Issue 78

V. I. Kolesikov et alii, Fracture and Structural Integrity, 78 (2026) 220-232; DOI: 10.3221/IGF-ESIS.78.13

Specifically, a normal compressive load of 33 P =− 100 MPa was applied towards the z-direction (top plate), while a simple shear was realized along the xz -plane. All other components in Eqn. (1) indicated by asterisks were left free to evolve naturally. These boundary conditions satisfy the mutual exclusiveness of ˙ F and P as well as prevent rotation (undefined P off-diagonal components). To achieve stable convergence and smooth result plots with all captured features, the simulations were run consequently in there stages: 1) up to 4 s with 80-time steps and sampling of every 2 nd step, 2) from 4 to 20 s with 800-time steps and sampling of every 40 th step, and 3) from 20 to 120 s with 600-time steps and sampling of every 10 th step. Assuming that hydraulic systems under heavy braking conditions typically operate at pressures of ~17 MPa (in automobiles), 1 MPa (in trains), and 30 MPa (in aircrafts), a level of applied load of 100 MPa was taken being physically reasonable. This is due to the fact that the actual contact area is extremely small. In doing so, the pressure localization becomes comparable with the value of material hardness. This high level of 33 P was also chosen to ensure well-manifested visualization of RVE deformations as well as to reach the maximum material strengths during the simulations. For the composite RVE shown in Fig. 1 b, two variants were first reconstructed representing columnar and equiaxial microstructures (see Tab. 1). In addition, two distinct “soft” and “hard” materials (phases) were considered: Cu and 40CrNiMo alloy, respectively.

−

Aspect Ratio

Axis ODF

Crystal ODF

Shape Type

ESB (av, min,

max) ⁄ ⁄

Euler angles

Euler angles

Microstructure

90°, - 90°, - 90°

Super Ellipsoid Super Ellipsoid

30, 27, 33 36, 15, 49

Columnar/Rolled

3.4 0.1

10

1

1

10 2 0.1

0.1

1 50000

Random

3.5 0.4

20

2

1

10 2

1

1

Random

Equiaxial

Table 1: Parameters to define two types of the microstructure in RVE (with Dream 3D for DAMASK crystal plasticity simulations). The meaning of all statistical parameters are given in [17]. Fig. 1 c illustrates the preferential z -axis orientation of columnar grains along the main axis and random crystallographic orientation in both phases. In order to ensure compatibility with the DAMASK software, the use of Dream 3D reconstruction required multiple pipelines and additional scripting to renumber and rename grain and phase identifiers within the composite RVE. Similar CP simulations of interfacial contacts between Cu and 40CrNiMo phases (RVEs of soft/hard and hard/hard composites: i) “Cu/40CrNiMo/Cu” and ii) “40CrNiMo/40CrNiMo/40CrNiMo”) as well as between columnar and equiaxial microstructures of the 40CrNiMo phase (RVE of hard/hard composite “40CrNiMo/40CrNiMo/40CrNiMo”) were also carried out, as described in details in [17]. The DAMASK Spectral Solver was utilized, which employs the following phenomenological model of plasticity [22]: ( ) : S m n α α α τ = ⊗ (2)

w α

τ τ

( ) α τ

α γ γ =  

(3)

sgn

0

α

0

= ∑

' 1 s N h α αα = ′

α ′

α





τ

γ

(4)

0

a



   

α

 

 

τ τ

' q h 

0

=

h

(5)

0 1

 − 

'

αα αα

 

∞

223