RESIDUAL STRESS DISTRIBUTION FOR A SINGLE PASS WELD IN PIPE

Heat input due to the welding of mild steel pipe causes a temperature gradient in the parent metal. After welding and temperature cooling down, residual stresses appear around welding zone which reduces the weld strength. Residual stresses are a result of the temperature gradient and the dependency of material properties on the temperature, such as yield strength, elasticity modulus


RESIDUAL STRESS DUE TO PIPE WELDING:
Residual stresses are formed by the plastic deformations during the thermal cycle of welding.Before welding, the structure is assumed to be at room temperature and free of stresses.During the weld thermal cycle, material mechanical properties change drastically, especially when material approaches melting point temperature.Therefore, due to the temperature dependence of material properties and the large deformation in fusion welding, material and geometrical non-linearity have to be taken into account.The initial expansion material due to the temperature increase is constrained by material placed away from the heat source, therefore generating compressive stress.At a temperature higher than material critical temperature, the material starts exhibiting thermal softening where heating results in decrease of flow stress.As phase change occurs deviatory stress becomes zero and considerable plastic deformation occurs in the weld metal and the base metal regions near the weld.As temperature decreases during the cooling phase, the stress in the solidifying material increases, and becomes tensile due to the positive temperature gradient.The region placed away from the weld line, will therefore, be in compression since the resultant force and the resultant moment induced by residual stress evaluated in any plane section must satisfy translation and rotational equilibrium.The plastic strains resulting from the heating causes stress , which in turn produce internal forces that may cause buckling , bending , and rotation .These displacements are in general called distortion.The residual stress combined with distortion and degradation of the material mechanical properties influence the buckling strength and fatigue life of welded structure [Meo, 2003].

MATHEMATICAL MODEL:
In a girth-welded pipe, shrinkage of the weld in the circumferential direction induces shearing force, Q, and bending moments, M, to the pipe as shown in Fig. (1).the angular distortion caused by butt welding also induces bending moment.Distribution of residual stresses is affected by the following [Koichi, 1980]: 1-The diameter and wall thickness of the pipe.2-The joint design (square, butt, vee, x ….etc).3-The welding procedure and sequence (welded on outside only, welded on both sides, outside first, or welded on both sides, inside first).4-The welding parameters (current, voltage, speed, electrode diameter, type of electrode…etc).5-Material properties.The tendon force locked into a weld is defined as the imaginary line load which would produce the observed shrinkage parallel to the weld, and is approximately independent of restraint.It may therefore be estimated on the basis of the assumption of infinite restraint against any hoop wise expansion of the heat material during welding.Then, the residual hoop stress at any point is a function of the maximum temperature reached, and the hoop tendon force is obtained by integrating the stress distribution.
For a surface weld bead, the maximum temperature as a function of the distance r from the weld centerline is given approximately by [Norman, 1984]: Where ζ is the arc efficiency, q the weld power, v the weld travel speed, and ρC p the volumetric specific heat.
Inside the region where the thermal strain αTmax . is greater than twice the yield strain σ y /E , yield occurs in compression during heating, and then again in tension during cooling.For thermal strains between 2σ y /E and σy/E, the material yields in compression during heating, but unloads to a sub-yield tensile strain during cooling.Material whose maximum thermal strain is less than σ y /E does not yield, and ends at zero stress for the idealized conditions of infinite hoop wise restraint.Where E modulus of elasticity, α thermal expansion coefficient, and σy yield strength of the pipe material.

Fig. 2 Hoop tensile zone at girth weld
The total force locked into the tensile zone is given by: F=A w σ yw + (1.17*2t o r-A w ) σ y (3) Where A w and σ yw are the area and yield strength of the weld, and the factor 1.17 allows for the subyield tensile stresses between r and 2 r.
The inward radial deflection of a circular cylindrical shell loaded symmetrically with respect to its axis [Timoshenko, 1959]: And hence:   4), ( 5) and ( 6) gives the radial deflection and its derivatives at any distance from the weld.
The axial bending stresses σ zb on the inner and outer surfaces at any section inside or outside the tensile zone are a function of the curvature:

FINITE ELEMENT MODELING PROCEDURES:
The FE analysis was carried out in two steps.A non-linear transient thermal analysis was conducted first to obtain the global temperature history generated during and after welding process.A stress analysis was then developed with the temperatures obtained from the thermal analysis used as loading to the stress model.The general purpose FE package ANSYS 8.0 was used for both thermal and stress analysis performed sequentially.The mesh used in the stress analysis was compatible to that in the thermal analysis.The material properties of the weld meld and base metal are assumed to be the same in this analysis and it is temperature dependent.The thermal and mechanical material properties are listed in table ( 1) & (2) respectively.
In the thermal analysis, the heat was input in four load steps as shown in figure (4) .The nodal temperature solution obtained from the thermal analysis were read as loading into the stress analysis .In order to capture the residual stress induced due to the heating and cooling cycle , the temperature history needed to be read at a sufficient large number of time points, especially where the temperature gradient is large .However, the greater the number of the thermal solution steps used, the greater the computational time and the larger store space required.

RESULTS AND DISCUSSIONS:
The sample of calculations was made on a single span ASTM214-71 mild steel pipe with (1 m) length, (25.4 mm) radius, (1.5 mm) thickness.The welded pipe was formed by joining two (0.5 m) pipes by single pass fusion arc welding.The amount of heat input was found as the product of arc efficiency, voltage, and current (Power arc welding =f 1 f 2 VI), Where: f 1 =heat transfer efficiency, f 2 =melting efficiency, V=voltage, and I=current.We take f 1 =0.9, f 2 =0.6, V=30 volt, I=300 Amp, using an electrode type E7010-G to make a straight pipe 1m length with welding on its mid span.During the welding process, the temperature is locally increased to the melting point of mild steel.Moreover, in the heat affected zone of the weld, the temperature reaches high values.The mechanical properties of mild steel such as yield strength and elasticity modulus are highly depending on the temperature.After welding, the heat energy is dissipated due to convection with ambient air causing the steel to cool down and consequently gain its original yield strength.During this process of increasing and decreasing the temperature, residual stresses and plastic strains are developed.9).It can be seen from these figures that the stress is changed from compression at the centerline of weld and tension away from the weld centerline at the end of welding (t=3.5 sec) to tension at the centerline of weld and compression away from the weld centerline when it cooled (t=400 sec), which are a good agreement between the analytical and numerical results with the The average values of thermal properties over the applied temperature distribution were used to study the effect of temperature dependent material properties on the final residual stress results.The residual stress obtained from the FE analysis using constant thermal properties show a significant difference from the obtained using temperature dependent thermal and mechanical properties as shown in fig.( 13), especially in the heat affected zone due to the fact that the yield strength variation at higher temperature has less effect.This suggested that care must be taken to identity correctly the temperature-dependent yield strength of material which is often not easily determined.

CONCLUSIONS:
Analytical and finite element analysis are used to determine the residual stresses resulting from the single pass welding of mild steel pipe of 25.4 mm radius, 1.5 mm thickness.Following the main summarized conclusions raised by this paper: 1-Welding of a pipe induced residual stresses.It has been seen that these stresses changed from compression at the centerline of welding and tension away from the weld centerline at the end of welding to tension at the centerline of weld and compression away from the weld centerline when it cooled.2-The residual stress obtained by using constant thermal and mechanical properties show significant difference from that obtained using temperature dependent thermal and mechanical properties especially in the heat affected zone.

REFERENCES:
 Brown S. and Song H., "Finite element simulation of welding of large structures", Vol.114, November 1992.

Fig. ( 5 )
Shows the temperature time history at a point in the center of welding.Fig. (6) Shows the temperature time history at a path along the length of the pipe at times during and after welding predicted by FE analysis.Fig. (7) Shows the nodal solution of the temperature distribution along the pipe.It was seen that max.Temperature in a center line of welding equal (1566 ºC) at the moment of end welding then decreased and distributed along the pipe.
Fig. (8) Shows the longitudinal stress time history at a path along the length of the pipe at times during and after welding predicted by FE analysis.The nodal solution of residual stress distribution in Z-direction during and after welding along the top surface predicted by FE analysis is shown in fig.( published results [Wu, 2001; Erika, 2002].The Von Mises residual stress distribution is shown in fig.(10) at time equal 400 sec.Fig. (11) Illustrates the results of residual stress distribution along the pipe due to welding.It is clear that the predicted residual stress by FE analysis is very close to the analytical analysis at the center of welding.It shows a tension peak of σz=225 MPa at weld line and adjacent parent metal going into compressive at about Z=10 mm from weld centerline and then blending into the background elastic distribution at about Z=30 mm from weld centerline.At position remote from the weld, the stresses didn't go to zero, but tend towards a steady value of about 10 MPa compressions.These results agree well with theoretical studies of residual stresses, at girth welds in pipes [Norman, 1984].Fig. (12) Shows time variation of plastic strain at a centerline of welding.It is clear that the plastic strain increases rapidly during welding and then still constant during cooling.

Fig. 5 Fig. 8
Fig. 5 Temperature time history at a point in the center of welding