Effects of weld geometry and sheet thickness on stress intensity factor solutions for spot and spot friction welds in lap-shear specimens of similar and dissimilar materials

In this paper, three-dimensional finite element analyses for spot welds with ideal geometry in lap-shear specimens of different materials and thicknesses were first conducted. The computational results indicate that the stress intensity factor and J integral solutions based on the finite element analyses agree well with the analytical solutions and that the analytical solutions can be used with a reasonable accuracy. Three-dimensional finite element analyses based on the micrographs of an aluminum 6111 resistance spot weld, an aluminum 5754 spot friction weld, and a dissimilar Al/Fe spot friction weld were also conducted. The computational results indicate that the stress intensity factor and J integral solutions based on the finite element analyses for the aluminum 6111 resistance spot weld and aluminum 5754 spot friction weld with complex geometry are in good agreement with the analytical solutions for the equivalent spot welds with ideal geometry. However, the stress intensity factor and J integral solutions based on the finite element analysis for the Al/Fe spot friction weld with complex geometry are completely different from the analytical solutions for the equivalent spot weld with ideal geometry. Different three-dimensional finite element analyses based on the meshes that represent different features of the complex geometry of the Al/Fe spot friction weld were then conducted. The computational results indicate that the stress intensity factor and J integral solutions for the Al/Fe spot friction weld based on the finite element analysis agree reasonably well with the analytical solutions for the equivalent spot weld with consideration of gap and bend. The computational and analytical results suggest that the stress intensity factor and J integral solutions based on the finite element analysis and the analytical solutions with consideration of gap and bend may be used to correlate with the fatigue crack growth patterns of Al/Fe spot friction welds observed in experiments.     

Stress intensity factor solutions for estimation of fatigue lives of laser welds in lap-shear specimens

Fatigue behavior of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel is investigated based on experimental observations and two fatigue life estimation models. Fatigue experiments of laser welded lap-shear specimens are first reviewed. Analytical stress intensity factor solutions for laser welded lap-shear specimens based on the beam bending theory are derived and compared with the analytical solutions for two semi-infinite solids with connection. Finite element analyses of laser welded lap-shear specimens with different weld widths were also conducted to obtain the stress intensity factor solutions. Approximate closed-form stress intensity factor solutions based on the results of the finite element analyses in combination with the analytical solutions based on the beam bending theory and Westergaard stress function for a full range of the normalized weld widths are developed for future engineering applications. Next, finite element analyses for laser welded lap-shear specimens with three weld widths were conducted to obtain the local stress intensity factor solutions for kinked cracks as functions of the kink length. The computational results indicate that the kinked cracks are under dominant mode I loading conditions and the normalized local stress intensity factor solutions can be used in combination with the global stress intensity factor solutions to estimate fatigue lives of laser welds with the weld width as small as the sheet thickness. The global stress intensity factor solutions and the local stress intensity factor solutions for vanishing and finite kinked cracks are then adopted in a fatigue crack growth model to estimate the fatigue lives of the laser welds. Also, a structural stress model based on the beam bending theory is adopted to estimate the fatigue lives of the welds. The fatigue life estimations based on the kinked fatigue crack growth model agree well with the experimental results whereas the fatigue life estimations based on the structural stress model agree with the experimental results under larger load ranges but are higher than the experimental results under smaller load ranges.     

Fracture mechanics solutions to spot welds

Notch stress, stress intensity factors and J-integral at a spot weld are generally expressed by structural stresses around the spot weld. The determination of these parameters are then simplified as determining the structural stresses that can be calculated by a spoke pattern in finite element analysis. Approximate stress formulas for structural stress, notch stress and equivalent stress intensity factor are given for common spot-welded specimens. With the aid of the formulas, test data in terms of the original load can be easily transformed into the data in terms of the structural stress, notch stress or equivalent stress intensity factor at the spot weld. The formulas also facilitate the transfer of test data across different specimens. A measuring method is given for lap joints. The strain gauge technique developed for the tensile-shear specimen shows that all the structural stress, notch stress, stress intensity factors and J-integral at the spot weld can be determined by two strain gauges attached only to the outer surface of one sheet. The results presented here should be helpful for the analysis and testing of spot welds and for developing measuring methods for spot welds.     

Closed-form structural stress and stress intensity factor solutions for spot welds in commonly used specimens

Closed-form new structural stress and stress intensity factor solutions for spot welds in lap-shear, square-cup, U-shape, cross-tension and coach-peel specimens are obtained based on elasticity theories and fracture mechanics. The loading conditions for spot welds in the central parts of the five types of specimens are first examined. The resultant loads on the weld nugget and the self-balanced resultant loads on the lateral surface of the central parts of the specimens are then decomposed into various types of symmetric and anti-symmetric parts. Closed-form structural stress and stress intensity factor solutions for spot welds under various types of loading conditions are then adopted from the recent work of Lin and Pan to derive new closed-form structural stress and stress intensity factor solutions for spot welds in the five types of specimens. The selection of a geometric factor for square-cup specimens and the decompositions of the loads on the central parts of the U-shape, cross-tension and coach-peel specimens are based on the corresponding three-dimensional finite element analyses of these specimens. The new closed-form solutions are expressed as functions of the spot weld diameter, the sheet thickness, the width and the length of the five types of specimens. The closed-form solutions are also expressed as functions of the angular location along the nugget circumference of spot welds in the five types of specimens in contrast to the limited available solutions at the critical locations in the literature. The new closed-form solutions at the critical locations of spot welds in the five types of specimens are listed or can be easily obtained from the general closed-form solutions for fatigue life predictions.     

Failure mode and fatigue behavior of weld-bonded lap-shear specimens of magnesium and steel sheets

Failure modes and fatigue behaviors of ultrasonic spot welds in lap-shear specimens of magnesium AZ31B-H24 and hot-dipped-galvanized mild steel sheets with and without adhesive were investigated. The spot welded specimens failed from the kinked crack growth mode. The adhesive-bonded specimens failed from the cohesive failure through the adhesive and the kinked crack growth through the magnesium sheet. The weld-bonded specimens failed from the cohesive failure through the adhesive, the interfacial failure through the spot weld, and the kinked crack growth through the magnesium sheet. The estimated fatigue lives for the adhesive-bonded and weld-bonded specimens failed from the kinked crack growth mode are lower than the experimental results.     

Fatigue behaviour of dissimilar friction stir spot welds between A6061‐T6 and low carbon steel sheets welded by a scroll grooved tool without probe

A6061 and low carbon steel sheets, whose thicknesses were 2 mm, were welded by a friction stir spot welding (FSSW) technique using a scroll grooved tool without probe (scroll tool). Tensile‐shear fatigue tests were performed using lap‐shear specimens at a stress ratio R = 0.1, and the fatigue behaviour of dissimilar welds was discussed. Tensile‐shear force of the dissimilar welds was higher than that of the A6061 similar ones. Furthermore, the dissimilar welds exhibited nearly the same fatigue strengths as the A6061 similar ones, indicating FSSW by a scroll tool was effective technique for joining aluminium to steel sheet. Fatigue fracture modes of the dissimilar welds were dependent on load levels, where shear fracture through the interface between A6061 and steel occurred at high load levels, while crack grew through A6061 sheet at low load level.     

Fatigue life predictions of spot welds using coarse FE meshes

A new engineering method for fatigue life prediction of spot welds is presented. The method starts with a coarse finite element representation of each spot weld using shell elements and one beam element. Forces and moments at the spot weld are calculated using the finite element method and used in an analytical calculation of the stresses around the spot weld. Mode I and II stress intensity factors are calculated from these stresses. Thereafter, an equivalent stress intensity factor is calculated and the fatigue life prediction is made using one unique K N curve for spot welds. Good agreement is found between a K N curve derived from the Paris law and several experimental results from the literature, although in order to achieve this, a shear correction factor is required. This factor is discussed in relation to results from the literature.     

Geometric functions of stress intensity factor solutions for spot welds in cross-tension specimens

Stress intensity factor solutions for spot welds in cross-tension specimens are investigated by finite element analyses. Three-dimensional finite element models are developed to obtain accurate solutions. Various ratios of sheet thickness, half specimen width and half effective specimen length to nugget radius are considered. The computational results confirm the functional dependence on the nugget radius and sheet thickness of Zhang’s analytical solutions. The results also provide three geometric functions in terms of normalized half specimen width and normalized half effective specimen length to Zhang’s analytical solutions. Based on the analytical and computational results, the dimensions of cross-tension specimens and the corresponding approximate stress intensity factor solutions are suggested.     

Effect of weld orientation on static strength and failure mode of friction stir stitch welds in lap‐shear specimens of aluminium 6022‐T4 sheets

Stitch friction stir spot welding (FSSW) is performed on 6022‐T4 Al alloy using a concave shoulder tool with cylindrical pin. Stitch FSSW is an extension of the conventional spot FSW process where an elongated (oval) spot is produced instead of a circular spot. The main advantage of this process is that it gives appreciably higher strength than conventional spot FSW due to an increase in the joint area. In this research, an experimental and numerical approach is taken to understand the failure mechanism of stitch welds made in lap‐shear configuration. There are four ways (orientations) in which specimens can be welded to produce a lap‐shear specimen – two in transverse direction and two in longitudinal direction. The static strength of welds made with these orientations was found to be different. For stitch welds made in the longitudinal orientation, the failure always occurred near the keyhole at the tool retract position. For welds made in the transverse orientation, failure always occurred in the region of the highest stress. This difference in the weld strength can be attributed to the hook geometry and interface bond strength. The results are explained using a kinked cracked model approach and calculation of stress intensity factor at the hook geometry.     

Stress Intensities at Spot Welds

The stress intensities (notch stress, stress intensity factors and J-integral) at spot welds under typical loads of tensile-shear, cross-tension and coach-peel are derived as a number of simple formulas on the basis of an analytic solution where the stress intensities at spot welds are generally determined by the stresses around the spot welds and of some analytic solutions to circular rigid inclusions in plates with the inclusions simulating the weld nuggets. The derived formulas show consistently the trends in the stress intensities with the design parameters for spot welds such as nugget diameter and sheet thickness and additionally with spacing of force for cross-tension spot welds and load eccentricity for coach-peel spot welds. The stress intensities at spot welds under general loading conditions are estimated in terms of the forces and moments transferred by the spot welds based on the derivations. The theoretical predictions from the formulas are compared favorably with the finite element results. As an application example, some fatigue test data for spot welds in the form of load range versus life to failure are transferred into the form of stress intensities range versus life to failure with the scatterband of the fatigue test data being substantially reduced. This revised version was published online in August 2006 with corrections to the Cover Date.     

Failure mode of laser welds in lap‐shear specimens of high strength low alloy (HSLA) steel sheets

In this paper, the failure mode of laser welds in lap‐shear specimens of non‐galvanized SAE J2340 300Y high strength low alloy steel sheets under quasi‐static loading conditions is examined based on experimental observations and finite element analyses. Laser welded lap‐shear specimens with reduced cross sections were made. Optical micrographs of the cross sections of the welds in the specimens before and after tests are examined to understand the microstructure and failure mode of the welds. Micro‐hardness tests were also conducted to provide an assessment of the mechanical properties in the base metal, heat‐affected and fusion zones. The micrographs indicate that the weld failure appears to be initiated from the base metal near the boundary of the base metal and the heat‐affected zone at a distance away from the pre‐existing crack tip, and the specimens fail due to the necking/shear of the lower left load carrying sheets. Finite element analyses based on non‐homogenous multi‐zone material models were conducted to model the ductile necking/shear failure and to obtain the J integral solutions for the pre‐existing cracks. The results of the finite element analyses are used to explain the ductile failure initiation sites and the necking/shear of the lower left load carrying sheets. The J integral solutions obtained from the finite element analyses based on the 3‐zone finite element model indicate that the J integral for the pre‐existing cracks at the failure loads are low compared to the fracture toughness and the specimens should fail in a plastic collapse or necking/shear mode. The effects of the sheet thickness on the failure mode were then investigated for laser welds with a fixed ratio of the weld width to the thickness. For the given non‐homogenous material model, the J integral solutions appear to be scaled by the sheet thickness. With consideration of the plastic collapse failure mode and fracture initiation failure mode, a critical thickness can be obtained for the transition of the plastic collapse or necking/shear failure mode to the fracture initiation failure mode. Finally, the failure load is expressed as a function of the sheet thickness according to the governing equations based on the two failure modes. The results demonstrate that the failure mode of welds of thin sheets depends on the sheet thickness, ductility of the base metal and fracture toughness of the heat‐affected zone. Therefore, failure criteria based on either the plastic collapse failure mode or the fracture initiation failure mode should be used cautiously for welds of thin sheets.     

The optimization of welding parameters for friction stir spot welding of high density polyethylene sheets

Friction stir spot welding parameters affect the weld strength of thermoplastics, such as high density polyethylene (HDPE) sheets. The strength of a friction stir spot weld is usually determined by a lap-shear test. For maximizing the weld strength, the selection of welding parameters is very important. This paper presents an application of Taguchi method to friction stir spot welding strength of HDPE sheets. An orthogonal array, the signal to noise ratio (S/N), and the analysis of variance (ANOVA) are employed to investigate friction stir welding parameter effects on the weld strength. From the ANOVA and the S/N ratio response graphs, the significant parameters and the optimal combination level of welding parameters were obtained. Experimental results confirmed the effectiveness of the method.     

Stress Intensity Factors for Spot Welds Joining Sheets of Unequal Thickness

Determination of stress intensity factor (SIF) at spot welds is one of the main problems in fatigue assessment of spot-welded structures using fracture mechanics methods. After a brief overview of the issue, we suggest an improvement in determination of SIFs at spot welds between sheets of unequal thickness, by adding the contributions of transverse shear stresses on the spot weld edge. T-stress at the spot weld is also discussed. A simplified finite element model in conjunction with application of the results obtained is illustrated as well.     

Theoretical fatigue–effective notch stresses at spot welds

Notch stress formulae are derived for the application of a notch stress approach to the fatigue assessment of spot welds. A keyhole notch is assumed to describe the edge of the weld spot between the overlapping plates. The stress fields at the keyhole notch under 'singular' and 'non-singular' in-plane loading modes inclusive of the stress concentration factors K _t are derived from the relevant Airy stress functions. The formulae are applied to typical loading cases of spot welds and compared with finite element solutions. Fatigue-effective notch stresses inclusive of fatigue notch factors K _f are calculated by applying the microstructural support hypothesis of Neuber. The notch stresses at the keyhole are also derived for out-of-plane shear loading based on the relevant harmonic stress functions. The multiaxial notch stresses at the weld spot edge are thus completely described.     

Determining Mode-I Cohesive Parameters for Nugget Fracture in Ultrasonic Spot Welds

Ultrasonic spot welds have been used as a model system to investigate how to determine the mode-I cohesive parameters associated with interfacial fracture of a spot weld. Numerical analyses indicated that, while multiple combinations of the two cohesive parameters (characteristic strength, , and toughness, Γ _I) could result in virtually indistinguishable behaviors for individual geometries, only a single pair of parameters can provide a unique set of behaviors for different test geometries. This provides the basis for determining the cohesive parameters by comparing numerical predictions to experimental observations. In particular, a direct uniaxial tensile test was found to be particularly useful for measuring the characteristic strength of an ultrasonic weld. With the characteristic strength known, the toughness of the weld was determined by fitting numerical predictions to experimental observations of the load–displacement curves obtained from T-peel specimens bonded with the ultrasonic weld. These two parameters were then used without modification to predict the performance of welded U-peel specimens. The numerical predictions for this third configuration were in excellent agreement with the experimental results, verifying that it may be possible to use cohesive-zone parameters to predict the behavior of different geometries of spot welds formed under nominally similar conditions.     

Numerical investigation on J-integral testing of heterogeneous fracture toughness testing specimens: Part I – weld metal cracks

Based on extensive two‐dimensional (2D) finite element (FE) analyses, the present work provides the plastic η factor solutions for fracture toughness J‐integral testing of heterogeneous specimens with weldments. Solutions cover practically interesting ranges of strength mismatch and relative weld width, and are given for three typical geometries for toughness testing: a middle cracked tension (M(T)) specimen, single edge cracked bend (SE(B)) specimen and (C(T)) specimen. For mismatched M(T) specimens, both plane strain and plane stress conditions are considered, whereas for SE(B) and C(T) specimens, only the plane strain condition is considered. For all cases, only deep cracks are considered, and an idealized butt weld configuration is considered, where the weld metal strip has a rectangular cross section. Based on the present solutions for the strength mismatch effect on plastic η factors, a window is provided, within which the homogeneous J estimation procedure can be used for weldment toughness testing. The effect of the weld groove configuration on the plastic η factor is briefly discussed, concluding the need for further systematic analysis to provide guidance to practical toughness testing.     

Variable amplitude fatigue of spot welds

A new method for fatigue life prediction of spot welds subjected to variable amplitude loads is proposed. The method is based on the concept of crack closure and is experimentally verified with three different specimens and four different load signals with variable amplitude. Experimental fatigue lives were found to be within a factor of three from the predicted lives. To start with, the stress intensity factor history at the spot weld is calculated with a finite element analysis. Then, crack closure is taken into account: the crack opening stress intensity factor, which is assumed to be constant, is determined from the maximum and minimum in the history. All stress intensities lower than the crack opening level are filtered from the calculated history. The filtered history is then analysed with rain flow count. Finally, fatigue life is predicted with the Palmgren–Miner cumulative damage rule together with an effective (closure‐free) curve for spot welds. In addition, single overload tests were carried out to investigate the assumption of a constant crack opening stress.     

Resistance spot weldability and high cycle fatigue behaviour of martensitic (M190) steel sheet

Resistance spot welding characteristics of martensitic sheet steel (M190) was investigated using a peel test, microhardness test, tensile shear test and fatigue test. Tensile shear test provides better spot weld quality than conventional peel test and hardness is not a good indicator of the susceptibility to interfacial fracture. Unlike DP 600 steel, the maximum load carrying capability is affected by the mode of fracture. At high load low cycle range, weld parameters have a significant difference in the S–N curves. But, almost similar fatigue behaviour of the spot welds is noted at low load high cycle range. However, when applied load was converted to stress intensity factor, the difference in fatigue behaviour between welds and even DP 780 steel diminished. Furthermore, a transition in fracture mode, that is, interfacial and plug and hole type at about 50% of yield load were observed.
[* Note: Correction made on 16 Aug 2010 after first publication online on 28 June 2010. The authors' affiliations were corrected. Under Results and Discussion, in reference to the HAZ hazardness in the ‘Micro hardness profile’ section, Figure 2 was changed to Figure 3. In reference to the welding parameters under ‘Tensile properties’ section, note that Figure 4 represents 7/200 and Figure 5 represents 5/300. In reference to the low cycles behaviour of S‐N curves in the ‘Fatigue’ section, Figure 5 was changed to Figure 6.]     

Effects of weld strength mismatch on <Emphasis Type="Italic">J</Emphasis> and CTOD estimation procedure for SE(B) specimens

This work examines the effect of weld strength mismatch on fracture toughness measurements defined by J and CTOD fracture parameters using single edge notch bend (SE(B)) specimens. A central objective of the present study is to enlarge on previous developments of J and CTOD estimation procedures for welded bend specimens based upon plastic eta factors (η) and plastic rotational factors (r _p ). Very detailed non-linear finite element analyses for plane-strain models of standard SE(B) fracture specimens with a notch located at the center of square groove welds and in the heat affected zone provide the evolution of load with increased crack mouth opening displacement required for the estimation procedure. One key result emerging from the analyses is that levels of weld strength mismatch within the range ±20% mismatch do not affect significantly J and CTOD estimation expressions applicable to homogeneous materials, particularly for deeply cracked fracture specimens with relatively large weld grooves. The present study provides additional understanding on the effect of weld strength mismatch on J and CTOD toughness measurements while, at the same time, adding a fairly extensive body of results to determine parameters J and CTOD for different materials using bend specimens with varying geometries and mismatch levels.     

Mechanical performance of three thickness resistance spot welded low carbon steel

Abstract

Resistance spot welding is the dominant process for joining sheet metals in automotive industry. Despite the application of three thickness resistance spot welds in this industry, present guidelines and recommendations are limited to two thickness spot welds. Study towards better understanding of weld nugget growth and mechanical properties is the first step to understanding the welding behaviour and developing proper guidelines for the three thickness resistance spot welding. In this paper, weld nugget growth, mechanical performance and failure behaviour of three thickness low carbon steel resistance spot welds are investigated. Macrostrcutural and microstructural investigations, microhardness tests and quasi-static tensile–shear tests were conducted. Mechanical performance of the joint was described in terms of peak load, energy absorption and failure mode. In order to understand the failure mechanism, micrographs of the cross-sections of the spot welded joints during and after tensile–shear are examined by optical microscopy. Unlike two thickness resistance spot welded joint, weld nugget was formed in the geometrical centre of the joint (i.e. centre of the middle sheet). Weld nugget size along sheet/sheet interface was greater than that of along geometrical centre of the joint. Increasing welding time leads to increases in peak load and energy absorption of the joint and transition of interfacial failure mode to pullout failure mode, primarily due to the enlargement of weld nugget size along sheet/sheet interface.