PSI - Issue 25

5

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

116

 E  ,

 c

(16)

c

 E  .

 t

(17)

t

3. Results and discussion The methodology for calculating of the strain energy release rate developed in the previous section of the paper is applied here in order to study the effects of the beam cross-section on the lengthwise fracture behaviour of the inhomogeneous beam configuration shown in Fig. 1.

Fig. 1. Inhomogeneous beam configuration with lengthwise crack of length, a . The beam is simply supported in its ends. The material of the beam is continuously inhomogeneous in both height and length directions. A lengthwise crack of length, a , is located in the beam as shown in Fig. 1. The heights of the cross-sections of the lower and upper crack arms are denoted by 1 h and 2 h , respectively. The external loading consists of one vertical force, F , applied at the lower crack arm at distance, s , from the free end of the crack arm. The length of the beam is denoted by l . The lengthwise fracture behaviour is studied in terms of the strain energy release rate by using dependence (1). First, the lengthwise fracture behaviour is studied assuming the beam cross-section is an isosceles triangle of base, b , and height, h (Fig. 1). The distribution of the modulus of elasticity along the height of the beam cross-section is written as

m

2

  

  

h z



m h E E E E   U U



L

,

(18)

1

3

where

2 1 h z h    .

(19)

3

3