Local Stress Intensity Factor Solutions Research Articles

Three-Dimensional Finite Element Analyses of Local Stress Intensity Factor Solutions for Kinked Cracks of Spot Welds in Commonly Used Specimens

<div class="section abstract"><div class="htmlview paragraph">Local stress intensity factors (LSIFs) for kinked cracks of spot welds in four specimens, lap-shear, cross-tension, U-shaped, and coach-peel, were studied by three-dimensional finite element analyses. Finite element models for spot welds without and with kinked cracks were developed. Semi-elliptical cracks with various kinked crack lengths were assumed. Two dominant cracking modes for each specimen were considered. The global stress intensity factor (GSIF) solutions for spot welds without kinked cracks were first obtained to determine the analytical LSIF solutions for spot welds with infinitesimal kinked cracks. The LSIF solutions for spot welds with finite kinked cracks were then obtained. The LSIF solutions of the four specimens show similar general trends. As kinked crack length increases, the mode I LSIF solutions gradually increase and then decrease, while the mode II LSIF solutions show inverse trends. Finally, the applications of LSIFs for fatigue life estimations of various types of spot welds or spot joints are discussed.</div></div>

Stress intensity factor solutions and fatigue estimation for dual phase and low-carbon steel spot weld

In this paper, stress intensity factor solutions of kinked crack for unequal thickness resistance lap-shear specimens of advanced high strength steel and low carbon steel are investigated for fatigue life estimation. The global stress intensity factor solutions for the main cracks in the lap-shear specimens are developed via finite element analyses and analytical solutions, and the finite element solutions are in good agreement with the analytical solutions. The local stress intensity factor solutions for kinked cracks and the effects of crack shape, crack length and kinked angle to the local stress intensity factors are investigated via finite element analyses. The mode I stress intensity factor of kinked crack shows a smooth increase as the kinked length is less than 30 percent of sheet thickness, and it increases sharply as the kinked length exceeds 50 percent of sheet thickness. An equivalent stress intensity factor of the three dimensional kinked crack and a fatigue life estimation method based on the equivalent stress intensity factor are proposed in the present study. The crack propagation of through-thickness is divided into several sections and subsection integral based on the equivalent stress intensity factor is applied to estimate the fatigue life of lap-shear resistance specimens. Compared with the fatigue test, the fatigue estimation based on subsection integral of local equivalent stress intensity factor for the lap-shear resistance specimens agrees well with the experimental results.

Fatigue behavior of dissimilar ultrasonic welds in lap-shear specimens of AZ31 and steel sheets

Fatigue behavior of dissimilar ultrasonic welds in lap-shear specimens in magnesium and steel sheets is investigated. The welds were produced using a Sonobond ultrasonic spot welder to join magnesium AZ31B-H24 to two types of steel. The lap-shear specimens have been machined into a dog-bone profile to approximate a linear weld. The lap-shear linear welds were studied based on experimental observations, closed-form stress intensity factor solutions, and a fatigue life estimation model. Optical micrographs of the welds after testing were examined to understand the failure modes of the welds. The micrographs show that the welds tested under cyclic loading failed from kinked fatigue cracks growing through the magnesium sheets. The closed-form stress intensity factor solutions for each side of the weld are used to explain the location of fatigue crack initiation and growth. Two-dimensional finite element analyses of the lap-shear specimens with the welds were carried out to obtain the global and local stress intensity factor solutions for the main cracks and kinked cracks, respectively. A kinked fatigue crack growth model based on the global and local stress intensity factor solutions for finite kinked cracks obtained from the finite element analyses is adopted to estimate the fatigue life of the welds. The fatigue life estimations based on the kinked fatigue crack growth model generally underestimate the experimental results. The kinked crack growth model shows little sensitivity to the welding indentation or the thickness of the steel sheet.

Stress intensity factor solutions for welds in lap-shear specimens of dissimilar sheet materials with and without kinked cracks

Global stress intensity factor solutions for welds with various widths in lap-shear specimens of magnesium alloy AZ31 and high-strength low-alloy steel sheets are developed using finite element analyses. Results are compared to and validated with the analytical solutions based on the beam bending theory and semi-infinite planes with connection. Analyses are also conducted using modified elastic constants with a bimaterial constant of zero for specimens with small kinked cracks. Results indicate that the stress intensity factor solutions for a vanishing kink length can be approximated by the available analytical solutions for the zero bimaterial constant for fatigue cracks growth models. The results of the global stress intensity factor solutions and the local stress intensity factor solutions for kinked cracks with the experimentally observed kink angle as functions of the kink length can be adopted for fatigue life estimations of ultrasonic welds in lap-shear specimens of magnesium and steel sheets.

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.

Stress intensity factor solutions for adhesive-bonded lap-shear specimens of magnesium and steel sheets with and without kinked cracks for fatigue life estimations

In this paper, stress intensity factor solutions for adhesive-bonded lap-shear specimens of magnesium alloy AZ31 and hot-dip-galvanized (HDG) mild steel sheets with and without kinked cracks are investigated for fatigue life estimations. First, the kinked fatigue crack failure mode of the adhesive-bonded lap-shear specimens is briefly reviewed. Then, the analytical global J integral and effective stress intensity factor solutions for main cracks in lap-shear specimens of three dissimilar sheets under plane strain conditions are developed based on the beam bending theory. The global effective stress intensity factor solutions for the main cracks in the lap-shear specimens from the corresponding finite element analyses are then presented and validated by the analytical solutions. Next, the local stress intensity factor solutions for kinked cracks with the experimentally observed kink angle as functions of the kink length from the corresponding finite element analyses are presented and the computational solutions are also compared with the analytical solutions at small kink lengths. The results indicate that the computational local stress intensity factor solutions for kinked cracks approach to the analytical solutions as the kink length decreases to a small value and the kinked crack is under dominant mode I loading conditions. The computational results also indicate that the local stress intensity factor solutions at a small kink length of microstructural significance may be used as the stress intensity factor solutions for zero or near zero kink length for fatigue life estimations when the computational results are not available. The computational local stress intensity factor solutions are then adopted to estimate the fatigue lives of the lap-shear specimens based on a kinked crack growth model and available material constants for the Paris law. The fatigue life estimations are lower than the experimental results. However, the general trend of fatigue life estimations agrees with that of the experimental results.

Fatigue behavior of laser welds in lap-shear specimens of high strength low alloy steel sheets

In this paper, the fatigue behavior of laser welds in lap-shear specimens of non-galvanized SAE J2340 300Y high strength low alloy (HSLA) steel sheets is investigated based on experimental observations and a fatigue life estimation model. Optical micrographs of the laser welds before and after failure under quasi-static and cyclic loading conditions are examined. The micrographs show that the failure modes of laser welds under quasi-static and cyclic loading conditions are quite different. Under quasi-static loading conditions, 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 to the pre-existing crack tip, and the specimens fail due to the necking/shear of the lower left load carrying sheets. Under low-cycle loading conditions, the weld failure appears to be initiated from the pre-existing crack tips and the specimens finally fail from the ductile fracture through the lower left load carrying sheets. Under high-cycle loading conditions, the weld failure appears to be initiated from the pre-existing crack tips and the specimens finally fail from the kinked fatigue crack propagating through the upper right load carrying sheets. Finite element analyses of the laser welded lap-shear specimens with consideration of the weld bead protrusion were carried out to obtain the global and local stress intensity factor solutions for the main cracks and kinked cracks, respectively. The stress intensity factor solutions can be used to explain the kinked fatigue crack growth patterns under high-cycle loading conditions. The kinked fatigue crack growth model based on the global and local stress intensity factor solutions for finite kinked cracks obtained from the finite element analyses is adopted to estimate the fatigue lives of the laser welds. The fatigue life estimations based on the kinked fatigue crack growth model agree well with the experimental results.

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.

A fatigue crack growth model for spot welds under cyclic loading conditions

Based on the experimental results for spot welds in square-cup, lap-shear and coach-peel specimens of dual phase, low carbon and high strength steels, kinked fatigue crack paths near spot welds are first examined. A fatigue crack growth model is then developed for spot welds based on the local stress intensity factor solutions for kinked cracks. Various global stress intensity factor solutions for spot welds in the three types of specimens are used to obtain the local stress intensity factor solutions with the experimentally determined kink angles. The predicted fatigue lives based on the fatigue crack growth model are then compared with the experimental data. The results indicate that the fatigue crack growth model can predict reasonably well the fatigue lives of spot welds based on the global stress intensity factor solutions and the assumed material constants in the Paris law for fatigue crack growth.

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.

Stress intensity factors for spot welds and associated kinked cracks in cup specimens

In this paper, the stress intensity factors for spot welds in cylindrical-cup and square-cup specimens are investigated by finite element analyses. Axisymmetric and three-dimensional finite element models are developed for circular plates and cylindrical-cup specimens to establish the finite element meshes needed to obtain accurate global stress intensity factor solutions. The global stress intensity factors are compared with the existing analytical solutions for circular plates. Then a three-dimensional finite element model based on the finite element mesh for cylindrical-cup specimens is established to obtain the global stress intensity factors for square-cup specimens. Based on the computational results, a closed-form stress intensity factor solution is suggested for square-cup specimens. Next, based on the experimental observations of kinked crack growth mechanisms in square-cup specimens under cyclic loading conditions, axisymmetric finite element models are established to investigate the local stress intensity factor solutions for kinked cracks emanating from the main crack. Both circular and rectangular shaped notch tip and a sharp crack tip are considered for the main crack. Various kink lengths are considered. The local stress intensity factor solutions for kinked cracks are obtained. The results show that the local stress intensity factors for kinked cracks with finite kink lengths are much higher than those based on the closed-form solutions for kinked cracks with vanishing kink length. Finally, the implications of the local stress intensity factor solutions for kinked cracks on fatigue life prediction are discussed.

Fatigue life prediction for spot welds in coach-peel and lap-shear specimens with consideration of kinked crack behaviour

A fracture mechanics approach is adopted to examine the fatigue lives of spot welds in coach-peel and lap-shear specimens with consideration of kinked crack behaviour. The paths of fatigue cracks near the spot welds in these two types of specimens are first discussed. A fatigue crack growth model is then developed for spot welds in these two types of specimens based on the local stress intensity factor solutions for kinked cracks and the Paris law for crack propagation. Various global stress intensity factor solutions for spot welds in these two types of specimens are used to obtain the local stress intensity factor solutions with the experimentally determined kink angles. The results indicate that the fatigue life predictions based on accurate global stress intensity factor solutions can characterise the general trend of the experimental results. The effects of the kink angle on the fatigue life predictions are also 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.