Spot Welds In Lap-shear Specimens Research Articles

Closed-Form Structural Stress Solutions for Spot Welds in Square Plates under Central Bending Conditions

<div class="section abstract"><div class="htmlview paragraph">A new closed-form structural stress solution for a spot weld in a square thin plate under central bending conditions is derived based on the thin plate theory. The spot weld is treated as a rigid inclusion and the plate is treated as a thin plate. The boundary conditions follow those of the published solution for a rigid inclusion in a square plate under counter bending conditions. The new closed-form solution indicates that structural stress solution near the rigid inclusion on the surface of the plate along the symmetry plane is larger than those for a rigid inclusion in an infinite plate and a finite circular plate with pinned and clamped outer boundaries under central bending conditions. When the radius distance becomes large and approaches to the outer boundary, the new analytical stress solution approaches to the reference stress whereas the other analytical solutions do not. The Mode II stress intensity factor solutions based on the new structural stress solution for a rigid inclusion in a square plate under central bending conditions are improved by up to 3% for similar spot welds in lap-shear specimens of equal thickness when compared with those obtained from the corresponding finite element analyses.</div></div>

Accurate analytical structural stress and stress intensity factor solutions for similar and dissimilar spot welds in lap-shear specimens

New analytical closed-form structural stress solutions for a rigid inclusion in a finite square thin plate under counter bending, central bending, in-plane shear and tension are developed. The new solutions are used to derive new analytical structural stress and stress intensity factor solutions for similar and dissimilar spot welds in lap-shear specimens. The new analytical solutions can predict the stress intensity factor solutions for similar and dissimilar magnesium/steel spot welds in lap-shear specimens of equal thickness under pinned loading conditions with less than 6% differences when compared with the results of three-dimensional finite element analyses.

Stress intensity factor solutions for similar and dissimilar spot welds in lap-shear specimens under clamped loading conditions

In this paper, analytical stress intensity factor solutions for similar and dissimilar spot welds in lap-shear specimens under pinned and clamped loading conditions are derived. Closed-form solutions for similar welds in lap-shear specimens of equal thickness under pinned and clamped loading conditions are derived to show explicitly the effects of the clamped edges on the stress intensity factor solutions. Finite element analyses are also employed to obtain the stress intensity factor solutions for similar and dissimilar spot welds in lap-shear specimens under pinned and clamped loading conditions. Both computational and analytical solutions indicate that the clamped loading reduces the stress intensity factor solutions for the given specimen geometries by up to 7% for similar welds and by about 20% for dissimilar magnesium/steel welds.

Failure Mode and Fatigue Behavior of Dissimilar Friction Stir Spot Welds in Lap-Shear Specimens of Transformation-Induced Plasticity Steel and Hot-Stamped Boron Steel Sheets

Failure mode and fatigue behavior of dissimilar friction stir spot welds in lap-shear specimens of transformation-induced plasticity steel (TRIP780) and hot-stamped boron steel (HSBS) sheets are examined in this paper. Optical micrographs of the dissimilar TRIP780/HSBS friction stir spot welds made by a concave silicon nitride tool before and after testing are obtained and examined. These micrographs indicate that subject to quasi-static and cyclic loading conditions, the TRIP780/HSBS welds fail from cracks growing through the TRIP780 sheets where the tool was plunged into and the thickness was reduced. The bending moments and the transverse shear force near the welds are derived with consideration of the load offset, the weld gap, and the bend distance for calculation of analytical global stress intensity factor solutions for the welds in lap-shear specimens. A fatigue model of kinked crack growth is used to estimate fatigue lives based on the local stress intensity factor solutions for kinked cracks. The estimated fatigue lives with consideration of the weld gap and the bend distance are in agreement with the fatigue test results under low-cycle loading conditions and lower than the fatigue test results under high-cycle loading conditions. The estimated fatigue lives suggest that the weld gap and the bend distance can significantly affect fatigue lives of the friction stir spot welds in lap-shear specimens under cyclic loading conditions.

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.

Failure Modes of Friction Stir Spot Welds in Lap-Shear Specimens of Dissimilar Advanced High Strength Steels under Quasi-Static and Cyclic Loading Conditions

Failure Modes of Friction Stir Spot Welds in Lap-Shear Specimens of Dissimilar Advanced High Strength Steels under Quasi-Static and Cyclic Loading Conditions

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.

Fatigue lives of friction stir spot welds in aluminum 6061-T6 sheets

The fatigue lives of friction stir spot welds in aluminum 6061-T6 lap-shear specimens under cyclic loading conditions are investigated in this paper. The paths of fatigue cracks near friction stir spot welds in lap-shear specimens are first examined. The experimental observations suggest that under cyclic loading conditions, the fatigue crack is initiated near the possible original notch tip in the stir zone and propagates along the circumference of the nugget, then through the sheet thickness and finally grows in the width direction to cause final fracture. A fatigue crack growth model based on the Paris law for crack propagation and the local stress intensity factors for kinked cracks is then adopted to predict the fatigue lives of friction stir spot welds. The global and local stress intensity factors are used to estimate the local stress intensity factors of kinked cracks with experimentally determined kink angles. The results indicate that the fatigue life predictions based on the Paris law and the local stress intensity factors as functions of the kink length agree well with the experimental results.

Microstructures and failure mechanisms of friction stir spot welds of aluminum 6061-T6 sheets

Microstructures and failure mechanisms of friction stir spot welds in aluminum 6061-T6 lap-shear specimens are investigated based on experimental observations. Optical micrographs of the cross-sections of friction stir spot welds in lap-shear specimens before and after failure are examined. These friction stir spot welds show the failure mode of nugget pullout under lap-shear loading conditions. The experimental observations suggest that under lap-shear loading conditions, the failure is initiated near the possible original notch tip in the stir zone (SZ) and the failure propagates along the circumference of the nugget to final fracture. Microindentation hardness data of base metal (BM), heat affected zone (HAZ), thermal–mechanical affected zone (TMAZ) and SZ are obtained. The interface between the HAZ and the TMAZ is the softest region, where the cracks of friction stir spot welds in the lap-shear specimens under the loadings initiate and lead to fracture of the specimens.

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.

Mode I stress intensity factor solutions for spot welds in lap-shear specimens

The analytical solutions of the mode I stress intensity factor for spot welds in lap-shear specimens are investigated based on the classical Kirchhoff plate theory for linear elastic materials. First, closed-form solutions for an infinite plate containing a rigid inclusion under counter bending conditions are derived. The development of the closed-form solutions is then used as a guide to develop approximate closed-form solutions for a finite square plate containing a rigid inclusion under counter bending conditions. Based on the J integral, the closed-form solutions are used to develop the analytical solutions of the mode I stress intensity factor for spot welds in lap-shear specimens of large and finite sizes. The analytical solutions of the mode I stress intensity factor based on the solutions for infinite and finite square plates with an inclusion are compared with the results of the three-dimensional finite element computations of lap-shear specimens with various ratios of the specimen half width to the nugget radius. The results indicate that the mode I stress intensity factor solution based on the finite square plate model with an inclusion agrees well with the computational results for lap-shear specimens for the ratio of the half specimen width to the nugget radius between 4 and 15. Finally, a set of the closed-form stress intensity factor solutions for lap-shear specimens at the critical locations are proposed for future applications.

Geometric functions of stress intensity factor solutions for spot welds in lap-shear specimens

In this paper, the stress intensity factor solutions for spot welds in lap-shear specimens are investigated by finite element analyses. Three-dimensional finite element models are developed for lap-shear specimens to obtain accurate stress intensity factor solutions. In contrast to the existing investigations of the stress intensity factor solutions based on the finite element analyses, various ratios of the sheet thickness, the half specimen width, the overlap length, and the specimen length to the nugget radius are considered in this investigation. The computational results confirm the functional dependence on the nugget radius and sheet thickness of the stress intensity factor solutions of [Zhang, S., 1997. Stress intensities at spot welds. International Journal of Fracture 88, 167–185; Zhang, S., 1999. Approximate stress intensity factors and notch stresses for common spot-welded specimens. Welding Journal 78, 173s–179s]. The computational results provide some geometric functions in terms of the normalized specimen width, the normalized overlap length, and the normalized specimen length to the stress intensity factor solutions of [Zhang, S., 1997. Stress intensities at spot welds. International Journal of Fracture 88, 167–185; Zhang, S., 1999. Approximate stress intensity factors and notch stresses for common spot-welded specimens. Welding Journal 78, 173s–179s] for lap-shear specimens. The computational results also indicate that when the spacing between spot welds decreases, the mode I stress intensity factor solution at the critical locations increases and the mode mixture of the stress intensity factors changes consequently. Finally, based on the analytical and computational results, the dimensions of lap-shear specimens and the corresponding approximate stress intensity factor solutions are suggested.

A computational study of local stress intensity factor solutions for kinked cracks near spot welds in lap-shear specimens

In this paper, the local stress intensity factor solutions for kinked cracks near spot welds in lap-shear specimens are investigated by finite element analyses. Based on the experimental observations of kinked crack growth mechanisms in lap-shear specimens under cyclic loading conditions, three-dimensional and two-dimensional plane-strain finite element models are established to investigate the local stress intensity factor solutions for kinked cracks emanating from the main crack. Semi-elliptical cracks with various kink depths are assumed in the three-dimensional finite element analysis. The local stress intensity factor solutions at the critical locations or at the maximum depths of the kinked cracks are obtained. The computational local stress intensity factor solutions at the critical locations of the kinked cracks of finite depths are expressed in terms of those for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. The three-dimensional finite element computational results show that the critical local mode I stress intensity factor solution increases and then decreases as the kink depth increases. When the kink depth approaches to 0, the critical local mode I stress intensity factor solution appears to approach to that for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. The two-dimensional plane-strain computational results indicate that the critical local mode I stress intensity factor solution increases monotonically and increases substantially more than that based on the three-dimensional computational results as the kink depth increases. The local stress intensity factor solutions of the kinked cracks of finite depths are also presented in terms of those for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. Finally, the implications of the local stress intensity factor solutions for kinked cracks on fatigue life prediction are discussed.

Fatigue life estimation in resistance spot welds: initiation and early growth phase: Sheppard, S.D. and Strange, M. Fatigue Fract. Eng. Mater. Struct. June 1992 15, (6), 531–549

In this paper, the local stress intensity factor solutions for kinked cracks near spot welds in lap-shear specimens are investigated by finite element analyses. Based on the experimental observations of kinked crack growth mechanisms in lap-shear specimens under cyclic loading conditions, three-dimensional and two-dimensional plane-strain finite element models are established to investigate the local stress intensity factor solutions for kinked cracks emanating from the main crack. Semi-elliptical cracks with various kink depths are assumed in the three-dimensional finite element analysis. The local stress intensity factor solutions at the critical locations or at the maximum depths of the kinked cracks are obtained. The computational local stress intensity factor solutions at the critical locations of the kinked cracks of finite depths are expressed in terms of those for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. The three-dimensional finite element computational results show that the critical local mode I stress intensity factor solution increases and then decreases as the kink depth increases. When the kink depth approaches to 0, the critical local mode I stress intensity factor solution appears to approach to that for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. The two-dimensional plane-strain computational results indicate that the critical local mode I stress intensity factor solution increases monotonically and increases substantially more than that based on the three-dimensional computational results as the kink depth increases. The local stress intensity factor solutions of the kinked cracks of finite depths are also presented in terms of those for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. Finally, the implications of the local stress intensity factor solutions for kinked cracks on fatigue life prediction are discussed.