Progresses in Fracture and Strength of Materials and Structures

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Authors: Gang Wang, Shu Cai Li, Shu Gang Wang, Jing Long Li, Xiao Jing Li
Abstract: According to the theories of fracture mechanics and damage mechanics, the constructive model and fracture damage mechanism of brittle discontinuous jointed rockmass are systematically studied under the state of complex stress in this paper. By the aid of the method of equivalent strain energy, the constitutive relation of anchored brittle discontinuous jointed rockmass is derived under the state of compression-shearing. The constitutive relation under the state of tension-shearing is also developed according to the theory of self-consistence. Finally, based on the above constructive models, the three-dimensional finite element procedure has been developed to model the ground movements that occur when underground power-houses of pumped-storage power station are installed in discontinuous jointed rockmass. The anchor supporting is an important component of this underground power-houses excavation work. Besides the displacement field and the secondary state of stress induced by the excavation disturbance, the effect of anchoring and the damage evolution around the power-houses have been particularly described during the process of installation. The numerical results obtained by numerical simulation were compared with that of field monitoring in order to verify the validity of the proposed models.
Authors: Zhao Hui Ren, Tao Yu, Yue Gang Luo, Nai Hui Song, Bang Chun Wen
Abstract: Mechanical model and rubbing force model of a dual-disc overhung rotor-bearing system are set up respectively. By using an experiment rig to simulate rubbing fault, the nonlinear dynamic characteristics of rubbing rotor system are investigated and the dynamic characteristics of mid-disc and overhung disc are analyzed respectively. The numerical simulation results coincide with the experiment results and the research in this paper has practical reference value to the safe and stable run of the practical rotating machinery.
Authors: Yan Hai Xu, Li Guo, Hao Li
Abstract: Microstructure plays a significant role in the evolution of short fatigue cracks. The modelling procedure of microstructure for polycrystalline materials is presented in this paper. The factors that effect on the modelling of microstructure are discussed in detail. Firstly, the 2D microstructure of LZ 50 steel with straight grain boundary is simulated with the help of Voronoi tessellation. To validate the modelling results of the microstructure, two load cases are intentionally designed to verify the microstructure for the view of comparing the results with homogeneous material under the same load cases. The whole process is carried out with the application of FEM. From the comparison of mechanical properties generated by the simulated microstructure with anisotropic material property to the ones showed by macrostructure with homogeneous material property, the validity and convenience of the modelling process is shown. The simulated microstructure for polycrystalline materials can be used for the further research on the initiation and growth of short fatigue cracks.
Authors: Yan Hai Xu, Yong Xiang Zhao
Abstract: The behavior of short fatigue cracks under variable amplitude loading (VA) was investigated by FEM. The crack closure induced by the crack surface roughness was taken into consideration by using the contact between these crack surfaces. The effects of variable amplitude loading on the performance of short cracks are demonstrated with factors such as grain orientation and misorientation, crack length and the friction efficient between the contacted crack surfaces. Through the two indicators, crack tip opening displacement represented by "CTOD and "CTSD and the plastic strain range of crack tip, the characteristics of short cracks affected by loading blocks are discussed in detail. It is shown from the numerical results that the significance of the design of loading blocks in the fatigue experiments is evident and the performance of short cracks from the variable amplitude loading is more effective due to the closer to practice.
Authors: Yan Hai Xu, Yong Xiang Zhao
Abstract: The short fatigue crack initiation of LZ50 axle steel for railway vehicles was investigated by numerical simulation in this paper. The microstructure of LZ50 steel was constructed with the application of 2D Voronoi tessellation. The stress and strain distributions in the microstructure were obtained by FEM under the boundary condition shifted from loading level applied in fatigue specimen of this steel. Finally, the probability of short fatigue crack initiation was given with different loading cycles to illustrate the process of crack initiation of LZ50 steel under the given loading cycles based on the S-N curve of the material. The further work on the research of crack growth and collective evolution of short fatigue cracks can be conducted with the simulated results of crack initiation in the microstructure of LZ50 steel.
Authors: Tian Hui Ma, Ju Ying Yang, Zheng Zhao Liang, Yong Bin Zhang, Tao Xu
Abstract: Fracture formation on surfaces of bi-layered materials is studied numerically. A simplified two-layered materials model like growing tree trunk is present. This work is focused on patterns of fractures and fracture saturation. We consider the formation of crack pattern in bark as an example of pattern formation due to expansion of one material layer with respect to another. As a result of this expansion, the bark stretches until it reaches its limit of deformation and cracks. A novel numerical code, 3D Realistic Failure Process Analysis code (abbreviated as RFPA3D) is used to obtain numerical solutions. In this numerical code, the heterogeneity of materials is taken into account by assigning different properties to the individual elements according to statistical distribution function. Elastic-brittle constitutive relation with residual strength for elements and a Mohr-Coulomb criterion with a tensile cut-off are adopted so that the elements may fail either in shear or in tension. The discontinuity feature of the initiated crack is automatically induced by using degraded stiffness approach when the tensile strain of the failed elements reaching a certain value. The different patterns are obtained by varying simulation parameters, the thickness of the material layer. Numerical simulation clearly demonstrates that the stress state transition precludes further infilling of fractures and the fracture spacing reaches constant state,i.e. the socalled fracture saturation. It also indicates that RFPA code is a viable tool for modeling fracture formation and studying fracture patterns.
Authors: Lei Chen, Zhen Zhou Lu
Abstract: For general reliability analysis with fuzzy failure region F % , the general failure probability F P% is defined as the integral of product of μF% [g( y)] , the membership of performance function ( ) g y to F % , and joint Probability Density Function (PDF) f ( y) over , the total variable space, i.e. [ ( )] ( ) F F P μ g f d  % = ∫ ∫ % y y y L . On the basis of line sampling, an efficient method for random failure probability analysis with clear failure region, a new numerical method is presented to calculate F P% . In the presented method, the total integral region  is split into m clear sub-regions i F in a way that the value of g( y) in i F can be approximately viewed as i g , a constant independent of y , and the value of [ ( )] F μ % g y in i F can be viewed as a constant ( ) F i μ g % subsequently. Due to the closely invariant property of [ ( )] F μ g % x in i F and 1 2 m  = F I F ILI F , F P% is transformed into the sum of ( ) F i μ g % ( ) i F ∫L∫ f y dy , where ( ) i F ∫L∫ f y dy is the random failure probability with the clear failure region i F and can be obtained by line sampling. The high efficiency of the presented method resulted from that of the line sampling is demonstrated by the illustration.
Authors: Shu Fang Song, Zhen Zhou Lu
Abstract: For reliability analysis of implicit limit state function, an improved line sampling method is presented on the basis of sample simulation in failure region. In the presented method, Markov Chain is employed to simulate the samples located at failure region, and the important direction of line sampling is obtained from these simulated samples. Simultaneously, the simulated samples can be used as the samples for line sampling to evaluate the failure probability. Since the Markov Chain samples are recycled for both determination of the important direction and calculation of the failure probability, the computational cost of the line sampling is reduced greatly. The practical application in reliability analysis for low cycle fatigue life of an aeronautical engine turbine disc structure under 0-takeoff-0 cycle load shows that the presented method is rational and feasible.
Authors: Xiu Kai Yuan, Zhen Zhou Lu
Abstract: On the basis of Markov chain simulation, an efficient method is presented to analyze reliability sensitivity of structure. In the presented method, Markov chain is employed to draw the samples distributed in the failure region, and these samples are fitted in a form of hyperplane by the weighted regression. By use of the regressed hyperplane, it is convenient to complete the sensitivities of the failure probability with respect to the distribution parameters of basic random variables by the available method. The presented method is applied to some examples to validate its accuracy and efficiency. The obtained results show that the presented reliability sensitivity analysis method is far more efficient than Monte Carlo based method.
Authors: Chao Ma, Zhen Zhou Lu
Abstract: For reliability analysis of structure with implicit limit state function, an iterative algorithm is presented on the basis of support vector classification machine. In the present method, the support vector classification machine is employed to construct surrogate of the implicit limit state function. By use of the proposed rational iteration and sampling procedure, the constructed support vector classification machine can converge to the actual limit state function at the important region, which contributes to the failure probability significantly. Then the precision of the reliability analysis is improved. The implementation of the presented method is given in detail, and the feasibility and the efficiency are demonstrated by the illustrations.

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