PSI - Issue 83

Victor Rizov et al. / Procedia Structural Integrity 83 (2026) 85–94

87

where  is strain,  is stress, E , H ,  and  are parameters.

Fig. 1. Sketch of beam structure with longitudinal crack.

The material is graded through the thickness of the beam. As a result of this E and H change continuously along the thickness. The change of E from gr E on the upper surface of the beam to dl E on the lower surface obeys the law in Eq. (4).



 h E E dl 

2 h

  

  

gr

E E

z

 



,

(4)

1

gr

where

z h    .

2 h

(5)

1

2

In Eq. (4) the following notations are used: h - thickness, 1 z - vertical axis (shown in Fig. 1),  - parameter. The change of H through the thickness is