PSI - Issue 5

Amr A. Abd-Elhady et al. / Procedia Structural Integrity 5 (2017) 123–130 Amr A. Abd-Elhady et al / Structural Integrity Procedia 00 (2017) 000 – 000

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3.5 Effect of composite repair on the value of J-integral of stationary crack in steel pipe

As is already known, J -integral is a logical crack driving force in either linear elastic fracture mechanics or elastic plastic fracture mechanics. The J -integral concept examines the stress-strain conditions along an arbitrary contour away from the crack tip. The crack will grow theoretically when the potential energy available for crack extension reaches a critical value defined by J -integral. Therefore, decreasing J -integral in cracked pipe by the use of an adhesively bonded composite repair patch increases the life of this pipe. The effect of composite repair patch on the normalized value of J -integral ( J -integral in pipe with composite repair patch/ J -integral without composite repair patch) of stationary crack in steel pipe with different  and different fiber orientation ([0 o ] 8s uniaxial ply circumferentially, [0 o /90 o ] 4s Cross ply, and [90 o ] 8s uniaxial ply longitudinally) is illustrated in Fig. 6. Fig.6. a shows the results of crack length equaling 35 mm, while Fig.5.b shows the results for crack length equaling 75 mm. Generally, the efficiency of composite repair patch for reducing J -integral increased with an increase in the crack length for the same patch dimensions and location. This may be attributed to the increase of the surface of the crack subject to closure stress. The highest reduction in normalized J -integral was found for stationary crack with  = 30 o regardless of the fiber orientation, and is more pronounced at the longer crack length. This may be attributed to the value of mode of mixity ( K II / K I ) in each case. Recall Fig. 4, the mode of mixity of  = 30 o is equal to 1.2 and 0.7 for crack length = 35 and 75 mm, respectively. In the case of  = 60 o , the mode of mixity is equal to 0.5 and 0.4 for crack length = 35 and 75 mm, respectively. It is clear that, the mode of mixity decreased with an increase in the crack length for  = 30 o and 60 o .The highest values of K II , for crack length = 35 and 57 mm, were found for stationary crack with  = 30 o , while the corresponding values of K II for  = 90 o were 0, i.e., pure mode I. Furthermore, the ratio of K I in the case of  = 30 o to that in the case of  = 90 o is about 0.7 and 0.9 for the crack length = 35 and 75 mm, respectively. This means that, this ratio increased with increasing crack length. From the previous observations, it can be concluded that, the crack closure produced by adhesively bonded composite repair patch is more pronounced for larger crack length and high mode of mixity for the same patch dimensions and location.

0.6

0.6

(b)

a = 75 mm

(a)

a = 35 mm

0.5

0.5

0.4

0.4

0.3

[0]8s [0/90]4s [90]8s

0.3

[0]8s [0/90]4s [90]8s

0.2

0.2

0.1

0.1

0 Normalized J-Integral

0 Normalized J-Integral

30

60

90

30

60

90

Inclined crack angle, 

Inclined crack angle, 

Fig. 6. The effect of composite repair ([0 o ]

8s uniaxial ply (circumferentially), [0

o /90 o ]

4s Cross ply and [90 o ]

8s uniaxial ply (longitudinally),) on the

normalized value of J -integral of stationary crack in steel pipe under internal pressure.

For crack inclination angle = 30 o , i.e., high mode of mixity, there is a marginal effect of fiber orientation regardless of the crack length. In the other two cases, i.e., crack inclination angle = 60 o and 90 o , the effect of fiber orientation increased, but it is not that pronounced. The reduction in J -integral is not highly affected by fiber orientation due to the following two reasons. First, the ratio of the highest value of modulus of elasticity in composite laminates ( E 11 ) to the lowest one E 22 , E 11/ E 22 , is small, about 3.6. Second, the ratio of E 11 to the modulus of the steel pipe material ( E ), E 11/ E equals 0.27. Therefore, it is recommended to use the high modulus carbon fiber reinforced epoxy for repairing such cracked steel pipe, in order to increase the repair efficiency in the elastic range.