Plane Strain Solutions for Highly Undermatched Scarf Joint Specimens
The specimens considered in this chapter are welded plates with the weld inclined at some angle to the line of action of two tensile forces applied. This angle is denoted by π/2 − α. By assumption, the constraints imposed require that the rigid blocks of base material move along the line of action of the forces. A crack is entirely located in the weld. Edge cracks are excluded from consideration. The width of the plate is denoted by 2W, its thickness by 2B, the thickness of the weld by 2H, and the length of the crack by 2a (except the last solution of this chapter which deals with cracks of arbitrary shape in the plane of flow). The specimens considered in the previous chapter are obtained at α = 0. Since plane strain solutions are of concern in this chapter, integration in the thickness direction in volume and surfaces integrals involved in Eq. (1.4) is replaced with the multiplier 2B without any further explanation. For the same reason, the term “velocity discontinuity surface” is replaced with the term “velocity discontinuity curve (or line)”. The latter refers to curves (lines) in the plane of flow. Base material is supposed to be rigid.