PSI - Issue 28

Jelena Srnec Novak et al. / Procedia Structural Integrity 28 (2020) 53–60 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Table 1. Isotropic parameters identified from experimental data for the Voce and proposed models. Goodness-of-fit examined in terms of sum of squares of residuals (SSE) for each model and strain amplitude.

Strain Amplitude

Material Parameters

Error Index (SSE)

Material hardness

Voce

Proposed

Voce

Proposed

ε a (%)

R ∞ (MPa)

b

a

s

0.9 1.2 1.5

-94 -37

1.158 0.883 1.312 1.086 1 0.986 1.953 2.027 1.495 1 3.977 3.516 2.810 b all 1 b all 1

0.388 0.621 0.327 0.439 1 0.419 0.200 0.176 0.337 1 0.095 0.089 0.107 a all 1 a all 1

2.054 1.600 1.608 1.809 1 0.832 1.243 1.394 0.853 1 1.081 1.347 1.439 s all 1 s all 1

0.348 0.136 0.018

0.518 0.269 0.082

296 HV

-104 R ∞,ave

1

Single values

1.169

1.597

-78

0.9 1.2 1.8

-328 -289 -265 R ∞,ave -294 1 -271 -323 -356 R ∞,ave -306 1

4.749 0.240 0.077

0.347 0.157 0.048

420 HV

1

Single values

6.853

1.932

0.9 1.2 1.5

0.959 0.082 0.070 1.329

0.335 0.080 0.043 0.787

546 HV

1

1

1

1

b

a

s

Single values

all

all

all

3.510 1

0.098 1

1.215 1

1 parameters b strain values).

all , a all and s all are estimated from all experimental data merged together (whereas R ∞,ave is the average over all

Different values of R ∞ , b , a and s parameters characterize cycles with different strain amplitudes, see Tab. 1. This may represent a drawback, if commercial finite element codes have to be used, as they generally permit only one set of the isotropic parameters to be input. Furthermore, components subjected to cyclically loads usually undergo plastic deformations over different strain ranges. Therefore, adopted material parameters should be valid over a wider range of loading conditions. A possible compromise for solving this issue could be to take an average value R ∞,ave and to identify a single value b all , a all and s all by fitting Eqs. (3) and (5), respectively, to all the experimental data gathered together (see Tab. 1). A comparison between the fitted curve calculated with the Voce model considering b all , the TP model with a all and s all parameters and the experimental data is presented in Fig. 5.

Fig. 5. Isotropic model for ε a = 0.9% (42CrMo4 steel with 420 HV), calculated with b all , a all and s all parameters; Voce model (red line) and proposed model (blue line). Residual ∆e is also reported.