Issue34

N.R. Gates et alii, Frattura ed Integrità Strutturale, 34 (2015) 27-41; DOI: 10.3221/IGF-ESIS.34.03 29 This then leaves two possibilities for subsequent crack growth; the crack can either branch and grow in mode I on maximum tensile planes, or the crack can remain coplanar and grow in mode II or mixed-mode conditions until failure. Concerning the first possibility, there is a reasonable amount of literature available describing the processes governing the transition from stage I to stage II crack growth. Murakami and Takahashi [17] studied the behavior of small mode II cracks growing under near threshold conditions for pure torsion loading of medium carbon steel solid cylindrical specimens. They observed three different conditions for crack growth from a precrack. Cracks either started to grow in both modes I and II from the precrack tip, with the mode II cracks stopping after a short distance to give way to the more dominant mode I cracks, or only mode I cracks were observed to grow from the precrack tip, or the crack propagated in mode II for a short distance before eventually branching to grow in mode I. Crack branching was attributed to a higher threshold stress intensity factor (SIF) value for modes II and III as compared to mode I. They argued that this led to an arrest of shear-mode cracks as they dropped below their threshold value which gave way to mode I growth as cracks were still above the mode I threshold SIF value [7]. They concluded that the mode I SIF of the branched cracks governed the fatigue limit for small cracks in torsion and were able to predict the fatigue limit using an extension of the square root of area parameter [17]. Makabe and Socie [18] studied crack growth in precracked specimens of 4340 steel under torsion loading with and without the influence of static axial stresses. They observed that cracks grew longer in mode II before branching as the applied shear strain and/or static axial stress increased. This was attributed to decreased contact and friction between opposing crack faces and the resulting change in slip band density surrounding the crack tip. The eventual branching mechanism was described as a zig-zagging between perpendicular slip bands generated in the vicinity of the crack tip. It was concluded that in order for a crack to continue to grow in shear-mode, the driving force for shear deformation at the crack tip must be large enough to overcome the friction between crack faces. Considering the effects of crack face friction, Tong et al . [19] proposed a model to describe changes in local stress intensity factors during shear-mode crack growth based on an idealized crack face asperity angle and coefficient of friction. The model was developed for a two-dimensional edge crack growing nominally in pure mode II and relates theoretical crack sliding displacements computed using finite element analysis (FEA) to local displacement components due to wedging of crack face asperities. The local displacements are then used to compute a local reduction in mode II SIF due to friction and a local increase in mode I SIF due to wedging. Comparing the effective mode II SIF to the local mode I SIF provides a means of predicting crack branching. The model predictions were not compared directly to experimental results, but the predicted trends agreed with experimental observations. In an extension of the same work [20], the model was applied to mixed-mode I and II loadings and could be extended to other crack geometries as well, provided the appropriate weight functions and crack face loading distributions are known. More recently, Künkler et al . [21] predicted the two-dimensional crack propagation behavior of short cracks under uniaxial loading in the region of stage I to stage II transition using a microstructure sensitive modeling technique. They found that mode II growth occurs primarily on single slip systems within individual grains. Once the crack reaches a length where its plastic zone is large enough to activate additional slip systems in neighboring grains, the crack begins to transition to mode I growth by switching from a single slip mechanism to a double slip propagation mechanism. In double slip crack growth, shear displacements on the two different slip systems cause a crack tip opening which promotes mode I crack extension. The crack length at this transition was considered dependent upon crack geometry, grain size, and the orientation of slip systems in neighboring grains. In 2014, Pokluda et al . [10] reviewed research on shear-mode crack behavior in metallic materials. It was concluded that the main factor driving the branching of mode II cracks is crack face friction and wedging caused by surface asperities. These asperities result from microstructural level crack meandering due to differing orientations of slip systems, and their average inclination angle was shown to vary based on the crystallographic structure of the material. When mode II sliding displacements occur between opposing crack faces, the wedging effect of these asperities acts to simultaneously reduce the effective value of the mode II SIF and introduce a local mode I SIF component. When the conditions are such that the local mode I SIF value exceeds the mode I threshold, crack branching is considered to occur. The authors applied a simple crack branching criterion to predict whether or not crack branching would occur in the threshold region before a crack became non-propagating. They compared the predictions to experimental data of four different metals and reported good agreement. While the aforementioned studies deal with describing or predicting the development of a mode I branch from a mode II crack in the near threshold regime, far less literature is available concerning the conditions for continuous coplanar shear- mode propagation of a crack. Tschegg [11] discussed this issue in a study of mode III crack growth behavior in circumferentially grooved cylindrical specimens of 4340 steel. The change in fracture mode was found to coincide with the intersection of the mode I and mode III crack growth curves. At lower stress intensity values, where crack branching and