The purpose of this study was to gain a better understanding of the parameters affecting crack growth direction in unidirectional comµosite materials. To achieve this, the effect of anisotropy and biaxial loading on the direction of crack growth in unidirectional off-axis composite materials were investigated. Specific emphasis was placed on defining the crack tip stress field and finding a consistent criterion for predicting the direction of crack growth. Two models are presented to predict the crack tip stress field, an anisotropic elasticity solution and a singular isoparametric finite element formulation. After defining the crack tip stress field, three crack extension direction criteria, the Normal Stress Ratio, the Tensor Polynomial and the Strain Energy Density Criterion, were applied to predict the direction of crack extension. The theoretically predicted crack extension directions were then compared with experimental results. After comparison, it was determined that only the Normal Stress Ratio Criterion correctly predicts the direction of crack extension. / Master of Science

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This study develops new quantitative thermoelastic stress analysis (TSA) techniques for fracture and fatigue damage analysis of composite materials. The first part deals with the thermo-mechanical derivation of two quantitative TSA techniques applied to orthotropic composites with and without a transversely-isotropic surface coating layer. The new TSA test procedures are derived in order to relate the thermal infrared (IR) images with the sum of in-plane strains multiplied by two newly defined material constants that can be experimentally pre-calibrated. Experiments are performed to verify the TSA methods with finite element (FE) numerical results along with available anisotropic elasticity solution. The second part of this study applies the quantitative TSA techniques together with the Lekhnitskii's general anisotropic elasticity solution to calculate mixed-mode stress intensity factors (SIFs) in cracked composite materials. The cracked composite coupons are subjected to off-axis loadings with respect to four different material angles in order to generate mixed-mode SIFs. A least-squares method is used to correlate the sum of in-plane strains from the elasticity solution with the measured TSA test results. The mode-I and mode-II SIFs are determined from eccentrically loaded single-edge-notch tension (ESE(T)) composite specimens. The FE models and virtual crack closure technique (VCCT) are utilized for comparisons. In the third part, a new stochastic model is proposed to generate S-N curves accounting for the variability of the fatigue process. This cumulative damage Markov chain model (MCM) requires a limited number of fatigue tests for calibrating the probability transition matrix (PTM) in the Markov chain model and mean fatigue cycles to failure from experiments. In order to construct the MCM stochastic S-N curve, an iterative procedure is required to predict the mean cycles to failure. Fatigue tests are conducted in this study to demonstrate the MCM method. Twenty-one open-hole S2-glass laminates are fatigue-cycled at two different stress levels. The coupon overall stiffness and surface-ply TSA damage area have been used as two damage metrics. The MCM can satisfactorily describe the overall fatigue damage evolution for a limited number of coupons (less than 6) subjected to a given specific stress level. The stochastic S-N curve can be constructed using at least two sets of fatigue tests under different stress levels. Three available fatigue tests for different E-glass laminates from the literature are also investigated using the proposed MCM approach. The results show the MCM method can provide the stochastic S-N curves for different composite systems and a wide range of fatigue cycles.