Search Results

An analytical load distribution solution for calculation of the loads exerted by the rolling elements on the outer raceway in cylindrical roller bearings under radial loading is proposed in this paper. The loads exerted by the rolling elements are obtained based on an assumption that the profile of the maximum contact pressures of rolling elements resemble the profile of the contact pressure of the corresponding lumped cylinder. Based on this assumption, an analytical load distribution solution which gives the loads exerted by the rolling elements on the outer raceway is derived based on the non-conforming contact solution of Hertz and the conforming contact solution of Persson. These loads can be calculated from the analytical solution with the total applied load and the normalized contact pressure profile of the corresponding lumped cylinder. Two-dimensional finite element analysis was conducted to validate the proposed analytical solutions.

In this paper, analytical stress intensity factor solutions for spot welds with ideal geometry in lap-shear specimens of different materials and thicknesses are presented 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 a three-dimensional finite element analysis for a dissimilar spot weld with ideal geometry in a lap-shear specimen. Finally, selected stress intensity factor 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 presented in the normalized forms as functions of the ratio of the specimen width to weld diameter.

Closed-form structural stress solutions are investigated for fatigue life estimations of flow drill screw (FDS) joints in lap-shear specimens of aluminum 6082-T6 sheets with and without clearance hole based on three-dimensional finite element analyses. The closed-form structural stress solutions for rigid inclusions under counter bending, central bending, in-plane shear and in-plane tension are first presented. Three-dimensional finite element analyses of the lap-shear specimens with FDS joints without and with gap (with and without clearance hole) are then presented. The results of the finite element analyses indicate that the closed-form structural stress solutions are quite accurate at the critical locations near the FDS joints in lap-shear specimens without and with gap (with and without clearance hole) for fatigue life predictions.

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.

In this paper, an analytical method is proposed for determining the stress distributions in steering knuckle/tapered stud assemblies. The method is based on solutions of the plane stress thick cylinder interference fit problem with modifications to account for the effects of stud taper and dissimilar component materials. The analytical solutions are applied to knuckle/tapered stud assemblies. The results from the analytical solutions are compared to those from a finite element analysis. It is shown that the analytical and FEA results are in good agreement for several load and frictional conditions, and the hoop and radial stress solutions presented in this paper are good engineering solutions to the knuckle/tapered stud problem where the draw distance is provided.

In this paper, the differences of the residual stresses due to rolling in a finite elastic-plastic plate by rigid and elastic deformable rollers at very high rolling loads are investigated by two-dimensional plane strain finite element analyses using ABAQUS. In the finite element analyses, the rollers are modeled both as rigid and linear elastic, and have frictionless contact with the elastic-plastic finite plate. The plate material is modeled as an elastic-plastic power-law strain hardening material with a non-linear kinematic hardening rule for loading and unloading. Two new numerical schemes are developed to represent the elastic roller to model the indentation and rolling. The results of the contact pressure and subsurface stress distributions from the two numerical schemes are almost identical.

In this paper, the evolution equation for the active yield surface during the unloading/reloading process based on the pressure-sensitive Drucker-Prager yield function and a recently developed anisotropic hardening rule with a non-associated flow rule is first presented. A user material subroutine based on the anisotropic hardening rule and the constitutive relation was written and implemented into the commercial finite element program ABAQUS. A two-dimensional plane strain finite element analysis of a crankshaft section under fillet rolling was conducted. After the release of the roller, the magnitude of the compressive residual hoop stress for the material with consideration of pressure sensitivity typically for cast irons is smaller than that without consideration of pressure sensitivity. In addition, the magnitude of the compressive residual hoop stress for the pressure-sensitive material with the non-associated flow rule is smaller than that with the associated flow rule.

In this investigation, dissimilar 5754/7075 and 7075/5754 spot friction welds were first made under different processing conditions. The spot friction welds in lap-shear specimens were tested under quasi-static loading conditions. The optimal processing times to maximize the failure loads of the 5754/7075 and 7075/5754 welds under lap-shear loading conditions are identified. The maximum failure load of the 7075/5754 welds is about 40% larger than that of the 5754/7075 welds. Optical micrographs of both types of spot friction welds made at different processing times before and after failure are examined. The micrographs show different weld geometries and different failure modes of spot friction welds made at different processing times. The failure modes of the 5754/7075 and 7075/5754 spot friction welds appear to be quite complex and strongly depend on the geometry and the strength of the interfacial surface between the two deformed sheet materials.

Effects of roller diameter and number on the contact pressures, subsurface stresses and the fatigue lives of cam roller follower bearings are investigated in this paper. Finite element analyses under plane strain conditions were conducted to identify the effects of the diameter and number of the rolling elements and the thickness of the outer ring. The fatigue life of the inner pin generally increases as the roller diameter increases. But, reducing the number of rollers to accommodate larger rollers does not necessarily increase the fatigue life. The inevitable decrease of the thickness of the outer ring due to the increase of the roller diameter results in the increase of compliance for the outer ring. This increase of compliance leads to excessive deformation of the outer ring and consequently more load must be carried by fewer number of rolling elements.

In this paper, residual stresses due to single indentation and rolling on a finite plate at very high rolling loads are investigated by two-dimensional plane strain finite element analyses using ABAQUS. In the finite element analyses, the roller is modeled as rigid and has frictionless contact with the finite plate. The plate material is modeled as an elastic-plastic power-law strain hardening material with a non-linear kinematic hardening rule for loading and unloading. For indentation and rolling at high rolling loads with extensive plastic deformation, the computational results show that the contact pressure distributions are quite different and they are also significantly different from the elastic Hertzian pressure distribution. The computational results for the rolling case show a significantly higher longitudinal compressive residual stress and a lower out-of-plane compressive residual stress along the contact surface when compared to those for the single indentation case.

Failure mode and fatigue behavior of dissimilar laser welds in lap-shear specimens of aluminum and copper sheets are investigated. Quasi-static tests and fatigue tests of laser-welded lap-shear specimens under different load ranges with the load ratio of 0.1 were conducted. Optical micrographs of the welds after the tests were examined to understand the failure modes of the specimens. For the specimens tested under quasi-static loading conditions, the micrograph indicates that the specimen failed through the fusion zone of the aluminum sheet. For the specimens tested under cyclic loading conditions, two types of failure modes were observed under different load ranges. One failure mode has a kinked crack initiating from the interfacial surface between the aluminum and copper sheets and growing into the aluminum fusion zone at an angle close to 90°.

In this paper, failure modes of dissimilar laser welds in lap-shear specimens of low carbon steel and high strength low alloy (HSLA) steel sheets are investigated based on experimental observations. Micro-hardness tests across the weld zones of dissimilar laser welds were conducted. The hardness values of the fusion zones and heat affected zones are significantly higher than those of the base metals. The fatigue lives and the corresponding failure modes of laser welds as functions of the load ranges are then examined. Optical micrographs of the laser welds before and after failure under quasi-static and cyclic loading conditions are then examined. The failure modes and fatigue behaviors of the laser welds under different loading conditions are different. Under quasi-static loading conditions, a necking failure occurred in the upper low carbon steel sheet far away from the laser weld.

Failure mode and fatigue behavior of flow drill screw (FDS) joints in lap-shear specimens of aluminum 6082-T6 sheets made with different processing conditions are investigated based on the experimental results and a structural stress fatigue life estimation model. Lap-shear specimens with FDS joints without clearance hole and lap-shear specimens with stripped FDS joints with clearance hole were made and then tested under quasi-static and cyclic loading conditions. Optical micrographs show the failure modes of the FDS joints without clearance hole (with gap) and the stripped FDS joints with clearance hole under quasi-static and cyclic loading conditions. The fatigue failure mode of the FDS joints without clearance hole (with gap) in lap-shear specimens is similar to those with clearance hole. The fatigue lives of lap-shear specimens with FDS joints without clearance hole are lower than those with clearance hole for given load ranges under cyclic loading conditions.

Failure mode and fatigue behavior of flow drill screw (FDS) joints in lap-shear specimens of aluminum 6082-T6 sheets of different thicknesses are investigated based on the experimental results and a structural stress fatigue life estimation model. Lap-shear specimens of different thicknesses with FDS joints with clearance hole were made and tested under quasi-static and cyclic loading conditions. Optical micrographs show the failure modes of the FDS joints with clearance hole in lap-shear specimens of different thicknesses under quasi-static loading conditions. Under quasi-static loading conditions, as the thickness increases, the FDS joint failed from the penetration of the screw head into the upper sheet to the failure of the screw between the two sheets. Optical micrographs also show the failure modes of the FDS joints with clearance hole in lap-shear specimens of different thicknesses under cyclic loading conditions.

Failure mode and fatigue behavior of friction stir spot welds made with convex and concave tools in lap-shear specimens of dissimilar high strength dual phase steel (DP780GA) and hot stamped boron steel (HSBS) sheets are investigated based on experiments and a kinked fatigue crack growth model. Lap-shear specimens with the welds were tested under both quasistatic and cyclic loading conditions. Optical micrographs indicate that under both quasi-static and cyclic loading conditions, the welds mainly fail from cracks growing through the upper DP780GA sheets where the tools were plunged in during the welding processes. Based on the observed failure mode, a kinked fatigue crack growth model is adopted to estimate fatigue lives of the welds. In the kinked crack fatigue crack growth model, the stress intensity factor solutions for fatigue life estimations are based on the closed-form solutions for idealized spot welds in lap-shear specimens.

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 are investigated. Ultrasonic spot welded, adhesive-bonded, and weld-bonded lap-shear specimens were made. These lap-shear specimens were tested under quasi-static and cyclic loading conditions. The ultrasonic spot weld appears not to provide extra strength to the weld-bonded lap-shear specimen under quasi-static and cyclic loading conditions. The quasi-static and fatigue strengths of adhesive-bonded and weld-bonded lap-shear specimens appear to be the same. For the ultrasonic spot welded lap-shear specimens, the optical micrographs indicate that failure mode changes from the partial nugget pullout mode under quasi-static and low-cycle loading conditions to the kinked crack growth mode under high-cycle loading conditions.

Failure mode of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel is investigated in this paper. The experimental results from quasi-static tests show that the laser welds failed in a ductile necking/shear failure mode near the heat affected zone. In order to understand the failure mode of these welds, a finite element analysis under plane strain conditions was conducted to identify the effects of the different plastic behaviors of the base metal, heat affected zone, and weld metal on the ductile failure. The results of the finite element analysis show that the higher effective stress-plastic strain curves of the weld metal and the heat affected zone results in the necking/shear failure mode. The deformed shape of the finite element model near the weld matches well with that of a failed weld.

Failure modes of friction stir spot welds in lap-shear specimens of dissimilar high strength dual phase steel (DP780GA) and hot stamped boron steel (HSBS) sheets are investigated under quasi-static and cyclic loading conditions based on experimental observations. Optical micrographs of dissimilar DP780GA/HSBS friction stir spot welds made by a concave tool before and after failure are examined. The micrographs indicate that the failure modes of the welds under quasi-static and cyclic loading conditions are quite similar. The micrographs show that the DP780GA/HSBS welds mainly fail from cracks growing through the upper DP780GA sheets where the concave tool was plunged into during the welding process. Based on the observed failure modes, a kinked fatigue crack growth model is adopted to estimate fatigue lives.

A failure prediction methodology that can predict sheet metal failure under arbitrary deformation histories including rotating principal stretch directions and bending/unbending with consideration of damage evolution is reviewed in this paper. An anisotropic Gurson yield criterion is adopted to characterize the effects of microvoids on the load carrying capacity of sheet metals where Hill’s quadratic anisotropic yield criterion is used to describe the matrix normal anisotropy and planar isotropy. The evolution of the void damage is based on the growth, nucleation and coalescence of microvoids. Mroz’s anisotropic hardening rule, which was proposed based on the cyclic plastic behavior of metals observed in experiments, is generalized to characterize the anisotropic hardening behavior due to loading/unloading with consideration of the evolution of void volume fraction. The effects of yield surface curvature are also included in the plasticity model.

Fatigue behavior of spot friction welds or friction stir spot welds in lap-shear specimens of dissimilar aluminum 5754-O and 7075-T6 sheets is investigated based on experimental observations and two fatigue life estimation models. Optical micrographs of the 5754/7075 and 7075/5754 welds after failure under cyclic loading conditions are examined to understand the failure mechanisms of the welds. The micrographs show that the 5754/7075 welds mainly fail from the kinked fatigue crack through the lower sheet thickness. Also, the micrographs show that the 7075/5754 welds mainly fail from the kinked fatigue crack through the lower sheet thickness and from the fracture surface through the upper sheet thickness.