PSI - Issue 25

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

118

7

pk 2 2

da dC

b G F 

,

(23)

where the compliance of the beam, C , is defined as

F C w  .

(24)

The vertical displacement, w , of the application point of the external force that is involved in (24) is determined by applying the integrals of Maxwell-Mohr. It should be mentioned that the strain energy release rate obtained by the compliance method is exact match to that found by the methodology developed in section 2 of the paper. This fact is a verification of the analysis of the strain energy release rate. The geometry of the cross-section of the beam is characterized by h b / ratio (Fig. 2). The ratio, s a / , is introduced in order to characterize the location of the application point of the external force (Fig. 1). The effect of the geometry of the beam cross-section on the lengthwise fracture behaviour is illustrated in Fig. 3 where the strain energy release rate in non-dimensional form is plotted against h b / ratio at three s a / ratios for 0.5 /  UB LB E E , 0.7 /  UB UD E E , 0.6 /  LB LD E E , / 0.8 1  h h and / 0.4  a l . One can observe in Fig. 3 that the strain energy release rate decreases with increasing of h b / ratio. It can also be observed in Fig. 3 that the strain energy release rate decreases with increasing of s a / ratio.

Fig. 3. The strain energy release rate in non-dimensional form plotted against h b / ratio (curve 1 – at /

0.4  s a , curve 2 – at

/ 0.6  s a and curve 3 – at / 0.8  s a ). The lengthwise fracture behaviour of the inhomogeneous beam configuration shown in Fig. 1 is investigated also assuming that the beam cross-section is an antiparallelogram. The methodology developed in section 2 of the paper is applied to calculate the strain energy release rate. The results obtained are verified by the compliance method. The lower and the upper bases and the height of the antiparallelogram are denoted by b , 1 b and h , respectively (Fig.