PSI - Issue 13

A. Prokhorov et al. / Procedia Structural Integrity 13 (2018) 1521–1526 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

1525

5





1

T T      ε u u u u .

(15)

2

Elastic Green-Lagrange strain tensor and Piola-Kirchhoff stress tensor are related according to the isotropic Hook’s law:   1 2 I     e e P ε E ε . (16) Additive decomposition of strain tensor is replaced by multiplicative decomposition of deformation gradient F : e p   F F F , where e F - elastic deformation gradient, p F - plastic deformation gradient. Plastic and elastic Green-Lagrange strain tensors are determined by:   p T p p   ε F F E , (17)

1 2





1       e ε F ε ε F . T

(18)

p

p

p

Boundary and initial conditions (8)-(12) were used for the simulation.

4. Results and discussion

Results of numerical simulation is presented in figure 3. During the numerical experiment, maximum of temperature field has moved from steel 316LN side to steel P91 side, as it has been observed in field experiment.

Fig. 3. Evolution of surface temperature (K) during quasistatic loading of P91-SS316LN specimen. Results of simulation (upper part of the specimen is SS316 LN steel)

Such behavior can be explained by difference in mechanical behavior of the P91 and SS316LN steels. Initial yield stress of the SS316LN steel is smaller than yield stress of the P91 steel and at the first stage of deformation SS316LN side of the specimen is in the plastic conditions while P91 side is in the elastic conditions. However, at some level of the plastic strain (which is approximately 22%) plastic flow in the P91 side overtakes plastic flow in the SS316LN side due to the various strain hardening rates of these materials and we can see temperature localization in the P91 steel side of the specimen. Figure 4 presents surface temperature evolution in P91-SS316 steel specimen when large plastic strains are taking into account. We can see that large plastic strains describe the same effect with the more pronounced localization zone. Moreover, large plastic strains allow illustration of necking of the specimen in the localization zone.