The Bueckner work conjugate integral for a permeable crack in piezoelectric materials |
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Authors: | Q Li Y -H Chen |
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Affiliation: | (1) School of Aerospace, Xian Jiao-Tong University, Xian City, 710049, P. R. China |
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Abstract: | Summary The Bueckner work conjugate integral for cracked piezoelectric materials is studied. The analysis is based on the permeable
crack model to avoid the unphysically impermeable crack assumption. It is proved that the values of the Bueckner integrals
are dependent on the normal electric displacement component on the crack surfaces and the coordinates of the starting point
and the end point of the integral contour on the lower and upper crack faces, respectively. This means that, strictly speaking,
the Bueckner integral for the permeable crack model is path-dependent unless a special condition is satisfied, i.e., the horizontal
coordinates of the starting point and the end points of the integral contour are the same. The present conclusions are quite
different from those derived from the impermeable crack model, where the Bueckner integral is strictly path-independent. The
universal relation between the Bueckner integral and the J-integral existing in the impermeable crack model is also proved
not to be always valid for the present permeable model unless the special integral contour is taken. This implies that the
crack electric boundary condition in piezoelectric materials yields some significant influence on the properties of the Bueckner
work conjugate integral. |
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