PSI - Issue 13

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

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where the plus sign is for the direct and minus – for the reverse transformation. The value of F fr is derived from the transformation characteristics: F fr = q 0 ( M s – T 0 )/ T 0 . The process of the mechanical twinning (reorientation) of martensite “through virtual austenite” is also considered. It is assumed that the reorientation is controlled by the mechanical part of the driving force F pi and, besides, that the dissipative force F fr tw for the reorientation can be different from that for the transformation. It is also assume that the reorientation of martensite in a grain can occur only if this grain is purely martensitic (  M = 1) and the condition of the reverse martensitic transformation are not satisfied for every variant of martensite. 2.2. Defect Densities and criterion of fracture To find the variation law of variables b pi following to Belyaev et al. (2015) and Volkov et al. (2015) the micro plastic flow conditions are formulated in the form similar to that for classic plastic flow:  F pi MP – F pi   = F pi y , ( F pi MP – F pi  ) dF pi MP > 0, (7) where F pi MP is the generalized force conjugated with the parameters b pi : According to Evard et al. (2006) and Volkov et al. (2015) the deformation defects generated by the microplastic flow are divided in two groups: oriented defects b pi mentioned above and scattered defects f pi . Evolution equations for them are formulated in the form: ), H( 1 * MP pi pi MP pi pi MP pi pi b b b          = − (8) where β * and r are the material constants, H( x ) is the Heaviside’s step function. The last term in (9) describes softening caused by the reverse transformation. It is assumed that the irreversible defects give rise to the isotropic hardening and the reversible ones – to the kinematic hardening. So the defect densities f pi and b pi are related to F pi y and F pi  by the so-called closing equations, which are chosen in the simplest linear form , , pi pi pi y y pi F a b F a f   = = (10) 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 of the model specimen the deformation-and-stress criterion of fracture proposed in the work of Belyaev et al. (2018) for TiNi SMAs is used: . Here T σ is the von Mises stress for the stress tensor σ , τ F is the shear strength, k 1 , k 2 are the 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. This criterion, being a generalization of the von Mises criterion of maximum shear stress intensity, allows predicting accumulation of fracture both for one-side loading and thermal and mechanical cycling. It takes into account the fact that the hydrostatic pressure hinders the damage, the oriented defects      ), H( r f f = + −  −     ) ( 0 pi pi pi MP pi pi f (9) p T +  =   1   b k k tr 1 F pi    + + 1 3 ( )  2 *  . pi MP pi b F G   = − Here F pi y and F pi  are the forces describing the isotropic and kinematic hardening.