PSI - Issue 28

Fedor S. Belyaev et al. / Procedia Structural Integrity 28 (2020) 2110–2117 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The stress-strain diagrams at room temperature, which corresponds to the martensitic state for the both specimens, are presented in fig. 1. According to (Sagaradze and Afanas’ev (2015)) additional aging at 720°C results in partial dissolution of the VC particles causing a slight decrease of the yield stress and a significant increase of plasticity. Cyclic loading of the specimens was performed in the pulsating regime, with the minimum stress σ min = 0 MPa and the maximum stress σ max which was varied. For an as-received specimen with σ 02 = 787 MPa the number of cycles to fracture is around N = 2000 at σ max = 800 MPa. When σ max decreases to 500 MPa, N increases to 192000 – 300000 cycles (fig. 2). As for the specimens subjected to additional aging the stress values mentioned above exceed the yield limit and the cyclic life is less: around 8000 cycles at σ max = 800 MPa and around 115000 cycles at σ max = 500 МPа.

after additional annealing as-received

600 700 800 900 1000

 max  MPa

2 1

500

1000

10000

100000

N

Fig.2. Number of cycles to failure vs. maximum stress σ max of the loading cycle. Curve 1 - as-received specimens (after quenching from 1150°С and annealing 12 hours at 650  С); curve 2 – specimens after additional annealing for 3 hours at 720°С.

3. Modeling 3.1. Microstructural model

The microstructural model for calculation of the phase deformation for FeMnSi-based SMA was described in detail in the works by Evard et al. (2016) and Belyaev et al. (2018). In this model it was supposed that the representative volume consists of grains characterized by orientations  of the crystallographic axes. The sub-volumes (domains) inside a grain can be occupied either by austenite or by any of the N crystallographically equivalent orientation variants of martensite. The fcc  hcp transformation in FeMnSi-based alloys is realized by one of the three simple shears by 1/6   112 fcc on each second {111} fcc plane. So for these SMA there exist N = 12 possible variants of the martensitic transformation. All the martensite variants were divided into four triplets (zones) related to the four {111} planes. The total amount of martensite belonging to zone p ( p = 1,2,3,4) is characterized by vector  p with components  pi ( i = 1,2,3 is the number of the direction of the shear). The sum of the components  pi characterizes the total amount of martensite in the zone:

     3 1 i zon p

.

pi

The total amount of martensite in a grain is calculated as the sum of martensite over all zones:

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1 p      . gr zon p