Calculation of Strain Energy Release Rate for Deformation Modes I, II and III

Abstract

Show that the strain energy release rate for the deformation modes I, II and III of a crack is given by

EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa % aaleaacaaIXaaabeaakiabg2da9iaaikdadaqadaqaamaalaaabaGa % am4AaiabgUcaRiaaigdaaeaacaaIYaGaam4AaiabgkHiTiaaigdaaa % aacaGLOaGaayzkaaGaamOCamaaBaaaleaacaaIWaaabeaakiaadEfa % daWgaaWcbaGaaGymaaqabaaaaa!4497!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$ {G_1} = 2\left( {\frac{{k + 1}}{{2k - 1}}} \right){r_0}{W_1} $$

(1)

EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa % aaleaacaWGjbGaamysaaqabaGccqGH9aqpcaaIYaWaaeWaaeaadaWc % aaqaaiaadUgacqGHRaWkcaaIXaaabaGaaGOmaiaadUgacqGHRaWkca % aIZaaaaaGaayjkaiaawMcaaiaadkhadaWgaaWcbaGaaGimaaqabaGc % caWGxbWaaSbaaSqaaiaadkfaaeqaaaaa!458B!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$ {G_{II}} = 2\left( {\frac{{k + 1}}{{2k + 3}}} \right){r_0}{W_R} $$

(2)

EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa % aaleaacaWGTbaabeaakiabg2da9iaadkhadaWgaaWcbaGaaGimaaqa % baGccaWGxbWaaSbaaSqaaiaad2gaaeqaaaaa!3CCF!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$ {G_m} = {r_0}{W_m} $$

(3)

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