Mixed-Mode Elastic-Plastic Fractures: Improved $R$-Criterion

For elastic-plastic materials, the plastic core region around a crack tip generally has a limited dimension, and therefore, the corresponding radius $r_p$ from the crack tip to the elastic-plastic boundary can be considered as a critical parameter. However, neither the critical radius $r_{p\text{I}c}$ for mode I nor the critical radius $r_{p\text{II}c}$ for mode II can be applied solely as the critical parameter to predict mixed-mode fractures well. In current work, a new parameter combining $r_{p\text{I}c}$ with $r_{p\text{II}c}$ has been proposed, and accordingly, the preexisting $R$-criterion has been improved. The improved $R$-criterion not only can predict crack initiation angle but also can predict the critical load, which is more significant in predicting material fractures. A series of fracture tests using the semicircular bend specimens with different mode mixities were conducted on polycarbonate (PCBA), and the test results were compared with the predictions of several criteria. This comparison shows that the test results agree well with the improved $R$-criterion. Finally, the advantage of using a combination of mode I and mode II fracture toughness in a criterion is analyzed.