We have investigated the fracture of Antarctic shelf ice core using two fracture mechanics test methods: the chevron-notched short-rod specimen loaded in tension and the chevron-notched round-bar specimen loaded in three-point bending. These tests have been used to measure the fracture initiation toughness, Kinit, at which crack growth starts, on samples taken through the entire thickness of the Ronne Ice Shelf, from low-density firn through consolidated meteoric ice to basal marine ice. The fracture data are presented together with depth profiles of relevant physical and mechanical properties derived from the test specimens: temperature, density, elastic modulus, and grain size. It is found that the trend in measured fracture toughness closely reflects changes in ice density and elastic modulus. We augment the experimental study by presenting a fracture mechanics analysis of ice shelf surface and basal crevassing which directly incorporates our measurements. For the examined ice shelf profiles, basal crevasses are found to be inherently unstable unless an external restraining force is imposed, which has important implications for overall ice shelf stability. On the other hand, surface crevassing is shown to be innately stable at depth. Our fracture mechanics model is used to predict local ice shelf back stresses in the vicinity of basal crevassing and is validated directly against field observations of crevasse penetration on the Ronne Ice Shelf.