Geometric correction factors determined by force balance method for center cracked specimens

Abstract

In Part X of this series [1], the force balance method (FBM) has been applied to determine the geometric correction factor of the center cracked specimen loaded by linearly distributed stresses with the maximum value occurring at the crack tip. Such a case and the previously considered cases [2] may be used to account for fatigue crack closure effects, extrinsic toughening mechanisms like zone shielding and contact shielding [3,4], crack-face cohesive forces and/or bridging stresses in composite materials [5-10]• There are several types of crack bridging models in brittle-matrix fiber-reinforced composite materials, such as constant bridging stress [10], shear lag [11][12][13], fiber pressure [14] models. Obviously, in the constant bridging stress model the bridging stress was assumed to be unchanged over the entire bridged area. The geometric correction factor for this case has been deduced in Part VIII [2]. In both the shear lag and the fiber pressure models, the bridging stress increases with increasing distance from the crack tip. In other words, the bridging stress is linearly distributed in the fiber pressure model and is zero at the crack tip in the shear lag model [14][15][16]. In addition, the following power-law has been utilized to describe the bridging stress distribution [ 16],where ob,(x ) is the bridging stress distribution along the crack wake, oh, is the maximum bridging stress, a is the half-crack length for the center cracked tension (CCT) specimen, x is the distance from the center of the notch/crack, d is the diameter of the initial center notch, n is an exponent characterizing the shape of the bridging stress distribution. Clearly, the exponent n equal to 0 and 1 corresponds to a constant and linear stress distribution beginning at the crack tip, respectively.Int ~u r n of Fracture 81 (1996) R64Based on these bridging stress models presented in the literature and in view of the fact that all of the practically-used specimens are of finite dimension, it is vitally important to determine the geometric correction factor, or sometimes called non-dimensional stress intensity factor, for the cases of the bridging stress distributions.Since the geometric correction factor for the case of n--0 in (la) has been calculated in [2], the case of n=l is considered only in the current paper. For simplicity, 6b,~ ` and a-d~2 in (la) are replaced by ~ and b, respectively, then (la) becomes: