On problems with the determination of the fracture resistance for materials with spatial variations of the Young's modulus

摘要

The paper considers the near-tip J-integral , the far-field J-integral , and the experimental J-integral in a material with sinusoidal variation of the Young's modulus . The evaluations of and are based on the concept of configurational forces; is evaluated from the area below the load point displacement curve, as prescribed by the standard testing procedures. Analytic expressions and/or approximation formulae are derived, how and depend on the system parameters of the material, i.e. wavelength and amplitude of the -variation and its phase shift with respect to the crack tip position, and the global specimen dimensions. The analyses show that and exhibit a strong dependency on the phase shift, but not the experimental J-integral . This is the reason why the current procedures for fracture mechanics testing are not suitable to determine the true values of the fracture initiation toughness or the crack growth resistance of a material, if the material properties exhibit a spatial variation in the direction of crack propagation. Relations are given to estimate the possible errors.