affected by reversing the direction of applied electric field with reference to the poled direction for a central crack in an infinite body made of PZT-4 material. The crack tip energy density function dW/dV is first computed using the equations of linear piezoelectricity. An energy density factor S near the crack tip can thus be defined; it has the units of energy release rate. The initiation of stable crack growth and rapid crack propagation correspond to dW/dV and S reaching their respective critical values, (dW/dV)c and Sc. Numerical results are presented to illustrate how the energy density factor is affected by sign change of the applied electric field while the energy release rate criterion has failed to account for such a behavior in the past. 2. THROUGH CRACK MODEL Depicted in Fig. 1 is a central crack of length 2a in an infinite body. A remote electric field E and uniform mechanical stress σ are applied such that the macrocrack would extend along the x1-axis while poling is directed in the positive x3-axis. Plane strain in the x 1x3-plane is assumed. Figure 1: Line crack under electrical Figure 2: Crack tip decay of volume and mechanical load. energy density 2.1 Coupling of electrical and mechanical effects A complete description of cracking involves the process of initiation, growth and termination. For a solid subjected to both electrical and mechanical disturbances, the energy density function based on the theory of linear piezoelectricity can be computed as i D o i ij o ij d E dD dV dW i ij ∫ ∫ = σ γ + γ . (1) In eq. (1), σij and γij are, respectively, the stress and strain components while Ei and Di are components of the electric and displacement field. Even though the mechanical and electrical portion of the energy density function would appear to be separated in eq.(1), the equivalents forms of expressing eq. (1) in terms of stresses and electric displacements i ij j ij ijk k D D 2 1 H 2 1 dV dW = σ σ + β l l (2) or in terms of strains and electric fields i ij j ij ijk k E E 2 1 C 2 1 dV dW γ + ε = γ l l (3) show that the mechanical and electrical parts of dW/dV are always coupled. They cannot be separated as it was assumed in [3]. In eq. (2), Hijkl and βij are the elastic and dielectric compliance constants while those in eq. (3) given by Cijkl and εij are the elastic and dielectric constants.
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