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.

Stress Intensities at Spot Welds

Stress singularity, notch stress and structural stress at spot-welded joints

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.

Fracture mechanics solutions to spot welds

The stress intensities (stress intensity factors and J-integral) around a spot weld between sheets of dissimilar materials and different thicknesses are generally expressed by the local stresses around the spot weld. The derivations are established on an interface crack model which represents the radial cross-sections of the spot weld with the local stresses varying from point to point along the periphery of the nugget. The J-integral is determined analytically by applying the equilibrium conditions and the elementary plate theory to the model. The stress intensity factors are then separated by following a load decomposition procedure and an analytic solution to interface cracks. The thermal stress intensities are also obtained for the spot weld. Application examples are given for a tensile-shear specimen.

Stress Intensities Derived from Stresses Around a Spot Weld

Overload failure curve and fatigue behavior of spot-welded specimens

A J-integral approach was used in this study to predict the fatigue lives of spot welds subjected to tensile-shear loads. Using a three-dimensional finite element program, J-integral values were computed for spot welds that reflect the overall weld stiffness

A J-Integral Approach to Fatigue Resistance of a Tensile-Shear Spot Weld

An enhanced head-and-neck restraint system is provided for use with a vehicle having a passenger compartment with a seat assembly and a safety belt assembly mounted therein. The restraint system includes first and second collar straps each having an inflatable cushion integrated thereto. A first end of each collar strap is attached to a headrest portion of the seat assembly to transition between a retracted position, in which the collar straps are substantially inside the headrest portion, and a use position, in which each collar strap attaches to a belt webbing of the safety belt system. A fluid dispensing apparatus is in fluid communication with the inflatable cushions, and operable to selectively transition the inflatable cushions from a non-expanded state to an expanded state when the collar straps are in the use position.

Kon-Mei W. Ewing

Papers

A J-Integral Approach to Fatigue Resistance of a Tensile-Shear Spot Weld

Retractable supplemental inflatable restraint system for vehicle head rest