Estimation of the plastic volume fraction from a linear-elastic finite element analysis

The plastic volume fraction is one of a range of parameters used in the design of rotating components that are subjected to an overspeeding cycle as part of the manufacturing process. Overspeeding is carried out in order to impart favourable residual compressive stresses and thereby improve the component's fatigue life. However, the amount of material that becomes plastic during overspeeding needs to be controlled carefully if pre-machined manufacturing tolerances are to be maintained. The plastic volume fraction expresses the volume of material in which yield has occurred as a fraction of the total volume, the actual value of which may only be determined through non-linear plastic analysis. The complexity and associated cost of such analyses are of such a level that a linear-elastic approximation to the plastic volume fraction is often used in lieu of the exact quantity. This paper presents a scheme for estimating the plastic volume fraction as a post-processing operation conducted on the results of a three-dimensional linear-elastic finite element analysis. The performance of the scheme is evaluated through numerical examples using element types typically found in commercial finite element codes. In addition to considering how the scheme is able to approximate the linear-elastic plastic volume fraction, plastic analysis is used to illustrate the way in which this quantity approximates the actual plastic volume fraction. The paper concludes with the analysis of a centrifugal impeller; a component drawn from the author's own field of interest. This analysis enables the various strands of the paper to be brought together and provides an example through which it is possible to discuss suitable limiting values for the plastic volume fraction. The examples indicate a plastic volume fraction of 0.05 to be a reasonable limiting value for the linear-elastic approximation adopted in this paper.