Byusingthemethodofstressfunctions,theproblemofmode-ⅡGriffithcrackindecagonalquasicrystalswassolved.First,thecrackproblemoftwo-dimensionalquasicrystalswasdecomposedintoaplanestrainstateproblemsuperposedonanti-planestateproblemandsecondly,byintroducingstressfunctions,the18basicelasticityequationsoncouplingphonon-phasonfieldofdecagonalquasicrystalswerereducedtoasinglehigherorderpartialdifferentialequations.Thesolutionofthisequationundermixedboundaryconditionsofmode-ⅡGriffithcrackwasobtainedintermsofFouriertransformanddualintegralequationsmethods.Allcomponentsofstressesanddisplacementscanbeexpressedbyelementalfunctionsandthestressintensityfactorandthestrainenergyreleaserateweredetermined.
