PSI - Issue 8

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

268

4

Table 2. Material mechanical properties Tensile test

Charpy test (23 ◦ C)

Grain size

σ y0.2% (MPa)

σ u (MPa)

A % Z % KV(kJ) Test 1

KV(kJ) Test 2

KV(kJ) Test 1

− 6

996 . 8

1087

15.4

56.1

68

73

71

1000

800

σ ( MPa )

600

400

200

0 10 20 30 40 50 60 70 0

ϵ (%)

Fig. 2. Tensile tests on the AISI 4140 (engineering strain-engineering stress).

2.2. Campaign setup

The Bauschinger e ff ect consists of the loss of material yielding performance when load is reversed after having experienced a plastic tensile strain. A typical σ − uniaxial path for a material exhibiting Bauschinger e ff ect is shown in Fig.3. Once the tensile yield point σ (L) y has been crossed over, a reduction of the reverse yield strength σ (U) y takes place. When, at unloading, the σ − curve overcomes σ (U) y , a significant hardening modulus is experienced (Parker et al. (2003b); Chen (1985)). Both σ (U) y and the hardening modulus are function of the maximum equivalent tensile plastic strain experienced at loading p . (Chen (1985); Gibson et al. (2005, 2012); Troiano et al. (2006, 2012)) .

Load reversal

ϵ p

σ

(L) σ y

E

σ y

α

σ y

ϵ

Hardening after reverse yielding (U) σ y

Fig. 3. Typical true stress-true strain cycle for a material exhibiting Bauschinger e ff ect.

In the present paper the FE formulation adopted for reconstructing the Bauschinger e ff ect is an elastic-plastic model where elasticity is isotropic with Young’s modulus E and Poisson’s ratio ν and where plasticity is Von-Mises based, including kinematic hardening and isotropic softening (with backstress α , radius of the yield locus σ y as shown in Fig.3)(Auricchio and Taylor (1995)). The aim of the test campaign is investigating the unloading behavior of the AISI 4140 steel for a range of tensile