Elastic constants microcracking

One type of pore that is worthy of further consideration is the extreme case of a microcrack. In Section 2.9 it was shown that thermal expansion anisotropy can lead to residual stresses in ceramics and, in some cases, the formation of localized (spontaneous) microcracking. Microcracks may only represent a small fraction of porosity in a body but their ability to concentrate stress can lead to substantial reductions in the elastic constants. For a random array of circular microcracks, radius a, the SC approach shows the elastic constants ix and B of the microcracked material can be approximated by... 

Figure 3.22 Elastic constant data for a-SiC, TiBj and a SiC material containing 15 vol.% TiB2 particles. The data for the composite lie below the values predicted from the constitutive relationships, indicating the presence of microcracks. The data are all corrected to zero porosity. (Reproduced courtesy of Plenum Press, New York.)...

This initial microcrack formation is reflected in a stress-strain curve by the deviation from the linear range of the elastic constants. In fact, the failure is analogous to the microcracks that form between spherulites when a semi-crystalline polymer is deformed. (Source Osswald, T.A. and G. Menges, Material Science of Polymers for Engineers, Hanser Publishers, New York, 1996). Refer also to Vulcanization, Peroxides, Peroxide Cross-Linking, Sulfur Vulcanization, and Vulcanizing Agents. 

Gudmundson P. and Ostlund S. (1992) Numerical verification of a procedure for calculation of elastic constants in microcracking composite laminates. Journal of Composite Materials, 26(17), 2480-2492. 

The above elastic crack curving criterion requires that r0material constant which specifies the characteristic crack tip region in which the off-axis microcracks enlarge and connect to the main crack tip, as shown schematically in Fig. 3.3. The angular deviation of the crack from its original direction of self-similar crack extension is given in Ref. 21. 

All these measures are applicable to monitor the development of the properties of the rock during loading and deformation. The development of the dilatancy can be divided very roughly into three phases. Phase I characterizes a decrease of the volume attributed to elastic compression of the rock salt, a decrease of permeability and an increase of seismic velocity. The volume becomes nearly constant at the end of Phase I. It can be assumed that elastic compression processes and dilatancy processes balance at this point. Dilatant microcracking generates only weak AE activity. 

Dunn, M L. 1995. Effects of grain shape anisotropy, porosity, and microcracks on the elastic and dielectric constants of polycrystalline piezoelectric ceramics. Journal of Applied Physics 78 [3] 1533-1541. 

---