not include a systematic study of these factors. The work reported here uses a multiple-pass butt weld in a cylindrical pipe to study in detail the effects of advanced material modeling methods on residual stress. Deposition of material during the welding is carried out in multiple weld passes. At the melting temperature, all accumulated elastic and plastic strains are set to zero. The interaction of this strain zeroing with the isotropic and kinematic hardening is examined in terms of the effect on the distribution of residual stress and welding-induced distortion.

KEYWORDS

Residual stress, kinematic hardening, isotropic hardening, strain accumulation, welding, finiteelement analysis.

INTRODUCTION

Accurate modeling of the material response to welding represents a significant challenge in welding simulations ([1] and [2]). The large temperature change associated with welding generates a complex material response. These temperature changes produce difficulties in both the thermal and mechanical analysis in a welding simulation. However, the material response in a mechanical analysis represents a greater challenge than the thermal response to the numerical analyst. The mechanisms of plastic deformation and evolution of the yield surface during welding continues to be a point of discussion among organizations conducting welding simulations.

To determine the influence of different techniques for modeling plastic deformation during welding, the International Institute of Welding (IIW) conducted a round robin of residual stress

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prediction. Eleven well-recognized organizations conducted analyses of a butt girth weld in a pipe. The IIW provided each participant with the finite-element mesh, the net heat input of welding, and the temperature-dependant material properties. The residual stress predictions from these 11 organizations contained significant scatter [3]. A detailed review of the analysis techniques used by the participants suggests the plasticity routines generated the majority of the scatter. The work reported here examines the effect of two critical components of welding simulation, namely the effects of the hardening model (isotropic versus kinematic) and zeroing the plastic strain during material melting.

COMPUTATIONAL MODELS

The analyses conducted here utilize an axisymmetric idealization of a pipe girth butt weld. The finite-element mesh used in the IIW round robin forms the basis for all analyses conducted in this work. The mesh in the weld region contains significant refinement with a coarsening as the mesh moves away from the weld (see Figure 1).

The analyses consist of a sequentially coupled technique where the thermal analysis is conducted first. All analysis used the commercial code ABAQUS. A double-ellipsoid function with a Gaussian distribution of heat flux [4] models the arc heating effects during welding. User routine DFLUX is utilized to implement a moving body heat input due to welding. Surface convection is applied at the inner and outer surfaces of the pipe. Radiation heat transfer effects are not accounted for in this analysis. The initial, and interpass, temperature of the model was room temperature.

Each weld pass is modeled discretely using an element-rebirth technique. In this technique, the element sets representing each weld pass are generated along with the finite-element analysis meshes for the base material, see Figure 1. During analysis, elements associated with higher numbered passes are first removed and then reactivated at the beginning of the appropriate weld pass.

When a group of weld pass elements is activated, specified initial temperatures are imposed for all nodes associated with the weld pass elements. In reality, rebirth of the weld pass elements occurs at the melting temperature. However, numerical studies indicate [5] that predicted residual stress distributions do not seem sensitive to prescribed initial conditions for the weld metal. Thus, rebirth of the higher pass elements occurs at room temperature in the present analysis.

The material is assumed to follow the von Mises yield criterion and associated flow rules. Linear isotropic and kinematic hardening models were analyzed. Strain rate effects and phase transformation effects are not considered in the present analysis. Temperature-dependent thermal-physical properties used in thermal analysis and material properties for stress analysis are taken from Reference [3]. These analyses utilize a strain resetting technique, included into ABAQUS via a UMAT that eliminates all accumulated plastic strains for material once it exceeds the solidus temperature.

RESULTS AND DISCUSSION

The first set of results presented in this section show the evolution of different variables at Point A located within the weld filler metal that are deposited during Pass 1 (see Figure 1). This point experiences melting during Pass 1 and re-melting during Pass 2, see Figure 2. As indicated previously, the solidus temperature for this material equals 1455°F. Thus, Point A, remains in the molten state over 0.5 sec ≤t≤ 4 sec for Pass 1, as indicated by the region between the dashed lines in Figure 2(a). Point A, becomes molten again for approximately 5 sec (5,012 sec <t≤5,017 sec) during Pass 2, as shown by the dashed lines in Figure 2(b).

Figure 3 presents the transient equivalent plastic strain at Point A1. Each figure compares an analysis where the strains accumulated through the entire welding cycle (dashed line) with an analysis for which the strains are reset (solid line) at all points where the temperature exceeded the solidus temperature of the material. The resetting algorithm effectively reduces the equivalent plastic strain for Point A1 to zero while the material melts and re-melts. Thus, the analyses that do not include resetting accumulate significantly more plastic strain than the analyses with resetting. The plastic strains presented in Figure 3 appear independent of the hardening model (isotropic or kinematic).

Figure 4 shows the variation of the plastic strain in the hoop direction, e, as a function of time at Point A1. The resetting algorithm influences this plastic strain component in a similar manner as the equivalent plastic strain. However, the examination of e permits a physical interpretation of the results to determine the applicability of the resetting algorithm. Introducing the resetting algorithm changes the direction of the hoop plastic strain from compression to tension. The tensile plastic strain represents a more physically reasonable result. The weld metal must contract on cooling after each pass. Thus, the weld metal should experience a tensile strain. As with the equivalent plastic strain, the strains shown in Figure 4 appear independent of the hardening model.

The hoop stress computed from these strains using an isotropic hardening model appear in Figure 5 (all stresses are normalized by the room-temperature yield strength, σ). As Pass 1 heats the material, a large compressive stress initially develops (σ/σ =-1.1). Additional heating during Pass 1 decreases the stress to near zero due to the decrease in yield strength and Young's modulus of the material. After the material solidifies, the hoop stress becomes tensile and attains a value of σ/σ = 1.5 at the end of Pass 1. The evolution of stress at Point A1 for Pass 2 appears in Figure 5(b). During Pass 2, Point A1 experiences re-heating, re-melting, and cooling. Reheating drives the hoop stress from a tensile value of σ/σ = 1.5 to a maximum compressive value of σ/σ = -0.7 before the material loses strength and stiffness. In the re-melting region, the hoop stress at Point A1 approaches zero. Cooling of the material generates a large tensile stress (σ/σ = 1.2).

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A direct comparison of the analyses with and without the resetting algorithm indicates strain resetting does not influence the residual stress at any point during the analyses, for the case of

isotropic hardening shown in Figure 5. Resetting the strains does not influence the residual stress due to the lack of influence of these strains on the yield surface, as shown in Figure 6. By definition, the yield surface may not shift for isotropic hardening. Thus, the yield surface for isotropic hardening remains unchanged during the resetting of the strains. This unchanged yield surface produces a constant residual stress since the stress state must remain on the yield surface during plastic flow.

Figure 7 shows the variation of hoop stress with time for the kinematic hardening case. Figure 7(b) shows the dramatic influence of strain resetting on residual stress prediction. For kinematic hardening, the yield surface radius does not change with plastic flow. Instead, the yield surface translates. Figure 8 shows the evolution of the back stress for Passes 1 and 2. For the case of strain resetting, the yield surface origin returns to the coordinate origin due to an elimination of the back stress. This modification of the yield surface origin produces the difference in hoop stress observed in Figure 7.

Figure 9 summarizes the effect of strain resetting on the hoop stress for both isotropic and kinematic hardening models. Figure 9(a) shows there is no influence of strain resetting on the hoop residual stress over the entire welding cycle for isotropic hardening. The stresses at Point A1 attain a value of approximately 1.5 times the yield stress early in the welding and maintain that value (except in the transients during welding). Figure 9(b) shows the strong influence of strain resetting over time. For Pass 1, the residual stress attains a value of approximately 2.0 times the yield stress. However, the addition of new material reduces the residual stress to yield level at the completion of the weld.

Figure 10 shows the final hoop and axial residual stresses along the weld centerline for all cases. The kinematic hardening results show the influence of the strain resetting technique used here. The isotropic case and kinematic case with resetting show the closest agreement for the hoop stress. All three cases show reasonable agreement for the axial stress case.

In additional to residual stress, welding simulations may provide predictions of distortion. Figure 11 shows the axial and radial displacement along the internal diameter of the pipe for all cases considered. For both plots, the origin of the x axis occurs at the symmetry plane of the weld. Strain resetting does not influence the residual stress for analyses using isotropic hardening. However, the axial and radial displacements show an effect of strain resetting. The effect of resetting strains appears much greater for kinematic hardening. Without strain resetting, isotropic and kinematic hardening provide dramatically different displacements. However, resetting the strains drives the two analyses towards each other.

SUMMARY AND CONCLUSIONS

This work examines the effect of strain resetting during melting in welding simulations. The resetting procedure does not influence the residual stress prediction for isotropic hardening. The resetting procedure does not alter the yield surface radius. Thus, the residual stress predicted from the simulation does not change. For kinematic hardening, the modification of the back stress produces a strong effect on the residual stress. Strain resetting does alter the predicted