An analytical solution for the correct determination of crack lengths via cantilever stiffness

TL;DR

This paper introduces an analytical solution for accurately determining crack lengths in microscopic cantilever fracture specimens, improving precision and reducing reliance on simulations.

Contribution

The paper presents a new compact analytical relationship based on classical beam theory that accounts for actual beam geometry and significantly improves accuracy over existing models.

Findings

Model reduces deviation to 1.6% from 15%.

Agrees well with finite element simulations.

Facilitates comparison of microcantilever fracture experiments.

Abstract

The present work provides an analytic solution for the stiffness to crack length relation in microscopic cantilever shaped fracture specimens based on classical beam theory and substitution of the crack by a virtual rotational spring element. The resulting compact relationship allows for accounting of the actual beamgeometry and agrees very well with accompanying finite element simulations. Compared with the only other model present in literature the proposed relationship reduces the deviation between model and data to a maximum of 1.6% fromthe previous minimumof 15%. Thus, the novel solution will help to reduce the necessity for individual simulations and aim to increase the comparability of elastic-plastic microcantilever fracture experiments in the future.