PSI - Issue 23

Jan Poduška et al. / Procedia Structural Integrity 23 (2019) 293–298 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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2. FEM model of the multilayer pipes

The lifetime calculation method used in this paper is based on the assumption that the slow crack growth in PE can be described by linear elastic fracture mechanics parameters, namely the stress intensity factor K I . The necessary small-scale yielding condition is met, as the process zone in front of the crack tip in PE is usually very small. If the crack growth rate da/dt in a certain PE grade is measured and plotted as a function of the respective K I , it forms a linear dependency in a log-log scale that can be fitted with a power law in the form of: = ( ( )) (1) where A and m are material parameters that need to be obtained experimentally. The estimation of pipe ’ s lifetime can be obtained by integration of the equation (1). FEM simulation of the pipe is necessary, because it provides the dependency of stress intensity factor on the crack length K I (a) in the pipe which is then used in the lifetime calculation. The FEM simulation allows to include various loads and other factors that act on the pipe and affect the overall lifetime. A FEM model of 3-layer pipe with a propagating crack was set up. The diameter of the pipe was d = 90 mm, the total thickness of its wall was s = 8.2 mm. The wall of the pipe consisted of 3 layers. The thickness of the layers was divided by the ratio of 0.25:0.5:0.25 which means the inner layer thickness was s i =2.05 mm, the outer s o =2.05 mm and the middle layer s m =4.1 mm. The material model was linear elastic isotropic. It was assumed, that the virgin material and the recycled material have approximately similar Young’s modulus and Poisson’s ratio. The values of E = 1030 MPa an Poisson’s ratio µ = 0.3 were used. The pipe with a crack is symmetrical which allows to create only a quarter of the pipe and use symmetrical boundary conditions. A semi-elliptical crack was created in the model. The dimensions of the semi elliptical crack front were determined according to Hutař (2011) where an equation is published that determines the ratio of the ellipse’s axes. The pipe was loaded by internal pressure.

Fig. 1. The mesh of the multi-layer pipe model with loads and boundary conditions, the crack front is pictured in the detail The mesh of the model is shown in Fig. 1, the applied boundary conditions are highlighted. A detail of the fine mesh close to the crack front is also pictured. The fine mesh is necessary to accurately describe the stress field close to the crack tip. Stress intensity factors were calculated for several crack lengths a . Then the stress intensity factors were fitted with polynomials to obtain the needed stress intensity factor dependency.