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Compact Shear Specimen for Mode II Fracture Tests: Analysis and Fracture Interpretation

The work presents theoretical analysis and fracture interpretation of Compact Shear (CS) specimen for Mode II fracture testing of materials. Two fracture criteria are used: the maximum circumferential stress criterion and the criterion of minimum strain energy density. The problem for two parallel crack s in an infinite body under shear loading as in the CS specimen is simplest model for this investigation. Previously obtained results for stress intensity factors (Petrova, Sadowski, 2012) are used in this investigation. The interaction of the cracks leads to mixed-mode loading conditions near the crack tips. The dominant stress intensity factor is Mode II KII, but KI is also non-zero. Using the fracture criteria the direction of crack propagation as well as the critical condition under which the crack would initiate is calculated. The influence of the geometry of the problem, i.e. the crack inclination angle to the remote shear loading, distance between the cracks, on the main fracture characteristics is investigated. Introduction Many materials, such as cement pastes, concretes, wood, different composites, are generally weak in shear [1] and also reveal shear fracture under compression [2]. The shear fracture is also observed and intensively investigated for geomaterials [3]. Hence the study of materials response to shear load is important in fracture mechanics of materials. For experimental shear Mode II fracture tests the geometry of the specimen and loading conditions should be chosen so that to induce shear with minimal influence of normal stresses, to minimize influence of edges of the specimen on the crack tips, to prevent friction between the cracked faces. The friction between the faces behind the crack tips can cause a significant increase in values of Mode II stress intensity factor KII [4,5]. Besides, it was shown in [4] that the compressive stresses ahead of the crack tip significantly affect the Mode II fracture. The general expression for the stress intensity factors (Mode I and Mode II) is written as a P f K II I II I , ,  , where P is applied load, a is the crack length and fI,II is the geometric correction factor. All geometrical effects are reflected in fI,II. The fracture parameters are measured in a test on any specimen, provided fI,II is known for the configuration. Because of analytical solutions are not available for the real specimen geometries finite element analysis and boundary element analysis are used for determination of fI,II. Different types of Mode II specimens are used, a review of these specimens can be found, for example, in [6] and in the stress intensity factors handbook [7]. One of these specimens, the compact shear (CS) specimen was introduced in [8,9], Fig. 1. This specimen is convenient for Mode II fracture testing, but experimental and numerical investigations show significant differences in the values of the stress intensity factors have resulted from minor geometrical differences [8,9,10]. Therefore the problem for study CS specimens in order to get the optimal specimen geometry remains important for planning the Mode II fracture experiment. It has been observed that a crack under mixed mode loading and, in particular, under Mode II loading will not follow a straight path, but will deviate at an angle φ with respect to the crack axis. For mixed mode cases special fracture criteria are formulated, which determine the critical conditions for crack propagation and the direction of this propagation, i.e. the angle φ. Discussion on applicability of existing fracture criteria can be found in [11]. In the present paper two of the most widely used criterion will be considered: the maximum circumferential stress criterion (Cherepanov, 1963; Erdogan and Sih, 1963; Panasyuk and Berezhnitskij, 1964, see for references [12,13,14]) and the criterion of minimum strain energy density [11,15]. Previously obtained results for stress intensity factors [16] are used in this investigation and are cited here for the sake of completeness. The problem for the cracks under shear loading corresponding to the loading in CS specimen in an infinite body was considered in [16] and analytical and semi-analytical solution based on the singular integral equations was obtained. In [17] numerical analysis was done by other approach, Finite Element Method implemented in FRANC2D/L code. Analytical and FEM calculations were also compared and discussed. This work is concentrated on studying of the application of fracture criteria for fracture interpretation of the results that is important for experiments. Formulation of the problem and solution The scheme of the CS specimen for the Mode II fracture test is presented in Fig.1a. The Fig.1b shows the experimental CS specimen made from concrete, the shear fracture experiment has been done in [18].