PSI - Issue 25

Victor Rizov / Procedia Structural Integrity 25 (2020) 112–127 Author name / Structural Integrity Procedia 00 (2019) 000–000

120

9

/ 0 1  b b the strain energy release rate for the beam of antiparallelogram cross-section is lower

Fig. 5). At

compared to that for the beam whose cross-section is an isosceles triangle (refer to Fig. 3 and Fig. 5).

Fig. 5. The strain energy release rate in non-dimensional form plotted against h b / ratio (curve 1 – at / 0.0 1  b b

, curve 2 – at

/ 1  b b

0.3

/ 1  b b

0.6

and curve 3 – at

).

An analysis of the lengthwise fracture behaviour of the inhomogeneous beam (Fig. 1) is performed also for the case when the cross-section has a T-shape. The base and the height of the cross-section are denoted by b and h , respectively (Fig. 6). The thicknesses of the flange and the stem are denoted p and q , respectively (Fig. 6). The modulus of elasticity is distributed along the height of the beam cross-sections according to the following power law:   m m L U U c z h E E E E 1 2     , (29) where

1 1 2 c z c    .

(30)

The quantities, 2 c and 1 c , which are involved in (26) and (27) are obtained by formulae

2

2

2 1

 

qh bp c h qh bp   2

,

(31)