ࡱ> TVSmCzU@|bjbj 2CbFFFFjjj"jjj8^<"ۀGMDP$$RXjaYaCGaYaYFF&^^^aYFj^aY^^`Rzj{ ǻ=j {V0ۀ"{`;]N;0{~d@FFFF{;j{5QRS^/UTV5Q5Q5Q""d^"" SHAPE \* MERGEFORMAT  Strength mismatch effect on yield load in X-shaped weldment with centre crack D. Kozak*, N. Gubeljak**, J. Predan**and F. Mateji ek* University of Osijek, Mechanical Engineering Faculty in Slavonski Brod, Trg Ivane Brli-Ma~urani 18, HR-35000 Slavonski Brod, Croatia* University of Maribor, Faculty of Mechanical Engineering, Smetanova ulica 17, SI-2000 Maribor, Slovenia** e-mail: dkozak@sfsb.hr Abstract This paper provides yield load solutions for the single edged fracture toughness specimen subjected to bending SE (B) with present X-shaped weld joint. The weld centre crack is located in the overmatch weld part. The corresponding fully plastic yield loads were obtained directly by plane strain finite element analysis for five characteristic a/W ratios: 0,1; 0,2; 0,3; 0,4 and 0,5. Also, the influence of the systematically varied weld root width 2H on the fracture behaviour has been evaluated. It was found that yield load decreases with increasing of the weld root, because the undermatched region ahead the crack tip plays the dominant role. Keywords: X-shaped weld, plastic yield load, strength mismatch, constraint effects. Introduction Welded components have wide application in many engineering fields today. However, welded joints present very often potential places for the crack initiation and propagation, what may lead to the catastrophic failure of the structure. Therefore, an integrity assessment of the welded structure with defects should be required using some of usual failure assessment procedures (R6, FAD or SINTAP). Such procedure demands the yield load FY, which has to be determined mainly by finite element method (FEM) or slip line field (SLF) analysis. One of the most used documents for assessing the significance of crack-like defects in joints with mechanical heterogeneity (such as welded joints) is EFAM ETM-MM 96 see Schwalbe et al [1]. It includes a number of yield load solutions for homogeneous materials FY and mismatch yield load solutions FYM for a lot characteristic configurations as well. Moreover, the influence of the weld slenderness and crack length on the yield load solution was analysed recently see Kim and Schwalbe [2]. Also, the stresses and strains distribution in the neighbourhood of the cracked strength mis-matched weld joint in the moment of rupture may assist by complete fracture behaviour assessing see Kolednik [3]. Having in mind that all performed analyses suppose weld as completely homogeneous (either strength overmatched or strength undermatched related to the base metal) and as idealised (a simple strip butt weld configuration), some of yield load solutions are still opened. Inhomogeneity present within the weld is often consequence by application of welding repair technique. Gubeljak et al [4] analysed the influence of the distance from the crack tip to the interface of the mismatched weld materials on the crack driving force, where one halve of the X-shaped weld was performed as overmatch and the second halve as undermatch. Such performance makes sense also by weld joints where possible cold hydrogen assisted cracking can appear. First analysis, which includes the weld heterogeneity effects on the yield load generally, varying simultaneously the width in the root of simple strip butt weld 2H and crack length ratio a/W was made by Konjatic et al, see [5]. In this paper an initial geometry of the SE(B) fracture toughness specimen with present heterogeneous X-weld, proposed by Gubeljak, was intentionally varied using the same materials as in the [4], with the crack tip positioned in the overmatched halve. The goal was to estimate the plastic yield load for such heterogeneous weld configurations, comparing obtained values with those calculated by assumption that all-weld is performed as either whole overmatch or whole undermatch. The influence of the shape of the weld joint on the yield load value was also evaluated. Limit load solutions for the SE(B) fracture toughness specimen with present homogeneous simple butt weld The mismatch yield load solutions for SE(B) fracture toughness specimen made as all-base material or with homogeneous I-shaped weld joint are given in the Ref. [1] for both plane strain and plane stress. They were obtained by limit load finite element analysis, which assume elastic-ideally plastic (non-hardening) materials in the joint. This approach reduces the complexity of the problem, simplifying the material behaviour, but still can provide qualitative information. When assessing the effect of mechanical mis-match on the fracture behaviour of a component, the behaviour of the all base plate component is taken as the reference. The base material properties are kept constant, while the weld metal properties vary. This variation is described by mis-match factor:  EMBED Equation.DSMT4  (1) where sYW and sYB present the yield strength of the weld metal and the yield strength of base metal, respectively. The weld metal is commonly produced with a yield strength greater than that of the base plate; this case is designated as overmatching (OM) with the mis-match factor M > 1. However, an increasing use of high strength steels forces the fabricator to select a consumable with lower strength to comply with the toughness requirements, what is designated as undermatching (UM), where M < 1. The basic equation used in this work for the yield load determination in the case of the SE(B) specimen made all from base metal and cracked in the middle is given by Equation (2). Plane strain reference yield load for all-base metal plate:  EMBED Equation.DSMT4  (2) where  EMBED Equation.3  and S = 4 W. This value is usually used as the reference value to the yield load solution of the mismatched SE(B) specimen with present homogeneous OM or UM weld. This enables comparison of particular solutions FYM to the referent solution FYB. Overmatching (OM):  EMBED Equation.3  (3) where  EMBED Equation.3  Equation (3) is the general solution for the case when the yielding zone spreads through the remainder ligament of the weld metal. Undermatching (UM):  EMBED Equation.3  (4) where  EMBED Equation.3 . Equation (4) presents the solution for the case when the plastic deformation is fully confined to the weaker weld metal, determined from the slip line field analysis. The aim of this work was to found the yield load solutions for the combined weld joint, half welded by overmatch and half by undermatch consumable. The yield strength of the base metal was 545 MPa and mis-match ratio-M were M=1,19 and M=0,86 in the case of overmatch and undermatch weld metals, respectively. Finite element modelling of the SE(B) fracture toughness specimen with heterogeneous X-weld In order to evaluate the mismatch yield load variation by SE(B) fracture specimen (Figure 1) with different geometries, it is necessary first to consider which influencing geometrical parameters should be varied and in which range. In this work the influence of the weld root 2H and crack length ratio a/W on the plastic mismatch yield load value FYM has been in focus of the investigation. They are systematically varied as follows: H=W/4, W/6, W/8, W/10, W/16 and as a/W=0,1; 0,2; 0,3; 0,4 and 0,5. This means different geometrical in-plane constraints within the specimen. Also, technological possibilities to perform the welded joints with such widths in the root were also getting into account. The results for the mismatch yield load were normalised by all-base metal yield load for 25 analysed combinations in total. The groove angle of X-shaped butt welded joint was idealised as 10. The crack was located in the centre of the specimen, completely in the strength overmatch metal advancing to the undermatched region. Heat affected zone is not modelled as particular material. The height of the overmatched weld part is approximately the same as the height of the undermatched weld part.  EMBED Word.Picture.8  Figure 1: SE(B) fracture toughness specimen with X-weld For mismatched specimens, plastic deformation pattern is very complex, due to influence of not only (W-a)/H parameter, but also on value of mis-match factor M. Typical finite element mesh employed in the present investigation is depicted in the Figure 2 (a/W=0,3 and W=6H), by using commercial FEM programme ANSYS. Due to symmetry, only one half of the specimen was modelled. The weld centre crack was located in the overmatched part of the weld, although in the case of a/W=0,5 where the crack tip was positioned at the interface between OM and UM part. All materials were considered as isotropic bilinear elastic-plastic, with the same hardening after yielding point amounts E =500 MPa. The number of elements and nodes is equal to about 1200 and 3700, where the first fan of elements was sized by about 100 mm. Stress concentration was assigned to the crack tip location with the first row of singular elements generated automatically around the crack tip. The mesh density was very fine in the regions where material changes and where the steep stress gradients may be expected. The loading was given as the pressure distributed on the very narrow area, what corresponds to the contact area between the specimen and the rollers. The magnitude of applied pressure should be large enough to bring the specimen to its fully yielding state through the net section. The equilibrium stress and strain fields are computed after each increment of pressure. An increment of the loading near the yield load value has to be very fine to be able to estimate the yield load value as precisely as possible.  EMBED Word.Picture.8  Figure 2: One half of the finite element meshed SE(B) specimen with inhomogeneous X-weld Plane strain yield load solutions for the SE(B) specimen with present heterogeneity in the X-weld In practice, inhomogeneous multipass weld joint with half OM- and half UM weld metal is usually used for repair welding of weld joints. Undermatched weld part satisfied high toughness requirements, while overmatched weld halves has the crack shielding effect. It is the question how accurately may be used the yield load solutions, given earlier for the case of homogeneous weld, if the weld is heterogeneous? Also, these yield load solutions are derived for the simple butt weld joint (I-shaped weld), so it is necessary to estimate the influence of the weld shape on the yield load magnitude. The conservative approach means to calculate the yield load solution assuming the weld made wholly from UM. This approach is near reality for the specimen with a/W=0,5, where the region in the front of the crack is undermatched, but considering the shallow crack, it can underestimate the yield load value. Such approach becomes more incorrect with the weld root width 2H decreasing, what is obviously from the Figure 3. Namely, as the weld is narrower, its influence on the complete fracture behaviour decreases. Therefore, the yield load values converge to those obtained for all-base metal, especially for low values of crack depths.  EMBED Excel.Chart.8 \s  Figure 3: Plane strain mismatched yield load solutions for the SE(B) specimen with heterogeneous X-weld It is evident from the Figure 3. that the crack resistance is the lowest for the crack length ratio a/W=0,5 regardless the weld root half width H actually. Increasing of the weld width by constant crack length causes the lower yield loads, generally. It is worthy note that yield load drops after some amount of crack advancing (mainly after about a/W=0,3). The influence of undermatch region by components with shallow crack is less, what may be of some help, shielding such components of unplanned failure. The value of the weld slenderness (W-a)/H is calculated for the different values of a/W and H. Its magnitude drops with a/W increasing, by H=const. It also drops with H value increasing, by a/W=const. In this investigation the slenderness ranges from 2 (a/W=0,5 and H=W/4) to 14,4 (a/W=0,1 and H=W/16). Fig. 4 shows an example of effects of (W-a)/H on the weld mis-match yield load solutions FYM, for different crack lengths.  EMBED Excel.Chart.8 \s  Figure 4: Plastic yield load solutions for the SE(B) specimen depending on the weld slenderness The curve has very low slope for the configurations with shallow cracks and it seems almost horizontal. It depends very few on the slenderness value. The load carrying capacity of the component with short crack, which is positioned deeply in the OM part of the heterogeneous weld, is dominantly dictated by OM region ahead the crack tip. On the other hand, the fracture behaviour of deeply cracked specimens is strongly affected by slenderness value (W-a)/H. It is also interesting to compare these yield load solutions for the SE(B) specimen with heterogeneous X-weld to the specimen with heterogeneous I-weld, given in Ref. [5]. This comparison is given on the Figure 5 for the characteristic values of weld root width: W=4H, 8H and 16H.  EMBED Excel.Chart.8 \s  Figure 5: The comparison of plane strain mismatched yield load solutions for the SE(B) specimen with heterogeneous X-weld or I-weld, but with the same width 2H in the weld root One can remark that the shape of the curves for the same weld root width is similar, but with difference in limit load value up to 10%. In the case when the crack is located in the OM part of the heterogeneous weld, it can be expected that X-welded joints will be more inferior related to the I-weld. The reason is predominant role of the material properties in the direction where the yielding zones spread by load increasing. In our case, it is about material with lower material properties  UM. Finally, the Mises equivalent stress seq distribution through the ligament has been analysed. The material in the joint yields in the region, where the seq stress is greater than the yield strength of the particular material. It is evident from the Figure 6 that the higher stresses are located in the OM weld part. The shape of the yielding zones is for different weld root widths relatively similar .   Figure 6: Yielding zones spread through the different materials of heterogeneous X-weld joint with different weld root half width W, by a/W=0,3 Concluding remarks This paper compiles the yield load solutions for the SE(B) fracture toughness specimen with the crack in the centre of heterogeneous X-weld, obtained by plane strain finite element analysis. The inhomogeneity in the weld was intentional due to the practical application of the weld performed as one half overmatched and one half undermatched by repair welding. The aim was to compare the crack resistance of such performed configuration with the similar evaluated in the Refs. [1, 5]. Most influenced geometrical parameters on the yielding constraint as a/W and (W-a)/H were varied systematically in practical range of values. It is found by heterogeneous X-weld with the crack tip located in overmatched weld halve that yield load FYM decreases with increasing of the weld width H, generally. Also, the crack resistance is the lowest for the crack length ratio a/W=0,5, almost regardless the weld root half width H. The load carrying capacity of the component with short crack, which is positioned deeply in the OM part of the heterogeneous weld, is dominantly dictated by OM region ahead the crack tip. On the other hand, the fracture behaviour of deeply cracked specimens is strongly affected by slenderness value (W-a)/H. In the case when the crack is located in the OM part of the heterogeneous weld, X-weld joint will be more inferior related to the I-weld. The reason is predominant role of the material properties in the direction where the yielding zones spread by load increasing. Therefore, the configuration with the crack tip located in the UM weld part will probably show better resistance to the fracture, because the material crucial in the front of an advancing crack is OM. 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References K.-H. Schwalbe, Y.-J. Kim, S. Hao, A. Cornec, M. Koak (1997) EFAM ETM-MM 96: The ETM method for assessing the significance of crack-like defects in joints with mechanical heterogeneity (strength mis-match), GKSS Research Center, GKSS/97/E9, Germany Y.-J. Kim, K.-H. Schwalbe (2001) Mismatch effect on plastic yield loads in idealised weldments I. Weld centre cracks, Engineering Fracture Mechanics, 68, 163-182 O. Kolednik (2000) The yield stress gradient effect in inhomogeneous materials, International Journal of Solids and Structures 37, 781-808 N. Gubeljak, O. Kolednik, J. Predan and M. Oblak (2003) Effect of Strength of Mismatch Interface on Crack Driving Force, Key Engineering Materials Vols. 251-252, 235-244 P. Konjatic, D. Kozak, N. Gubeljak, J. Predan, F. Matejicek (2005) Yield load solution for the SE(B) fracture toughness specimen with heterogeneous weld joint, accepted for 3rd M.I.T. 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