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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Besides that, carbon fibers have high resistance against corrosion and low coefficient of thermal expansion that are beneficial for RTP to some extent. Nonetheless, the impact resistance and cost of carbon fibers are lower than those of glass fibers that makes glass fibers the most favorable reinforcing layers in RTP. Lastly, Suvorova et al. (1991) mentioned glass fiber has so many good characteristics such as low moisture absorption, high tensile strength and chemical resistance like carbon fibers, and cheap prices. Therefore, glass fibers are used as the reinforcement layers for RTP in this study. The Table 1 below shows the properties of different types of fibers for a clear understanding. 1.2. Orientation of the reinforcement layers Clyne and Hull (2019) conducted research using the netting analysis for cylindrical pressure vessels shows the optimum fiber orientation for fully end-capped composite pipes is ±54.7° when assuming only fibers carrying loads. Various experiments about the relationship between matrix materials and pressure capacity were implemented by Meiras (1973). The experimental results illustrated a knee of a curve in the stress-strain plot that could be explained that the resin failed before the fibers broke. This statement was also proved through the results of the research of Hull et al. (1978) about the failure of glass reinforcement pipes. His pipe samples had ±54.44° winding angles with an opening end and a closed end. In addition, by using standard microscopic devices to check the failure mechanisms, Jones and Hull (1979) verified that a leakage from matrix cracking at approximately 20% of the composite pipes’ burst pressure happened because the fibers fractured. Studies by Alrsai et al. (2021) and Taraghi et al. (2021) reported efficiency of wrapping angle on pressure resistance of reinforced rigid steel pipes and pressure vessels, respectively. Spencer and Hull (1978) experimentally assessed RTPs with ±75°, ±65°, ±45° and ±35° winding angles under opening and closed ends. Their research showed that there is a strong relationship between deformation/ leakage/ fracture and winding angles. Following up with the research of Spencer and Hull, another study conducted by Rosenow (1984) used six RTPs with different winding angles ranging from ±15 to ±85° demonstrating that the state of loading can have a significant influence on not only the optimum winding angles but also the pressure capacity. Rosen ow’s study showed that optimum winding angles for the closed-end loading circumstance is ±55°, but the failure in the pipe still occurred before the fibers were broken. The similar results were also shown in the study of Takayanagi et al. (2002) when experimenting RTPs with ±30° and ±70° winding angles. A more detailed study had been conducted by Evans and Gibson (2002) to investigate the connection between materials and optimum winding angles. Their study shows the ratio of reinforcement stiffness, and the matrix affects the optimum winding angles. Recently more studies have been carried out to research the RTP s’ mechanical behaviors subjected to internal pressure. Experiments on RTPs with two layers of aramid cords under internal pressure were conducted by Kruijer et al. (2005). When comparing the experimental results with the result of a mathematical model originating from the characterization of plane strain, there were a noticeable difference in hoop and axial strains of modelling and experiments suggesting that material non-linearity should be considered. Furthermore, their experiments show the ratio of 2.25:1 between hoop and axial stresses results in very little stiffness in hoop direction and too much stiffness in axial direction. Other RTP studies under the internal pressure consisting of HDPE and aramid fibers for reinforcement was conducted by Bai et al. (2013). Their methods included the theoretical, numerical, and experimental approaches. As a result, their experimental measurements are 16.5% and 19.6% smaller than theoretical values and numerical simulations, respectively, since non-linear behavior of HDPE is not considered in theoretical and numerical approaches. Bai et al. (2012) continued to study similar RTPs with the previous studies but use different approaches including experiments, analyzing and Finite Element (FE) modelling. By applying the progressive damage modelling in fiber-reinforced materials in the study of Lapczyk and Hurtado (2007), they determined the failure and the damage of reinforced fibers at the beginning. In this study, the deviations of experimental results with analytical approach and FE modelling are 26.4% and 18.1%, respectively. The failure of the whole tested pipes is due to the fiber breakage causing the crack in RTP ’s outer layer. 2. Theoretical analysis Considering the RTP as an infinitely long, thick-walled orthotropic cylinder that has fix ends and its centre is the origin of the polar coordinate system with r , θ and z representing radial, circumferential, and longitudinal axis respectively. To determine stresses of cylindrical shapes, the polar coordinate system should be used. Figure 1 (b)