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.     

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.     

Modeling of failure mode of laser welds in lap-shear specimens of HSLA steel sheets

Failure mode of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel sheets is investigated in this paper. The experiments for laser welds in lap-shear specimens under quasi-static loading conditions are briefly reviewed first. The experimental results showed that the laser welds failed in a ductile necking/shear failure mode and the ductile failure was initiated at a distance away from the crack tip near the boundary of the base metal and heat affected zone. In order to understand the failure mode of these welds, finite element analyses under plane strain conditions were conducted to identify the effects of the different plastic behaviors of the base metal, heat affected zone, and weld zone as well as the weld geometry on the ductile failure. The results of the reference finite element analysis based on the homogenous material model show that the failure mode is most likely to be a middle surface shear failure mode in the weld. The results of the finite element analysis based on the multi-zone non-homogeneous material models show that the higher effective stress–plastic strain curves of the weld and heat affected zones and the geometry of the weld protrusion result in the necking/shear failure mode in the load carrying sheet. The results of another finite element analysis based on the non-homogeneous material model and the Gurson yield function for porous materials indicate that the consideration of void nucleation and growth is necessary to identify the ductile failure initiation site that matches well with the experimental observations. Finally, the results of this investigation indicate that the failure mode of the welds should be examined carefully and the necking/shear failure mode needs to be considered for development of failure or separation criteria for welds under more complex loading conditions.     

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.     

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.     

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.     

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.     

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.     

A parametric study on fatigue strength of spot‐weld joints

Fastening elements usually lead to high stress concentrations; fatigue failure thus becomes the most critical failure mode for a fastening element itself or the region around it under fluctuating stresses. A designer should seek the ways of increasing fatigue strength of a joint to ensure the safety of the whole structure. Resistance spot welding is the most preferred method to join metal sheets. The design variables for spot‐weld joints affecting their strengths are basically sheet thickness, spot‐weld nugget diameter, number of spot welds and the joint type as exemplified in tensile shear (TS), modified tensile shear (MTS), coach peel (CP) and modified coach peel (MCP) specimens. In this study, the effects of these parameters on the fatigue life of spot‐weld joints have been investigated. For this purpose, one of the most reliable fatigue assessment models, Coffin–Manson approach, was used. In order to accurately determine the stress and strain states, a nonlinear finite element analysis was carried out taking into account plastic deformations, residual stresses developed after unloading and contacting surfaces. The results provide designers with some guidelines to foresee the impact of design changes on fatigue strength of spot‐weld joints.     

A hybrid polygonal element method for fracture mechanics analysis of resistance spot welds containing porosity

A hybrid polygonal element (HPE) method is presented in this study for evaluating the effects of micro-porosity on the fracture behavior of resistance spot welds. The HPE method uses an arbitrarily shaped n-sided polygonal grid to characterize porosity distribution in a weld nugget. Compared with traditional finite element methods, HPE method possesses a number of unique features and advantages, such as mesh simplicity, computational efficiency, and easiness in performing parametric studies. Randomly distributed porosity in a resistance spot weld can be directly modeled using this method. The interactions between porosity and the main crack around the periphery of a weld nugget can be easily quantified. This is of particular importance for aluminum resistance spot welds as the automotive industries strive to produce light-weight vehicles by using more and more aluminum alloys. To demonstrate its effectiveness, HPE method was applied to carry out a series of fracture mechanics analyses for aluminum spot welds with various distributions of micro-porosity. Both lap shear and lap tension specimens were analyzed. The analysis results shed light on the effects of porosity on the fatigue strength of aluminum spot welds.     

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.     

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.     

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.     

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.     

Cohesive-zone modelling of the deformation and fracture of spot-welded joints

The deformation and failure of spot‐welded joints have been successfully modelled using a cohesive‐zone model for fracture. This has been accomplished by implementing a user‐defined, three‐dimensional, cohesive‐zone element within a commercial finite‐element package. The model requires two material parameters for each mode of deformation. Results show that the material parameters from this type of approach are transferable for identical spot welds in different geometries where a single parameter (such as maximum stress) is not. The approach has been demonstrated using a model system consisting of spot‐welded joints made from 5754 aluminium sheets. The techniques for determining the cohesive fracture parameters for both nugget fracture and nugget pullout are described in this paper. It has been demonstrated that once the appropriate cohesive parameters for a weld are determined, quantitative predictions can be developed for the strengths, deformations and failure mechanisms of different geometries with nominally identical welds.     

Effect of process parameters on the strength of resistance spot welds in 6082-T6 aluminium alloy

In this study the microstructural and mechanical behaviour of resistance spot welds (RSW) done on aluminium alloy 6082-T6 sheets, welded at different welding parameters, is examined. Microstructural examinations and hardness evaluations were carried out in order to determine the influence of welding parameters on the quality of the welds. The welded joints were subjected to static tensile-shear tests in order to determine their strength and failure mode. The increase in weld current and duration increased the nugget size and the weld strength. Beyond a critical nugget diameter the failure mode changed from interfacial to pullout. Taking into consideration the sheet thickness and the mechanical properties of the weld, a simple model is proposed to predict the critical nugget diameter required to produce pull-out failure mode in undermatched welds in heat-treatable aluminium alloys.     

Overload failure behaviour of dissimilar thickness resistance spot welds during tensile shear test

Abstract

Resistance spot welding is the dominant process for joining sheet metals in automotive industry. Even thickness combinations are rarely used in practice; therefore, there is clearly a practical need for failure behaviour investigation of uneven thickness resistance spot welds. The aim of the present paper is to investigate the failure mode and failure mechanism of dissimilar thickness low carbon steel resistance spot welds during tensile shear overload test. Microstructural investigations, microhardness tests and tensile shear tests were conducted. Mechanical properties of the joints were 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. It was found that for well established weld nuggets, the final solidification line is located in the geometrical centre of the joint. In pull-out failure mode, failure is initiated by necking of the base metal at the thinner thickness sheet. Finally, it was concluded that weld nugget size, weld penetration and the strength of the thinner sheet are the main controlling factors of the peak load and energy absorption of dissimilar thickness spot welds.     

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.