PSI - Issue 8

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

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6

0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

ϵ (%)

ϵ (%)

10 20 30 40 50 60 70

10

20

30

40

Step

Step

(a) Cycle 1.

(b) Cycle 2.

Fig. 5. Testing cycles for total strain levels = 0 . 75 , 1 . 00 , 1 . 50 , 2 . 00 , 2 . 50 and 3 . 00%

1000

1000

500

500

σ ( MPa )

σ ( MPa )

1000 - 500 0

1000 - 500 0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

ϵ (%)

ϵ (%)

(a) Cycle 1.

(b) Cycle 2.

Fig. 6. Results of the experimental campaign (engineering strain-engineering stress).

3. Formulation of the Finite Element model

3.1. General hypothesis

The model has been built in order to be able of fitting the results shown in Sec.2.3. The model is intended to be implemented in a standard commercial FE code ( ANSYS ) and, for this purpose it was translated in a suitable discrete formulation. All physical quantities will exhibit the subscript n if the formula refers to their values at a given iteration. As anticipated in Sec.2.2 the model is Von-Mises based with yield locus radius σ y and back-stress vector α , with the plastic flow vector n defined by an associated flow rule, as shown in Eq.1 (the jacobian matrix and the discrete return map have been implemented according to Auricchio and Taylor (1995)).

σ − α | σ − α |

n =

(1)

| σ − α | = σ y

According to the considerations of Sec. 2.3 and 2.2 the model should fulfill the following requests:

1. when yielding condition is not verified, the behavior is elastic with E and ν at loading and unloading.