PSI - Issue 25

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

119

8

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

4). The distribution of the modulus of elasticity along the height of the beam cross-section is expressed as





 m

h z

m h E E E E   U U

1 

L

,

(25)

g

where

d g h z h    1 .

(26)

g h and d h , which are involved in (26) and (27) are found by formulae

The quantities,

1 1 2 3 b b h h b b g    2 3 b b h h b b d   

,

(27)

1

.

(28)

1

U E and L E in the length direction of the beam are expressed by (20) and (21), respectively.

The distributions of

Fig. 4. Trapezoidal beam cross-section.

The geometry of the beam cross-section is characterized by b b / 1 and h b / ratios. The effects of b b / 1 and h b / ratios on the lengthwise fracture behaviour of the beam are studied. For this purpose, the strain energy release rate in non-dimensional form is plotted against h b / ratio in Fig. 5 at three b b / 1 ratios for / 0.4  s a . The curves in Fig. 5 indicate that the strain energy release rate decreases with increasing of b b / 1 and h b / ratios. It should be mentioned that at / 0 1  b b the strain energy release rate for the beam of antiparallelogram cross-section is exact match to that for the beam whose cross-section is an isosceles triangle at / 0.4  s a (refer to Fig. 3 and