Issue 33

C. Gao et alii, Frattura ed Integrità Strutturale, 33 (2015) 471-484; DOI: 10.3221/IGF-ESIS.33.52

D ETERMINATION OF MODEL PARAMETERS

A

luminum and its alloys are widely used in aerospace and automotive industries because of their good mechanical properties [27]. CNTs can be an ideal reinforcement to design aluminum matrix nanocomposites (CNT/Al) to improve their wear and creep properties. So a typical CNT-reinforced MMNC (CNT/Al) is chosen as the example in this paper. Determination of model parameters for pure aluminum matrix As the matrix model is relatively independent to the strengthening component in the composite model, the material parameters in the matrix model in Eq. (10) can be determined firstly. For the pure aluminum matrix, the two reference strain rates 0 s   and 0   can be evaluated in advance. The two parameters lie in logarithmic functions and produce a smaller influence than 1  and 2  together with them. So their evaluation errors can be offset by fitting of 1  and 2  . The value of 0   is evaluated as 7 1 1 10 s   , and the value of 0 s   can be estimated as 9 1 1 10 s   which is generally two orders greater than 0   . The remaining seven parameters, ath  , ˆ Y , n , 1  , 2  , p , q , can be determined by a global multi-variables nonlinear optimization method, i.e. generic algorithm (GA) as used in [23], based on a group of experimental stress-strain curves of pure aluminum [9, 28] at different strain rates and temperature. A Matlab program has been developed to realize the optimization calculations. The optimized results of the matrix model parameters were listed in Table 1.

Model Parameters

Theoretically allowed ranges

optimized results

units MPa MPa



[0, 20]

12.0 456

ath

ˆ Y

[100, 1000]

n

[0, 1]

0.293

/

1  2 

1/K 1/K

6 5 9 10 , 9 10     ] 6 5 9 10 , 9 10     ]

5 1.11 10   -5 1.04 10 

[ [

p

(0, 1] [1, 2]

0.939 1.712

/

q

/ Table 1 : Optimized results of the material parameters of the Al matrix model

Determination of model parameters for CNT/Al composite For the CNT/Al composite in [9], the average original length and diameter of CNTs can be known as 0 1 l m   and 0 25 D nm  . The CNT strength parameters in the composite model of Eq. (24) can be first ascertained as 30 f GPa   and 100 fb GPa   [29]. The shear yield strength of perfect bonding interface should be equal to that of the matrix, 45 i y MPa   . The parameters in the distribution function of misorientation angle were evaluated as 0.874 B  and 6.47 k  . The CNT weight fractions were transformed into volume fractions by using the measured density, and the congruent relationship of weight fractions and volume fractions for CNT/Al was listed in Table 2.

0 0.5 1.5 2.0

Weight fractions wt ( % ) Measured density  (

2.636 2.642 2.638 2.625

3 g cm )

f v ( % )

Volume fractions

0 0.68 1.88 3.12

Table 2 : The congruent relationship of volume fractions and weight fractions for CNT/Al

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