The mode III fatigue crack growth threshold for mild steel

Fatigue cracks grow perpendicular to the maximum principal applied tensile stress, or put more precisely into fracture mechanics terms, in mode I. Like most generalizations this one has its exceptions, but it does mean [I] that fatigue crack growth data can conveniently be analyzed in terms of the range of mode I stress intensity factor, AK I. A threshold value of AKI, AKIt must be exceeded before a crack will propagate. Various techniques can be used to determine AKIt ; a simple approach is to define the threshold in terms of the fatigue limit of cracked specimens. Conventional specimens used to determine fatigue crack growth behaviour have the initial crack oriented perpendicular to the applied stress. In practice components fail by fatigue from crack-like flaws that are not necessarily at right angles to the maximum principal stress, and crack growth will be in general not be in the plane of the initial crack. Definition of threshold behaviour in terms of the fatigue limit of cracked specimens extends naturally to such combined mode situations; for example, AKIIIt may be defined as the critical value of AKIIIt , the range of the shear mode stress intensity factor necessary to cause growth with leads to failure, even though crack growth is not in the plane of the initial crack. It has recently been found [2] that the fatigue crack growth thresold behaviour of mild steel for pure mode II and combined mode I and II loadings depends on two separate factors: firstly, whether or not a mode I branch crack forms at or near the precrack tip under the loading being applied, and secondly, whether the loading is sufficient to cause continued crack growth from the branch. If such a branch forms easily, or is already present, threshold behaviour is controlled by AK I for the branch crack. If for some reason branch crack formation is suppressed, higher apparent threshold values are obtained. It follows that, for the understanding of mode Ill threshold behaviour, the stress intensity factor for a mode I branch at a mode III crack is required. Two dimensional cases involving small branch cracks have been extensively discussed, for example, [3]. The problem of a mode I branch at a mode III crack is more difficult because of its three dimensional nature. Approximate solutions to branched crack problems in the two dimensional case can be obtained [3] by solving the problem of an application of the prior traction on the branch, but merely ensuring that the "extended branch" (Fig. I) is traction free. Application of this method to a mode III branch at a mode III crack gives KIII (branch) = KIII [main), and is independent of the branch angle @. For an element of a mode I branch (Fig. 2), K I [branch) = KIII (main), but geometrical incompatabilities prevent assembly of these elements into a crack. Consideration of various possible configurations suggests [4] K I (branch) =