Issue 58

K. Benyahi et alii, Frattura ed Integrità Strutturale, 58 (2021) 319-343; DOI: 10.3221/IGF-ESIS.58.24

influence of the variation of the volume fraction of inclusions on the mechanical characteristics. Then, once the effective mechanical properties of the composite were known, a damage model was introduced to study the response of the microstructure. The effective mechanical properties of the representative volume element ( )  , eff eff E are those obtained from the periodic homogenization method, corresponding to each volume fraction. The volume element is stressed in pure tension. The loading is done with displacement imposed in three-dimensional strain. The characteristics of composite are defined in Tab. 4:

Matrix- Spheroidal inclusions

E h (MPa)

ν h

A C

B C

A t

B t

ε D0

Volume Fraction (%)

10 15 20 25 30

3440.43 3764.60 4264.90 4779.03 5324.70

0.333 0.335 0.326 0.316 0.312

1.4 1.4 1.4 1.4 1.4

240.83 263.52 298.54 334.53 372.73

0.8 0.8 0.8 0.8 0.8

2752.35 3011.68 3411.92 3823.23 4259.76

0.001 0.001 0.001 0.001 0.001

Matrix- Ellipsoidal inclusions

E h (MPa)

ν h

A C

B C

A t

B t

ε D0

Volume Fraction (%)

10 15 20 25 30

3391.73 3787.73 4240.37 4784.43 5320.80

0.340 0.333 0.328 0.321 0.312

1.4 1.4 1.4 1.4 1.4

237.42 265.14 296.82 334.91 372.46

0.8 0.8 0.8 0.8 0.8

2713.39 3030.19 3392.30 3827.55 4256.64

0.001 0.001 0.001 0.001 0.001

Matrix- Cylindrical inclusions

F tj (MPa)

(MPa)

E h (MPa)

ε 0 ( % )

τ u (MPa)

ω ( % )

ν h

θ 0

ϕ (mm)

l f (mm)

47.76 47.76 47.76 47.76

3.46 3.46 3.46 3.46

5247.08 7780.74 10360.73 13033.63

0.342 0.335 0.327 0.320

0.21 0.21 0.21 0.21

0.04 0.04 0.04 0.04

0.8 0.8 0.8 0.8

7 7 7 7

5

0.405 0.405 0.405 0.405

10 15 20

Table 4: The effective properties and damage parameter of a composite.

In a first case, we represent in Figs. 15-16 the local stress-strain response and the evolution of the damage respectively, depending on the strain of a volume element loaded in pure tension, and under various volume fractions. We set the parameter t A and made the parameter t B varied.

Figure 15: Influence of the variation of the volume fraction inclusions on the local stress-strain behavior.

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