PSI - Issue 8

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

274

10

L

2b

r θ

z

p

z

2a

Fig. 9. Finite Element model of the autofrettaged cylinder.

600 - 400 - 200 0

σ θθ ( MPa )

Bauschinger Elastic - Perfectly Plastic

30

40

50 r ( mm )

60

70

Fig. 10. σ θθ profile with and without Bauschinger e ff ect.

noting that the impact if the Bauschinger e ff ect and the behavior of the programmed model are qualitatively in line with available literature (Chen (1985); Livieri and Lazzarin (2001); Parker et al. (2003a); Parker; Parker et al., 1998); Gibson et al. (2005, 2012); Troiano et al. (2006, 2012); ASME (1997)). This confirms that the proposed model has the potential of describing properly the autofrettage process.

6. Conclusions

A set of uniaxial tension-compression tests have been performed on AISI 4140 carbon steel, with the aim of investigating its unloading behavior and the impact of the Bauschinger e ff ect. Basing on the acquired stress-strain curves a model for describing the Bauschinger e ff ect in autofrettaged components, depending on a limited set of parameters, has been proposed. The key points for programming the model in a commercial Finite Element code have been discussed. Downstream the model has been tuned referring to unloading experimental data, obtaining very good agreement using only a limited set of parameters. In the end it has been implemented in the Finite Element model of an autofrettaged cylinder and the results obtained are consistent with the Residual Stress profiles commonly available in literature. More in general the presented model has the capacity of accounting of the complex first unloading behavior occurring when low tensile plastic strains are present (the model, as formulated in this paper, can be easily expanded). Moreover its uniaxial response can be fully expressed with explicit formulas thus siplifying the identification of consititutive parameters. The main further development consists carrying out a bigger experimental campaign for achieving a statistically valid tuning of this model and verifying experimentally its response directly in autofrettaged components.