كتاب أساسيات المرونة واللدونة أسامة محمد المرضي

‫ك‬‫ـ‬‫أساس‬ ‫تاب‬‫ـ‬‫امل‬ ‫يات‬‫ـ‬‫والل‬ ‫روىة‬‫ـ‬‫دوىة‬
Fundamentals of Elasticity and Plasticity
‫تأل‬‫ــ‬‫يف‬
‫سليمان‬ ‫املرضي‬ ‫حممد‬ ‫أسامة‬
‫النيل‬ ‫وادي‬ ‫جامعة‬ ، ‫اهلندسة‬ ‫كلية‬ ، ‫مساعد‬ ‫استاذ‬
Author
Osama Mohammed Elmardi Suleiman
Assistant Professor, Faculty of Engineering, Nile Valley
University
‫يياير‬ ‫األوىل‬ ‫الطبعة‬0222‫و‬
‫أكتوبر‬ ‫َّة‬‫امليقح‬ ‫الثاىية‬ ‫الطبعة‬0204‫و‬

‫ك‬‫ـ‬‫أساس‬ ‫تاب‬‫ـ‬‫امل‬ ‫يات‬‫ـ‬‫والل‬ ‫روىة‬‫ـ‬‫دوىة‬
Fundamentals of Elasticity and Plasticity
‫تأل‬‫ــ‬‫يف‬
‫املرضي‬ ‫حممد‬ ‫أسامة‬‫سليمان‬
‫النيل‬ ‫وادي‬ ‫جامعة‬ ، ‫اهلندسة‬ ‫كلية‬ ، ‫مساعد‬ ‫استاذ‬
Author
Osama Mohammed Elmardi Suleiman
Assistant Professor, Faculty of Engineering, Nile Valley
University
‫يياير‬ ‫األوىل‬ ‫الطبعة‬0222‫و‬
‫َّة‬‫امليقح‬ ‫الثاىية‬ ‫الطبعة‬‫أكتوبر‬0204‫و‬

i
‫لرحيم‬‫ا‬‫لرمحن‬‫ا‬‫اهلل‬‫بسم‬
‫وعرفان‬ ‫شكر‬

iii
‫مم‬‫ـ‬‫ذمح‬
i.e.

iv
‫املوفق‬ ‫واهلل‬
‫انمؤنف‬
‫ضهٍمان‬ ً‫انمرض‬ ‫محمذ‬ ‫أضامح‬‫خٍال‬
Osama Mohammed Elmardi Suleiman Khayal
‫أكتىتر‬6102‫و‬

v
‫انمح‬‫ـ‬‫تىٌاخ‬
i
iii
v
1.11
1.11
1.11
1.11
1.1.16
1.1.19
1.1.111
1.111
1.1.111
1.1.111
1.1.111
1.1.116
1.111
1.116
1.112
1.119
1.111
1.111
1.111

vi
1.111
1.116
1.613
1.312
1.212
1.111
1.111
1.111
1.111
1.111
1.611
1.311
1.211
1.911
1.1161
1.169
1.131
1.121
6.121
6.126
6.126
91
91

‫خيال‬ ٌ‫سلينا‬ ‫املرضي‬ ‫حمند‬ ‫أسامة‬ :‫تأليف‬ ‫واللــدوىة‬ ‫املــروىة‬ ‫أساســيات‬ ‫كــتاب‬
Properties of Engineering Materials
0.0Introduction
( 1/ complexity of extraction 2/ higher cost of technology used )
unmanned drones
0.0Importance of Metals in Industry
i.e.corner stone
ferrous and non- ferrous metals

0.1
Physical and Mechanical Properties of Metals)
Physical Properties
0Density{ }
0(Thermal and Electrical Conductivity)
1Specific Heat Capacity
Q
2Light Reflection

3X-Ray Penetration
4Magnetizability
5Fluidity
6Local Fusibility
Mechanical Properties
0Ductility
tension
compressionbendingtorsiondrawing
wire and tube drawing

0Malleability
compression
i.e.(forging)
rolling
1Toughness or Strength
2Divisibility
3Hardness
(Hardness: is the ability of a material to withstand scratching or identation)
1.1i.e.
0.2(Engineering Materials Testing)
tensioncompression
torsionimpacthardness

‫تشكٍم‬ ( ‫انتصنٍع‬ ‫طرق‬)‫انمطهىب‬ ‫انشكم‬ ‫إنى‬ ‫انمعادن‬ ‫تشغٍم‬ ‫او‬
(Metal forming and machining)
( ً‫داخه‬ ‫تحىٌم‬Internal conversion)
‫وانكٍمٍائٍح‬ ‫انفٍسٌائٍح‬ ‫انخىاص‬
( ً‫خارج‬ ‫تحىٌم‬(External conversion
ً‫انمٍكانٍك‬ ‫انتشكٍم‬ ‫وضائم‬
‫انمعادن‬ ‫اضتخالص‬
Metal extraction
‫انثترول‬ ‫تنمٍح‬
Petroleum refining
‫انحرارٌح‬ ‫انمعانجح‬
Heat treatment
‫انمٍىعح‬
Fluidity
‫نالنصهار‬ ‫انماتهٍح‬
Fusibility
‫انهذونح‬
Plasticity
‫نالنشطار‬ ‫انماتهٍح‬
Divisibility
‫انمعذن‬ ‫وانطٍاب‬ ‫ضٍىنح‬
‫انمنصهر‬
‫انطثاكح‬ ‫عمهٍاخ‬
‫انمنصهرج‬ ‫انمعادن‬ ‫انتصاق‬
‫نماط‬ ‫خالل‬
‫انهحاو‬ ‫عمهٍاخ‬
‫وانهذونح‬ ‫انمطاطٍح‬
Ductility and plasticity
‫انتشكٍم‬ ‫عمهٍاخ‬
‫انرائش‬ ‫إزانح‬
Chip removal
‫انتشغٍم‬ ‫عمهٍاخ‬
‫انرمهٍح‬ ‫انطثاكح‬sand casting
‫تانمىانة‬ ‫انطثاكح‬‫(تثالهٍح‬ ‫انذائمح‬
)‫وضغط‬Gravity and pressure
die casting
‫انمركسي‬ ‫انطرد‬ ‫تاضتخذاو‬ ‫انطثاكح‬
Centrifugal casting
‫انغاز‬ ‫نحاو‬Gas welding
ً‫انكهرت‬ ‫انمىش‬ ‫نحاو‬
Electric arc welding
‫اننمطح‬ ‫نحاو‬spot welding
‫انمىنح‬ ‫نحاو‬brazing welding
‫انمصذٌر‬ ‫نحاو‬soldering welding
‫انحذادج‬forging
‫انذرفهح‬rolling
‫انثثك‬extrusion
‫انطحة‬drawing
‫انكثص‬pressing
‫انثرادج‬fitting
‫انخراطح‬machining
‫انتفرٌس‬milling
‫انكشط‬planing
‫انتثمٍة‬drilling
‫انتجهٍخ‬grinding
( ‫شكم‬0.0‫انمىاد‬ ‫تخىاص‬ ‫وارتثاطها‬ ‫انمختهفح‬ ‫انتصنٍع‬ ‫طرق‬ )

0.2.0Tension Test
i
ii
iii
F
1.11.1
0:
(Modulus of Elasticity or Young Modulus)
i.e.
E =i.e.
stress

straini.e.
0Yield Stress
1Ultimate Stress
2Resilience

2
1


)‫(أ‬‫ناشف‬ ‫صهة‬‫لصف‬ ‫أو‬‫طري‬ ‫صهة‬ )‫(ب‬
0.0
)‫(ج‬‫ناشف‬ ‫صهة‬‫لصف‬ ‫أو‬‫طري‬ ‫صهة‬ )‫(د‬
0 1

3
0.2.0Impact Test
recess
1 1
Hh
w
 k
2
/
)(
cmkg
A
hHw
k


A
Brittleness
0.1 – 0.2 kg/cm112
kg/cm

0 2Charpy impact test
1111
0.2.1Hardness Test
0Brinell Hardness Test
√
Brinell hardness number)
kg
mm
mm
0Rockwell Hardness Test
111

11160 kg10 kgRHA
2.5mm100 kg10 kgRHB
111150 kg10 kgRHC
0.2.2Vickers Hardness Test
116
5 kg140kg
11
0.3Metals Preparation Methods
0.3.0

ferrous metals
(steel
(cast-iron)1
61
0.3.0Iron Ore
1.1
mining
industriesmetallurgical processes
hematitemagnetite
0.3.1
i.e.

ISemi-Finished Products
0Raw Metal
Molten Metal
Pigs
0Prepared Metal

( Cupola furnace)
1(Castings)
2Forming Lugs
plastic forming
hammering100 kg
3Semi-Rolled Lugs
initial rolling
4
5Square Block
160 cm
6( Rods)

(rolling)extrusion(drawing)
7(Forgings)
02Structural Sections
TI(angleL(channel)∪
00Wire
drawingi.e.
2mm
00Sheet Metals
2mm
bolts
(springs)
press work
metal cutting
i.e.

IIFinished Products
0.3.2Plastic Forming of Metals
0Metal Rolling
beams
anglesi.e.
0Rolling Machines
1 1
gear box
alloy steel

0 3
1Calculation of Angle of Contact
1 6
∝angle of contact











 






 


d
tt
d
tt
211
21
1cos
1cos


d
t
t

0 4
0 5
2

N
FNF1.3
̅
̅
̅
N
F
S
Q
S= N cos∝ + F sin∝
Q = F cos∝
1P = N sin∝
QP
)4(
22





PQ
PQ
P , Q11
)5(sincos  NF 

F
)6(NF 
𝛍
μ∅
)7(tan 
163
)8(tantan
sincostan
sincos
sincos








NN
NN
NF
∝∅
angle of friction
angle of contact1121111
11
3Types of Rolling Machines

Primary Reduction Mills
Structural Sections Mills
beams
rodsangles
Finishing Mills
sheets.
iTwo High Rolls
iiReversing Rolls
1 2
0 6

iiiThree High Rolls
1 9
0 7
iv(Four High Rolls)
)( forming rolls
(supporting rolls)
1 11

0 02
vMulti High Rolls
10mm
30mm
viUniversal Rolling Mills
1000mm
4Cold Rolling Processes
1
1

1
(internal stresses)
i.e.
5(Hot Rolling Processes)

Chip Generation
0.0(Introduction)
elastic deformationpermanent plastic deformation
i.e.
1.1(mild steel)
iA(Limit of Proportionality)
Hook's law
iiBElastic Limit
iiiCi.e.Yield
Point
ivD
Maximum or Ultimate Stress Point

vEFracture Point
0.0
slip planes
0.0(Types of Chips)
0.0.0Discontinuous Chips

0.0.0Continuous Chips
60m/min
1
1
1
1
1
i
ii
iii
6
0.0.1(Inhomogeneous Chips or Heterogeneous Chips)
∅
1
1

0.0.2(Fractured Chips)
cracks
0.1
Martensitic Structure
Tool face
0 0

0.2(Forming Operations without Chip Formation)
0.2.0Press Work
punch and die
(The First Type)
Piercing
Blanking
(The Second Type)
Bending
Deep Drawing
0(Shear Processes)
(Piercing and Blanking)

i.e.
1 11 1
1 1
0 10 2

0 3
0(Forming Processes)
i(Bending)
ii(Deep Drawing)
1 6

iii(Stamping Processes)
0 4

Materials Testing and Experimental Methods
1Tensile Tests
ductile materialmild steel
i.e.
i.e.
i.e.
1The Working Portion of the Specimen
wedge
i.e.0.01d

1Testing Machines
in the elastic range(extensometer)
(strain gauge)
(pair of dividers and graduated rule)
1Effect of Rate of Loading
hardened steel
1
(Variation of Elongation with Gauge Length and Cross – Sectional Area )
1

1
el
e = a + bl
= 100e/l = 100a/l + 100b
Unwina
AC √A100a100b=B
B
l
AC
l
e
100

BCB=20C =70
B. S. 18
 Al 4
1Overstrain and Repeated Loading
i.e.)
Hook's law
1

1
1Proof Stress
1
1

OTPQOTQ
OP = 0.1%Q
OT
1Compression Tests
BucklingLength=minimum
breadth
1(Failure in Brittle Materials)
11
𝛉 ∅
∅
∅
𝛉

𝛉
𝛉
𝛉 ∅
1.1AP
σ𝛉∅
σ P /A
BB = A/ cos θ
PN
(Q)

1.2P




 22
cos.cos
cos/
cos

A
P
A
p
B
N
N


tancos
tancos 2
2

A
P
θσr
P

(*)tancoscossin 2
  fQr
σr
𝛉
  

 
 
#2/45
902
902
)902tan()290tan(tan
2cot
2sin
2cos
cossin2
sincos
tan
tancossin2sincos
0tancossin2cossin
0)sincos2tan
)cos()cos(cossinsin
22
22
22
2

































d
d
zero
d
d
r
r

(Strain Energy Methods)
1.0(Internal Strain Energy)
PU
LAE
1
LTU
GJ
2
LMU
I
3

(Positive scalar quantity).
1.6(Sign Conventions)
1.4(Castigliano's Theorem)
1.1
(Application to Statically Determinate Problems)

(fictitious force)
1
(Application to Statically Indeterminate Problems)
1.2(Assumption and Limitations)
(law of Superposition)
1.4(Solved Examples in Strain Energy)
0
P

(a) (b)
1.0
(4 1 (a) )
ALE
(Linear)( (b) )P
B
OBA
U

B
P
∫
6
T(torque).
1.6
(4 2 (b) )
BOBA
(a) o
T
𝚯T
T A
(b)
𝜽

U
∫
4

4 3B
OAB
∫
1.4

1.4(Derivation of Castigliano Theorem)
4 4
n123
n
n

1.1
1
34

1.4(Solved Examples in Castigliano Theorem)
1
∫

∫
∫ ∫ * +
5
∫ ∫
∫ ∫

∫ ∫
2
∫ ∫
∫
∫
∫ ∫

4
∫
∫
∫ ( )
∫

4
∫ ∫
∫ ∫
( )
∫ ∫ ( )

∫ ∫ ( )
4
P
∫ ∫
P:
∫ ∫

∫ ∫
∫ ∫
01
9
∫ ∫

∫ ∫
∫ ∫
∫
00
RBA
PA

∫
∫
∫
∫ ∫
[ ]
60
A11

A
∫
∫
∫
∫ ( )
[ ]
40

Q
∫
∫
∫ [ ]
∫ [ ( ) ]
01

∫ ∫
∫ ∫
( )
∫ ∫ ( )
∫ ∫ [ ]
* + * +

1.01(Exercises in Castigliano Theorem)
0
13P
, ( )-
6
, -
4

, -
1
PA
, -
5
A11
, -

2
A
, -
4
ABP
, -
4
7P
{ }

4
A
, -
01
{ }
00
P11

{ }
06
{ }
04
RAB
PB
{ }

5.0(Introduction)
5 1
5.0
𝑄 𝑃
𝑄 𝑃‫الخضوع‬ ‫إجهاد‬‫اإلجهاد‬
‫اإلنفعال‬

5.6(Method of Determining Critical Load)8
0Bending Moment Diagram Methods))
0

6
4

6(Virtual Work Method)
i
ii
iii
iv

1
P
( )


5
2

∫
[ ( )]
A

4

(A)
( ) ( )
4

( ) ( )
4

B
B
C
123

01

P3P
P
( )
3P
( ) ( )

5 4
(Exercises in Plastic Collapse of Beams and Simple Frames)
0
{ }
6
{ }

4
{ }
1
{ }
5
{ }

2
{ }
4
{ }
4
{ }

4
{ }
9

(Plastic Theory of Bending)
2.0(Bending Beyond the Yield Stress)
(edge stress)
(mild steel)
i.e.
1121

2.6(Assumptions in the Plastic Theory)
1
2
3
4
2.4(Moment of Resistance at a Plastic Hinge)
(a) )
(b))
(c)

(a)(Rectangular Section)8
2.0
bd
Z

Si.e.
13
23
12
56
0
72mm30mm

3
6 1 (b)

(b)I(I – Section)8
(flange)(web)
1 152
6
I

(i)(ii)
(c)(Unsymmetrical Section)8
6 2
2.6

4
6 3
8

2.4
‫انمىفك‬ ‫واهلل‬:::::::::::::::::
‫سليمان‬‫املرضي‬‫حممد‬‫أسامة‬
‫امليكاىيكيــة‬ ‫اهليدســة‬ ‫قســه‬
‫والتقييــة‬ ‫اهليدســة‬ ‫كليــة‬
‫الييــل‬ ‫وادي‬ ‫جامعــة‬

1www.jalalalhajabed.com
1
1111
1
The Iraqi Journal for Mechanical and Material Engineering
11119
1111
1991
611
1111
3
1119
2
1113
91113
111922

11
1931
11111
1991
11
1111
11111
1111
Mikell P Groover, "Fundamentals of Modern Manufacturing”, John Wiley and
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th
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3 Mills B , and Redford A H , "Machinability of Engineering Materials”, Applied
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Berg R T , "Fundamentals of Turning”, Metal Cutting: by the editors of
American Machinist, McGraw Hill, New York, (1979).
Trent E M , "Metal Cutting”, nd
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Addison – Wesley Publishers Company, USA, (1992).
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Macmillan Publishers Company, N. Y. and London, (1988).

Schley J A , "Introduction to Manufacturing Processes”, 3rd
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edition, (2011).
20. R. S. Khurmi, "Strength of Materials (Mechanics of Solids) (S.I. Units)", (2014).
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22. Gere J. , and Timoshenko S. P., "Mechanics of Materials", 3rd
edition, PWS –
Kent, Boston, (1990).
23. Boresi A. P., and Chong K. P., "Elasticity in Engineering Mechanics", nd
edition,
Wiley, Hoboken, N. J., (2000).
24. Ansel C. Ugural and Saul K. Fenster, "Advanced Mechanics of Materials and
Applied Elasticity: Analysis of Stress", The Trusted Technology Learning Source,
July 20 (2011).
25. G. H. Ryder, "Strength of Materials", A. M. I. Mech. I., (1969).
26. William A. Nash, "Schaum's Outline of Strength of Materials", Fifth Edition,
McGraw Hill, August 12 (2010).

‫املــــؤلف‬ ً‫عـ‬ ‫ىبـــذة‬
1966
1991
1998
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كتاب أساسيات المرونة واللدونة أسامة محمد المرضي

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كتاب أساسيات المرونة واللدونة أسامة محمد المرضي