Single and Double Cantilever Beam Large Displacement Mixed Mode Fracture Toughness Test Methods and J-integral Analyses

The J-integral is applied to the single cantilever beam (SCB) and double cantilever beam (DCB) test specimens subjected to both mixed mode I and II loading and large displacements. The methods proposed and resulting closed form theoretical equations allow for the instantaneous evaluation of J during laboratory tests, requiring only the applied load and angular rotation of the specimen loading link, loading points and remaining ligament. These measurands can be acquired using a common load cell and markers, digital video camera, and video analysis software. In general, the equations do require knowledge of the specimen elastic moduli and shear moduli, as well as the specimen linear dimensions. Since the test data can be analyzed and J determined throughout the test instantaneously, and since, due to geometric non-linearities, the ratio of mode I and mode II loading will likely vary significantly throughout the test, each specimen can be used to generate multiple data points. If crack length is determined throughout the test, presumably by directly measuring the crack length optically, then when the crack advances, critical values of J for mixed mode loading can be determined using the methods and results presented. It is noted that moderate to large translational and rotational displacements actually improve the accuracy of the results using these methods. The results are applicable to standard purely mode I or purely mode II SCB and DCB tests as well and reduce to known equations in those special cases.