PSI - Issue 25

Victor Rizov / Procedia Structural Integrity 25 (2020) 112–127

117

6

Author name / Structural Integrity Procedia 00 (2019) 000–000

In (18) and (19), U E and L E are, respectively, the values of the modulus of elasticity in the upper and lower surfaces of the beam, m is a material property that controls the material inhomogeneity along the height, 1 z is a vertical centroidal axis of the beam cross-section. The distributions of U E and L E in the length direction of the beam are expressed as

n l E E E E    l E E E E    UD UB U f LD LB L

n

x

UB

,

(20)

f

x

LB

,

(21)

where

x l   0 .

(22)

In (20) and (21), UB E and UD E are, respectively, the values of U E in the left-hand and right-hand ends of the beam, n is a material property that controls the material inhomogeneity along the length direction on the upper surface of the beam, LB E and LD E are, respectively, the values of L E in the left-hand and right-hand ends of the beam, f is a material property that controls the material inhomogeneity along the length direction on the lower surface of the beam, x is the lengthwise axis of the beam (Fig. 1).

Fig. 2. Triangular beam cross-section. The strain energy release rate for the lengthwise crack in the beam shown in Fig. 1 is presented in non dimensional form by using the formula   G G E b UB N /  . The calculations of the strain energy release rate are carried-out assuming that 0.010  b m, 0.400  l m, 0.6  m , 0.6  n and 0.6  f and 5  F N. It should be noted that the strain energy release rate obtained by applying the methodology developed in the previous section of the paper is verified by using the compliance method. According to the compliance method, the strain energy release rate is expressed as