PSI - Issue 35

Domen Šeruga et al. / Procedia Structural Integrity 35 (2022) 150–158 Sˇ eruga et al. / Structural Integrity Procedia 00 (2021) 000–000

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Fig. 1. a) Model of the analysed pipe bend and b) mesh of the pipe bend with boundary conditions. Control points serve for examination of simulation results.

The stress-tensor increment can be calculated as (Nagode et al. (2021)) ∆ σ i j = 2 µ ∗ T (2) ∆ ε i j + λ ∗ T (2) ∆ ε kk δ i j , (3) where T (2) , µ ∗ T (2) and λ ∗ T (2) stand for the temperature in the current step and Lame´ constants considering temperature-dependent elastoplastic material properties. The calculation procedure utilises play operators in the mod ified Haigh–Westergaard coordinate space which connect the stress and the strain tensors in a unique closed-form solution (Nagode et al. (2021)). The pipe bend with the outer diameter of 100 mm and the wall thickness of 5 mm has been meshed with 68000 nodes and 48000 solid finite elements (type C3D8, 8-node linear bricks). The sweep technique has been used for meshing. Between two and three layers of finite elements have been applied across the thickness of the cross-section. The boundary conditions and the load application may not represent realistic loads of the pipe bend. However, they have been chosen so as to ensure the elastoplastic stress-strain response of the pipe bend. Since the same boundary conditions have been applied in the case of both the Prandtl and the reference models, the simulated stress-strain results and their influence onto the fatigue life prediction can be compared. Moreover, the computational power of the models can also be considered. The pipe bend has been clamped on one end and exposed to internal pressure of 10 bar at 20 ◦ C in load step 1 (Figs. 1 and 2). Additionally, an alternating mechanical load cycle has been applied to the free end of the pipe bend between load steps 2 and 8. The temperature has been initially set to 20 ◦ C (until load step 4) and has been then increased to 300 ◦ C in load step 5 where it has been kept until the last load step (load step 8). Every load step has been assumed to last 10 s. However, the size of the time step does not a ff ect the results of the simulation since elastoplastic material properties are time-independent. Two control points have been chosen to analyse the simulation results and predict fatigue lifetime. They are pointed out in Fig. 1b. Ferritic stainless steel EN 1.4512 (Nagode et al. (2012); Sˇ eruga et al. (2014)) has been chosen for the material of the pipe bend, its material properties used in the simulation are listed in Tables 1 and 2. Their graphical representation is given in Fig. 3. The cyclic stress-strain curves of the material have been described by the Ramberg-Osgood relationship (Ramberg and Osgood (1943)) and the durability properties have been given by the Manson-Co ffi n relationship (Manson (1952), Co ffi n (1954)). The material parameters of the reference model (Besseling (1958)) have been determined from the same cyclic curves (Fig. 3). Fatigue lifetime calculation has been performed using the Prandtl damage operator approach (Nagode et al. (2010)). During this calculation, the resulting stress tensors and the temperature have been used to estimate the accumulated fatigue damage considering the linear damage accumulation rule and the critical plane (mode I) type of crack initiation.

3. Results and discussion

The implemented Prandtl operator approach enables simulation of a temperature-dependent elastoplastic response of the pipe bend exposed to an arbitrary thermomechanical load history. If the equivalent von Mises stress field is first examined (Fig. 4), it can be noticed that equivalent stresses over 200 MPa occur in the pipe bend. This value is over