Tài liệu Machine Design Databook P1 doc

CHAPTER

1

PROPERTIES OF ENGINEERING

MATERIALS

SYMBOLS5;6

a area of cross section, m2 (in2

)

original area of cross section of test specimen, mm2 (in2

)

Aj area of smallest cross section of test specimen under load Fj, m2

(in2

)

Af minimum area of cross section of test specimen at fracture, m2

(in2

)

A0 original area of cross section of test specimen, m2 (in2

)

Ar percent reduction in area that occurs in standard test

specimen

Bhn Brinell hardness number

d diameter of indentation, mm

diameter of test specimen at necking, m (in)

D diameter of steel ball, mm

E modulus of elasticity or Young’s modulus, GPa

[Mpsi (Mlb/in2

)]

f" strain fringe (fri) value, mm/fri (min/fri)

f
stress fringe value, kN/m fri (lbf/in fri)

F load (also with subscripts), kN (lbf)

G modulus of rigidity or torsional or shear modulus, GPa

(Mpsi)

HB Brinell hardness number

lf final length of test specimen at fracture, mm (in)

lj gauge length of test specimen corresponding to load Fj, mm

(in)

l0 original gauge length of test specimen, mm (in)

Q figure of merit, fri/m (fri/in)

RB Rockwell B hardness number

RC Rockwell C hardness number

Poisson’s ratio

normal stress, MPa (psi)

The units in parentheses are US Customary units

[e.g., fps (foot-pounds-second)].

1.1

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Source: MACHINE DESIGN DATABOOK

b transverse bending stress, MPa (psi)

c compressive stress, MPa (psi)

s strength, MPa (psi)

t tensile stress, MPa (psi)

sf endurance limit, MPa (psi)

0

sf endurance limit of rotating beam specimen or R R Moore

endurance limit, MPa (psi)

0

sfa endurance limit for reversed axial loading, MPa (psi)

0

sfb endurance limit for reversed bending, MPa (psi)

sc compressive strength, MPa (psi)

su tensile strength, MPa (psi)

u ultimate stress, MPa (psi)

uc ultimate compressive stress, MPa (psi)

ut ultimate tensile stress, MPt (psi)

sub ultimate strength, MPA (psi)

suc ultimate compressive strength, MPa (psi)

sut ultimate tensile strength, MPa (psi)

y yield stress, MPa (psi)

yc yield compressive stress, MPa (psi)

yt yield tensile stress, MPa (psi)

syc yield compressive strength, MPa (psi)

syt yield tensile strength, MPa (psi)

torsional (shear) stress, MPa (psi)

s shear strength, MPa (psi)

u ultimate shear stress, MPa (psi)

su ultimate shear strength, MPa (psi)

y yield shear stress, MPa (psi)

sy yield shear strength, MPa (psi)

0

sf torsional endurance limit, MPa (psi)

SUFFIXES

a axial

b bending

c compressive

f endurance

s strength properties of material

t tensile

u ultimate

y yield

ABBREVIATIONS

AISI American Iron and Steel Institute

ASA American Standards Association

AMS Aerospace Materials Specifications

ASM American Society for Metals

ASME American Society of Mechanical Engineers

ASTM American Society for Testing Materials

BIS Bureau of Indian Standards

BSS British Standard Specifications

DIN Deutsches Institut fu¨r Normung

ISO International Standards Organization

1.2 CHAPTER ONE

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PROPERTIES OF ENGINEERING MATERIALS

SAE Society of Automotive Engineers

UNS Unified Numbering system

Note:
and with subscript s designates strength properties of material used in the design which will be used and

observed throughout this Machine Design Data Handbook. Other factors in performance or in special aspects are

included from time to time in this chapter and, being applicable only in their immediate context, are not given at

this stage.

For engineering stress-strain diagram for ductile steel,

i.e., low carbon steel

For engineering stress-strain diagram for brittle

material such as cast steel or cast iron

The nominal unit strain or engineering strain

The numerical value of strength of a material

Refer to Fig. 1-1

Refer to Fig. 1-2

" ¼ lf l0

l0

¼
l

l0

¼ lf

l0

1 ¼ A0 Af

A0

ð1-1Þ

where lf ¼ final gauge length of tension test

specimen,

l0 ¼ original gauge length of tension test

specimen.

s ¼ F

A ð1-2Þ

where subscript s stands for strength.

Particular Formula

Point P is the proportionality

limit. Y is the upper yield limit.

E is the elastic limit. Y 0 is the

lower yield point. U is the

ultimate tensile strength point.

R is the fracture or rupture

strength point. R0 is the true

fracture or rupture strength

point.

FIGURE 1-1 Stress-strain diagram for ductile material.
Subscript s stands for strength.

PROPERTIES OF ENGINEERING MATERIALS 1.3

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PROPERTIES OF ENGINEERING MATERIALS

The nominal stress or engineering stress

The true stress

Bridgeman’s equation for actual stress (
act) during r

radius necking of a tensile test specimen

The true strain

Integration of Eq. (1-6) yields the expression for true

strain

From Eq. (1-1)

The relation between true strain and engineering

strain after taking natural logarithm of both sides of

Eq. (1-8)

Eq. (1-9) can be written as

¼ F

A0

ð1-3Þ

where F ¼ applied load.

tru ¼
0 ¼ F

Af

ð1-4Þ

where Af ¼ actual area of cross section or

instantaneous area of cross-section of

specimen under load F at that instant.

act ¼
cal

1 þ

4r

d

ln

1 þ

d

4r

 ð1-5Þ

"tru ¼ "0 ¼
l1

l0

þ

l2

l0 þ
l1

þ

l3

l0 þ
l1 þ
l2

þ ð1-6aÞ

¼

ðlf

l0

dli

li

ð1-6bÞ

"tru ¼ ln
lf

l0

ð1-7Þ

lf

l0

¼ 1 þ " ð1-8Þ

ln
lf

l0

¼ lnð1 þ "Þ or "tru ¼ lnð1 þ "Þ ð1-9Þ

" ¼ e

"tru 1 ð1-10Þ

Particular Formula

There is no necking at fracture for

brittle material such as cast iron or low

cast steel.

FIGURE 1-2 Stress-strain curve for a brittle material.

1.4 CHAPTER ONE

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PROPERTIES OF ENGINEERING MATERIALS