As the weldment is locally heated, the weldmetal and HAZ adjacent to it are at a temperature substantially above that of the unaffected base metal. As the molten pool solidifies and shrinks it causes shrinkage stresses on the surrounding weld metal and HAZ area. In the beginning, the contraction the weld metal applies is small, the metal is hot and weak. As it solidifies, the weld metal applies increasing stresses on the weld area, the base metal may yield.

The sequence of thermal events in welding is far from simple and is not easily amenable to mathematical analysis. It is possible to describe qualitatively the contraction of a weld and to ascribe to the different stages empirical data established by observations made over a period of many years.

5.4.1 Thermal Expansion and Contraction

To understand residual stresses and distortion let us consider the shrinkage that occurs dur­ing welding when the source of heat has already passed. This is made up of three components or stages

(a) Liquid contraction (liquid to liquid)

(b) Solidification shrinkage (liquid to solid)

(c) Solid metal contraction (solid to solid)

From Fig. 5.12 we can see that as the solification front proceeds to the weld centre line, the solid metal occupies a smaller space than the liquid metal it replaces (i. e., its density increases). The molten metal also contracts.

• The surface of weld pool should recede below the original level (formation of weld crater at the end of the weld bead, when the heat source is suddenly removed). However, at the same time further molten metal from the leading edge of the weldpool is fed into the area, the actual shrinkage is thus not shown up.

5.4.2 Contraction of Solid Metal

Contraction of weld metal is volumetric. It could be estimated along the length and across it. Longitudinal contraction is given by

l1 = l0 (1 - a A 0) = l0 - l0 a A 0 where l0 = original length, a = coefficient of linear expansion = 14.3 x 10-6/oC l1 = length after cooling through temperature change A0

For 1 meter length of weld, the shrinkage along length

l0 a A 0 = 1000 mm x 14.3 x 10-6/oC x (1500 - 20)oC = 1000 x 14.3 x 10-6 x 1480 mm = 21.2 mm/meter length

The value 21 .2 is based on a which does not remain constant over the range of tempera­ture, but it indicates that the contraction is appreciable.

In practice, the measured contraction is significantly less.

• The practical observation shows 1 mm/m. This is because of the restraint provided by the adjoining cold plates.

• When the weld metal tries to contract, its contraction is restrained, so it is plastically deformed.

• Tensile forces ultimately set-up in the weld region and corresponding compressive forces are set in the plate by reaction (Fig. 5.13).

• If the cold plates are perfectly rigid, the welded joint will be of the same length as the original plates. The compressive stresses are of considerable magnitude exceeding the yield stress of the parent plate. The result is that the plates get deformed so reducing the overall length of the joint and thus resulting in 1 mm/meter contraction shrinkage quoted above. A compressive force of about 150-170 N/mm2 is required to achieve a compressive strain of about 1 mm/meter.


Fig. 5.12 Shrinkage during solidification


Weld is stretched by plates. Tensile stresses in weld. Compressive stresses in plate on either side of weld.



Fig. 5.13 Deformation of a weld metal element during cooling.

Fig. 5.14 Estimation of transverse shrinkage in T butt joint


■ Average^ width

Single-V Double-V

Fig. 5.15 Transverse shrinkage in ‘V’ butt welds.

5.4.3 Transvers Shrinkage

Similar conditions apply when look at shrinkage to the weld, where the contracting weld metal tries to pull the plates towards the centre-line of the joint and as a result the whole joint area is in transverse tension. Again we have a situation where, because the hot weld metal has a lower yield stress than the cold plates, deformation first takes place in the weld but, at a later stage of cooling, as the relative yield stresses become more equal, some yielding of the parent material occurs and the overall width of the welded plates is reduced.

Strictly, the amount of transverse shrinkage which takes place depends on the total volume of weld metal, but’ as a general rule, for a given plate thickness, the overall reduction in width transverse to the joint at any point is related directly to the cross-sectional area of the weld. Similarly, as we would expect, the total shrinkage increases with the thickness of the plate, since the weld area is greater. It is possible to state this relationship in a general way:


transverse shrinkage = k —

where k = an empirical factor with a value between 0.1 and 1.17

A = cross-sectional area of weld t = thickness of plate

This formula can be used to predict the shrinkage that will occur in a butt joint (Fig. 5.14) and has been found to give good correlation with practical observations. In the case of a single-V butt joint the calculation can be simplified, since the ratio A/t is equal to the average width and the formula is reduced to

Transverse shrinkage = k x average width of weld

It should be noted that for a double-V weld the average width is not zero but is the value for one of the V s.

Estimation of Transverse shrinkage in a ‘T butt joint (Fig. 5.14)

Transverse shrinkage = 0.1 x —

A = a + b + c

= 1 x 5 x (12 + 3) + (3 x12) + 1/2 x 12 x 12) 2

= 145.5 mm2

Transverse shrinkage = 0.1 x 145.5/12 = 1.21 mm.

Estimation of Transverse shrinkage in ‘V’ butt welds, (Fig. 5.15).


a = — x w x t 2


= 0.1 x


Area of weld, Transverse shrinking


0.1 x

— x w X t 2


= 0.1 x w/2

= 0.1 x average width.

5.4.4 Angular Distortion and Longitudinal Bowing

(b) Asymmetrical shrinkage tends to produce distortion.

Taking both longitudinal and transverse shrinkage, based on what has been said above the final shape of two plates welded together with a butt joint should be as shown in Fig. 5.6 (a). In practice, however, such a simple treatment does not apply, principally because the shrinkage is not distributed uniformly about the neutral axis of the plate and the weld cools progres­sively, not all at one time.



(a) Changes in shape resulting from

shrinkage which is uniform throughout the thickness

Fig. 5.16 Change in shape and dimensions in butt-welded plate.

If we look at a butt made with a 60° included-angle preparation, it is immediately apparent that the weld width at the top of the joint is appreciably greater than at the root.

Since the shrinkage is proportional to the length of metal cooling, there is a greater contraction at the top of the weld. If the plates are free to move, as they mostly are in fabricating operations, they will rotate with respect to each other. This movement is known as angular distortion (Fig. 5.16 b) and poses problems for the fabricator since the plates and joint must be flattened if the finished product is to be acceptable. Attempts must be made, therefore, to reduce the amount of angular distortion to a minimum. Clamps can be used to restrain the movement of the plates or sheets making up the joint, but this is frequently not possible and attention has to be turned to devising a suitable weld procedure which aims to balance the amount of shrinkage about the neutral axis. In general, two approaches can be used: weld both sides of the joint or use an edge preparation which gives a more uniform width of weld through the thickness of the plate (Fig. 5.17).

In the direction of welding, asymmetrical shrinkage shows up as longitudinal bowing Fig. 5.18. This is a cumulative effect which builds up as the heating-and-cooling cycle progresses along the joint, and some control can be achieved by welding short lengths on a planned or random distribution basis, Fig. 5.19. Welding both sides of the joint corrects some of the bow­ing, but can occasionally be accompanied by local buckling.

Original preparation


Angular distortion and longitudinal bowing are observed in joints made with fillet welds (Figs. 5.20 and 5.21), Angular distortion is readily seen, in this case as a reduction of the angle

Original preparation


Fig. 5.17 Edge preparation designed to reduce angular distortion

(a) Double-V joints balance the shrinkage so that more or less equal amounts of contraction

occur on each side of the neutral axis. This gives less angular distortion than a single 'V'.

(b) It is difficult to get a completely flat joint with a symmetrical double 'V' as the first weld run always produces more angular rotation than subsequent runs; hence an asymmetrical prepa­ration is used so that the larger amount of weld metal on the second side pulls back the

distortion which occurred when the first side was welded.

(c) Alternatively, a single-U preparation with nearly parallel sides can be used. This gives an approach to a uniform weld width through the section.


Direction of welding Fig. 5.18 Longitudinal bowing or distortion in a butt joint

Fig. 5.19 Sequences for welding short lengths of joint to reduce longitudinal bowing

Fig. 5.20 Longitudinal bowing in a fillet-welded 'T' joint 1 3 2

. 1st weld


(a) Distortion caused (b) Use of presetting to correct (c) Distortion of

by fillet weld distortion in fillet welded 'T' joint flange

1 = plate centre-line before


2 = plate centre-line after

first weld

3 = plate centre-line after

second weld

between, the plates and is greatest for the first weld. Although the second weld, placed on the other side of the joint, tends to pull the web plate back into line, the amount of angular rota­tion will be smaller. With experience, the joint can be set up with the web plate arranged so that the first angle is greater than 90° and thus ends up with the web and flage at right angles. Even so, warping in the flage plate cannot be ignored.

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