Issue 46

V. Rizov, Frattura ed Integrità Strutturale, 46 (2018) 158-177; DOI: 10.3221/IGF-ESIS.46.16

delamination fracture analysis of the multilayered functionally graded non-linear elastic circular shaft loaded in bending and torsion.

Figure 11 : The strain energy release rate in non-dimensional form plotted against

1 D p property at three

1 3 / B B p p ratios for the

shaft configuration shown in Fig. 7a (curve 1 – at

, curve 2 – at

/ 1 B B p p  and curve 3 – at

).

/ B B p p 

/ B B p p 

0.5

1.5

1

3

1

3

1

3

P ARAMETRIC INVESTIGATIONS

P

arametric investigations of delamination fracture in the multilayered functionally graded non-linear elastic circular shaft are performed in order to elucidate the effects of material gradients, cylindrical delamination crack location, non-linear mechanical behavior of the material and load combinations. For this purpose, calculations of the strain energy release rate are carried-out by formulae (41) and (62). The results obtained are presented in non-dimension form by using the formula 3 / N B G G s R  . Two three-layered functionally graded circular shafts loaded in centric tension and torsion are analyzed in order to elucidate the influence of the cylindrical delamination crack location on the fracture behavior (Fig. 7). A cylindrical delamination crack is located between layers 2 and 3 in the shaft configuration shown in Fig. 7a. A shaft with cylindrical delamination crack located between layers 1 and 2 is also under consideration (Fig. 7b). In both shaft configurations, the thickness of the layers is t (Fig. 7). It is assumed that 50 T  Nm, 300 F  N and 0.01 t  m. In order to elucidate the influence of the load combination on the fracture behavior, two three-layered functionally graded circular shafts loaded in bending and torsion are also analyzed (Fig. 8). In the shaft shown in Fig. 8a, a cylindrical delamination crack is located between layers 2 and 3. A cylindrical delamination crack is located between layers 1 and 2 in the shaft configuration in Fig. 8b. The thickness of each layer is 0.01 t  m in both shafts (Fig. 8). The loading is 50 T  Nm and 40 M  Nm. The strain energy release rate in non-dimensional form is presented as a function of 1 D s material property ( 1 D s controls the gradient of 1 s property in layer 1) in Fig. 9 for the four shaft configurations shown in Fig. 7 and Fig. 8. It is assumed that 2 3 / 0.3 D D s s  , 1 3 / 2 B B s s  , 2 3 / 1.8 B B s s  , 1 3 / 0.3 D D p p  , 2 3 / 0.2 D D p p  , 3 3 / 0.4 D D p s  , 1 3 / 1.7 B B p p  ,

2 3 / 1.9 B B p p  , 3 / 1.1 B B f s  , 3

/ B D p p 

f 

f 

3 3 / 0.5 D D f s  ,

1 3 / 1.7 B B f f  ,

2 3 / 1.6 B B f f  , 3 / 0.8 B B g s  . 3

f

f

,

,

,

0.9

/

0.4

/

0.3

D D

D D

3

3

1

3

2

3

g 

g 

3 3 / 0.4 D D g s  ,

1 3 / 1.5 B B g g  ,

2 3 / 1.9 B B g g 

g

g

/

0.2

/

0.5

,

,

and

D D

D D

1

3

2

3

Curves in Fig. 9 indicate that the strain energy release rate decreases with increase of 1 D s . This behavior is due to the decrease of the shaft stiffness. It can also be observed in Fig. 9 that the strain energy release rate increases when the cylindrical delamination crack position is changed from this shown in Fig. 7a and Fig. 8a to that shown in Fig. 7b and Fig.

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