PSI - Issue 68

Eren Çelikses et al. / Procedia Structural Integrity 68 (2025) 1045–1050

1048

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E. C¸ elikses et al. / Procedia Structural Integrity 00 (2024) 000–000

3. Numerical Modeling

The numerical model is established using the micrographs of the DP800 samples. A Python script is utilized to convert the two phased microstructure to a finite element model. Explicit finite element analysis is performed with Abaqus and the material parameters are identified to the fit experimental tensile test data. The constitutive behavior of ferrite and martensite are represented with rate-independent J 2 plasticity model with isotropic hardening following the relation presented in Pierman et al. (2014) for both banded and dispersed DP800 samples. The hardening behavior of martensite is described by the following equations

1 n M    a +

q   

bC M

1 / 3 M , k M =

ε p n M ) , σ

(1)

σ y , M = σ y 0 , M + k M (1 − e

y 0 , M = 300 + 1000 C

C M C 0

1 +

where ε p is the equivalent plastic strain, C m is the martensite carbon weight percentage and a , b , C 0 , q , n m aremodel constants. Carbon contents of the martensite phase is calculated using ThermoCalc. The hardening of ferrite phase is described by

σ y , F = σ y 0 , F (1 + H F ε p ) n F

(2)

Parameters of the ferrite phase are calibrated to match experimental data of the DP800 samples. The calibrated set of parameters are listed in Table 2.

Table 2: Model parameters.

Martensite

a [MPa]

b [MPa]

C 0

q

n M

C M

33 × 10 3 33 × 10 3

36 × 10 4 36 × 10 4

DP800 Banded DP800 Dispersed

0.7 0.7

1.45 1.45

120 120

0.3547 0.3233

Ferrite

σ y 0 , F [MPa]

H F

n F

DP800 Banded DP800 Dispersed

420 415

250 390

0.14 0.14

DP steel microstructures are modelled as 2D plates using plane stress elements (CPS3), with 0.1 × 0.1 mm dimen sions. The left hand side is held in x direction, and the bottom is held in y direction. A master node is assigned at the top right node of the models by linking top and right surface nodes. In both banded and dispersed DP models, there are 44402 elements in total. To simulate the damage initation, an equivalent plastic strain controlled element deletion is performed. Critical values of equivalent plastic strain are identified separately for ferrite and martensite phases. Fig. 3 shows the maximum principal stress contours for the two microstructures, captured at their respective peak stress points, which also indicate the onset of element deletion. A more homogeneous stress distribution is observed in simulations with tension applied in the y-direction. When the models are loaded parallel to the martensite band direction, the dispersed martensite model displays similar uniform stress response. However, in the banded model, regions of highly localized stress appear around the martensite bands, potentially driving early crack initiation in martensite grains and leading to premature strain localization. Stress vs. strain curves are shown in In Fig. 4. Since martensite is heavily banded in the x-direction, a significant di ff erence is observed in both hardening response and failure behavior between the simulations in di ff erent directions for the banded microstructure. However, for the dispersed martensite microstructure, the hardening behavior shows minimal variation, though some di ff erences in failure strain are still observed. The reason might be that the failure simulations based on plastic strain might not be adequate to correctly capture the complex failure mechanisms in dual-phase mictostructure. The initiation of element deletion is also a ff ected by the mesh resolution in this model. To overcome such issues, more advanced modelling techniques such as cohesive zone elements or phase field fracture method can be utilized (see e.g. Aydiner et al. (2024); Tatli et al. (2024)).