Size-dependent energy release rate formulation of notched beams based on a modified couple stress theory

Highlights
• A size-dependent energy release rate for notched beams has been developed.
• The energy release rate of notched beams under three-point bend condition has been formulated.
• The energy release rate is a function of the ratio of the length scale to beam depth.
• The results are in good agreement with the experimental observations.
• The energy release rate of the Timoshenko model is greater than Euler–Bernoulli one.

The modified couple stress theory is employed in this paper in order to formulate the size-dependent strain energy release rate of Euler–Bernoulli and Timoshenko notched beams. As a case study, the normalized energy release rate of the aforementioned beams has been developed for three-point bending as a function of the ratio of material length scale parameter to the beam depth. The results of the current model are compared to the experimental data. The good agreement between the present results and the experimental values indicates that the current model can be successfully applied to evaluate size dependent energy release rate of structures.