Browsing by Subject "Fracture Mechanics"
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Item The Mechanics of a Cantilever Composite Beam with two Dissimilar Isotropic Materials with an Embedded Horizontal Crack Subjected to an end Transverse Force(2023-01-01) serna, oscar j; Charalambides, Panos; Zhu, Weidong; Mechanical Engineering; Engineering, MechanicalABSTRACT This study addresses the mechanics of a cantilever bimaterial beam with an embedded horizontal interface crack and subjected to a transverse force applied at its free end. This work expands on previous contributions by Fang and Charalambides wherein the related mechanics of a homogeneous beam with an embedded crack were established. In this work, a four-beam model is also used to establish the macro-mechanical response of the bimaterial beam with an embedded interface horizontal crack. Mid-crack force and moment resultants are established as a function of the beam geometry and material heterogeneity. The free-end deflection is also established analytically. Relevant bimaterial beam theories used in the development of the four-beam model are presented in a related Appendix. In parallel studies, a Two-Dimensional (2D) finite element model was also developed and used to validate the analytical four-beam model predictions. The analytical and finite element results were found to be in excellent agreement. The finite element model was also used to extract the near-tip fracture mechanics of the interface crack. Emphasis was placed on determining the near-tip energy release rate for a broad range of bimaterial systems and various crack locations. Arguments regarding the structure of the transition fields and induced force and moment discontinuities at the crack tip cross sections led to unique separation of the mode-mixity as discussed elsewhere, thus revealing the dominant fracture mode II nature of the beams and loading considered. The analytical four-beam model predictions were then used in conjunction with a J-integral approach as well as the compliance method to obtain analytical predictions of the near-tip energy release rates. Those predictions were then compared to results obtained using the 2D finite element model which were also found to be in good agreement. The near-tip energy release rate trends with crack depth location and bimaterial severity were established. The finite element model was also used to obtain the beam surface curvatures which were plotted against the beam axis. Top as well as bottom surface curvatures were obtained. Appreciable and measurable curvature deviations were shown to exist in the crack location region. Such deviations from an otherwise smooth profile for a similar beam without a crack can be used in damage and crack detection studies as discussed elsewhere. For example, the results of this study would allow for the detection of the presence of such cracks. More specifically, this study can be used in the interpretation of experimental methods that can establish through surface scanning, the surface curvatures of bimaterial beams loaded in the form considered in this study. Through such efforts, the presence of an interface crack can be detected. The study allows for the specific determination of the crack center location at a point where the experimatal surface curvature profile in the disturbed region matches that of a projected healthy structe. The study also allows for the determination of the crack size as measured through the peak values of the disturbed curvature profiles while also allowing for the determination of the crack along the beam height using the model estimates of maximum curvature deviations caused by the presence of such cracks.