11 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Chapter 8: Mechanical Properties of Metals

ISSUES TO ADDRESS

22 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

8.1 Introduction

Mechanical behavior of a material reflects its response or deformation inrelation to an applied load or force.

Key mechanical design properties: stiffness, strength, hardness, ductility andtoughness

ASTM (American Society for Testing and Materials) Standards(http://www.astm.org)

Role of engineers

33 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

8.2 Concepts of Stress and Strain

Tension Test (Tensile Test)

Compression Test

Shear and Torsional Tests

Geometric Considerations of theStress State

0

0

FA

ll

44 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Elastic Deformation

F F

55 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Plastic Deformation (Metals)

F

F

66 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

8.3 Elastic Deformation

Elastic deformation (nonpermanent): When the applied load is released, thepiece returns to its original shape.

Linear elastic materials: = E Hooke's Law)E

F

F

77 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Mechanical Properties

The elastic modulus is proportional to the slope of the interatomic forceseparation curve at equilibrium spacing:

Callister & Rethwisch 9e. Callister & Rethwisch 9e.

0r r

dFEdr

88 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

E

Callister & Rethwisch 9e.

Young’s Moduli: Comparison

99 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Poisson's ratio,

The axial elongation is accompanied by lateral contraction.Lateral strain is proportional to the axial strain.Poisson’s ratio: the ratio of the lateral strain to the axial strain

Most of materials: = 0.25 ~0.35Cork: = 0 (e.g. wine cap)Rubber: = 0.5 (incompressible material)Limitation on Poisson’s ratio

Units:

Typical values of Poisson’s ratio

Callister & Rethwisch 9e.

lateral strainaxial strain

yx

z z

110 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

• Elastic shear modulus, G:G

Other Elastic Properties

M

M

• Special relations for isotropic materials:

• Elastic bulk modulus, K:

V0V

P

P P

P

K

G

0

VP KV

2(1 )EG

3(1 2 )EK

0

VV

111 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Basic Concepts in Mechanics of Materials

Three basic equations of linear elasticity

Terminologies

112 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

T Tmelt

8.4 Plastic Deformation

Plastic deformation: permanent or nonrecoverable deformation

Simple tension test:

p

Callister & Rethwisch 9e.

113 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Tensile Test

Tensile test to understand the mechanical behavior of materialsStandard: ASTM (American Society for Testing and Materials)

• Typical tensile specimen

Callister & Rethwisch 9e

114 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Stress Strain Curve

Typical stress strain curve of mildsteel

115 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Yield Strength and Yield Criteria

Yield strength: stress at whichnoticeable plastic deformationhas occurred.

von Mises yield criterion: the yielding ofmaterials begins when the seconddeviatoric stress invariant J2 reaches acritical value.

y

Callister & Rethwisch 9e.

y

p

3 32 2 2

1 2 2 3 3 13 1 ( ) ( ) ( )2 2v ij ij

i j

116 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Callister & Rethwisch 9e.

Yield Strength: Comparison

y

117 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Work Hardening or Strain Hardening

T Kn

F Ao

nn

y

y1

y0

118 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Tensile Strength (Ultimate Strength)

Callister & Rethwisch 9e.

yF

TS

119 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Tensile Strength: Comparison

TS

Callister & Rethwisch 9e.

220 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Ductility

A0

AfA0RA

L0

L0LfEL

LfA0 AfL0

e

EL

EL

Callister &Rethwisch 9e.

221 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Energy to break a unit volume of materialApproximate by the area under the stress strain curve.

Toughness

Callister & Rethwisch 9e.

e

222 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Elastic Energy Density & True Stress & Strain

Elastic Energy Density (Resilience) True Stress & Strain

Callister& Rethwisch 9e.

y dUr 0

yyrU 21

iT AF

oiT ln

1ln1

T

T

Callister & Rethwisch 9e.

223 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Hardness

Resistance to permanently indenting the surface.Hardness measurement: simple, inexpensive, nondestructiveLarge hardness means:

dD

224 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Hardness Measurement

225 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Design or Safety Factors

Design uncertainties mean we do not push the limit.Factor of safety, N

Example: Calculate a diameter, d, to ensure that yield does not occur in the1045 carbon steel rod below. Use a factor of safety of 5.

Ny

w N

/4kN 2202d

Ny

working

y

TS

F

d

Lo

d