PSI - Issue 28

Paolo S. Valvo et al. / Procedia Structural Integrity 28 (2020) 2350–2369

2351

2

P.S. Valvo / Structural Integrity Procedia 00 (2020) 000–000

Nomenclature

a

crack length

B crack width = out-of-plane thickness of cracked body

c xx crack-tip flexibility coe ffi cient = relative displacement in x -direction due to unit forces in x -direction c xz crack-tip flexibility coe ffi cient = relative displacement in x -direction due to unit forces in z -direction c zx crack-tip flexibility coe ffi cient = relative displacement in z -direction due to unit forces in x -direction c zz crack-tip flexibility coe ffi cient = relative displacement in z -direction due to unit forces in z -direction C position of crack tip

C − position of crack tip on bottom crack face C + position of crack tip on top crack face C crack-tip flexibility matrix D position of propagated crack tip F x crack-tip force in x -direction F c x crack-tip force in x -direction at local contact F z crack-tip force in z -direction F c z crack-tip force in z -direction at local contact F crack-tip force vector G energy release rate G I mode I contribution to energy release rate G II mode II contribution to energy release rate

k xx crack-tip sti ff ness coe ffi cient = nodal force in x -direction due to unit displacement in x -direction k xz crack-tip sti ff ness coe ffi cient = nodal force in x -direction due to unit displacement in z -direction k zx crack-tip sti ff ness coe ffi cient = nodal force in z -direction due to unit displacement in x -direction k zz crack-tip sti ff ness coe ffi cient = nodal force in z -direction due to unit displacement in z -direction K crack-tip sti ff ness matrix p distributed contact pressure

q x distributed crack closure force in x -direction q z distributed crack closure force in z -direction Q x crack closure force in x -direction Q I x mode I crack closure force in x -direction Q II x mode II crack closure force in x -direction Q II , a x mode II crack closure force in x -direction, sub-step a Q II , b x mode II crack closure force in x -direction, sub-step b Q z crack-tip closure force in z -direction Q I z mode I crack closure force in z -direction Q II z mode II crack closure force in z -direction Q II , a z mode II crack closure force in z -direction, sub-step a Q II , b z mode II crack closure force in z -direction, sub-step b O origin of reference system x Cartesian coordinate ¯ x direction of crack-tip force vector corresponding to contact z Cartesian coordinate ¯ z direction of crack-tip force vector corresponding to mode I fracture Γ ellipse of crack-tip flexibility ∆ a crack length increment ∆ A crack area increment ∆ u x crack-tip relative displacement in x -direction ∆ u c x crack-tip relative displacement in x -direction at local contact