Volume 19, Issue 1 (January 1991)
Improved Wide Range Expressions for Displacements and Inverse Displacements for Standard Fracture Toughness Specimens
Wide range expressions (interpolating polynomials) for displacements for standard ASTM fracture testing specimens have been developed. The strategy was to fit displacements as a function of crack length for all the specimens using a similar form of nondimensional displacement. Different forms appear in different ASTM standards for the same or similar specimens. The criterion used to establish the degree of polynomial fit and number of significant figures for the coefficients of the polynomial was for the polynomial to agree with the best available numerical displacement solutions to within 1% or better. Once the polynomials for displacement as a function of crack length were developed, inverted forms of the specific interpolating polynomials were obtained to determine relative crack length (a/W) as a function of displacement. Since the inverted polynomial will be used in tandem with the interpolating polynomial, the inverted polynomial was fit to the interpolating polynomial and not the numerical solution for displacement. Three forms of nondimensional displacements were used to invert the interpolating polynomials. The criterion used to establish the degree of polynomial and the number of significant figures of the coefficients of the polynomial was for the predicted relative crack length to agree with the actual relative crack depth to within 0.0005W. A sensitivity analysis was performed to suggest which form of interpolating polynomial should be used for standards.