PSI - Issue 13

M.R. Ayatollahi et al. / Procedia Structural Integrity 13 (2018) 735–740

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Ayatollahi et al. / Structural Integrity Procedia 00 (2018) 000–000

Numerous researches have been conducted considering the effect of higher order terms of stress on the accuracy of fracture behaviour predictions (Larsson and Carlsson, 1973; Rice, 1974; Betegon and Hancock, 1991; Ayatollahi et al., 2015; Ayatollahi et al., 2016; Razavi et al., 2018). In the present research, the crack growth paths for PMMA specimens of five different geometries are evaluated theoretically using two fracture criteria namely the Generalized Strain Energy Density (GSED) criterion and the Generalized Maximum Tangential Stress (GMTS) criterion. The theoretical results were then compared to the experimental results reported in a recently published research by the Ayatollahi et al. (2016). It is shown that the specimen’s geometry can strongly influence the crack growth path under mode-I loading condition. The GSED criterion was found to be able to successfully predict the crack instability in the tested specimens.

Nomenclature a

crack length biaxiality ratio

B E G K I

axial modulus of elasticity shear modulus of elasticity mode-I stress intensity factor mode-I fracture toughness mode-II stress intensity factor effective stress intensity factor

K Ic K II K eff

applied load

F

r , θ

polar coordinates with the origin located at the crack tip

critical distance

r c S T

strain energy density factor

T -stress

the angle between the initial direction and the direction of new crack growth increment

θ o σ ij σ t

stress components ( i, j = r , θ )

ultimate strength Poisson’s ratio

ν α

dimensionless form of the critical distance

2. Experimental procedure Five specimens of different shapes including: the compact tension (CT), two geometries of double cantilever beam (DCB) and two geometries of tapered double cantilever beam (TDCB) were tested by Ayatollahi et al. (2016 and the crack growth paths of the tested specimens were extracted. The specimens’ geometries were selected in a way to have a wide range of T -stress in the vicinity of the crack tip in these specimens. Fig. 1 illustrates the schematic view of the test specimens all with a thickness of 10 mm. The tested PMMA had the elastic modulus, tensile strength and Poisson’s ratio of E = 2.9 GPa, σ t = 55 MPa, ν = 0.35. More details about the experimental procedure can be found in the paper published by Ayatollahi et al. (2016).

F

F

F

30

30

30

45

75

15

150

90

30

CT specimen

DCB

1 specimen

DCB 2 specimen

F

F

F

F

F

30

30

90

90

75

45

90

150

F

TDCB 1 specimen

F

TDCB 2 specimen

Fig. 1. A scheme of specimen geometries (not scaled) (Ayatollahi et al., 2016).