13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- The effect of thickness on components of the non-singular T-stress under mixed mode loading Yury G. Matvienko1,*, Alexander S. Chernyatin1, Igor A. Razumovsky1, Hui-Ji Shi2, Zhao-Xi Wang2,3 1 Mechanical Engineering Research Institute of the Russian Academy of Sciences, 101990, Russia 2 Department of Engineering Mechanics, Tsinghua University, 100084, China 3 Suzhou Nuclear Power Research Institute, 215004, China * Corresponding author: ygmatvienko@gmail.com Abstract. Distributions of the singular (KI, KII) and the non-singular (Txx, Tzz) terms along the 3D crack front are analyzed for the case of mixed (mode I and II) loading. Relations between the singular, non-singular terms and specimen thickness are calculated in the specimen middle plane for different values of the mixity parameter. The values of the mixity parameter are varied through 1 (pure mode I), 0.75, 0.5, 0.25–0 for pure mode II. It is shown that the increase of thickness in 8 times influences on values of KI , KII and Tzz . The strong effect of thickness and mixed mode loading conditions on the Tzz-stress is observed. At the same time, there is not the effect of thickness on the non-singular Txx at the same loading conditions. Keywords T-stress, Mixed mode, In-plane and out-of-plane constraint, Specimen thickness Introduction The development of modern fracture mechanics is closely related to the formation of two-parameter approaches and criteria, which introduce and nonsingular components of the stress field at the crack tip, such as the T-stress. Primarily it is due to the fact that the fracture toughness of structural materials shows a significant effect of the specimen geometry and thickness, load conditions, etc. (e.g. [1, 2]). The results of analytical and numerical calculations show that stress fields in the vicinity of the crack tip, in many cases, are strongly dependent on the non-singular terms of the stress field [3, 4]. Introduction of an additional parameter, namely, the nonsingular Txx-stress in the criteria allows to eliminate the above-mentioned effects [5, 6]. It should be noted that the Txx-stress describes in-plane constraint. In contrast to the Txx-stress, out-of-constraint is connected with the Tzz-stress. However, investigation of joint influence of the nonsingular T-stress (Tzz and Txx) terms on the fracture mechanics parameters is not carried out yet. Present paper deals with numerical analysis of three-dimensional stress fields in the vicinity of through-thickness crack tip under mixed mode (I + II) loading. The combined effect of thickness on the effective stress intensity factor and T-stress terms are discussed. Statement of the problem An analysis of 3D stress field in the vicinity of the crack front is performed on the CCCD-specimen with the thorough-thickness crack of arbitrary space orientation. The specimen is loaded by 2 compressive forces acting in the vertical direction (Fig. 1). This configuration of the specimen is very suitable to create different conditions of mixed loading [7]. Finite element method is employed to estimate the 3D stress field in the vicinity of crack front. The orientation of the crack plane with respect to the disk can be arbitrary, since it is determined by both the angle α (Fig. 1) and the other two spatial angles. Changing the combination of angles can provide almost any relationship between the magnitudes of the KI, KII, KIII. The geometrical parameters of the model are given in dimensionless form, namely, b=B/R, l=a/R (Fig. 1). Note that the developed procedure for the construction of the model allows taking into account the spatial symmetry of the problem and getting the best mesh in terms of accuracy and speed of calculation.
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