Question

It is desired to develop a strong Aluminum-based alloy with a shear strength on the order of G/100 by precipitation hardening, where G is the shear modulus. Calculate the necessary precipitate spacing, and estimate the required percentage of the precipitate phase. Assume that the precipitate phase consists of spherical particles of radius of R=40 nm with centers uniformly distributed in simple cubic lattice. Does it matter whether the precipitates strain the matrix locally around the interface or not?

Answer 1

a) L = 50.01 nm

b) 99.98%

Step-by-step explanation:

Determine the necessary precipitate spacing and estimate the required percentage of precipitate phase

Given that the shear strength = G/100 by precipitation hardening

G = shear modulus

Radius of particles = 40 nm

attached below is the detailed solution

a) precipitate spacing ( L ) = √( 2π / f ) * R₁

= √ ( 2π / 0.00719956 ) * 1.693 nm

hence L = 50.01 nm

b) Determine The percentage of precipitate phase that is required

( precipitation strength / peak strength ) * 100

= ( 18.4583 / 18.4604 ) * 100

= 99.98%