First- and second-order approaches for the direct determination of bridging stresses from R-curves

A procedure is presented that allows the simple estimation of bridging stresses from crack growth resistance curve (R-curve) data. The first-order approximation results by taking the derivative of the R-curve. For an increased degree of accuracy a second-order solution is suggested. This step includes straight-forward integration of the first-order results. The procedure is outlined in detail and applied to fatigue threshold R-curve results for a MgO + Y2O3-doped silicon nitride (MgY-SN) and an 99.5% pure alumina obtained with compact tension specimens, and fracture toughness R-curve results for a MgO + La2O3-doped silicon nitride (MgLa-SN) obtained with notched bending bars. The approximate bridging stresses are compared with the “full solutions” computed with much more effort by solving a system of integral equations.