The present investigation of the crack problem inpiezoelectric materials is performed based on the non-localtheory.After some manipulations,the impermeable crack,the permeable crack(the crack gap is full of NaCI solution),and the semi-permeable crack(the crack gap is full of air orsilicon oil)are reduced to a uniform formulation by assum-ing the normal electric displacement on the crack surfaces tobe an unknown variable.Thus,a triple integral equation withthe unknown normal electric displacement is established.Byusing the Newton iterative method and solving the triple inte-gral equation,it is found that the normal electric displacementon the crack surfaces is no longer a constant as determinedby previous studies,rather,it depends upon the remote com-bined electromechanical loadings.Numerical results of thestresses and electric displacement fields show that there areno singularities at the crack tips so that the stresses remainfinite.It is of great significance that the concrete electricboundary condition on the crack surfaces exerts significantinfluence on the near-tip fields and in this way plays an impor-tant role in evaluating the crack stability in the non-localpiezoelectric materials.More specifically,the impermeablecrack model always overestimates the finite stresses at thecrack tips,whereas the permeable crack model always under-estimates them.
Q. Li Y. Chen School of Aerospace, Xi’an Jiao-Tong University,710049 Xi’an, China
