# Axisymmetric Solutions for Highly Undermatched Tensile Specimens

## Abstract

The specimens considered in this chapter are axisymmetric welded solid or hollow circular cylinders with the weld orientation orthogonal to the axis of symmetry which is also the line of action of forces applied. An axisymmetric crack is entirely located in the weld. The outer radius of the cylinder is denoted by *R*, the inner radius (when it is applicable) by *R* _{0}, and the thickness of the weld by 2*H*. Also, \( u_{r} \) stands for the radial velocity and \( u_{z} \) for the axial velocity in a cylindrical coordinate system (*r*, θ, *z*). The solutions are independent of θ. Therefore, velocity discontinuity surfaces are referred to as velocity discontinuity curves (or lines) which are in fact the intersections of the velocity discontinuity surfaces and a plane \( \theta = {\text{constant}} . \) Moreover, integration with respect to θ in volume and surface integrals involved in Eq. (1.4) is automatically replaced by the multiplier \( 2\pi \) without any further explanation. Base material is supposed to be rigid.

## Keywords

Radial Velocity Plastic Zone Cylindrical Coordinate System Limit Load Velocity Discontinuity## References

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