Experiments on a Quasibrittle Material: Strength and Fracture Properties

Abstract

This study investigated the strength and fracture properties of a typical quasibrittle solid, Dunnville sandstone, using digital image correlation (DIC) and acoustic emission techniques. Fracture experiments were conducted with three-point and four-point bend beams, notched and smooth boundary respectively, using 20 specimens of three sizes: large (span 484 mm × depth 164 mm), medium (242 mm × 82 mm), and small (121 mm × 41 mm), for a total of 60 geometrically similar beams. Only the results from the large specimens are reported because the medium and small beams experienced some damage such that the Young’s moduli were 30% and 40% lower than the large beams. For the large, notched specimens, the fracture process zone (FPZ) was characterized based on a cohesive zone representation, and DIC was used to determine the critical crack opening ω_c, FPZ length l_p, and the effective crack tip. The latter was assessed using a displacement gradient method, which involved analyzing two slopes of the gradient variation along the ligament, one associated with the FPZ and the other with elastic behavior. By identifying the position of the effective tip and ω_c, which is assumed to equal the maximum crack opening at peak load, the length of the process zone, l_p, was determined. The average FPZ length is 18 mm for the large notched specimens and 11 mm for smooth boundary specimens; the average crack opening at peak load is 31 µm at the notch tip and 10 µm at the bottom fiber for smooth boundary beams. An alternative geometry is developed with ease of loading and efficient material usage in mind. The specimen design is an internally-pressurized thick-walled cylinder, with a solid elastomeric cylinder placed inside the cavity to generate internal pressure. The interaction problem is solved to obtain a relation between axial stress applied to the elastomeric cylinder and the internal pressure generated within the cavity; calibration experiments with an aluminum specimen confirmed the relation. The cavity diameter of the rock specimen is changed from 22.7 mm to 45.2 mm to investigate a size effect, and a square plate, 164 × 164 mm, is substituted for the cylinder; finite element analysis indicated virtually no change in the stresses near the cavity. Nineteen cavity expansion strength tests showed a size effect, where nominal strength σ_t = 4.28 MPa and 2.20 MPa for small (22.7 mm) and large (45.2 mm) cavity sizes, respectively. Assuming linear elastic fracture mechanics (LEFM) applies for the large, notched beams, fracture toughness K_IC = 0.339 MPa∙m0.5 for cracking parallel to the bedding direction. Taking this K_IC value, the crack lengths for these two holes sizes are calculated to be 5 mm and 16 mm. In summary, the failure of quasibrittle materials due to fracture is influenced by size effects on specimen structural strength, where the failure process can be characterized by the formation of the FPZ. Within the context of a cohesive zone model, the critical crack opening is assumed to form at the point of unstable crack growth, which is the peak load. The process-zone length is determined from a detailed analysis of the (opening) displacement gradient, where the tip was identified by the gradient variation along the crack length.