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

125 3

(a)

(b)



D

Dr

L

Fig.1. (a) A schematic repaired pipe used in the present investigation. (b) Stationary inclined crack

The unidirectional stiffness properties of the GFRP lamina composite repair material which was used in this investigation are tabulated in Table 2 extracted from Shouman and Taheri (2011). The steel plate modeled as isotropic material and elastic-plastic behavior is considered in the present analysis. The mechanical properties of the present steel plate are given in Table 2. Eight angle plies in Uniaxial laminates [0 o ] 8s (perpendicular to pipe axis), perpendicular laminates [90 o ] 8s (parallel to pipe axis) and cross ply laminates [0 o /90 o ] 4s are simulated with solid elements, and the material properties of GFRP are defined as an engineering constant with using the mechanical properties included in Table 2.

Table 2. Material properties and strength data, Shouman and Taheri (2011) Symbol Value Property Glass epoxy composite repair wrap material’s properties E 11 55 Young's modulus in fiber direction (GPa) E 22 15.2

Young's modulus in the transverse direction (GPa) (In Y direction) Young's modulus in the transverse direction (GPa) (In Z direction)

E 33 G 12 G 13 G 23

15.2

In- plane shear modulus (GPa) ( X-Y plan) In- plane shear modulus (GPa) ( X-Z plan) In- plane shear modulus (GPa) ( Y-Z plan)

4.7 4.7

3.28 0.254 0.254 0.428

Poisson's Ratio ( X-Y plan) Poisson's Ratio ( X-Z plan) Poisson's Ratio ( Y-Z plan)

 12  13  23

Steel pipe material’s properties E 205

Young’s modulus (GPa)

Poisson’s ratio

0.3 413



Minimum yield stress (MPa)

 ym

0.5%

Yield strain

 y

2.2 Contact and loading regime

Pressure was loaded inside the pipe surface, P , at 100 MPa. In the present model, penalty friction formulation is used to simulate the contact properties of crack surface. Coefficient of friction of 0.4 for steel-steel is used to simulate the crack surface property (from Abd-Elhady and Sallam 2015). Master – slave contact interactions "surface to surface" were applied between the outer surface of pipe and inner surface of composite repair as a tie contact.

2.3 X-FEM and fracture parameters (J-integral and stress intensity factor) Calculation

A 3-D elastic FE model has been developed using the ABAQUS program (ABAQUS 2002) to account for the geometric and material behavior of composite repaired steel pipe. X-FEM has been used to simulate the fracture crack path (Elguedj et al. 2006) in various crack analysis problems with different stationary inclined crack angles in pipe. The X-FEM method enables simulation of crack propagation without reformulation of the finite elements mesh. In the present work, the domain integral method is used to extract J -integral and stress intensity factors (SIFs) for steel plate joint (Gosz and Moran 2002). The stress intensity factors K I , K II and K III (mode I, mode II, and mode III SIF) are usually used in linear elastic fracture mechanics to characterize the local crack-tip/crack-line stress and displacement fields. They are related to the energy release rate (the J -integral) through: