Machine Design Handbook.pdf

Source: MACHINE DESIGN DATABOOK

CHAPTER

PROPERTIES OF ENGINEERING

MATERIALS

SYMBOLS 5 ; 6

area of cross section, m 2 (in 2 )

original area of cross section of test specimen, mm 2

(in 2 )

A j

area of smallest cross section of test specimen under load F j ,m 2

(in 2 )

A f

minimum area of cross section of test specimen at fracture, m 2

(in 2 )

A 0

original area of cross section of test specimen, m 2

(in 2 )

A r

percent reduction in area that occurs in standard test

specimen

Bhn

Brinell hardness number

diameter of indentation, mm

diameter of test specimen at necking, m (in)

diameter of steel ball, mm

modulus of elasticity or Young’s modulus, GPa

[Mpsi (Mlb/in 2 )]

f "

strain fringe (fri) value, m m/fri ( m in/fri)

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

load (also with subscripts), kN (lbf)

modulus of rigidity or torsional or shear modulus, GPa

(Mpsi)

H B

Brinell hardness number

l f

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

l j

gauge length of test specimen corresponding to load F j ,mm

(in)

l 0

original gauge length of test specimen, mm (in)

ﬁgure of merit, fri/m (fri/in)

R B

Rockwell B hardness number

R C

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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PROPERTIES OF ENGINEERING MATERIALS

1.2 CHAPTER ONE

transverse bending stress, MPa (psi)

compressive stress, MPa (psi)

strength, MPa (psi)

tensile stress, MPa (psi)

endurance limit, MPa (psi)

endurance limit of rotating beam specimen or R R Moore

endurance limit, MPa (psi)

sfa

endurance limit for reversed axial loading, MPa (psi)

sfb

endurance limit for reversed bending, MPa (psi)

compressive strength, MPa (psi)

tensile strength, MPa (psi)

ultimate stress, MPa (psi)

ultimate compressive stress, MPa (psi)

ultimate tensile stress, MPt (psi)

ssu

ultimate strength, MPA (psi)

suc

ultimate compressive strength, MPa (psi)

sut

ultimate tensile strength, MPa (psi)

yield stress, MPa (psi)

yield compressive stress, MPa (psi)

yield tensile stress, MPa (psi)

syc

yield compressive strength, MPa (psi)

syt

yield tensile strength, MPa (psi)

torsional (shear) stress, MPa (psi)

shear strength, MPa (psi)

ultimate shear stress, MPa (psi)

ultimate shear strength, MPa (psi)

yield shear stress, MPa (psi)

yield shear strength, MPa (psi)

torsional endurance limit, MPa (psi)

SUFFIXES

axial

bending

compressive

endurance

strength properties of material

tensile

ultimate

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

DIN

Deutsches Institut fu ¨ r Normung

ISO

International Standards Organization

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BSS

British Standard Speciﬁcations

PROPERTIES OF ENGINEERING MATERIALS

PROPERTIES OF ENGINEERING MATERIALS 1.3

UNS

Society of Automotive Engineers

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.

and

Particular

Formula

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

Refer to Fig. 1-1

Refer to Fig. 1-2

" ¼

l f l 0

l 0 ¼ l

l 0 ¼

l f

l 0 1 ¼

A 0 A f

A 0

ð 1 - 1 Þ

where l f ¼ ﬁnal gauge length of tension test

specimen,

l 0 ¼

original gauge length of tension test

specimen.

The numerical value of strength of a material

s ¼

ð 1 - 2 Þ

where subscript s stands for strength.

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. R 0 is the true

fracture or rupture strength

point.

FIGURE 1-1 Stress-strain diagram for ductile material.

Subscript s stands for strength.

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SAE

Uniﬁed Numbering system

Note:

PROPERTIES OF ENGINEERING MATERIALS

1.4 CHAPTER ONE

Particular

Formula

The nominal stress or engineering stress

A 0

where F ¼ applied load.

The true stress

tru ¼ 0 ¼

A f

where A f ¼ actual area of cross section or

instantaneous area of cross-section of

specimen under load F at that instant.

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

radius necking of a tensile test specimen

act ¼

ln 1

cal

The true strain

" tru ¼ " 0 ¼ l 1

l 0 þ

l 2

l 0 þ l 1

l 3

l 0 þ l 1 þ l 2 þ

ð 1 - 6a Þ

ð l f

dl i

l i

ð 1 - 6b Þ

l 0

ln l f

l 0

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

strain

" tru ¼

From Eq. (1-1)

l f

l 0 ¼ 1 þ "

ð 1 - 8 Þ

ln l f

l 0

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 ln ð 1 þ "Þ

" tru ¼ ln ð 1 þ "Þ

ð 1 - 9 Þ

" ¼ e " tru

ð 1 - 10 Þ

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.

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PROPERTIES OF ENGINEERING MATERIALS

PROPERTIES OF ENGINEERING MATERIALS 1.5

Particular

Formula

Percent elongation in a standard tension test specimen

" 100 ¼

l f l 0

l 0 ð 100 Þ

ð 1 - 11 Þ

Reduction in area that occurs in standard tension test

specimen in case of ductile materials

A r ¼

A 0 A f

A 0

ð 1 - 12 Þ

A 0 A f

A 0 ð 100 Þ

Percent reduction in area that occurs in standard

tension test specimen in case of ductile materials

For standard tensile test specimen subject to various

loads

A r100 ¼

ð 1 - 13 Þ

Refer to Fig. 1-3.

The standard gauge length of tensile test specimen

FIGURE 1-3 A standard tensile specimen subject to various

loads.

l 0 ¼ 6 : 56 p

ð 1 - 14 Þ

The volume of material of tensile test specimen

remains constant during the plastic range which is

veriﬁed by experiments and is given by

Therefore the true strain from Eqs. (1-7) and (1-15)

A 0 l 0 ¼ A f l f

l f

l 0 ¼

A 0

A f ¼

d 0

d f

" tru ¼ ln A 0

A f

¼ ln l f

l 0 ¼ 2ln d 0

d f

ð 1 - 16 Þ

where d f ¼

minimum diameter in the gauge length

l f of specimen under load at that

instant,

minimum area of cross section of

specimen under load at that instant.

" ftru ¼ ln 1

1 A r

A r ¼

The true strain at rupture, which is also known as the

true fracture strain or ductility

ð 1 - 17 Þ

where A f is the area of cross-section of specimen at

fracture.

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