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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Interfacial bonding mechanism in Al/coated steel dissimilar refill friction stir spot welds

Defect-free dissimilar Al/zinc coated steel and Al/AlSi coated steel welds were successfully fabricated by refill friction stir spot welding. However, Al alloy and uncoated steel could not be welded under the same welding condition. Al-Zn eutectic layer formed at the Al/zinc coated steel interface showed non-uniformity in thickness and nanoscale intermetallic (IMC) produced was discontinuous. The bonding formation between the Al-Zn layer and the surrounding materials was attributed to a liquid/solid reaction mechanism. Bonding formation at Al alloy and AlSi coated steel interface was attributed to a solid/solid reaction mechanism, as the joining process did not involve with melting of base metals or AlSi coating materials. Kissing bond formed at the weld boundary acted as a crack initiation and propagation site, and the present study showed that weld strength of Al 5754/AlSi coated steel was greatly influenced by properties of original IMC layer.     

Local melting and tool slippage during friction stir spot welding of Al-alloys

Local melting and tool slippage during friction stir spot welding of different Al-alloy base materials is examined using a combination of detailed microscopy and temperature measurement. The stir zone peak temperature during welding is limited by either the solidus of the alloy in question or by spontaneous melting of intermetallic particles contained in the as-received base material. When spontaneous melting occurs this facilitates tool slippage at the contact interface. Accurate stir zone temperature and grain size measurements are essential elements when estimating the strain rate using the Zener–Hollomon relation. In Al 2024 and Al 7075 spot welds spontaneous melting of second-phase particles produces a drastic reduction in strain rate values. In Al 5754 and Al 6061 spot welds there is a strong correlation between tool rotational speed and estimated strain values. Local melted films dissolve rapidly in the high temperature stir zone and when the spot weld cools to room temperature following welding. Evidence of local melting is observed in Al 7075 friction stir spot welded joints made using a combination of rapid quenching, high plunge rates, and extremely short dwell time settings.     

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.     

Fatigue performance and fatigue damage parameter estimation of spot welded joints of aluminium alloys 6111‐T4 and 5754

In the present study, fatigue behaviours of spot welded joints of aluminium alloys 6111‐T4 and 5754 have been experimentally investigated. Fatigue results indicate that fatigue strength of spot weld primarily depends on specimen loading type and gauge thickness. Effects of base material and load ratio on fatigue resistance of welded specimen are insignificant. An equivalent stress based fatigue damage parameter is derived to consolidate empirical data and develop predictive capabilities for automobile designers. The fatigue damage parameter defined in this study is proven effective in consolidating a large amount of fatigue data into a narrow band and is especially suitable for the comparative fatigue strength evaluation of components and specimens.     

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.     

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.     

Mechanical characterization of spot friction stir welded joints in aluminum alloys by combined experimental/numerical approaches: Part I: Micromechanical studies

This paper is part I of a two part paper, which summarizes recent studies carried out to characterize the weld zone mechanical properties in aluminum alloy 6111 spot friction stir welded joints at both the macromechanical and micromechanical levels. In this paper, micromechanical level investigations are reported for joints welded with different processing times. Apart from microstructural studies and microhardness tests, a new approach to characterize the distribution of weld zone modulus using modal vibration tests on micron scale cantilever array specimens with a micro-scanning laser vibrometer and the corresponding finite element simulations has been developed. Microcantilever array samples were designed in such a way that each microcantilever represents one of the weld zones. Microscopic studies reveal a partial metallurgical bond formed in the direction of flow, which is governed by the tool used and Vickers hardness numbers in those regions were found to be considerably lower than those of the base metal. From the analysis of microcantilever arrays, it was concluded that the variation of modulus in the weld zones is minimal and there is no significant reduction in the weld zone modulus when compared to that of the base metal.     

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.     

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.