Effect of stress biaxiality on fracture energy and microstructures of tensile cracks

The onset of crack propagation is often described with a unique threshold and intrinsic material property, the fracture energy. However, in geomaterials, this parameter varies with environmental and loading conditions (e.g., temperature, confining pressure, humidity, loading rate, etc.). This can be explained by more elaborate models in which the fracture energy is set by the weakening mechanisms at stake during material breakdown. Variations in fracture energy may then be attributed to a change in the failure mechanisms occurring in a dissipative region located very near the crack tip. Here, we show how stress biaxiality can cause a shift in the mechanisms dictating crack propagation and how they consequently affect the fracture energy.

 

To this end, we performed modified ring tests (MRT) and wedge splitting tests (WST) on Carrara marble. These tests were selected for their stable configurations, while they have opposite stress biaxiality levels; -8 and +5 MPa respectively for MRT and WST. These tests also allow continuous fracture energy measurements thanks to a compliance method previously calibrated on PMMA experiments. We halted crack propagation and extracted thin sections at the tip, on which we acquired backscatter electron (BSE) and electron backscatter diffraction (EBSD) maps using a scanning electron microscope.

 

These experiments showed that the fracture energy is test dependent: it ranges between 20 to 30 J/m² on the MRT, and 20 to 80 J/m² on the WST, depending on the crack tip position. Interestingly, the variations of fracture energy seem correlated with variations of stress biaxiality and associated microstructures. The BSE and EBSD scans show that the crack is mostly intra-granular and straight at a negative stress biaxiality level on the MRT. While at a positive level on the WST, the crack travels through grain boundaries with significant branching and higher tortuosity. These observations are in good agreement with theoretical studies on crack path in heterogeneous materials. However, one may expect that a shift from inter-granular (WST) to intra-granular (MRT) fracture would be associated with higher fracture energy, as the crack crosses through tough grains rather than weak grain boundaries. The opposite is measured as “en-passant” cracks occasionally form on the crack path during wedge-splitting tests. It creates bridging patches that oppose crack opening and double the fracture energy. These microstructures might be key to large variations of tensile fracture energy observed in geomaterials, whose fracture behavior is strongly influenced by stress biaxiality.