Issue 78

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

Of key interest are the negative values of P , which indicate shear induced “locking” effect within the material. While tending to displace along the x -axis, adjacent elements/grains/nodes impede this movement, giving rise to localized compression/squeezing along the x -axis, which results in negative 11 P values. Unlike shear, tension is a single dimensional deformation; it i) lacks the geometric nonlinearity that generates normal reactions, ii) does not lock motion, and iii) does not impose contact constraints along the x -axis. Therefore, there is no reason for localized compression to develop along the x -axis under tension; thus 11 P remains positive. Figs. 3a and 3e show that crystal orientation within the individual grains is changed as compared to the non-deformed state (illustrated with uniform IPF colors). This suggests not only slip activation but also complex rotation of slip planes due to interactions with neighboring grains [24, 25]. It is noteworthy that strain maps (visualized with the use of ParaView) display the deformed geometry by recomputing new node coordinates from the deformation gradient tensor and by applying them to the Eulerian grid (fixed DAMASK mesh). As a result, the RVE is transformed into a “parallelogram”, but out of the pixel scale. Generally speaking, it is also possible to reconstruct a Lagrangian mesh by integrating the deformation gradient tensor and regenerating node coordinates. However, DAMASK software naturally utilizes a fixed Eulerian grid; the material remains represented by the same pixel-based mesh: i) its grain ID does not change, ii) the grain boundaries never fluctuate (i.e., the material does not transit into neighboring pixels). Instead, all internal fields evolve within initial pixels. Thus, the used maps provide a realistic visualization of the results of the DAMASK CP simulations. Depending on carbon content and tempering, bcc-martensite in Fe-C steels typically exhibits tensile strengths in the range of 1.2–2.4 GPa [26, 27]. However, given compressive nature of stress state in our simulations, this does not necessarily indicate imminent fracture for RVE of hard/hard composite “40CrNiMo/40CrNiMo/40CrNiMo” (see Figs. 2 and 3 at t =144 s as well Figs. 4). A quantitative assessment would require a calibrated ductile fracture locus for this material. Note that a c τ 〈 〉 values were calculated from the magnitudes of all 24 slip systems; therefore, the a c τ 〈 〉 values are inflated by inactive systems and latent hardening since the hardening of one slip system affects many others even if they are not active. As a result, a c τ 〈 〉 values are higher compared to those from active slip systems in the active vM c M σ τ = relation, where M ≈2.5 –3.5 is the Taylor factor. Thus, / active c vM M τ σ 〈 〉 =〈 〉 values can also be easily accessed from vM σ 〈 〉 plots.

40CrNiMo/40CrNiMo/40CrNiMo RVE 〈〈 ττ cc aa 〉〉 a)

40CrNiMo/40CrNiMo/40CrNiMo RVE 〈〈 σσ vv MM 〉〉 b)

40CrNiMo/40CrNiMo/40CrNiMo RVE

〈 τ c α ⟩ / 〈 σ vM ⟩ 〈 τ c α ⟩ / 〈 σ vM ⟩

c)

100

1.2E+09

2.30E+09

1.0E+09

8.0E+08

2.25E+09

〈τ c α ⟩/〈σ vM ⟩

〈τ c α ⟩, Pa

10

〈σ vM ⟩, Pa

6.0E+08

2.20E+09

4.0E+08

2.15E+09

2.0E+08

〈ε vM ⟩

〈ε vM ⟩

〈ε vM ⟩

1

2.10E+09

0.0E+00

5.E-05

5.E-04

5.E-03

5.E-02

0.00001

0.001

0.1

1.E-05

1.E-03

1.E-01

Figure 4: The volume-averaged plots of a) resistance against the plastic slip, b) the von Mises equivalent stress, and c) the plastic flow resistance indicator for columnar (cyan markers) and equiaxial (orange markers) microstructures versus von Mises equivalent strain in RVE of hard/hard composite “40CrNiMo/40CrNiMo/40CrNiMo”. In this regard, Figs. 4 a and 4 c should be analyzed in terms of trends and mechanisms, while the calculated vM σ 〈 〉 values in Fig. 4 b are physically reasonable. Regarding trends and mechanisms, Fig. 4 demonstrates that up to vM ε 〈 〉 ≈ 10 -3 , there is negligible slip and an elastic response only, followed by plastic deformations with a work-hardening

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