Modelling of size effects on strengthening of multiphase Al based composites

Some considerations on modelling and homogenization of multiphase light alloys

“…According to the variant of Cosserat theory adopted, [17] , the following relations holds among the parameters of initially micropolar matrix:…”

“…The size sensitivity of the model depends on the dimensionless parameter D i /l 0 through the average Eshelby tensor component (b m − b 0i ), [16], [17], where l 0 is intrinsic length of the initial matrix and D i is inclusion's diameter.…”

“…Herein it is assumed (as in many investigations [16], [17], [20] concerning the application of centrosymmetric micropolar theory) that the Cosserat parameter κ is in order of the shear modulus of initial matrix. If the inclusions (pores) are much smaller than the characteristic length l 0 , the term b 0i converges to 1/5.…”

“…Approximate analytical formulae are derived in order to assess and analyze the influence of pore size on the elastic properties of porous composite with higher porosity. The homogenization technique based on DEM theory and modified Mori -Tanaka two-phase model [16], [17] for the case of spherical inclusions is further developed incorporating an additional size dependent term to one of the classical Eshelby's tensor components. The consequences of this new assumption are demonstrated on a few limiting cases.…”

“…Further the homogenization scheme (1) is used as a representative of (8) , see [17], [16], leading to the system:…”