PSI - Issue 77

Victor Rizov et al. / Procedia Structural Integrity 77 (2026) 389–396 Author name / Structural Integrity Procedia 00 (2026) 000–000

392 4

Q Q −

(

) Qi b

i β

i α

Q Q

R R −

= +

,

(9)

i

i ε

i

b

∆

Qi

P P −

(

) Pi b

i β

i α

P P

R R −

= +

,

(10)

i

i ε

i

b

∆

Pi

i α and i β , refer to inner and outer surface of the layer, i R is the radius of the inner surface,

where the subscripts,

Gi b , Hi b , Si b , Ei b , Qi b and Pi b are parameters. In order to determine the SERR for the delamination crack, one has to derive the parameters of the mechanical behaviour of the member in Fig. 1. These parameters are derived from the following equations. ( ) 3 4 2 1 l l a R a R L L D vb B vq T κ γ γ ϕ − + = + , (11) 3 4 2 l L L M ϕ κ = , (12) ∑∫∫ ∑∫∫ = = = = = δ λ τ τ i i A i i A L L i i i i RdA RdA 1 ( ) 1 ( ) 2 3 , (13) where δ and λ are the number of layers in the internal delamination arm and in the member, vq γ and vb γ are the shear strains on the surface of the internal delamination arm and on the surface of the member in portion, 2 3 L L , the quantity, 3 4 L L κ , is the curvature of member in portion, 3 4 L L . Equations (11) and (12) are composed by applying the integrals of Maxwell-Mohr. Equation (13) is composed by considering the equilibrium of section, 2 L , of the member ( i τ and L L i 2 3 τ are the shear stresses in the layers of the internal delamination arm and in portion, 2 3 L L , of the member, respectively). When composing Eqs. (11), (12) and (13), it is taken into account that R R B vq γ γ = , (14) R R D vb L L γ γ = 2 3 , (15) v t vq vq = γ , (16) v t vb vb = γ , (17)

z L L

L L ε

κ =

,

(18) (19)

3 4

3 4 1

v L L κ

t

κ

=

,

3 4

3 4

L L

where B R is the radius of the cross-section of the internal delamination arm,

3 4 L L ε is the strain in portion,

3 4 L L , of the member, 1 z is the centric axis of the cross-section of the member, vq v , vb v and unknown velocities. These velocities are determined from Eqs. (11), (12) and (13) by the MatLab. Formula (20) is applied for determining the SERR, G , for the delamination crack in the plane member shown in Fig. 1. 3 4 L L v κ are

*

dU

G

=

,

(20)

B π 2

R da

where