Stress Intensity Factor Using Quarter Point Element

Abstract

The finite element analysis to determine stress intensity factors (SIF's) is complex but useful. It is complex due to the stress singularity that exists at the crack tip, which requires a large number of conventional elements to model satisfactorily. Its usefulness lies in its generality because of the limited capabilities of analytical tools to calculate SIF's for general crack geometries, complicated boundary conditions and material nonlinearity. The necessity of a very fine mesh of conventional elements in the vicinity of crack tip regions can be overcome by using special elements which incorporate or can generate the required stress singularity. The accuracy and efficiency achieved by the use of these elements will vary. The mathematical expressions are often rigorous, and usually share the common disadvantages, such as the lack of interelement continuity and the constant strain term, excessive programming and error‐prone determinations of SIF. The quarter point element (QPE) is free from these weaknesses, is simple, efficient and requires no additional programming. Due to the accuracy of QPE results, QPE is preferred over any other special cracktip element.