Review and Model Development
Since the 1950s, more than one hundred separate and distinct weldability tests aiming at assessing the solidification and liquation cracking susceptibility have been devised and completely new or modified tests are under continued development. However, the design and fabrication of solidification crack-free structures has not been completely successful despite tremendous effort. A critical problem remains the lack of adequate techniques to quantify the stress/strain variations during the solidification process. There are concerns in appropriately quantifying laboratory weldability testing results. This can be seen by comparing the results of Arata et al [16 and 18] in which the materials were tested under similar welding conditions. It was found that the ductilities in the BTR measured by the MISO technique were often an order of magnitude higher than those measured by the augmented strain of the Trans-Varestraint test, whereas the BTR itself generally showed little change. In fact, the minimum ductilities obtained by the MISO technique were often quite measurable for alloys that are generally regarded as being highly susceptible to weld solidification cracking, .
More importantly, it is extremely difficult to reliably apply laboratory weldability testing results to the actual fabrication problems, since the mechanical driving force under the actual fabrication conditions has rarely been quantitatively determined.
Studies of hot cracking require more accurate models. It is important to have a correct description of the material behavior in order to have an accurate model. The more important mechanical properties are Young’s modulus, thermal dilatation and parameters for the plastic behavior. The influence of these properties at higher temperatures is less pronounced on the residual stress fields. The
material is soft and the thermal strains cause plastic strains even if the structure is only restrained a little as the surrounding, initially cold material acts as a restraint on the heat-affected-zone. If a cut-off temperature is used, the strain and strain rate are expected to be under-estimated and stress over-estimated.
According to the Feng’s et al  study, direct observation of the solidification cracking of Type 316 stainless steel in the Sigmajig test has revealed that the weld centreline cracking was often initiated at a location some distance behind the apparent trailing edge of the weld pool, i. e., at a temperature below the bulk solidus of 316 steel (1645 °K). This study assumes that depending upon the testing conditions, cracking would initiate anywhere between 1600 °K and 1300 °K as long as the stress/strain condition and the microstructure at that particular temperature favoured such an event.
Feng et al  have discussed development of finite element models that included the solidification effect in the weld pool. The
In the Sigmajig test, a specimen is pre-stressed by a pair of steel bolts before welding. The pre-stress is maintained by two stacks of Bellville washers in the load train, which have a displacement/load curve with a slope of 6.167xl0“4 mm/N for each stack of washers, Figure 8-3:
Figure 8-3: Geometry representation of the Sigmajig test and boundary conditions in the mechanical model used by Feng et al .
models are used to calculate the local stress/strain evolution in the solidification temperature range in which weld solidification cracking takes place. The results presented in his study indicate the possibility of using the finite element analysis, when properly formulated, to capture the local stress/strain conditions in the vicinity of a moving weld pool. The models not only show very good agreement with the quantitative measurements of deformation patterns in the vicinity of the weld pool in aluminium alloys, but also correlate very well with the experimental observations of cracking initiation behaviour of a nickel-based super-alloy under various welding and loading conditions during the Sigmajig weldability test. Figure 8-4 shows the welds with cracks in some selected specimens.
14.8 mm/s 172 MPa
4.23 mm/s 68.9 MPa
4.23 mm/s 172 MPa
14.8 mm/ j free specimen
14.8 mm/s bfi.9 MPa
Figure 8-4: Appearance of welds and solidification cracks. Welding direction was from left to right. From top to bottom: 4.23 mm/s free; 4.23 mm/s 68.9 MPa-, 4.23 mm/s 172 MPa', 14.8 mm/s free; 14.8 mm/s 68.9 MPa', 14.8 mm/s 172 MPa, adopted from .
Experiment has revealed that the centreline solidification cracking, if it occurs, would initiate at the starting edge of the specimen. Centreline cracks were observed at the high and low loading conditions, while the medium loading condition did not cause any centreline crack, Figure 8-4.
Intuitively, it is difficult to comprehend why centerline cracking occurs in the stress-free specimen but not in a moderately prestressed specimen based on the threshold pre-stress concept. However, this phenomenon can be readily interpreted in terms of the local stress evolution at the crack initiation site located in the starting edge of the weld. Figure 8-5 plots the transverse stress evolution at the crack initiation site only. Compressive transverse stresses initially develop upon solidification from 1600 °K, then changing to tension before the temperature drops to 1500 °K for all three pre-stress conditions. However, the tensile stress in the 68.9 MPa case is always lower than the other two cases over the entire crack initiation temperature range, .
Figure 8-5: Transverse stress evolution responsible for centerline cracking initiation at the starting edge of the specimen, adopted from .
According to Figure 5-24, the compressive stress region is larger and tends to shift towards the rear of the weld pool for a faster weld. This is the effect observed by Chihoski and suggests the faster weld would be less susceptible to hot cracking because more of the temperature region susceptible to hot cracking is in compression. Data of this type would be also useful to compare with Sigmajig test data.
Dangerously misleading results obtained by conventional Charpy F-notch (CVN) testing of narrow zones in electron beam welds were reported by Goldak and Nguyen [5 and 11]. The fracture appearance of the various weld zones as measured with a binocular microscope and a scanning electron microscopy SEM is showed in Figure 8-6.
Figure 8-6: Charpy impact fracture paths for the notch: a) at the first notch position -30°C or -22°F and 5.4 joules (fusion zone) ; b) at the second notch position -31 °С or -24°F and 4 joules', c) at the third notch position -19°C or -2°F and 68 joules (grain coarsened HAZ)
A careful study of the fracture path revealed the disturbing fact that no tough fractures were ever observed in the weld metal for this weld at any temperature, Figure 8-7. The absorbed energy versus temperature curve for the Charpy F-notch test is often used to characterize the ductile-brittle transition in steels.
TEMPERATURE "F (°С )
Figure 8-7: CVN test results showing fracture traveled in base metal above -40 °С (-40°F) and in the weld metal below -80°C (~112°F)
Figure 8-8: SEM fractograph of cross weld Charpy test specimen (6 kJ/in. or 0.24 kJ/mm, -3 °С or +17.6 °F and 46 ft-lb or 62.4 J) showing cleavage facets indicative of brittle fracture on the weld in the lower half of the photograph; the base metal has failed ductilely.
Figure 8-9: SEM fractograph of cross weld Charpy test specimen (6kJ/in. or 0.24kJ/mm, +21 °С or +70°F and 48 ft-lb or 65.1 J). The fracture in the weld metal on the lower half of the figure is entirely brittle; the base metal has failed ductilely by void coalescence
Figure 8-10: SEM fractograph of cross weld Charpy test specimen (6kJ/in. or 0.24kJ/mm, +50 °С or + 122°F and 50 ft-lb or 67.8 J). The fracture in the weld in the center of the photograph shows both cleavage facets and ductile dimples; the lower third of the photograph shows a ductile fracture in the base metal.
Above the CVN (FATT) all fractures occurred in base metal by a plastic hinge mechanism. Below the CVN FATT all fractures were brittle and traveled in the weld metal. At -3 and 21 °С (27 and 70 °F) the CWCT results shown in Figures 8-8 and 8-9 illustrate a completely brittle fracture in the fusion zone comprised entirely of cleavage facets. At +50 °С or 122 °F, Figure 8-10 shows equal areas of cleavage fracture and ductile dimpling in the fusion zone indicating a “FATT’ for the fusion zone in the CWCT.
Tvergaard and Needleman [21 and 22] have applied a micromechanically based material model in a plane strain analyses of the Charpy F-notch test and have found that the experimentally observed behavior is well reproduced by the computations. The ductile-brittle transition for a weld is investigated by numerical analysis of Charpy impact specimens by Tvergaard and Needleman . In this study, plane strain analyses of the Charpy F-notch test are carried out for different welded joints, to investigate the ductile - brittle transition in different parts of the weld, Figure 8-11. The HAZ is of thickness w2 and the weld material lies between the two HAZ
regions. Attention is focused on two cases. In one case, x2c = 0 giving a weld that is symmetrical about the notch, while in the other case, xc = 6.5 mm, so that one HAZ is located directly in front of the notch.
In relation to the procedures prescribed in European Standards, the planar analyses can directly represent impact test specimens with the notched face parallel to the surface of the test piece, while specimens with the notched face perpendicular to the surface of the test piece would generally require a full three dimensional analysis. The micromechanically based material model is used to represent the elastic-viscoplastic properties and the failure behavior in the base material, the weld material and the HAZ and specimens with a number of different notch locations in and around the weld are analyzed.
A convected coordinate Lagrangian formulation is used with the dynamic principle of virtual work written as, adopted from :
j T^SE^dV = J Tdu^S - jp ^Su^V (8-1)
V S у dt
Eu = ^(uij+ujj+ukjukj)
where tv are the contravariant components of Kirchhoff stress on the deformed convected coordinate net (TJ = Jo", with o" being the contravariant components of the Cauchy or true stress and J the ratio of current to reference volume), v. and u. are the covariant
components of the reference surface normal and displacement vectors, respectively, p is the mass density, V and S are the volume and surface of the body in the reference configuration, and () ,. denotes covariant differentiation in the reference frame. The boundary conditions are:
щ = 0 at x2 = ±A / 2 and x1 = 0 (8-3)
m, = - V(t) for xl = В and - ap < x2 < ap (8-4)
where ap= 2 mm is the distance along the specimen axis over which the striker and the specimen are in contact and:
V(t) = Vxt/tr for t < tr
V(t) = Vx for t>tr (8-5)
The impact loading on the Charpy specimen is modeled using Vx =5mis and tr = 20jus .
The finite element mesh used in the calculations by Tvergaard and Needleman  is shown in Figure 8-12 and curves of force versus imposed displacement for selected cases are shown in Figure 8-13.
(«) (b) (с)
Figure 8-12: Finite element mesh. Each quadrilateral consists of four “crossed” triangles, (a) Region analyzed numerically, the full mesh has 1480 quadrilaterals. The total number of degrees-of - freedom is 6110', (b) and (c) near the notch for two configurations; the material in the heat affected zone (HAZ) is dark gray and the weld material is the light gray region between the two heat affect zones, adopted from .
The force computed in the plane strain calculation is multiplied by the 10mm Charpy specimen thickness to give the value plotted. Two of the curves are terminated when extensive cleavage occurs and the computations become numerically unstable with the time steps used. Complete brittle fracture can be computed using smaller time steps, but this only changes the work to fracture by a relatively small amount, and is computationally intensive. When ductile failure occurs, the curves are terminated at an imposed displacement, U, of 5 mm. In all cases, the work to fracture is then computed as the area under curves such as those in Figure 8-13.
Figure 8-13: Representative curves of force, P, versus imposed displacement, U,
for the comparison material properties. 0(Ш/ is the value of the initial
temperature and b and с refer to the weld configurations in Figure 8-12b and 8- 12c, adopted from .
At t = 0, the specimen is assumed to be stress free (so that any effect of residual stresses is ignored) and to have the uniform initial temperature Qunt.
The effect of weld strength undermatched or overmatched is investigated by Tvergaard and Needleman  for a comparison material and analyses are also carried out based on experimentally determined flow strength variations in a weldment in HY100 steel. The flow strengths of the base and HAZ materials are taken to be (7gase =930MPa and <7^AZ =1674MPa. For a 50% undermatched weld cr0weW = 465 MPa, while for a 50% overmatched weld qweid _i365MPa. The flow strength values used for the HY100 steel are CTbQase = 790MPa, = 890MPa andcr(fz = 1140 MPa.
For the symmetric configuration 8-12b, the transition temperature for the 50% undermatched weld is about -110°C, while it is about +20°C for the 50% overmatched weld. However, in the ductile
regime the work to fracture is higher for the overmatched weld than for the undermatched weld. The transition temperature difference and the difference in ductile work to fracture are both direct outcomes of higher flow strength of the overmatched weld.
For the weld configuration in Figure 8-12c, fracture takes place by cleavage over the entire temperature range. The reason for this brittle behavior is that for this weld geometry, the region of enhanced triaxiality overlaps the HAZ. At the higher temperatures, the work to fracture is greater for the overmatched weld because the higher flow strength leads to greater plastic dissipation.
The best understanding of the weld toughness is obtained from curves as those in Figures 8-14 and 8-17 showing the work to fracture as a function of the location of the notch relative to the welded joint. With the notch placed well outside the weld fracture behavior of the base material is modeled, and in the cases studied by Tvergaard and Needleman, where the notch is small relative to the region of weld material, a centrally placed notch gives a good measure of the weld material fracture behavior. Testing Charpy specimens with notch locations near the HAZ gives a good impression of the embrittlement resulting from this thin layer of hard material. It is noted in Figure 8-14 for the comparison material that the worst location of the notch is not exactly the same in the overmatched and undermatched cases.
Figure 8-14: Work to fracture versus the location of the HAZ relative to the notch as measured by the parameter xc for the comparison material properties at initial
temperature 0/ш7 = 0°С, adopted from .
Figure 8-15: Contours of maximum principal stress O’;. Undermatched
weld, 0/mV = 0°С, comparison material properties, at U=2.62 mm. (a) x2c =3mm,
(b) xc =5mm, adopted from .
Figure 8-16: Work to fracture versus initial temperature for the HY100 material properties for the two weld configurations in Figure 8-12 b and c. For comparison purposes, the curve for a Charpy specimen made of the pure base material is also shown, adopted from .
Figure 8-17: Work to fracture versus the location of the HAZ relative to the notch as measured by the parameter xc for the HY100 material properties at
©/«я = О С and -40°C, adopted from .
Fracture in the Charpy F-notch test for a welded joint has been analyzed by Tvergaard and Needleman based on a material model that accounts for ductile failure by the nucleation and growth of voids to coalescence as well as cleavage failure. Pervious ductile - brittle transition studies for homogenous Charpy F-notch specimens have shown that this material model is well suited to predict the transition temperature as well as the more brittle behavior under impact than in slow bending, which results from the material strain - rate sensitivity.