*Article* **A Theory of Autofrettage for Open-Ended, Polar Orthotropic Cylinders**

### **Marina Rynkovskaya 1,\*, Sergei Alexandrov 2,3 and Lihui Lang 2**


Received: 1 January 2019; Accepted: 19 February 2019; Published: 22 February 2019

**Abstract:** Autofrettage is a widely used process to enhance the fatigue life of holes. In the theoretical investigation presented in this article, a semi-analytic solution is derived for a polar, orthotropic, open-ended cylinder subjected to internal pressure, followed by unloading. Numerical techniques are only necessary to solve a linear differential equation and evaluate ordinary integrals. The generalized Hooke's law connects the elastic portion of strain and stress. The flow theory of plasticity is employed. Plastic yielding is controlled by the Tsai–Hill yield criterion and its associated flow rule. It is shown that using the strain rate compatibility equation facilitates the solution. The general solution takes into account that elastic and plastic properties can be anisotropic. An illustrative example demonstrates the effect of plastic anisotropy on the distribution of stresses and strains, including residual stresses and strain, for elastically isotropic materials.

**Keywords:** residual stress; residual strain; open-ended cylinder; autofrettage
