PSI - Issue 8

Matteo Loffredo / Procedia Structural Integrity 8 (2018) 265–275 M. Lo ff redo / Structural Integrity Procedia 00 (2017) 000–000

273

9

1000

500

σ ( MPa )

●

●

●

1000 - 500 0

●

● ●

0.000 0.005 0.010 0.015 0.020 0.025 0.030

ϵ ( mm / mm )

Fig. 7. Identification of the unloading yielding line based on filtered unloading experimental data for cylcles of type 1.

1000

500

σ ( MPa )

1000 - 500 0

- 0.02 - 0.01 0.00

0.01

0.02

0.03

ϵ ( mm / mm )

Fig. 8. Comparison of model response (red lines) and experimental data of cycles of type 1 (blue dots).

4 k = 0

max − min − 2 σ y / E 5

σ E ( k ) − σ C ( k ) σ (L) y

1 5

(10)

Err =

k = min + k

The error has been calculated, by the function defined in Eq.10, for each σ − curve and averages among five total strain levels the relative error between experimental unloading stress σ E and calculated unloading stress σ C for a set of spanning through in the plastic unloading part. The strain corresponding to the first reverse yielding ( max − 2 ∗ σ y / E ) is excluded since the model presents a discontinuity due to its formulation, that is not reflected by experimental data. The tuning described above resulted, for all curves, in an error below 3% (Fig.8).

5. Application to the Finite Element model of an autofrettaged cylinder

The constitutive law defined in this paper has been programmed in ANSYS FE code by a customized UPF . In this way the customized constituve law is made available in ANSYS software and the end-user is able to account for it using ANSYS standard environment. In order to verify UPF proper functionality in a non-uniaxial geometry, it has been implemented in the FE model of a cylinder autofrettaged in open end conditions. The internal radius was a = 30 mm, external radius b = 72 . 5 mm and axial length L = 4 b . The autofrettage pressure p = 750MPa (Fig.9). Fig.10 compares the hoop RS σ θθ profiles obtained on the cylinder mid-section accounting for the Bauschinger e ff ect with the model presented in this paper and using a conventional elastic-perfectly plastic model. It is worth