PSI - Issue 8

L. Landi et al. / Procedia Structural Integrity 8 (2018) 3–13 L. Landi et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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To increase the predictive precision of the material’s model, we have decided to carry out a more precise least squares linear regression of the equation (8), using the Johnson- Cook’s constitutive model, with the only “static” terms A, B and n different from 0. It requires minimizing the least square error, limiting ourselves to the curve in (8) until about = 0.27 alligned with the data reported in Børvik (2001). Indeed, as we have explained, the experimental curves, found in literature for non-alloy steels, are incompletes or even misleading beyond the necking, when the real curves of stress-deformation are treated. The optimization leads to a model (RMS) reported on the table 4, which will be used on the simulations of that article to link the numerical models to the experimental results. In addition the c and m parameters have not been changed at all and are again taken the same as the previous one. The T m parameter in this RMS model has been taken from a technical furniture sheet of a DC01 and not assumed from Weldox as in the past.

Table 4. Root mean square DC01 JC constitutive model RMS JC parameters

Data

̇ 0 c m

A, B [MPa] , 0 [K] n [s -1 ]

210, 506.5

0.0001

1800, 300

0.488

0.02

0.7

In the figure 2 we have reported the graph of the static models of DC01 for Hollomon in black, of JC by Landi and Amici (2016) in dashed blue and of least squares in red.

Fig. 2. DC01 static models comparison.

Fig. 3. DC01 JC dynamic models comparison, strain rate of 1000 1/s