PSI - Issue 13

Fedor S. Belyaev et al. / Procedia Structural Integrity 13 (2018) 988–993 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

992

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characterized by the variables b pi serve as the stress concentrators and the material damage due to the micro plastic deformation reduces the deformation resistance of material. A representative volume is considered fractured if at least for one of the martensite variants in any grain the criterion of failure on the micro level is fulfilled. 3. Results of simulation To verify the model and its predictive ability, simulations of mechanical cycling of FeMn-based SMA until fracture were carried out and the calculated values of the number of cycles to failure were compared with the available experimental data. The values of the material constants specifying the elastic, thermal and phase deformation of SMA were chosen to represent the properties of a FeMn-type SMA (Table 1).

Table 1. Values of the material constants.

Material constant

Value

Characteristic temperatures M f, M s, A s, A f

310, 380, 440, 510 K

Latent heat q 0

-65 MJ/m 3

Number of martensite variants N 12 Lattice deformation matrix D by Schumann (1964) (to be symmetric) 1 1 2 ( 1 1 1 1 1 1 −2 −2 −2 ) � Elastic modulus of austenite E A 200 GPa Elastic modulus of martensite E M 200 GPa Poisson’s ratio of austenite  A 0.33 Poisson’s ratio of martensite  M 0.33 Critical reorientation force F fr tw 45 MJ/m Isotropic hardening factor a y 500 MPa Kinematic hardening factor a  1000 MPa Oriented defects saturation factor β* 10 Parameter of softening r 0.001 Parameter of the hydrostatic pressure influence on fracture k 1 0 Parameter of the oriented defects influence on fracture k 2 1 Damage scaling factor B 1

Figure 1(a) demonstrates stress-strain curves at isothermal alternating strain-controlled cycles in the martensitic state. According to Sawaguchi et al. (2006, 2015), Nikulin et al (2015, 2016) and other authors this regime is the most promising for full-scale FeMn-based dampers and isolators. For this regime simulations of the fatigue fracture of the FeMn-based alloy were performed. In fig. 1 (b) the calculated results of the number of cycles for fracture are shown depending on the strain amplitude, which varied in the interval 0.5 – 2.0% for two-sided deformation (tension compression). They are compared to the experimental results obtained by Nikulin et al. (2016). One can see that the results obtained with the developed fracture criterion are in a good agreement with the experimental data on the fatigue fracture of FeMn SMA. So the criterion can be used for estimation of the cyclic life of such materials. 4. Conclusions The microstructural model of the deformation of SMA admits natural generalization for FeMn-based SMA. Taking into account the specific features of the martensitic transformation and the micro plastic deformation together with a proper deformation-and-stress criterion of fracture allows describing deformation and fatigue fracture of these alloys. There is a good agreement between the calculation and the available experimental data. The model can also be used for further estimations of the cyclic life of SMA working elements in different thermal and mechanical regimes, thereby allowing finding the optimum characteristics of such elements and ensuring the required cyclic life.