PSI - Issue 45

Thi D. Le et al. / Procedia Structural Integrity 45 (2023) 109–116 "Thi D. Le" / Structural Integrity Procedia 00 (2022) 000 – 000

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fibers are divided into two sections including tests for Young’s and shear moduli and other tests for Poisson’s Ratio. In terms of Young’s and shear moduli, twelve GF samples of 0/90° fiber orientations and five GF samples of 45° fiber orientation are tested. An Instron 6800 is used for tensile tests at standard displacement rate of 2.0 mm/min and the samples are tabbed in both ends to ensure the samples are not failed near the grips. Before testing, the width and thickness of specimens are measured by a digital caliper at five different points. Table 3 shows the average results of GF samples.

100 125 150 175 200

Ø20mm Ø25mm Ø32mm

True stress ( MPa)

0 25 50 75

0

0.5

1

1.5

2

2.5

True Strain (mm/mm)

Figure 2. True stress-strain curve of HDPE samples.

E (GPa) (MPa) E shear (GPa) ℎ (MPa) ν ( mm/mm )

Table 3. Average results of GF specimens. Coupon ID Fiber orientation

Strain rate ( mm/min )

t ( mm ) 1.09 1.13

GF90 GF45

0/90°

2 2

27.07 11.42

363.86 122.42

N/A 3.89

N/A

0.149

45° N/A Note: t is the thickness of GF specimens; E is modulus (hoop and longitudinal moduli are the same for this type of GF); E shear and ℎ are shear modulus and ultimate stress of GF samples, respectively. Poisson’s Ratio for glass fibers are based on tests according to the Standard Test Method for Tensile Properties of Polymer Materials ASTM E132-04. The average measured Poisson’s ratio of GF is 0.149 (mm/mm) . According to Craig and Summerscales (1988), the Poisson’s Ratio for woven roving laminate ranges from 0.14 to 0.166, so the obtained Poisson’s ratio of GF (0.149 mm/mm) is within this range which can validate for this result. 4. Finite Element Analysis and Validation Assuming an orthotropic tube with 150mm inner radius, 0.6 mm thickness and 3000 mm length under internal pressure of 2.2 MPa. The material made of this tube has the hoop and longitudinal moduli of 24821.14 MPa, radial modulus of 60673.88 MPa, Poisson’s ratios (v rz and v θz ) of 0.09 and v rθ of 0.23. Both ends of this tube are fixed. The theoretical stress and displacement are calculated from equations in Section 2 while stress and displacement of finite element analysis FEA are obtained from utilizing ANSYS Structural Static Analysis. 61.21

Table 4. Comparison between theoretical analysis and FEA.

Theoretical Analysis

Difference (%)

FEA

Internal radial displacement External radial displacement

u r ( mm ) – Equation (9) u r ( mm ) – Equation (9) ( MPa ) – Equation (10) ( MPa ) – Equation (11) ( MPa ) – Equation (12)

3.30 3.30 2.20

3.26 3.25 2.24

1.5 1.5 2.0

Radial stress Hoop stress

551.10

549.08

0.40

Longitudinal stress 5.7 Table 4 summaries internal and external displacements, and stresses in radial, hoop and longitudinal direction of theoretical analysis and FEA. It can be seen from that the difference between displacements and stresses are all under 6% meaning that the FEA method produces accurate results and can be used for the parametric study. 49.52 52.33