PSI - Issue 68

Minghua Cao et al. / Procedia Structural Integrity 68 (2025) 828–834 M. Cao et al. / Structural Integrity Procedia 00 (2025) 000–000

830

3

the statistical analysis of microscopic images (Cao et al. (2023)). Nodular graphite was modelled as a sphere with a diameter of 15 µm, equal to the length of the major axis of a vermicular graphite particle, represented as an oblate spheroid (Fig. 2).

"

!

$)50#*)6%7*-0#%=09.)(*.0* $).#%6*7'#<)&D*2!>3

$)50#*)6%7*;D#.%&)(*.0* $).#%6*7'#<)&D*2!!3

!

"

#

/01'()#*+#),-%.D*2/3

!D#$%&'()#*+#),-%.D

4)50#*)6%7*8 4%90#*)6%7*8*

:%)$D.D#*8

Fig. 2. Geometry of numerical models

2.2. Constitutive behaviours There is significant variation in the available data for both graphite and the matrix in CGI of different grades (Sirtuli et al. (2024)). Due to inherently soft and brittle nature of graphite inclusions, previous numerical studies typically modelled graphite particles with limited plasticity (Seldin (1966); Greenstreet et al. (1973); Andriollo et al. (2015)). In terms of thermal properties, both constant (C-CTE) (Cao et al. (2023)) and temperature-dependent (T-CTE) (Rodriguez et al. (2018)) coefficients of thermal expansion were considered in this study. The inter-particle distances within CGI are smaller than the dimensions of the models, necessitating the assignment of effective properties to the metallic-matrix domain, consistent with those applied in our previous two-dimensional studies (Palkanoglou et al. (2022a); Palkanoglou et al. (2022b)). The matrix properties were selected based on the stress–plastic strain curve from our prior experimental work on CGI. The J2 flow theory was employed to characterize the mechanical behaviour of both the graphite inclusions and the metallic matrix (Palkanoglou et al. (2020)). The CTE of matrix was 1.2× 10 !" , higher than that of the graphite domain (Fig. 3c).

MP4

MG4

M:4

)E

)"!

$E!

$!!

)!

#"E

)E!

#E

#"!

)!!

#!

'"E

#E!

#!!

'E

'"!

/89P.+5: /29P.+5:

'E! *+,-../M12P4

*+,-../M12P4

'!

!"E

'!!

E

!"!

/

E!

<=->>5:5-S+/=>/+?-,@P9/-ABPS.5=S/M8C%4

!

!

;!"E

!"!

!"#

!"$

!"%

!"C

!"!

!"#

!"$

!"%

!"C

'"!

'"#

!

'!!

#!!

)!!

$!!

E!!

*+,P5S/MT4

a-@B-,P+b,-/Mc<4

*+,P5S/MT4

Fig. 3. Parameters of CGI constituents: (a) matrix; (b) graphite; (c) Coefficients of thermal expansion of graphite inclusions. The constitutive parameters for the graphite and matrix phases were selected according to our previous work (Palkanoglou et al. (2022)). A damage model was implemented to capture the constitutive behaviour of graphite, limiting its response to the elastic region. Damage initiation was assumed to occur when a plastic-strain-based criterion was met. Following the damage initiation, the stiffness of the material gradually degraded to 0. The integral ductile damage criterion is described as (Hooputra et al. (2004))