PSI - Issue 25

A.Yu. Smolin et al. / Procedia Structural Integrity 25 (2020) 477–485 A.Yu. Smolin et al. / Structural Integrity Procedia 00 (2019) 000 – 000

481

5

The expression for tangential interaction of movable cellular automata is similar to Hooke's relations for non diagonal stress tensor components and is pure pairwise:

.

(12)

2 ( G τ   

γ

)

ij

ij

The difference in automaton rotation leads also to the deformation of relative “bending” and “torsion” ( the last only in 3D) of the pair. It is obvious that the resistance to relative rotation in the pair causes the torque, which value is proportional to the difference between the automaton rotations:

(13)

    K (

ω ω

G G

   t )

)(

ij

i

j

j

i

Eqs. (1) – (8), (11) – (13) describe the mechanical behavior of a linearly elastic body in the framework of the MCA method. Note that Eqs. (7), (8), (11) – (13) are written in increments, i.e., in the hypoelastic form. Smolin et al. (2009) showed that involving the rotation allows the movable cellular automata to describe the isotropic response of material correctly. A pair of elements might be considered as a virtual bistable automaton having two stable states (bonded and unbonded), which permits simulation of fracture and coupling of fragments (or crack healing) by MCA. These capabilities are taken into account by means of corresponding change of the state of the pair of automata. A fracture criterion depends on the physical mechanisms of material deformation. An important advantage of the formalism described above is that it makes possible direct application of conventional fracture criteria, which are written in tensor form. Herewith the two-parameter Drucker-Prager criterion is used for silicon coating. This criterion utilizes two parameters such as the tensile strength and the compression strength of the material.

3. Description of the Model

In this paper, the MCA method is applied to study a three-dimensional nitinol bar covered by silicon coating subjected to flexural loading. It is assumed that nitinol possesses linear elastic properties and characterized by Young’s modulus E = 40 GPa and Poisson’s ratio ν = 0.32 (martensitic phase). Silicon is assumed to be an elastic brittle material with Young’s modulus E = 131 GPa, Poisson’s ratio ν = 0.26, tensile st rength σ t = 16.7 MPa and strength in compression σ c = 690 MPa.

a)

b)

Fig. 2. The model specimen as the packing of movable cellular automata (a) and a scheme of its loading (b).

The geometry of the model is shown in Fig. 2. We consider a nitinol bar of the length of 0.7 mm with a square cross- section with a side size of 95 µm. The thickness of the silicon coating is 5 µm; it is shown in Fig. 2,a by blue color. To mimic the three-point flexural test we fixed the automata at the lines along the X -axis located on both left and right sides from the coordinate plane XOZ at a distance of 0.25 mm (cyan lines in Fig. 2,b; the distance between them l = 0.5 mm). The loading is applied by moving the automata at the center cross-section (marked by red in Fig.