Title

Theoretical Strength of Perfect Crystalline Materials

Description

A mathematical procedure is presented for applying the Born stability criteria to the determination of the mechanical stability of cubic crystals in the presence of applied forces and deformations. The general procedure is suitable for use in conjunction with an electronic computer and is independent of the specific model of interatomic interactions that can be used in numerical calculations. In this report, specific calculations are performed for a body-centered cubic (B.C.C.) crystal lattice with a uniaxial tensile force applied perpendicularly to a face of a unit cell. The atoms in the crystal are assumed to interact through a two-body Morse interatomic potential function appropriate to B.C.C. iron. Two ranges of stability, a B.C.C. phase and body-centered tetragonal (B.C.T.) phase were found to exist: . The B.C.T. phase has a theoretical strength of 0.9 x 1011 dyne/cm2 (1 dyne/cm2 = 1.45 x 10-5 psi) with a corresponding theoretical strain of about 7 percent. These values are fairly close to the values of 1.3 x 1011 dyne/cm2 tensile strength and about 5 percent strain experimentally observed for fine iron whiskers.

Identifier

AD0717698

AD0717698

DTIC Record Exists

Yes

Report Availability

Full text available by request

Distribution Conflict

No

Distribution Classification

1

Subject

Crystal Structure -- Mechanical Properties

Composite Materials

Deformation

Whiskers (Crystals)

Tensile Properties

Iron

Stability

Abstract

A mathematical procedure is presented for applying the Born stability criteria to the determination of the mechanical stability of cubic crystals in the presence of applied forces and deformations. The general procedure is suitable for use in conjunction with an electronic computer and is independent of the specific model of interatomic interactions that can be used in numerical calculations. In this report, specific calculations are performed for a body-centered cubic (B.C.C.) crystal lattice with a uniaxial tensile force applied perpendicularly to a face of a unit cell. The atoms in the crystal are assumed to interact through a two-body Morse interatomic potential function appropriate to B.C.C. iron. Two ranges of stability, a B.C.C. phase and body-centered tetragonal (B.C.T.) phase were found to exist: . The B.C.T. phase has a theoretical strength of 0.9 x 1011 dyne/cm2 (1 dyne/cm2 = 1.45 x 10-5 psi) with a corresponding theoretical strain of about 7 percent. These values are fairly close to the values of 1.3 x 1011 dyne/cm2 tensile strength and about 5 percent strain experimentally observed for fine iron whiskers.

Creator

Milstein, Frederick

Publisher

Santa Monica, CA : The RAND Coporation

Date

1970

Format

vii, 35 pages, : ill. ; 28 cm.

Type

report

Date Issued

1970-12

Corporate Author

The RAND Corporation

Report Number

RM-6379-PR

Contract

F44620-67-C-0045

Access Rights

THIS DOCUMENT HAS BEEN APPROVED FOR PUBLIC RELEASE AND SALE; ITS DISTRIBUTION IS UNLIMITED.

Index Abstract

Contrails and DTIC condensed

Photo Quality

Not Needed