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Metallurgical Transactions A

, Volume 21, Issue 1, pp 289–303 | Cite as

The physics of mechanical alloying: A first report

  • D. R. Maurice
  • T. H. Courtney
Transformations

Abstract

In this paper, we present a first attempt to define the basic geometry, mechanics, and physics of the process of mechanical alloying. The geometry of the collision events which lead to particle fragmentation and coalescence is modeled on the basis of Hertzian contacts between the grinding media which entrap a certain amount of material volume between the impacting surfaces. This geometry essentially defines the volume of material affected per collision, and from this information and characteristics of the specific mill and the material being processed, impact times, powder strain rates and strains, powder temperature increase, powder cooling times, and milling times can be approximated.

Keywords

Metallurgical Transaction Nusselt Number Powder Particle Impact Velocity Mechanical Alloy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

a

deceleration of particle due to factional drag

A

particle surface area

Cp

specific heat

CR

charge ratio (mass of grinding balls/mass of powder)

Dm

diameter of SPEX mill

E

Young’s modulus

Eeff

effective Young’s modulus of impacting media having different Young’s moduli

f

fluid mechanics friction factor

fp

fractional powder volume (powder volume/ (mill volume - tool volume))

FD

fluid mechanics factional drag force

g

gravitational constant

gp

geometrical constant relative to pressure developed in a Hertzian collision

gr

geometrical constant relative to Hertzian radius

gT

geometrical constant relative to collision time

h

height of powder cylinder impacted during collision

ho

initial height of powder cylinder impacted during collision

ht

heat transfer coefficient

hf

height of fluid above reference line as a result of rotational velocity

k

thermal conductivity of powder

K

coefficient in constitutive plasticity equation for powder aggregate

l

interlamellar thickness in powder particle

lo

initial interlamellar thickness in powder particle

L

length of SPEX mill

m

mass of colliding grinding media

n

strain-hardening coefficient of powder aggregate

nB

number of balls in SPEX mill

nc

number of powder collision events

Nu

Nusselt number

p

pressure

pmax

maximum pressure generated in a Hertzian collision

Pr

Prandtl number

r

effective powder particle radius

rd

radius of horizontal ball mill

rh

Hertz radius

ro

radius of attritor

R

radius of grinding balls

R1,2

radii of curvature of impacting spherical bodies

Ro

distance from center of attritor tank

Re

Reynolds number

t

time

to

time between powder particle collisions

tcb

time between grinding media collisions

tf

time for completion of mechanical alloying

tp

processing time

T

temperature

Ta

ambient mill temperature

Tb

bulk temperature of powder particles

Ts

postimpact temperature of powder particles (=T a +ΔT)

Ts

surface temperature of powder particles

u

relative velocity of two contacting particles

up

plastic work per unit volume on powder during impaction

UE

elastic strain energy associated with a Hertzian collision

Up

plastic work on powder during impaction

v

precollision relative velocity of impacting media

v

instantaneous relative velocity of impacting media

va

ball velocity in attritor

Uair

air velocity in SPEX mill

vg

ball velocity component due to gravity in a horizontal ball mill

ut

transverse velocity component of ball in a horizontal ball mill

V

particle volume

VB

total ball volume in mill

Vc

powder volume impacted during collision

VM

mill volume

Vp

total powder volume in mill

Vs

sound velocity

Vs

volume swept by grinding balls between collisions

V

bulk stream velocity

x

distance

y

vertical drop distance of ball in horizontal ball mill

α

thermal diffusivity

β =−R2/R

whereR 2 is magnitude of radius of curvature of impacted surface

γ

proportionality constant

δ

(linear) measure of deformation of impacting media

δmax

maximum center of mass displacement in a Hertz collision

ε

powder strain during collision

εmax

maximum powder strain per collision

ε

powder strain rate during collision

E

accumulated strain during mechanical alloying

Ef

critical accumulated strain for alloying completion

η

viscosity

μ

coefficient of friction

p

density

σ

stress experienced by powder during collision

σo

coefficient in plasticity constitutive equation of powder aggregate

τ

half-duration of impact during Hertzian collision

v

Poisson’s ratio

ϕ

proportionality constant

ω

angular velocity of attritor or ball mill

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Copyright information

© The Minerals, Metals & Materials Society - ASM International - The Materials Information Society 1990

Authors and Affiliations

  • D. R. Maurice
    • 1
  • T. H. Courtney
    • 1
  1. 1.Department of Materials ScienceUniversity of VirginiaCharlottes ville

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