PSI - Issue 37

Carl Fällgren et al. / Procedia Structural Integrity 37 (2022) 948–955 Carl Fällgren / Structural Integrity Procedia 00 (2019) 000 – 000

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in Fig. 2 together with red frames symbolising the finite element model geometry derived from the symmetric characteristic of the real specimens. The specimens have two bores intersecting at an angle of 90°. The bore diameter for all specimens was 5 mm. The thicker specimen shown in the upper left of Fig 2. has a height h of 12.5 mm, leading to a ratio of h/d = 2.5 while the thinner, weakened specimens had a ratio of h/d = 2. The finite element model was generated with the software package Abaqus/CAE and boundary conditions taking the exploitation of symmetry into account were applied. Then the material model described in section 2.1 was applied. 3.1. Autofrettage simulation Different autofrettage pressures were applied to the model. The pressures were estimated by numerically calculating the bursting pressures of the component-like specimens with a linear-elastic ideally-plastic approach as described by Thumser (2009). The maximum pressure for autofrettage was then set at around 92 % of the calculated bursting pressures. For the thicker specimens, h/d = 2.5, two more autofrettage states were considered. For the weakened specimens, h/d = 2, five different autofrettage states were selected. The autofrettage pressures for the component-like specimens are listed in Tab. 2.

Table 2: Approximated bursting pressures and autofrettage pressures for the two specimen geometries. Geometry ratio Calculated bursting pressure in MPa Applied autofrettage pressures in MPa h/d = 2.5 1855 1700, 850 h/d = 2.0 1419 1300, 1100, 900, 600, 300

As known from previous works (cf. Beier et al. (2017), Thumser et al. (2002) and Vormwald et al. (2018)), cracks nucleate as quarter circles at the bore intersections and grow in the midplane. Their growth rate is determined by the rate of the crack front position along the bisector line of the bore intersections. For this reason, the residual stresses perpendicular to the crack propagation plane along the bisector line were examined. The results from the FEA are shown in Fig. 3. From the figure it is obvious, that the absolute values of the compressive residual stresses at the notch of the bore intersections become even lower with higher autofrettage pressures. Additionally, it can be seen, that the minimum (identical to the maximum of the absolute value) of the residual stress fields changes its location from the intersection notch into the material depth with higher autofrettage pressures, too.

Figure 3: Residual stress distribution along the bisector line for different autofrettage pressures. Left: for thick specimen geometry h/d = 2.5, Right for the weakened geometry h/d =2.

For the thicker specimen geometry, h/d = 2.5, this is only the case for the applied maximum autofrettage pressure of 1700 MPa (17000 bar). For the weakened specimen geometry, h/d = 2, the effect can be seen for the maximum autofrettage pressure of 1300 MPa and the lower autofrettage pressure of 1100 MPa.