PSI - Issue 28

6

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

2115

(10)

y n F a f  y n

,

,

F a b  

n

n



where a y and a ρ are material constants. From conditions (6) and (7) and formulae (8), (9), (10) the equations relating the increments of the internal variables  pi , b pi , f pi and ε �� � � to the increments of the stress and temperature are derived. Formulae (1) – (4) allow calculating the reversible and irreversible macroscopic strain. To calculate the fracture the deformation-and-stress criterion proposed in the work of Belyaev et al. (2018) was used:

b

     1

T      1  

3 ( ) 

.

pi

k tr 1

k

F

2 *

p



Here T σ is the von Mises stress for the stress tensor σ , F  is the shear strength, k 1 , k 2 are material constants, p is the damage variable which is assumed to be proportional to the total micro plastic strain in the grain:

,   p i

MP pi

|

|,

p B 

 

where B is a material constant. The representative volume was considered to be fractured if at least for one of the martensite variants in any grain the criterion of failure on the micro level was fulfilled. 3.2. Model material and results of simulation To verify the model simulations of mechanical cycling of FeMnSi-based SMA until fracture were carried out and the calculated values of the number of cycles to failure were compared with the experimental data for the specimens with additional aging, as for these specimens we have more experimental data in the low-cycle fatigue range. The values of the material constants specifying the elastic, thermal and phase deformation of SMA were chosen to represent the properties of such material (Table 1). The σ max - N diagram for the model material is presented in fig. 3 simultaneously with the experimental results. One can see that the results obtained with the developed fracture criterion are in a good agreement with the experimental data. So the microstructural approach and the criterion can be used for the estimation of the cyclic life of such materials. 4. Conclusions The precipitation hardening austenitic steels Fe – 0.40 С – 18 Mn – 2 Si – 2 V steel (mass percent) demonstrates rather high yield stress and significant homogenous strain before the failure. These parameters can be controlled by additional aging. The microstructural model of the deformation of FeMnSi-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, is an adequate tool for describing fatigue fracture of high-strength precipitation-hardening steels undergoing fcc-hcp martensitic transformation. There is a good agreement between the calculation and the 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.

Table 1. Values of the material constants.