Based　on　the　concept　of　the　hoop　field　intensity　factors　of　an　initial　crack　prior　to　any　kink,　an　apparent　hoop　mechanical　(strain)　energy　release　rate　(MERR)　is　defined　to　approximate　the　MERR　of　a　piezoelectric　crack　with　an　infinitesimal　kink　at　any　arbitrary　angle.　The　validity　and　the　efficiency　of　the　simplified　approximation　are　examined　by　numerical　examples　using　the　boundary　element　method　(BEM).　The　generalized　crack-opening-displacements　or　displacement　jumps　are　computed　by　the　traction　boundary　integral　equations　(BIEs).　By　using　the　displacement　extrapolation　method,　the　crack-tip　field　intensity　factors　of　any　arbitrarily　kinked　crack　in　linear　piezoelectric　materials　are　obtained　and　the　BEM　results　are　validated　by　comparing　them　with　the　available　reference　analytical　results.　Then,　the　differences　between　the　conventional　field　intensity　factors　and　MERR　of　an　infinitesimally　kinked　crack　and　the　hoop　field　intensity　factors　and　hoop　MERR　of　the　main　crack　prior　to　any　kink　are　numerically　analyzed.　Finally,　the　crack　propagation　in　an　infinite　linear　piezoelectric　material　is　numerically　simulated.　The　paths　of　the　crack　growth　are　predicted　by　adopting　four　different　fracture　criteria,　namely,　the　maximum　hoop　stress　intensity　factor　(SIF)　and　MERR　fracture　criteria　for　the　main　crack-tip　before　the　next　propagation,　and　the　maximum　K-1　and　MERR　fracture　criteria　for　the　kinked　tip　of　the　main　crack　with　an　infinitesimal　branch　at　an　arbitrary　kinking　angle　evaluated　by　using　a　trial　crack　extension　technique.　The　comparisons　among　these　results　show　that　the　present　simplified　approximation　can　efficiently　provide　a　sufficient　accuracy　for　numerical　simulation　of　crack　growth　in　linear　piezoelectric　materials.　(C)　2017　Elsevier　Ltd.　All　rights　reserved.