Crack Profiles in Applied Moment Double Cantilever Beam Tests
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Crack profiles in applied moment double cantilever beam tests C. H. Hsueh, E. Y. Sun, P. F. Becher, and K. P. Plucknett Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6068 (Received 24 July 1997; accepted 21 April 1998)
In situ observations of crack propagation in an applied moment double cantilever beam specimen were used previously to obtain the R-curve behavior of ceramic composites. To predict the R-curve using constitutive models, knowledge of the crack profile is required to derive the bridging stress distribution along the crack length and to analyze the toughening effect. To predict the crack profile in an applied moment double cantilever beam test, both the deformation of the crack surface due to the bending moment and the movement of the crack surface due to the rigid body motion of the loading fixture need to be considered. The analytical solution for the crack profile is derived in the present study. The predicted crack profiles agree well with experimental measurements.
I. INTRODUCTION
The strength of brittle materials is characterized by their resistance to crack propagation (i.e., the fracture toughness).1 To obtain the fracture toughness, various techniques have been developed and the measurement of the crack length in the specimen is required for most of the techniques. One approach has been to develop loading fixtures and specimen configurations which result in an applied stress intensity that is independent of the crack length. Three specimens of this type have been developed: the tapered double cantilever beam (DCB),2 the double torsion DCB,3–5 and the applied moment DCB.6 It has been noted that machining of a tapered specimen is difficult and the crack shape of a double torsion specimen is not geometrically simple. However, these aspects can be remedied in the applied moment DCB specimen.6 To improve the fracture toughness of brittle materials, dispersed inclusions (such as fibers, whiskers, or second phases) have been incorporated into brittle matrices to form composites.7–9 The fracture toughness of these composites is not a single valued parameter. The measured fracture resistance can increase and asymptotically approach a plateau value as the crack extends (i.e., the R-curve behavior).9–14 In many cases, the R-curve behavior is attributed to bridging of the matrix crack by reinforcing phases. As the R-curve behavior can influence the flaw size sensitivity of the fracture strength and the mechanical reliability, it is desirable to obtain the entire R-curve for each material. Recently, in situ observation of crack propagation in an applied moment DCB specimen has been used to investigate the R-curve behavior.15,16 Constitutive modeling has also been developed to predict the R-curve. However, knowledge of the crack profile is required in order to derive the bridging stress distribution along the crack length and to analyze the toughening effect.15–19 The deflection of a J. Mater. Res., Vol. 13, No. 9, Sep
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