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.     

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.     

Analytical stress intensity factor solutions for resistance and friction stir spot welds in lap-shear specimens of different materials and thicknesses

In this paper, analytical stress intensity factor and J integral solutions for resistance and friction stir spot welds without and with gap and bend in lap-shear specimens of different materials and thicknesses are developed. The J integral and stress intensity factor solutions for spot welds are first presented in terms of the structural stresses for a strip model. Analytical structural stress solutions for spot welds without and with gap and bend in lap-shear specimens are then developed based on the closed-form structural stress solutions for a rigid inclusion in a finite thin plate subjected to various loading conditions. With the available structural stress solutions, the analytical J integral and stress intensity factor solutions can be obtained as functions of the applied load, the elastic material property parameters, and the geometric parameters of the weld and specimen. The analytical stress intensity factor solutions are selectively validated by the results of three-dimensional finite element analyses for a spot weld with ideal geometry and for a friction stir spot weld with complex geometry, gap and bend. The stress intensity factor and J integral solutions at the critical locations of spot welds in lap-shear specimens of dissimilar magnesium, aluminum and steel sheets with equal and different thicknesses are then presented in the normalized forms as functions of the ratio of the specimen width to the weld diameter. Finally, general trends and simple estimation methods of the stress intensity factor and J integral solutions at the critical locations of spot welds in lap-shear specimens of different materials and thicknesses are given for convenient engineering applications.     

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.     

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.     

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.     

Characterization of magnesium spot welds under tensile and cyclic loadings

Resistance spot welds of a magnesium alloy were characterized in terms of microstructure, hardness and monotonic and cyclic properties. Microstructural features in base metal and different zones in the weld region were discussed and the mechanical behavior of spot welds in tensile–shear configuration was studied. Effects of welding parameters were investigated on the micro- and macro-scale characteristics of magnesium spot welds. To this end, five sets of spot weld specimens were prepared, utilizing different welding parameters. The effect of cyclic loading was studied on microstructure and hardness of the base metal and the weld region, and it was shown that microstructural features do not change remarkably under cyclic loading. Fatigue crack initiation and propagation behavior was discussed for different specimen sets under both low and high cyclic loads. Fatigue cracks under high cyclic loading initiated close to the nugget edge, and decreasing the cyclic load nucleated the cracks farther from the nugget.     

FRACTURE MECHANICS ANALYSIS OF FATIGUE RESISTANCE OF SPOT WELDED COACH-PEEL JOINTS

Resistance spot welding is the most widely used joining method in automobile manufacture. The number, location, and quality of welds are some of the factors that influence the performance of welded subassemblies, and body panel structures. Therefore, design optimization requires knowledge of not only sheet metal behavior, but also weld behavior under service loadings. A linear elastic fracture mechanics approach was employed in this study to estimate the fatigue lives of spot welds subjected to tearing loads in a coach-peel specimen. Using a finite element method (FEM), the initial J-integral values for five coach-peel joints, each with different geometries, were calculated. Fatigue tests conducted on the same weld geometries provided life data. The experimental data were used to derive a relationship between the initial elastic J-integral values (ΔJ_e) and the fatigue life. It was found that the total fatigue life (N_f) of a weld at one applied stress range is related to its range of J-integral value such that a ΔJ_e vs N_f log-log plot gives a straight line relationship. This relationship can be used to evaluate the effects of geometrical variables on the fatigue life of coach-peel joints. The results show that, within the dimension range studied here, the effects of geometrical variables on the fatigue resistance can be ranked in the following decreasing order: weld eccentricity, sheet thickness and weld nugget diameter.     

Failure modes and fatigue life estimations of spot friction welds in cross-tension specimens of aluminum 6061-T6 sheets

Failure modes of spot friction welds (SFWs) in cross-tension specimens of aluminum 6061-T6 sheets are investigated. Micrographs of the SFWs before and after failure under quasi-static and cyclic loading conditions are examined. Two different nugget pullout failure modes can be seen. A fatigue crack growth model based on the paths of the dominant kinked fatigue cracks is adopted to estimate the fatigue lives of SFWs. The computational stress intensity factors for finite kinked cracks and the Paris law for fatigue crack propagation are considered. The fatigue life estimations based on this model agree well with the experimental results.     

Fatigue strength evaluation of self-piercing riveted Al-5052 joints under different specimen configurations

In this study, static and fatigue tests were conducted using coach-peel, cross-tension and tensile–shear specimens with Al-5052 plates for evaluation of the fatigue strength of the SPR joints. For the coach-peel, cross-tension and tensile–shear geometries, the ratios of the fatigue endurance limit to static strength were 11%, 14% and 34%, respectively, assuming fatigue cycles of 10⁶ for an infinite lifetime. The equivalent stress intensity factor range can properly predict the current experimental fatigue lifetime. Fatigue crack initiation occurred due to fretting damage between the upper and lower sheets and between the rivet and these sheets.     

Modeling of failure near spot welds in lap-shear specimens based on a plane stress rigid inclusion analysis

In this paper, the failure mechanism of resistance spot welds in dual-phase steel lap-shear specimens is investigated based on experimental observations, two-dimensional elasticity theories and two-dimensional finite element analyses. Optical micrographs of the cross sections of spot welds in lap-shear specimens of a dual-phase steel before and after failure are first examined to understand the failure mechanism. The experimental results suggest that under lap-shear loading conditions, a necking failure is initiated near the middle of the nugget circumference in the base metal and then the failure propagates along the nugget circumference in the sheet to final fracture. Based on the stress function approach of the elasticity theory, an analytic solution for an infinite plate containing a rigid inclusion subjected to a resultant shear force is developed and used to investigate the stress and strain distributions near the nugget in lap-shear specimens. The results of the elastic analytic solution and those of a two-dimensional elastic finite element analysis indicate that the initial yielding starts on the two side edges of the inclusion in the sheet. However, the results of a two-dimensional elastic-plastic finite element analysis indicate that as the applied displacement increases, the maximum equivalent plastic strain shifts from the two side edges of the inclusion to the middle of the inclusion along the inclusion circumference in the sheet. The computational results suggest that the location of the initial necking failure should occur near the middle of the nugget circumference in the sheet as observed in experiments based on the forming limit diagram (FLD) for ductile sheet metals.     

Effect of adhesive on fatigue property of Aural2 to AA5754 dissimilar aluminum alloy resistance spot welds

General Motors (GM) has developed a proprietary resistance spot welding (RSW) process using a multi-ring, domed electrode geometry that has been used successfully in automotive aluminum welding operations. To enhance structural performance, one-part epoxy adhesives are frequently applied prior to RSW to create weld-bonded joints. The addition of adhesive can result in additional porosity created within the weld nugget. Therefore, the adhesive's impact on mechanical properties, especially fatigue properties requires further investigation.Load-controlled fatigue testing was conducted on dissimilar aluminum alloy spot welds made of AA5754 wrought sheet and Aural2 die casting sheet with and without the addition of adhesive prior to welding. The same GM RSW electrode and weld schedule was used for both conditions. The results show that the addition of adhesive results in a larger nugget size, but similar maximum load in tension-shear testing. X-ray computed tomography during interrupted fatigue testing of the spot welds shows that the main fatigue crack initiates at the edge of the nugget in the plane of the faying interface and penetrates through the Aural2 die cast sheet in the thickness direction. Using the structural stress concept, it was also found that the structural stress range–fatigue life curve for these spot welds, both with and without adhesive, falls onto a single master curve indicating that the nugget size which corresponds to the tensile and bending strength dominates the fatigue life and that adhesive-induced porosity within the weld nugget does not harm fatigue performance.     

Effect of governing metal thickness and stack orientation on weld quality and mechanical behaviour of resistance spot welding of AA5754 aluminium

A study was carried out to investigate the effect of governing metal thickness (GMT) and stack orientation on weld quality and mechanical behaviour of resistance spot welded (RSW) AA5754 aluminium. Individual samples from 27 different joint stacks in three test geometries; lap-shear, coach-peel and cross-tension were evaluated for quasi-static and fatigue performance; micro examination was also conducted on some of the samples to assess weld quality. The results derived from over 1000 samples show that: the GMT has a significant effect on welding quality by controlling progression of weld nugget from under-developed to over penetrated. The GMT also determines the feasible quasi-static joint strength regardless of stacks in the three joint geometries tested, though the effect differs with respect to test geometry. The fatigue behaviour is dominated by the effect of GMT on attainable weld size, overall joint stiffness and stress concentration, providing good quality of weld nuggets is achieved. No notable effect of stack orientation on weld quality and joint strength was found with respect to the joint stack asymmetry and welding orientation to the electrodes. These fundamental relationships between weld qualities, joint strength, GMT and stack orientation for RSW of aluminium will have significant relevance to design and manufacturing communities.     

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.     

Three-Dimensional Finite Element Analysis of Tensile-Shear Spot-Welded Joints in Tensile and Compressive Loading Conditions

Three-dimensional finite element analysis is applied to verify mechanical behavior of spot welds for one, three and five spot welds under tensile and compressive loading conditions. The elastic-plastic stress distribution at edge of hot spot weld is used for strength calculations. To obtain exact and reliable results for finite element analysis of spot welds, which are generally very small relative to other dimensions, sub-modeling technique is applied. The proposed numerical calculation scheme allows one to take into account the material parameters and geometrical non-linearity effects related to a gap between thin plates, buckling, etc. We provide the analysis of elastic and elastoplastic behavior of specimens with various configuration of spot welds subjected to tensile and compressive axial loads.     

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.     

Fatigue crack growth assessments in welded components including crack closure effects: Experiments and 3-D numerical modeling

This work provides a numerical and experimental investigation of fatigue crack growth behavior in steel weldments including crack closure effects and their coupled interaction with weld strength mismatch. A central objective of this study is to extend previously developed frameworks for evaluation of crack closure effects on FCGR to steel weldments while, at the same time, gaining additional understanding of commonly adopted criteria for crack closure loads and their influence on fatigue life of structural welds. Very detailed non-linear finite element analyses using 3-D models of compact tension C(T) fracture specimens with center cracked, square groove welds provide the evolution of crack growth with cyclic stress intensity factor which is required for the estimation of the closure loads. Fatigue crack growth tests conducted on plane-sided, shallow-cracked C(T) specimens provide the necessary data against which crack closure effects on fatigue crack growth behavior can be assessed. Overall, the present investigation provides additional support for estimation procedures of plasticity-induced crack closure loads in fatigue analyses of structural steels and their weldments.     

Strength prediction of sheet to tube single sided resistance spot welding

Single-Sided Spot Welding (SSSW) procedure is considered as a feasible method to join hydroformed or closed section parts to others in vehicle productions. A ‘doughnut’ shaped or ring nugget can be formed between the two workpieces during this process. The strengths of conventional button spot welds can be determined by the attributes of weldments and many functions that link weld diameter, sheet thickness and material properties to weld strength have been established. For welds of sheet to tube joining, the strength prediction model is greatly different from that of conventional welds for the completely different nugget form. In this study, computer experiments were conduced using the concept of design of experiments (DOE) and the method of finite element used to simulate the tensile-shear tests. The stress and strain distribution contour clouds during tensile-shear process were analyzed and quantitative relationship models were established to link a weld’s geometric and material properties to its tensile-shear strength. The results can give a simple judgment whether a ring spot weld was good only by its appearance.     

Stress intensity factors in spot welds

This paper looks at stress intensity factors of cracks in resistance spot welded joints. Stress intensity factors have been used in the past to predict fatigue crack propagation life of resistance spot welds. However, the stress intensity factors from all previous work was based on assumed initial notch cracks at the nugget, parallel to the sheets. Physical evidence shows, however, that fatigue cracks in spot welds propagate through the thickness of the sheets rather than through the nugget. In this work, stress intensity factors of assumed notch cracks and through thickness cracks in tensile shear (TS) and modified coach peel (MCP) specimens were determined by the finite element method. The finite element results from the assumed notch cracks were compared with the results in the literature and were found to be in agreement with the results from Zhang’s equations [Int. J. Fract. 88 (1997) 167]. The stress intensity factors of assumed notch cracks were found to be different from those of through thickness cracks. To date, no analytic equations for stress intensity factors of through thickness cracks in spot welds have been published. In the current work, simple equations are proposed to estimate the K_I and K_II values of through thickness cracks in TS and MCP specimens.     

Stress intensity factors in spot welds

This paper looks at stress intensity factors of cracks in resistance spot welded joints. Stress intensity factors have been used in the past to predict fatigue crack propagation life of resistance spot welds. However, the stress intensity factors from all previous work was based on assumed initial notch cracks at the nugget, parallel to the sheets. Physical evidence shows, however, that fatigue cracks in spot welds propagate through the thickness of the sheets rather than through the nugget. In this work, stress intensity factors of assumed notch cracks and through thickness cracks in tensile shear (TS) and modified coach peel (MCP) specimens were determined by the finite element method. The finite element results from the assumed notch cracks were compared with the results in the literature and were found to be in agreement with the results from Zhang’s equations [Int. J. Fract. 88 (1997) 167]. The stress intensity factors of assumed notch cracks were found to be different from those of through thickness cracks. To date, no analytic equations for stress intensity factors of through thickness cracks in spot welds have been published. In the current work, simple equations are proposed to estimate the K_I and K_II values of through thickness cracks in TS and MCP specimens.