Fracture and Damage Mechanics V

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Authors: Liao Liang Ke, Yue Sheng Wang
Abstract: Fretting is a major cause of surface damage and fretting fatigue crack initiation at the interface between contact materials subjected to small oscillatory movements. In the present paper, a multi-layered model is developed to analyze fretting fatigue of functionally graded materials (FGMs) with arbitrarily varying shear modulus under plane strain-state deformation. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into several sub-layers and in each sub-layers the shear modulus is assumed to be a linear function while the Poisson’s ratio is assumed to be a constant. With the model, the problem of fretting contact of two similar functionally graded coated cylinders is investigated. By using the transfer matrix method and Fourier integral transform technique, the problem is reduced to two uncoupled Cauchy singular integral equations. The tangential contact pressures in the slip and stick zones are calculated by solving the equations numerically. The results show that appropriate gradual variation of the shear modulus can significantly alter the pressures in the contact zone. This may lead to suppression of fretting fatigue cracks at the edges of the contact zone and thus modify the fretting contact damage.
Authors: Hyeon Chang Choi
Abstract: An elastic-plastic finite element analysis (FEA) is performed to examine the opening behavior of fatigue crack, where the contact elements are used in the mesh of the crack tip area. The relationship between fatigue crack opening behavior and cyclic crack tip opening displacement was studied in the previous study. In this paper, we investigate the effect of the element size when predict fatigue crack opening behavior using the cyclic crack tip opening displacement obtained from FEA. The cyclic crack tip opening displacement is well related to fatigue crack opening behavior.
Authors: Yi Ming Fu, Xian Qiao Wang
Abstract: Based on the Talreja’s tensor valued internal state variables damage model and the Helmhotlz free energy of piezoelectric material, the constitutive relations of the piezoelectric plates with damage are derived. Then, the nonlinear dynamic equations of the piezoelectric plates considering damage are established. By using the finite difference method and the Newmark scheme, these equations are solved and the effects of damage and electric loads on the nonlinear dynamic response of piezoelectric plates are discussed.
Authors: Zhi Gang Yu, Fu Lei Chu, Yue Cheng
Abstract: In this paper, a method is presented to facilitate the computation of dynamic properties of non-uniform beams with any number of cracks. Based on the Frobenius method, an analytical solution of vibration equation of non-uniform beams is obtained. In combination with the line spring model of crack, the transfer matrices for non-uniform beam element and crack are established respectively. Then the global transfer matrix can be simply formulated, from which the frequency equation in the form of 2×2 determinant is derived. Due to the decrease in the determinant order as compared with previously developed procedures, significant savings in the computational task would be achieved by the present method.
Authors: De Ming Zhang, Gui Qing Chen, Chun Mei Zhang, Jie Cai Han
Abstract: The TiAl-based alloys sheet with 150 mm × 100 mm × 0.4 mm was fabricated successfully by using EB-PVD method. The fracture morphology and residual stresses of the sheet were analyzed by SEM, numerical calculation and X-ray stress analyzer. The results indicate that before stripping, the depositional layers have a higher compressive stress, and the substrate has a very lower tensile stress. For the isolated TiAl-based alloys sheet, the microstructure of as-deposited sheet is columnar crystal, and the residual stresses distribution on the free surface has a trend that its magnitude decreased gradually from center to edges. After vacuum annealing at 1273 K for 16 h, the columnar crystal transforms into the equiaxed, the residual stresses on the free surface are eliminated ultimately, and the fracture of the material is diverted from the manner of intergranular fracture to the mixed manner of intergranular fracture with cleavage fracture.
Authors: Yao Ling Xu, Wen Feng Tan
Abstract: Inhomogeneous materials with doubly periodic non-uniform cracks under antiplane shear is dealt with. By using conformal mapping technique and elliptic function theory, the stress field and stress intensity factor at the tip of each crack are derived in closed form. Numerical examples show the influences of some microstructure parameters of crack distribution on stress intensity factor.
Authors: Wan Cheng Zhu, Jin Chao Duan, Chun An Tang, Shan Yong Wang
Abstract: Rock and concrete are typical heterogeneous material that the meso-scale heterogeneity may have a significant effect on their macro-scale mechanical responses. In this work, a digital image-based (DIB) technique is employed to characterize and quantify the heterogeneity of concrete, and the obtained data is directly imported into a numerical code named RFPA (Rock Failure Process Analysis) to study the effect of heterogeneity on the failure process of concrete. The upgraded RFPA is capable to simulate the progressive failure of brittle materials such as rock and concrete, representing both the growth of existing fractures and the formation of new fractures, obviating the need to identify crack tips and their interaction explicitly. The simulated results are in reasonable agreement with experimental measurements and phenomenological observations reported in previous studies.
Authors: Yue Sheng Wang, Jun Lei, Dietmar Gross
Abstract: The paper considers a bi-material with a crack propagating rapidly, penetrating or deflecting at the interface under dynamic loading. The hybrid time-domain boundary element method, together with the multi-region technique, is applied to simulate the dynamic process of propagation and penetration or deflection of the crack. Moving of the crack tip in the matrix, penetration and deflection of the crack at the interface, and propagation of the crack along the interface are controlled by criteria developed from the quasi-static ones. A bi-material rectangular plate with an edged crack under impact loading is computed and compared with the photoelastic experiments. Good agreement between numerical and experimental results implies that the present boundary element numerical method can provide an excellent simulation for the dynamic crack propagation in a bi-material involving interfaces.
Authors: Jian Mei Wang, Qing Xue Huang, Chun Jiang Zhao, Li Feng Ma
Abstract: To solve the three-segment loop-like damage of sleeve under rolling load case, to quantitatively analyze bearing failure mechanism, a mathematical model of oil-film bearing for producing the 3-D contact pressure and shear stress distribution between sleeve and roll neck was developed by 3D elastic contact boundary element method. Some programs for automatically creating 3-D surface grid model have been developed to check data and display deformation, as well as to plot the deformation fields of roller and sleeve. Analytical results provide an effective way to decrease wear and adhesive damage of sleeve, and help to increase the load capacity of oil-film bearing and service life as well.
Authors: Norio Kawagoishi, Q. Chen, M. Oki, Qing Yuan Wang
Abstract: In order to investigate the effect of frequency on the crack growth behavior, ultrasonic fatigue tests were carried out for an extruded age-hardened Al alloy, 7075-T6, and the results were compared with those in rotating bending fatigue. Fatigue strength in ultrasonic was higher than that in rotating bending. This was mainly caused by the retardation of crack initiation. Growth direction of a crack changed from a tensile mode to a shear one in ultrasonic fatigue, though fracture occurred by the growth of a tensile mode in rotating bending. The growth direction of a shear mode crack was inclined about 55 degrees to the tensile axis. The relation between an applied stress σa and a crack depth at transition of growth direction T was expressed by a nT=C, where C and n are constants. These results were discussed from the points of view of the time dependent environmental effect and the texture of material.

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