In studying crack problems in a piezoelectric material, many crack models have been proposed and some fracture criteria have been established. The author of 1 presented a new permeable crack model. That is, a permeable crack is modeled as a rectangular hole having height h0. The first-order perturbation solution in terms of small parameter h0 is derived, and asymptotic electroelastic field, together with field intensity factors, local and global energy release rates are further determined. The obtained theoretical prediction agrees basically with experimental observation. Here, we would like to make some discussions on 1.

In deriving the results in 1, Eq. (45) is crucial. However, based on (44), (45) does not hold unless E˜XX,Y and E˜XaX,Y are linear functions with respect to variable Y and independent of variable X. The reason is that, if denoting  
fX,±hX=E˜XX,±hXE˜XaX,±hX,
(1)
the Fourier cosine transform of fX,±hX is  
0fX,±hXcosζXdX=0afX,±h0cosζXdX+afX,0cosζXdX,
(2)
rather than  
f*ζ,±h0sinaζζ,
(3)
where  
f*ζ,Y=0fX,YcosζXdX.
(4)
Consequently, (45), i.e.,  
f*ζ,±h0sinaζζ=0,0<ζ<,
(5)
cannot follow from (44), i.e.,  
fX,±hX=0,<X<,
(6)
where hx is given by (12) in 1.

In addition it is seen from (81)–(83)) that the height of a rectangular crack has been taken into account. However, for such a rectangular crack, (or strictly speaking a rectangular hole), σYZX,0,εYZX,0,DYX,0, and EYX,0 should have no singularity near the points ±a,0 since the points ±a,0 are not the crack tips h0>0. Instead, the electromechanical field near the apexes of the rectangle ±a,±h0 exhibits a singularity. Moreover, the singularity is no longer an inverse square-root singularity. The classical definition of field intensity factors is therefore employed directly except for the case of h0=0.

1.
Li
,
S.
,
2003
, “
On Global Energy Release Rate of a Permeable Crack in a Piezoelectric Ceramic
,”
Transactions of the ASME, J. Appl. Mech.
,
70
, pp.
246
252
.