PSI - Issue 17

S. Mousa et al. / Procedia Structural Integrity 17 (2019) 284–291 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Inner of specimen

Outer of specimen

Fig. 1 FGM specimen with pre-crack The bending stress distribution along the cross section of the simple beam is higher at outer surface of the cross section and decreases along the depth. The FGM technique was used to reduce the effect of the bending stress at the outer surface, by increasing the fibers density at outer surface and gradually decreasing it at higher depths. The fracture load and crack path of pre-cracked beam of the polyester fiber glass FGM under 3PB was explained as shown in figure 1. The pre-crack with length, a = 3 mm, with different seven inclination angles ( 0 o , 15 o , 30 o , 45 o , 60 o and 75 o ) were created using a jigsaw machine. Table 1: The properties of E-glass fiber and Polyester resin Properties E-glass fiber Polyester Density (kg/m 3 ) 2540 1720 Tensile modulus (GPa) 72.4 19.7 Tensile strength (MPa) 3450 206 Elongation % 3 3.47 Coefficient of thermal expansion (x10 -6 /ºC) 5 50 The average value of fiber volume fraction,  f , was 39 % and it was determined experimentally using the ignition technique according to BS3691 (Dry 1996). The unidirectional mechanical property of the FGM composite specimen was measured using the Universal Testing Machine INSTRON-8801 and it was listed in Table 2. The bending tests were made for FGM with pre-crack by using the Universal Testing Machine INSTRON-8801 at room temperature with a loading rate 0.5 mm/min. Five specimens were tested for each test condition and the average value was used for drawing the different relationships. Table. 2: Unidirectional mechanical properties for FGM composite material. E 11 (GPa) E 22 (GPa) E 33 (GPa) G 12 (GPa) G 13 (GPa) G 23 (GPa)  12  13  23 42 36 36 12 12 18 0.3 0.3 0.5 3. Numerical Work The main objective of the numerical part is to simulate the behavior of FGM specimen to study the effect of variation of the pre-crack angle and site of pre-crack on the crack path under 3PB. A three-dimensional finite element model by using ABAQUS program has been used to simulate these tests methods. As shown in figure 2, the numerical simulation is used to predicted the crack path for different pre-crack inclination angle,  , and for different pre-crack location, 2L . Extended finite element method (X-FEM) has been used to simulate the fracture crack path in various crack analysis problems with different plate widths (Sukumar and Prévost 2003, Asadpoure, Mohammadi et al. 2006, Elguedj, Gravouil et al. 2006). In the present simulation, X-FEM approach is used to attempt simulating the final failure of the specimen under the 3 point bend and compared it with the experimental. The crack growth direction in the present simulation was chosen normal to the direction of maximum tensile stress. In the present section XFEM models are used to model the failure of FGM composite specimen under 3 point bend