PSI - Issue 26

Victor Rizov et al. / Procedia Structural Integrity 26 (2020) 86–96 Rizov / Structural Integrity Procedia 00 (2019) 000 – 000

90

5

g l m m − r gC

r

gF

m m

x

= +

g

,

(14)

g

gF

3

−

r

d l m m m m = + r dC dF d

x

dF

,

(15)

d

3

−

r

l l m m m m = + r lC lF l

x

lF

,

(16)

l

3

g l s s − q gC

q

gF

x

s s

gF = +

g

,

(17)

g

3

−

q

d l s s s s = + q dC dF d

x

dF

,

(18)

d

3

−

q

l l s s s s = + q lC l lF

x

lF

l

,

(19)

3

f

f

−

p

gC

gF

x

f

gF f = +

g

,

(20)

g

3

p

l

g

f

f

−

p

f

dF f = +

x

dC

dF

,

(21)

d

d

3

p

l

d

f

f

−

p

f

lF f = +

x

lC

lF

,

(22)

l

l

3

p

l

l

where

x l   3 0 .

(23)

lF m , gF s , dF s , lF s , gF f , dF f and lF f are the

dF K ,

lF K ,

dF m ,

gF K ,

gF m ,

In formulae (11) – (22),

d f and l f in the free end of the beam,

d K ,

l K ,

d m ,

l m , g s , d s , l s ,

g m ,

g f ,

g K ,

values of

g K , d K , l K , g m , d m , l m , g s , d s , l s , g f , d f and l f in the clamping are lC K , gC m , dC m , lC m , gC s , dC s , lC s , gC f , dC f and lC f . The distributions of lF m , gF s , dF s , lF s , g f , d f and l f in the longitudinal direction of the

respectively. The values of

dC K ,

gC K ,

denoted by

dF K ,

lF K ,

gF m , dF m ,

gF K ,

beam is controlled by g n , d n , l n , g r , d r , l r , g q , d q , l q , g p , d p and l p , respectively. In principle, the complementary strain energy density is equal to the area that supplements the area enclosed by the stress-strain curve to a rectangle. Thus, the complementary strain energy density in the lower crack arm is written as

L * 0 = − 

u

u

.

(24)

L

0