Young's modulus for filled metal?

[dculp1]

I have a tin material (E = 7.35e6 psi, density = 0.268 lb/in^3) that is uniformly filled with 0.030" diameter steel shot (E = 28.0e6 psi, density = 0.280 lb/in^3). If the steel is 30% by weight of the total and assuming the surfaces of the steel shot are well-bonded to the tin, what value should I assume for the resulting modulus E? (I assume that the resulting filled material is isotropic on a macro scale.)

As a first guess I have adjusted the modulus according the the relative volumes occupied by the tin and steel, for which the resulting modulus is 13.28e6 psi. Is this approach correct? If so, is there any theoretical or empirical justification? If not, is there a better approach?


Thanks,
Don Culp

 

[GregLocock]

The vf method you suggest is commonly used for estimating the density and Young's modulus of mixtures, and I have seen it suggested in books such as Ashby and Jones.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[dculp1]

Greg --

Is "Engineering Materials 1: An Introduction to Properties, Applications and Design" the Ashby and Jones book to which you refer?

Thanks,
Don Culp

 

[GregLocock]

I think that'd be it, I've only got the lecture notes which they amplified and turned into a book.

Off the top of my head

Vf.2=1-Vf.1

Vf.1>=0
Vf.2>=0

Den.mix=Vf.1*Den.1+Vf.2*Den.2
E.mix=Vf.1*E.1+Vf.2*E.2

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[GBor]

Greg's on the mark. Vf.1 is a volume fraction...basically a ratio of how much of each substance is contributing to the overall modulus. I've always referred to it as the "Law of Mixtures"...don't know if that is the "true" name for it. It works for continuous fiber composites as well.

Garland E. Borowski, PE
Borowski Engineering & Analytical Services, Inc.
Lower Alabama SolidWorks Users Group

 

[GregLocock]

Now, that only works for plum puddings, not spaghetti bolognese!

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[dculp1]

Garland --

In searching for "Law of Mixtures" I found the following (

http://www.mse.cornell.edu/courses/engri119/Class_Notes/structure_of_teeth.html):

"We know that composites have a range of possible moduli depending on how the components are arranged. The law of mixtures for moduli gives the highest possible value, but if the hard and soft components are placed together randomly, the composite has a modulus of
1/(the average of (1/modulus)) which is much lower." [This equation does not appear to involve the volume fraction.]

Also see

http://www.chemweb.com/journals?type=issue&jid=00796425&iid=00510005:

"Mechanical properties of alloys consisting of two ductile phases by Sreeramamurthy Ankem; Harold Margolin; Charles A. Greene; Brett W. Neuberger; P. Gregory Oberson (pp. 632-709).

A large number of engineering alloys consist of two ductile phases; for example ?/? titanium alloys, ?/? brasses and dual phase steels. Whenever a material consisting of two or more component phases with different properties is subjected to stress, in general, the phases deform differently. This results in additional interaction stresses and strains and their magnitude depends on such factors as the property difference between phases, and morphology and volume fraction of phases. Due to these complexities, the properties of two-phase materials, in general, cannot be predicted on the basis of simple laws such as the law of mixtures."

Thoughts?

Don Culp

 

[GBor]

Don,

Your statements are absolutely true for randomly oriented, short-fiber composites. I specifically named continuous fiber composites for this reason. You can (and I have on many occasions with excellent agreement with test data) predict continuous fiber composite material properties using the Law of Mixtures SO LONG AS you understand your manufacturing process and recognize void fraction in the equation.

Garland