Stress-Intensity Factors for Single-Edge-Notch Specimens in Bending or Combined Bending and Tension by Boundary Collocation of a Stress Function

Abstract : A boundary-value-collocation procedure was used in conjunction with the Williams stress function to determine values of the stress-intensity factor K for single edge cracks of various depths in specimens subjected to pure bending. The results are of use in connection with K(sub Ic) fracture toughness tests, which utilize rectangular-section crack-notch beam specimens loaded in four-point bending, and are in good agreement with published results derived from experimental compliance measurements. The results are expressed in convenient, compact form in terms of the dimensionless quantity Y(exp 2)=K(exp 2)B(exp 2)W(exp 3)/M(exp 2), which is a function of relative crack depth a/W only, where B and W are the specimen width and thickness and M is the applied bending moment. On the assumption that the condition for a valid K(sub Ic) test is that the maximum nominal stress at the crack tip should not exceed the yield strength of the material, the K(sub Ic) measurement capacity of bend specimens was estimate as a function of a/W. The measurement capacity is proportional to the yield strength and to the square root of the specimen depth, and it is greatest for a/W in the range 0.2 to 0.3. Values of K for single-edge-notch specimens subjected to combined bending and tension were obtained by superposition of the present results and those of earlier work for specimens loaded in uniform tension. These values are of interest in connection with the use of single-edge-notch specimens that are off-center pin-loaded in tension. It is shown that the K(sub Ic) measurement capacity of such specimens is not very sensitive to the eccentricity of loading.