1 such that Hypothesis I is satisfied. Under the above considerations, the work in [7,8] gives the expression of S for the present problem: S (9) 2 14 1 E 44 E 2 11 1 B K 2B K K B K + + = in which a K1 =σ π and K E a E = π (10) where both σ and E are constants. The quantities B11 , B14 and B44 for PZT-4 can be found in [7,8]. Substituting eqs. (10) into eq. (9), it can be shown that [ ]2 44 14 11 2 1K B 2B p B p + + =S (11) Defined in eq. (11) is a load parameter p = E/σ. It is now more pertinent to examine whether a crack would grow longer or shorter when the direction of the applied electric field is reversed by using the solution for no applied electric field as the base of reference. 3. ENHANCEMENT AND RETARDATION OF CRACK GROWTH The phenomenon of crack growth enhancement and retardation due to applied electric field reversal has been known for sometime by experiments [1-3]. Attempts made in [3,6] to explain the observation have all failed because the energy release rate result could not distinguish a positive electric field from that of a negative one. Hence, the arguments presented for these unsuccessful attempts are also suspect. 3.1 Crack growth segments Consider the situation in Fig. 1 where the crack is subjected to σ and E. The superscripts +, o and – will refer to, respectively, as the positive, zero and negative E field. The corresponding crack growth segments are r1 , r , …, r1 , r o 2, …, and r1 , r2 , …, while the energy density factors are given by S1 , S2 , …, S1 , S , …, and S1 , . Application of Hypothesis III governed by eq. (5) renders + + 2 o S − − + + o o 2 − − 2 const r S r S r S r S r S r S dV dW 2 2 1 1 o 2 o 2 o 1 o 1 2 2 1 1 c ========== − − − − + + + + L L L . (12) For the jth segment of crack growth, eq. (12) gives − − + + = = j j o j o j j j r S r S r S , L j 1,2, = (13) What needs to be shown is that S > and S < for + j o j S − j o j S L j 1,2, = (14) and > and r < for + jr o jr − j o jr L j 1,2, = (15) Refer to Fig. 3 for an illustration of eq. (15). Recall that positive and negative electric field refer, respectively, to E being in the same and opposite direction of poling. 3.2 Interaction of mechanical and electrical field The interaction of mechanical and electrical field on crack growth can be exhibited by a plot of energy density factor and/or crack growth as a function of the parameter p or the ratio E/σ. Using the elastic,
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