Thesis (M.S.)--George Mason University, 2009. / Vita: p. 64. Thesis director: Rainald Löhner. Submitted in partial fulfillment of the requirements for the degree of Master of Science in Computational Sciences. Title from PDF t.p. (viewed June 10, 2009). Includes bibliographical references (p. 60-63). Also issued in print.

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

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This thesis is divided into six chapters. The first chapter provides a brief introduction concerning the behaviour of brittle materials. It also contains the justification for the undertaking of the study as well as a brief description of the method of approach adopted, and thesis layout. Chapter two provides a critical review of the current literature available at present in the failure prediction brittle materials. Both theoretical and experimental studies are discussed and the relevance to the present work is justified. Chapter three deals with the numerical analyses adopted within the thesis. Five different failure criteria were utilized in the initial analysis of the results presented. Among them, the empirical model using the Principle of Independent Action satisfactorily represents the biaxial fracture behaviour of brittle materials in both tension-tension and tension-compression quadrants. Its validity has never been tested before. Various statistical fracture models were used to analyze the failure of brittle materials under multiaxial states of stress, the experimental failure data for simple tension being a starting point for their calculation. It was shown that the Energy Density theory led to a better agreement with the experiments than any other well-known fracture criterion. The study investigates methods of evaluating the Weibull parameters which were crucial in the failure prediction of brittle materials. Monte Carlo simulation techniques are also presented as a method of evaluating the data ranking for the failure probability of brittle materials. Chapter four is devoted to the description of experimental techniques adopted in the study, using specially designed rigs. Six different tests were conducted to evaluate the performance of brittle materials in static loading and also to enable comparisons with the theoretical predictions. Attention was given to specimen casting, loading frames, alignment, measurement techniques and other relevant parameters. The use of the linear elastic fracture mechanics method to predict the behaviour of cracks in bodies, which are subjected to steady stresses, is discussed. The compliance function for the three-point notch bend specimen is presented in addition to the determination of the fracture toughness of Herculite LX plaster. The work was also supplemented by the use of scanning electron microscopy (SEM) to failure analysis of plaster material. This is an extremely important tool in the study of brittle materials since the dimensions of small defects and fracture features on individual grains are often pertinent information to the failure analysis. Chapter five details the analysis of the theoretical results as well as the experimental findings. Based upon the previously mentioned approaches, a comparison was made between theoretically predicted and experimentally observed data. The comparison indicates that discrepancies exist between the observed and predicted results, the reasons for the discrepancies have been justified in this work. Chapter six provides a brief summary of conclusions derived from the complete study, together with recommendations for future work.

Stability analysis of rock masses composed of small, discrete rock blocks that are in-place and interlocked should consider four components of failure: (1) Sliding between blocks. (2) Shearing through rock blocks. (3) Rolling blocks in a shear zone. (4) Crushing of rock blocks. Statistical rock mass description is used to define the characteristics of the rock blocks and the block assemblage. Clastic mechanics is one method of predicting stresses produced by the arrangement of rock blocks and the loading conditions. Failure begins at a point of maximum stress behind the slope. Progression of the failure is assumed if the first block fails because adjacent blocks will become overstressed. The location of the point of maximum stress is determined from the shape and arrangement of the constituent rock blocks. Because strength is mobilized block-by-block rather than instantaneously along a continuous shear surface, sliding between blocks shows less stability than a soil rotational shear analysis or a rigid block sliding analysis. Shearing through rock blocks occurs when maximum shear stress exceeds rock shear strength. Crushing of rock blocks is predicted if the normal stress exceeds the compressive strength of the rock block. A size-strength relationship is combined with the rock block size distribution curve to estimate crushing strength. Rotating blocks in a shear zone have been observed in model studies and as a mechanism in landslides. Stability analysis assumes that the rock mass is sufficiently loosened by blasting and excavation to allow blocks to rotate. The shear strength of rolling blocks is dynamic shear strength that is less than static sliding shear strength. This rolling mechanism can explain release of slope failures where there are no other obvious structural controls. Stability of each component of rock mass failure is calculated separately using capacity-demand reliability. These results are combined as a series-connected system to give the overall stability of the rock mass. This probability of failure for the rock mass system explicitly accounts for the four components of rock mass failure. Criteria for recognizing rock mass failure potential and examples applying the proposed method are presented.

An equivalent constant amplitude fatigue loading (Miner's stress) is developed for stationary random amplitude loadings. The effects of rainflow cycle counting and fatigue crack closure are included. A method for determining the opening stress in a random loading is also proposed. This research takes a fatigue damage factor approach. The damage factor is defined as the ratio of the wide band rainflow fatigue damage to the equivalent narrow band fatigue damage. The mathematical form of the damage factor equations is derived from theoretical derivations using the analytically tractable local range cycle counting method. Simulations of stationary Gaussian random processes are used to empirically derive the values of certain parameters dependent on the spectral shape for the rainflow cycle counting equations. There are five tasks in this research. (1) A simulation program for generating a Gaussian process has been written and is used to generate random loading histories for this study. (2) A previously proposed rainflow damage factor has been verified and refined with these simulations, without considering crack closure. (3) Using a sinusoidal approximation, the joint probability density functions between peaks, valleys and rises counted by the local range method are derived. (4) The resulting joint probability distributions are used to determine the theoretical damage with crack closure; simulations are again used to calibrate the parameters for rainflow stress cycles. (5) A procedure for finding an equivalent constant fatigue crack opening stress for stationary random loadings is described. An example application of the procedures and equations is given.

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