PSI - Issue 18

Riccardo Fincato et al. / Procedia Structural Integrity 18 (2019) 75–85 Author name / Structural Integrity Procedia 00 (2019) 000–000

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4. Numerical analyses The constitutive equations in section 2 were implemented via user subroutine for the commercial code Abaqus (ver. 6.14-4) and used for FE analyses on a single cubic element with reduced integration (i.e. Abaqus element type C3D8R). The element is isostatically constrained at the base and along two sides, see Fig. 2a.

a)

b) c) Fig. 2 (a) sketch of the cubic element and the boundary conditions, (b) impact loading sequence, (c) quasi-static loading sequence.

Table 1. Material parameters

Elastic modulus

206 [GPa]



0.3

h 1 , h 2

2.5, 5.0

575 [MPa] 5000 [MPa]

K

C 1 B 1 C 2 B 2 s 1 s 2 R e F 0 c

20

1200

35

200 0.9



1.25 [MPa]

1.1 0.2

381 [MPa]

A prescribed displacement is applied on top in order to give a fully reversed loading condition with two different amplitudes. The first amplitude applies the displacement under a high rate 12.5 v  [mm/s] ( 04 1.0 10 [s] t     ), simulating an impact load. The second amplitude applies the displacement under quasi-static loading conditions, 8 12.5 10 v    [mm/s] ( 04 1.0 10 [s] t     ). The total displacement in extension and compression is ±0.025 mm, for a total of 2 cycles (see Fig. 2b and c). The material parameters are reported in Table 1 . It is worth mentioning that the material parameters adopted in this work consider typical values for a generic carbon steel. The purpose of the paper is to compare the response of the DOSS model against a conventional overstress viscoplastic theory. Future works will focus the attention on reproducing experimental data. 4.1. Impact loading conditions In case of impact loading conditions, most of the conventional models based on the overstress concept (Ganjiani, 2018; Perzyna, 2016; Prager, 1962; Perić, 1993; Wang et al., 2016) predict a pure elastic response due to the fact that