Design Data Handbook

CHAPTER
1
PROPERTIES OF ENGINEERING
MATERIALS
SYMBOLS5;6
aarea of cross section, m2(in2)
original area of cross section of test specimen, mm2(in2)
Ajarea of smallest cross section of test specimen under load Fj,m
2
(in2)
Afminimum area of cross section of test specimen at fracture, m2
(in2)
A0original area of cross section of test specimen, m2(in2)
Arpercent reduction in area that occurs in standard test
specimen
Bhn Brinell hardness number
ddiameter of indentation, mm
diameter of test specimen at necking, m (in)
Ddiameter of steel ball, mm
Emodulus 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)
Fload (also with subscripts), kN (lbf)
Gmodulus of rigidity or torsional or shear modulus, GPa
(Mpsi)
HBBrinell hardness number
lffinal length of test specimen at fracture, mm (in)
ljgauge length of test specimen corresponding to load Fj,mm
(in)
l0original gauge length of test specimen, mm (in)
Qfigure of merit, fri/m (fri/in)
RBRockwell B hardness number
RCRockwell 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

btransverse bending stress, MPa (psi)
ccompressive stress, MPa (psi)
sstrength, MPa (psi)
ttensile 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)
uultimate stress, MPa (psi)
uc ultimate compressive stress, MPa (psi)
ut ultimate tensile stress, MPt (psi)
b
susu ultimate strength, MPA (psi)
suc ultimate compressive strength, MPa (psi)
sut ultimate tensile strength, MPa (psi)
yyield 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)
sshear strength, MPa (psi)
uultimate shear stress, MPa (psi)
su ultimate shear strength, MPa (psi)
yyield shear stress, MPa (psi)
sy yield shear strength, MPa (psi)
0
sf torsional endurance limit, MPa (psi)
SUFFIXES
aaxial
bbending
ccompressive
fendurance
sstrength properties of material
ttensile
uultimate
yyield
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 sdesignates 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
"¼lfl0
l0¼l
l0¼lf
l01¼A0Af A0ð1-1Þ
where lf¼final gauge length of tension test
specimen,
l0¼original gauge length of tension test
specimen.
s¼F
Að1-2Þ
where subscript sstands for strength.
Particular Formula
Point Pis the proportionality
limit. Yis the upper yield limit.
Eis the elastic limit. Y0is the
lower yield point. Uis the
ultimate tensile strength point.
Ris the fracture or rupture
strength point. R0is the true
fracture or rupture strength
point.
FIGURE 1-1 Stress-strain diagram for ductile material.
Subscript sstands 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
¼F
A0ð1-3Þ
where F¼applied load.
tru ¼0¼F
Afð1-4Þ
where Af¼actual area of cross section or
instantaneous area of cross-section of
specimen under load Fat that instant.
act ¼cal
1þ4r
dln 1þd 4r ð1-5Þ
"tru ¼"0¼l1
l0þl2 l0þl1
þl3
l0þl1þl2þ ð1-6aÞ
¼ðlf
l0
dli
lið1-6bÞ
"tru ¼ln lf
l0ð1-7Þ
lf
l0¼1þ"ð1-8Þ
ln lf
l0¼lnð1þ"Þor "tru ¼lnð1þ"Þð1-9Þ
"¼e"tru 1ð1-10Þ
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

Percent elongation in a standard tension test specimen
Reduction in area that occurs in standard tension test
specimen in case of ductile materials
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
The standard gauge length of tensile test specimen
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)
The true strain at rupture, which is also known as the
true fracture strain or ductility
"100 ¼lfl0
l0ð100Þð1-11Þ
Ar¼A0Af
A0ð1-12Þ
Ar100 ¼A0Af
A0ð100Þð1-13Þ
Refer to Fig. 1-3.
FIGURE 1-3 A standard tensile specimen subject to various
loads.
l0¼6:56 ffiffiffi a
pð1-14Þ
A0l0¼Aflfor lf
l0¼A0 Af¼d2
0
d2
fð1-15Þ
"tru ¼ln A0
Af¼ln lf l0¼2lnd0 dfð1-16Þ
where df¼minimum diameter in the gauge length
lfof specimen under load at that
instant,
Ar¼minimum area of cross section of
specimen under load at that instant.
"ftru ¼ln 1
1Arð1-17Þ
where Afis the area of cross-section of specimen at
fracture.
Particular Formula
PROPERTIES OF ENGINEERING MATERIALS 1.5
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PROPERTIES OF ENGINEERING MATERIALS