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This paper shows how the concise K and compliance formats can be used in analysis that are common in fracture mechanics evaluations. The concise forms of the stress intensity factor, K, solutions, and the corresponding compliance equations were introduced by Donoso and Landes at the 30th National Symposium. This form was based on the separability of the elastic form of the load and displacement relationships and was done as an analogy to the same separability for the plasticity relationships. The concise format could replace the present calibrations that require polynomial solutions in some cases where the application could benefit from a simpler K calibration format. A big advantage comes when the K or compliance functions are used in application models where a closed form evaluation would be desirable. The first example is the use of compliance to evaluate crack length or crack length change. Calculations using compliance are used to evaluate crack length in an elastic unloading compliance evaluation of physical crack length that would be used in a J-R curve fracture toughness evaluation. Using the concise format the compliance can be easily inverted to solve for crack length from the compliance expression. All evaluations of crack length can be done easily with a hand calculator. Other examples show how the relationship between the compliance change and the crack length change can be evaluated by a simple expression. This is used in the KIc test of E 399 or E 1820. Other examples presented in this paper, show how the plastic instability model of Paris and Vasquez can be evaluated in closed form using this formulation and how the K-R curve instability point can be calculated in closed form. Other uses of a separation approach to determining calibration functions could be applied. The separation format is already used for plasticity. The ranges of applicability could be better defined by using the elastic analogy.
linear-elastic fracture mechanics, calibration functions, elastic compliance, crack length
Universidad Técnica Federico Santa María, Valparaíso,
University of Tennessee, Knoxville, TN