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Computational Mechanics of Composite Materials part 10

Tham khảo tài liệu 'computational mechanics of composite materials part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Fracture and Fatigue Analysis of Composites 255 Since 5.70 is based on the assumption of the square-root stress singularity in the front of the sharp crack tip it does not precisely represent the stress distribution in the tubular adhesive layer in the stress concentration region. However this characteristic length serves to estimate upper bound on the finite element size at the crack-like damage tip. Figure 5.28. Pipe to pipe adhesive connection 3D and 2D views Then it is postulated that after the crack-like defect had nucleated it steadily propagates along the adhesive layer as the main single crack leading to an average stress increase over the distance d along with the number of load cycles N as T N 1 T N dX 1 T ad N dX T N d T A d i1 -D N A 5.71 where D N denotes the classical scalar damage variable which may be written in terms of the nucleated and propagating main crack a as follows D N aNl 5.72 a The defect propagation terminates according to the condition d n 1 . a N la 5.73 which corresponds to the loss of stiffness for all those finite elements in the adhesive layer that are placed on the crack propagation path. 256 Computational Mechanics of Composite Materials The boundary differential equation system which describes fatigue defect propagation along the adhesive layer of a composite pipe joint may be defined over the pipe element of length dla N dXA-da N as follows i equilibrium and damage equations dFp F N and F F N dơvn d2 -IF Td N n Ddla N p 4 up ip ad up a dơc n D - d2c Td N n Dicdla N c 4 uc ic ad ic a ii constitutive relations dwp -ƠA . dWc _ƠA dl N Ep and dl N Ec Tad N Ga ịrtp- iii boundary conditions dw 7 and dw ơ _ dl N Xa L Ep an dl N XA 0 Ec dwn p 0 XA 0 and dWc 0 dl N XA L 5.74 5.75 5.76 5.77 5.78 5.79 5.80 where Fp Fad Fc represent internal axial forces in a pipe adhesive layer and coupling respectively internal axial stresses in the pipe adhesive and coupling are denoted by ơp Tad and ơc. Let us assume that Ep Ec and Gad are the axial .