Prediction and control of distortion in EB welding

Having studied metallurgy and materials science at Cambridge Bruce Dance graduated in 1986 and joined TWI the following year. As senior research metallurgist now in the Electron Beam group he has worked on a wide range of EB welding and processing related subjects such as surface treatment, demagnetisation and more recently, electron beam weld distortion.

In many industries, electron beam (EB) welding is used for precision assemblies in which the amount of weld distortion is of some importance. For a new component design, an initial assessment of EB weld distortion can be made by practical experimentation, finite element analysis, or by estimation. Following recent research at TWI, Bruce Dance presents different methods for estimating EB weld distortion and compares them with experimental data. For many EB welding applications a good estimate alone is sufficient; in other cases, such an estimate is very useful because it will greatly reduce the amount of subsequent practical experimentation/modelling required.

The ability of electron beam (EB) welding to create very deep, accurate, low distortion welds has led to its adoption for many precision applications. In these applications, EB welding is used typically because it may allow finish machined parts to be joined, or alternatively minimal post weld machining may be adequate.

The amount of distortion that occurs in an EB weld depends on many things, including the joint/component design, the joint fit-up, the material type, and the welding parameters. One method of predicting the distortion is to model it, perhaps using a finite element analysis technique. If all the data are available, and the analysis is carried out correctly, this can give very useful results. However, such analyses are often not appropriate, particularly at the early stages of weld/component development. At this stage, the most appropriate prediction of distortion would be a good estimate, perhaps backed up by limited experimentation. This feature presents some of the techniques that can be used to estimate and control certain types of EB weld distortion. Although, inevitably, there is a mathematical content to this, an attempt is made to cast some light on some of the mechanisms and factors that can strongly influence EB weld distortion without relying exclusively on what might well be unfamiliar mathematics.

The total distortion in an EB welded component arises from a combination of any movement of the two halves of the joint (joint movement) and the intrinsic shrinkage associated with the weld metal (intrinsic distortion). The two are dealt with in separate sections below. Although both are influenced by the welding parameters used, joint movement is prevented or minimised by careful attention to component design, jigging, tacking, and welding procedure. By contrast, the intrinsic distortion is more a function of material type and welding parameters alone. In cases where distortion is to be minimised, it should be the objective of the welding engineer to devise a jigging, tacking, and welding sequence that produces little distortion in excess of the expected intrinsic distortion for that type of weld. Similarly, it should be the objective of the component design engineer to ensure that the weld location/component design are such that the intrinsic distortion may be accommodated without difficulty.

Intrinsic distortion in EB welding

The intrinsic distortion in EB welds is that which arises from the interaction of the welding beam with the material, rather than the details of the joint design and its alignment during welding. It is therefore primarily dependent on the characteristics of the material and the welding parameters, which can be adjusted to give a wide range of different results in a single material, Fig 1. The most significant distortion is usually the transverse weld shrinkage. The bulk of what follows thus concentrates on this issue.

Fig. 1. Various flat position EB weld melt runs in 2 x 6mm thickness 12% Cr steel. Although these welds cover a huge range of heat inputs, it is conceivable that any of them might be applied in practice

A basic understanding of intrinsic EB weld distortion

A good conceptual idea of the processes involved in transverse EB weld distortion may be obtained thus (Fig 2.): Imagine a melt run in virgin material. Simplistically, any heat running ahead of the weld will cause an attempted expansion of the heated material (h-zone), which is restrained by the surrounding cold material (c-zone), (2i). At the beam position, we now have a region of zero strength, comprising molten material (m-zone) and the 'keyhole' itself (k-zone). At this stage, (2ii), compression in the h-zone (which is still expanding) is relieved to some extent by movement of the two sides of the h-zone inwards, towards the weld position. It should be noted that the keyhole periphery is at boiling point of the material. This means that the average temperature in the m-zone is well above the melting point, ie there is some degree of superheat. Behind the beam itself, this superheat may actually back melt parts of the h-zone, expanding the m-zone further. As the weld solidifies, the h-zone continues to expand, pushing into and squeezing the m-zone as it does so, (2iii). Finally, the entire solidification process is complete, and the heat continues to flow away from the weld itself. In this case, only after the whole piece has cooled will a significant transverse shrinkage occur, provided the piece is not too small.

Fig. 2. Schematic transverse sections of an EB weld pool.

i) Ahead of the weld mainly c-zone (cold material), some well restrained h-zone (hot material).

ii) At and behind (iii and iv) the EB position, m-zone and k-zone (melt + keyhole) offer no restraint to the continued expansion of the h-zone.

Now, the absolute minimum heat input to make a weld might in principle be just sufficient to melt the material in the fusion zone alone. But in practice there are other factors; first, some heat always flows ahead and to each side of the weld, and second, the weld pool is full of superheated material. Each of these two factors is strongly influenced by the welding parameters and the material's properties. They also have a strong influence on the weld distortion. For example, if there were two materials with different boiling points, but otherwise similar properties, the material with the higher boiling point would be more likely to suffer more distortion because of the effect depicted in (2iii). Alternatively, if the h-zone is very large in relation to the m-zone, something rather odd will happen.

This is best thought of in terms of the following simple model. Imagine a large circular metal plate, with a small central hole. If the region immediately around the hole is heated, the diameter of the hole may actually decrease, due to the restraint of the surrounding material. If, however, the entire metal plate (or at least a good portion of it) is heated, the hole will not shrink in size but will expand with the rest of the material. Even if the circular plate is very large, and only part of it is heated, the hole may still expand, provided it is small in relation to the size of the heated zone. If we imagine this hole to be instead the weld pool and its associated keyhole, in a travelling, rather than stationary temperature field, the relevance of this simple model will be seen. Oddly, it seems to imply that in some instances a high heat input may actually result in lower than expected transverse shrinkage distortion, provided the weld itself is still small.

A good grasp of longitudinal and through-thickness distortion characteristics is also possible. If the weld is low heat input, a narrow, planar region extending beyond the fusion zone and the heat affected zone will all have become hot, and will have yielded due to the restraint offered by the surrounding colder material. Following this, it will then have cooled, still under conditions of high restraint. This results in tensile stresses up to yield magnitude in this region. For the purpose of estimating the likely distortion in the component, it is convenient to think of each weld pass shrinking, individually, which would, for example, indicate the 'tourniquet' effect seen in circumferential butt seams. A similar approach has been used for calculation as well as modelling of weld residual stress distributions.

Examples of each of the characteristics intrinsic to EB weld distortions can be seen in Fig 3, which gives the dimensions of a simple 109mm C-Mn steel cube after a melt run has been made in it.

Fig. 3. An example of intrinsic EB weld distortion. Normal shrinkages (in µm) of a 109mm C-Mn steel cube subjected to a central fully penetrating EB melt run ~5mm in width. The central 100µm shrinkage zone is evident for only ~1mm either side of the weld. NB: in longer seams, δ is more uniform. However, in steel the low value of δ near the start (due to an undeveloped h-zone) and high value of δ near the end of the joint (due to an extended h-zone) are typical.

Heat flow in EB welding

Some understanding of the nature of the heat flow is essential to a further understanding of the nature of EB weld distortion. The symbols used are given in the glossary.

	Glossary
T m	melting point (C)
T b	boiling point (C)
α	thermal expansion coefficient (C -1)
c	thermal conductivity (Wm -1K -1)
ρ	density (kg m -3)
C p	heat capacity (J kg -1K -1)
ν	Poisson's ratio
D T	thermal diffusivity (m 2s -1)
b w	weld width (m)
y	distance from weld centreline (m)
δ	transverse weld shrinkage (m)
t	plate thickness (and/or weld penetration) (m)
V	welding speed (m s -1)
η	welding process thermal efficiency
q	welding power (W)
F	longitudinal (Tendon) force (N)
β	angular distortion (degrees)
A b	average transverse area of protuberant weld bead (m 2)
A w	weld cross sectional area (m 2)

Reasonable predictions of heat flow in EB welding can be made by assuming an entirely 2-D characteristic, modelling the heat source as a line through the plate thickness after Rosenthal. The upshot of such models is, in the extreme, two types of heat flow, which are described below. The first, (Type A) occurs in situations of low thermal diffusivity/high welding speed, and results in little or no heat flow ahead of the weld. The second, (Type B) occurs in situations of high thermal diffusivity/low welding speed, and can result in considerable heat flow ahead of the weld.

By mathematical analysis of 2-D heat flow, Myers, Uyehara and Borman found that, over a wide range of conditions, the 'dimensionless temperature maximum',

at some point a 'dimensionless distance'

Vb _w(4D _T) ^-1=1 for a range of materials is given in Fig 4. Coincidentally, the range of practical EB welding conditions is usually similarly distributed, eg most of the viable EB welding conditions for stainless steels lie roughly along its Vb _w(4D _T) ^-1=1 line. This means that in a given material, the essential nature of the heat flow around an EB weld in a workpiece of reasonable size may not really vary greatly with weld width, plate thickness and welding speed. This implies that, for EB welds, it may be possible to obtain useful information knowing only the width of a single isotherm (eg T _m, b _w) and the material properties.

Fig. 4. Heat flow type, for different materials (plotting Vb _w (4DT) ^-1=1. For each material, Type A heat flow exists above the line. Since, in any given material, practical EB welding conditions lie along, rather than across these lines, the heat flow type is roughly constant, eg Type A in stainless steel, Type B in Cu and its alloys. Further D _T (x10 ^-6m ²s ^-1) values for some pure metals and alloys are as follows. Ag~172; Au~128; Cu~116; Al~97; Mg~88; Al alloys~50-90 (typ); W~67; Be~59.5; Mo~54; Ir, Rh~49; Sr~46; Li, Zn, Th, Sn~40-45; Fe, Ni, Ta, Cr, Pt, Pd~20-25; Re, Pb~15-20; Zr, Hf, U~12; Ti, V, Pr, Sc, Sm, La~10; steels, Ni alloys~2-10 ~(typ); Ti alloys 1~10 (typ).

Transverse Shrinkage

Leggatt has previously shown that for arc welds the transverse shrinkage may be predicted from the heat input alone, eg for an upper bound

When compared with experimental data eg Table 1 , it gives good results as an equality for EB welds in some materials. However, it gives high δ values in materials in which Type B heat flow is likely to occur. This is presumably because, in its derivation, a 1-D ( ie Type A) heat flow is assumed. However, this result implies that some of the heat input in type B heat flow EB welds is not related to transverse shrinkage, and it may be possible to provide an improved estimate by replacing the equations' ηq term with an expression related to the type of heat flow. Since the problem is very complex, it was decided to attempt to develop a semi-empirical formula. In terms of distortion, three elements of the heat input per unit length, (ηqV^-1) are significant, and might be expressed approximately as follows:

1) The heat required to melt the weld metal A_wρC_pT_m ,
2) The conductive losses K_cD_TA_w , where k c is a constant,
3) The melt zone superheat k_SρC_p(T_b - T_m)A_w , where k s is a constant. So, we can now write:
ηqV^-1=A_w(ρC_pT_m+k_cD_T+k_Sρ(T_bT_m)) for the heat input significant to EB weld distortion. Substituting into Leggatt's expression and re-arranging yields:
δb_w ^-1=α(1+ν)[T_m+k_ccT_m(ρC_p)^-2+k_s(T_b-T_m)].
By trial and error, a good fit with available experimental data is obtained with k c=-1x10 11, k s=2.5. A comparison of methods for obtaining/estimating δ and/or δ(b_w )^-1 is made in Table 2 .

Table 1 Experimentally obtained values of

Material	Pure Ti	Pure Fe	Pure Cu	Pure Ta	Pure Mo	316 s/s	'Manganin' 86 Cu,12 Mn, 2Ni
	0.065	0.075	0.02	0.06	0.02	0.12	0.09
Material	6082 Al alloy	Al,17Si alloy	Inconel 718	Cu, 30Ni	Ti, 6Al, 4V*	C C-Mn steel*
	0.04	0.02	0.075	0.11	0.05-0.065	0.045-0.08
* - δ in some materials varies with transformation characteristics and heat input, eg in steels, low heat input/high hardenability gives a martensitic/bainitic microstructure and lower distortion

Table 2 Comparison of methods for obtaining values of

Method		Comments	Drawbacks
1.		Direct measurement of melt run in coupon of known size.	May underestimate slightly if coupon small and D T large.
2.		Measurement of bead dimensions of melt run in coupon of unknown size.	As above; also underestimates if vapour/spatter generated. Overestimates if melt run contains porosity.
3.		Based on heat input, for Type A heat flow; also heat input not always known eg full penetration EB welds.	Overestimates for EB welds with Type B heat flow
4.		Simplest predictive formula, useful for quick 'Ball-park' estimates.	Overestimates for Type B heat flow. Can underestimate if D T is very low.
5.		Good estimate provided boiling behaviour during EBW is predictable and well controlled ( eg not Ag or Mg alloys).	Semi-empirical formula.

Intrinsic (free) angular distortion

Free angular distortion β_f is, in EB welds, very closely related to the fusion zone profile and intrinsic transverse shrinkage alone, since joints are usually made in a single pass. In practice, the observed angular distortion has plenty to do with the restraint too, but it is useful to be able to make an initial estimate of the free angular distortion. We have found that a good approximation to β_f is given by:
β_f = tan ^-1[δ(b_wt - b_wb) (tb_w)^-1] for a penetrating weld, where b wt and b wb are weld widths (making allowance for any obvious 'nail head' etc) at the top and bottom of the weld.

Longitudinal shrinkage

Shrinkage along the weld length does not usually significantly affect EB welded parts. There are two main exceptions to this; circular seams, and long seams in thin section material. The only readily visible longitudinal shrinkage in many welds is restricted to areas immediately adjacent to the weld, since the restraint is very high in most of these cases ( eg Fig 3 .). Remote from the ends of the joint, the 'Tendon' force 'F' is approximately proportional to: σ_yb_wt, where σ_y is the weld metal yield strength.

Since the width of the tensile zone is wider (typically by ~x4-x6) than the weld itself, F can be considerable, causing significant elastic contractions in flat panels. In circular joints, F can appear to result in angular distortion, even if the weld cross-section is not heavily asymmetric. In longer welds in flat material of thin cross-section, the tendon force F can cause a type of 'Euler buckling' to occur. Prediction of this is difficult, but a simplistic analysis indicates that, under otherwise similar circumstances, if the quantity σ_yb_wL²(Π²Ebt²)^-1 is increased then buckling of this type is more likely for a simple narrow panel of length L, width b and Young's modulus E. Weld asymmetry b_wt≠b_wb also increases buckling tendency. Distortion of this type is controlled using jigging, so that massive full-length clamps close to the weld are often used in EB and laser welding of thin sheet.

Through-thickness shrinkage

Restraint in this orientation is inevitably very high for all EB welds. Barely measurable shrinkage only exists immediately adjacent to the weld site ( eg Fig 3 ). The dimensional change caused by through-thickness shrinkage is rarely of any practical significance whatsoever.

Factors influencing joint movement

Tacking

Joint movement can be the main distortion source in EB welds. Careful attention to jigging and tacking will reduce it to acceptable levels with many joint designs. Although tack welding is a convenient means of preventing joint movement, if excessive, it can cause distortions that persist in the final component, since tack welds are usually partially penetrating, and therefore induce angular distortion in joints that are not well restrained in this respect. Tacking induced angular distortion can be made to work in favour of a reduction in overall angular distortion if tacking is applied to the rear of a simple butt joint, for example, prior to a main weld pass which causes a small amount of angular distortion in the reverse direction. If all tacking is done from the front, then a good solution can be to clamp the joint well to the rear, and then perform only tack welds that cause a small amount of angular distortion.

When welded, unintentional joint gaps can cause unpredictable distortion, since the usual weld heat flow and shrinkage is disrupted. We have observed that the maximum allowable joint gap is approximately equal to the expected transverse shrinkage δ, but control of both overall dimensions and fusion zone shape is difficult before this point is reached. Uneven transverse weld loading/restraint can cause the joint gap to change during welding. This most usually occurs in materials where the thermal expansion coefficient α varies significantly with temperature, since this will generate thermal loadings which will cause the joint gap to open at some point ahead of the weld. This can affect the required spacing of tack welds along the joint. As a general rule, tack welds should be spaced no more than 100-200mm apart in thick (>50mm) sections, and closer in thinner section/inherently flexible parts.

Tacking - variation in strategy with materials properties

Although this is a complex subject in which component geometry is important, devising an acceptable strategy is usually possible. A few general points are made in Table 3.

Table 3 Variation in tacking strategy with situation

Controlling joint movement in circular joints

Circular joints are unusual, in that they generally have a weld overlap and fade out (slope down) region. This involves welding some of the joint twice, and unsurprisingly we have observed increased distortion in this area. There are two basic joint geometries; planetary ( eg a ring weld in a plate) and circumferential butt.

Planetary welds

This is a typical precision application geometry ( eg gear welding) and there has been considerable work in this area. Least distortion is usually obtained by welding un-tacked interference/shrink fitted parts. To a first approximation, an elastically accommodated shrink fit should be equal to δ over the full diameter. By making a narrow weld, δ can be minimised. A shrink fit of this type may be useful anyway, since this weld geometry is capable of applying significant transverse restraint, particularly if the weld diameter is small and/or the parts (particularly the inner one) are solid/stiff in nature. The resultant increased likelihood of centreline solidification cracking thus can be offset in some materials by the use of a suitable shrink fit. If no shrink fit is used , then tacking is important, since the transverse weld shrinkage may otherwise cause a lack of concentricity during the second half of the main weld, particularly in larger diameter components. This can be controlled by using an incremental, or balanced tacking sequence. In most cases the main weld is completed by an overlap/fade out, in which transverse restraint is inevitably high, increasing the risk of weld cracking. Distortion is minimised by reducing the size of overlap/fade out. Alternatively, some component designs provide for the weld to start and stop in a hole, thus virtually eliminating this source of distortion.

Circumferential butt welds

The main distortion in these joints is an axial shrinkage, caused by transverse shrinkage of the weld, which is usually unrestrained. The weld tendon force (caused by longitudinal shrinkage) causes necking of the diameter, even if the weld is perfectly parallel sided. For a true tube to tube butt weld, formulae exist for estimating such necking in arc welds, although caution is advised when using them to estimate EB weld angular distortion. It should be noted that the extra restraint in a tube to flange weld can reduce such distortion significantly. The axial (transverse) shrinkage in a circumferential butt weld is usually uniform. However, the overlap/fade out region increases shrinkage locally, causing axial run out. As in planetary welds, this can be reduced by starting and stopping the weld in a hole, or by making the region as small as possible. Axial run out may also be minimised (at the expense of increased overall axial shrinkage) by using a double weld; the main weld overlaps most of the joint twice, so the position corresponding to the start of the original fade in is just overlapped the second time by the tail end of the fade out.

Summarising remarks

It is evident that, in many cases, distortion is most easily minimised by careful attention to design, jigging, tacking, and welding details. However, when these have been optimised, the intrinsic distortion remains. Easily the most significant intrinsic distortion is transverse shrinkage. It is tempting to minimise this by keeping the weld width down, and this is certainly worthwhile, provided weld quality is not compromised.

Several approaches exist to predicting transverse shrinkage, and providing a suitable method is chosen an accurate estimate is usually possible. Each of the equations in Table 2 has its place for estimating EB weld transverse shrinkage. To date, newly developed semi-empirical equation 5 has, in many cases, provided a good estimate of the distortion found in EB welds in previously unknown materials.