The Asymptotic Stress Field for Free Edge Joints under Small - Scale Yielding Conditions

In the complex engineering structures the use of bonded joints are often preferred to more traditional methods of fabrication such as bolts and welds since they are lighter and spread load more evenly. For determination the durability of such structures it is necessary to know well the stress field around stress concentrators. At the free edge of bonded joints between the adhesive and the adherend layers it is well-known that there exists an elastic singular stress field. However, little is known about the material behavior beyond the yield point. This paper presents the small-scale yielding plane-strain asymptotic field calculated for the interfacial free-edge joint singularity. Non-linear elasto-plastic materials with Ramberg-Osgood power-law hardening properties bonded to a rigid elastic substrate were considered. The leading order problem consists of five non-linear ordinary differential equations. The numerical solutions were obtained using a fourth order Runge Kutta numerical method fitted to the governing equations. For exemplification the singularity orders for the interfacial free-edge joint with an angle of 60◦ are shown plotted against hardening exponent.