2018
Version
10.0
Department of Informatics and Engineering Systems
EXAMINATION REFERENCE AND
EQUATION BOOKLET
MECE 2340/ENGT 2307: Materials Engineering
Robert Jones, PhD. and Jazmin Ley, MSE
DO NOT WRITE ON THIS BOOKLET
Booklet Number:________
1|Page
Equations
2
%IC = { 1 − 𝑒 [−0.25 (𝑥𝐴 −𝑥𝐵 ) ] } × 100
Percent Ionic Character
Vacancies
𝑁𝑣 = 𝑁 exp [−
Conversion
𝐶′′1 = (
ASTM Grain Number
Intercept Method
First Law of Diffusion
Second Law of Diffusion
True Stress – Strain
𝑄𝑣
]
𝑘𝑇
𝐶1
) 𝑥103
𝐶1 𝐶2
+
𝜌1 𝜌2
𝐶1 𝐴2
𝐶′1 = (
) 𝑥100
𝐶1 𝐴2 + 𝐶2 𝐴1
𝑀 2
𝑛𝑀 (
) = 2𝐺−1
100
𝐿𝑇
𝑙 − 𝑚𝑒𝑎𝑛 𝑖𝑛𝑡. 𝑙𝑒𝑛𝑔𝑡ℎ
𝑙̅ =
LT− total length
𝑃𝑀
nM  grains/in2 at mag, M, other
than 100X
𝐺 = −6.6457 log 𝑙 ̅ − 3.298
For l in mm
𝐽 = −𝐷
𝑑𝐶
𝑑𝑥
𝐶𝑥 − 𝐶0
𝑥
= 1 − 𝑒𝑟𝑓 (
)
𝐶𝑠 − 𝐶0
2√𝐷𝑡
𝑙𝑖
𝜀𝑇 = 𝑙𝑛 ( )
𝑙0
𝐹
𝜎𝑇 =
𝐴𝑖
𝜎𝑇 = 𝐾𝜀𝑇𝑛
Tensile Tests
%𝐴𝑅 = (
Hardness – Tensile Correlation
𝑈𝑇𝑆 (𝑝𝑠𝑖) = 500 × 𝐻𝐵
Yield Strength – Grain Size
𝜎𝑦 = 𝜎0 + 𝑘𝑦 𝑑 2
Fracture
𝐾 = 𝑌𝜎√𝜋𝑎
Creep
from wt% to atomic%
𝑁 = 2𝐺−1
Stress – Strain Power Law
Fatigue
from wt% to mass/volume
𝐴0 − 𝐴𝑓
) 𝑥100
𝐴0
𝑀 − 𝑀𝑎𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛
P – Intercepts
−𝑄𝐷
𝐷 = 𝐷0 𝑒𝑥𝑝 (
)
𝑅𝑇
𝑥2
= 𝐶𝑜𝑛𝑠𝑡
𝐷𝑡
𝜎𝑇 = 𝑠(1 + 𝑒)
𝜀𝑇 = 𝑙𝑛(1 + 𝑒)
%𝐸𝑙 = (
𝑙0 − 𝑙𝑓
) 𝑥100
𝑙0
𝑈𝑇𝑆 (𝑀𝑃𝑎) = 3.45 × 𝐻𝐵
−1
𝑑𝐴
= 𝐴(∆𝐾)𝑚
𝑑𝑁
𝑑𝜀
−𝑄𝑐
= 𝐾2 𝜎 𝑛 𝑒𝑥𝑝 (
)
𝑑𝑡
𝑅𝑇
Composites
𝐸𝐶 = 𝑣𝑓 𝐸𝑓 + 𝑣𝑚 𝐸𝑚
Cell Potential
∆𝑉 = (𝑉20 − 𝑉10 ) −
𝑅𝑇 [𝑀1𝑛+ ]
ln
𝑛𝐹 [𝑀2𝑛+ ]
∆𝐾 = 𝑌∆𝜎√𝜋𝑎
𝑑𝜀
𝑑𝑡
= 𝐾1 𝜎 𝑛 iff T = constant
𝑣𝑓 𝑣𝑚
1
=
+
𝐸𝐶 𝐸𝑓 𝐸𝑚
Nernst Equation
2|Page
Values of Selected Physical Constants
Symbol
SI Units
cgs Units
Avogadro's number
Boltzmann's constant
Quantity
NA
k
6.022 × 1023 molecules/mol
1.38 × 10−23 J/atom · K
Bohr magneton
Electron charge
Electron mass
Gas constant
Permeability of a vacuum
Permittivity of a vacuum
Planck's constant
μB
e
—
R
μ0
ϵ0
h
9.27 × 10−24 A · m2
1.602 × 10−19 C
9.11 × 10−31 kg
8.31 J/mol · K
1.257 × 10−6 henry/m
8.85 × 10−12 farad/m
6.63 × 10−34 J · s
Velocity of light in a vacuum
c
3 × 108 m/s
6.022 × 1023 molecules/mol
1.38 × 10−16 erg/atom · K
8.62 × 10−5 eV/atom · K
9.27 × 10−21 erg/gaussa
4.8 × 10−10 statcoulb
9.11 × 10−28 g
1.987 cal/mol · K
unitya
unityb
6.63 × 10−27 erg · s
4.13 × 10−15 eV · s
3 × 1010 cm/s
a in cgs-emu units.
b in cgs-esu units
Electronegativity Values for Elements
Figure 1: Adapted from Fig. 2.8, Callister & Rethwisch 9e.
3|Page
Characteristics of Selected Elements
Element
Symbol
Atomic
Number
Atomic
Weight
(amu)
(g/mol)
Density
of Solid,
20°C
(g/cm3)
Crystal
Structure,
20°C
Atomic
Radius
(nm)
Ionic Radius
(nm)
Most
Common
Valence
Melting Point (°C)
Aluminum
Argon
Barium
Beryllium
Boron
Bromine
Cadmium
Calcium
Carbon
Cesium
Chlorine
Chromium
Cobalt
Copper
Fluorine
Gallium
Germanium
Gold
Helium
Hydrogen
Iodine
Iron
Lead
Lithium
Magnesium
Manganese
Mercury
Molybdenum
Neon
Nickel
Niobium
Nitrogen
Oxygen
Phosphorus
Platinum
Potassium
Silicon
Silver
Sodium
Sulfur
Tin
Titanium
Tungsten
Vanadium
Zinc
Zirconium
Al
Ar
Ba
Be
B
Br
Cd
Ca
C
Cs
Cl
Cr
Co
Cu
F
Ga
Ge
Au
He
H
I
Fe
Pb
Li
Mg
Mn
Hg
Mo
Ne
Ni
Nb
N
O
P
Pt
K
Si
Ag
Na
S
Sn
Ti
W
V
Zn
Zr
13
18
56
4
5
35
48
20
6
55
17
24
27
29
9
31
32
79
2
1
53
26
82
3
12
25
80
42
10
28
41
7
8
15
78
19
14
47
11
16
50
22
74
23
30
40
26.98
39.95
137.33
9.012
10.81
79.90
112.41
40.08
12.011
132.91
35.45
52.00
58.93
63.55
19.00
69.72
72.64
196.97
4.003
1.008
126.91
55.85
207.2
6.94
24.31
54.94
200.59
95.94
20.18
58.69
92.91
14.007
16.00
30.97
195.08
39.10
28.09
107.87
22.99
32.06
118.71
47.87
183.84
50.94
65.41
91.22
2.71
—
3.5
1.85
2.34
—
8.65
1.55
2.25
1.87
—
7.19
8.9
8.94
—
5.90
5.32
19.32
—
—
4.93
7.87
11.35
0.534
1.74
7.44
—
10.22
—
8.90
8.57
—
—
1.82
21.45
0.862
2.33
10.49
0.971
2.07
7.27
4.51
19.3
6.1
7.13
6.51
FCC
—
BCC
HCP
Rhomb.
—
HCP
FCC
Hex.
BCC
—
BCC
HCP
FCC
—
Ortho.
Dia. cubic
FCC
—
—
Ortho.
BCC
FCC
BCC
HCP
Cubic
—
BCC
—
FCC
BCC
—
—
Ortho.
FCC
BCC
Dia. cubic
FCC
BCC
Ortho.
Tetra.
HCP
BCC
BCC
HCP
HCP
0.143
—
0.217
0.114
—
—
0.149
0.197
0.071
0.265
—
0.125
0.125
0.128
—
0.122
0.122
0.144
—
—
0.136
0.124
0.175
0.152
0.160
0.112
—
0.136
—
0.125
0.143
—
—
0.109
0.139
0.231
0.118
0.144
0.186
0.106
0.151
0.145
0.137
0.132
0.133
0.159
0.053
—
0.136
0.035
0.023
0.196
0.095
0.100
∼0.016
0.170
0.181
0.063
0.072
0.096
0.133
0.062
0.053
0.137
—
0.154
0.220
0.077
0.120
0.068
0.072
0.067
0.110
0.070
—
0.069
0.069
0.01-0.02
0.140
0.035
0.080
0.138
0.040
0.126
0.102
0.184
0.071
0.068
0.070
0.059
0.074
0.079
3+
Inert
2+
2+
3+
1−
2+
2+
4+
1+
1−
3+
2+
1+
1−
3+
4+
1+
Inert
1+
1−
2+
2+
1+
2+
2+
2+
4+
Inert
2+
5+
5+
2−
5+
2+
1+
4+
1+
1+
2−
4+
4+
4+
5+
2+
4+
660.4
−189.2
725
1278
2300
−7.2
321
839
(sublimes at 3367)
28.4
−101
1875
1495
1085
−220
29.8
937
1064
−272 (at 26 atm)
−259
114
1538
327
181
649
1244
−38.8
2617
−248.7
1455
2468
−209.9
−218.4
44.1
1772
63
1410
962
98
113
232
1668
3410
1890
420
1852
Adapted from Callister & Rethwisch 9e.
4|Page
Glass Transition Temperature (Tg) and Melting
Temperature (Tm) of Selected Polymers
Polymer
Tg (°C)
Tg (°F)
Tm (°C)
Tm (°F)
Aramid
375
Polyimide (thermoplastic)
280-330
Polyamide-imide (PAI)
277-289
Polycarbonate (PC)
150
Polyether-ether-ketone (PEEK)
143
Polyacrylonitrile (PAN)
104
Polystyrene (PS) (Atactic)
100
Polystyrene (PS) (Isotactic)
100
Polybutylene terephthalate (PBT)
Poly vinyl chloride (PVC)
87
Polyphenylene sulfide (PPS)
85
Polyethylene terephthalate (PET)
69
Nylon 6,6
57
Polychlorotriflouroethylene (PCTFE)
45
Poly methyl methacrylate (PMMA) (Syndiotactic)
3
Poly methyl methacrylate (PMMA) (Isotactic)
3
Polypropylene (PP) (Isotactic)
-10
Polypropylene (PP) (Atactic)
-18
Polyvinylidene chloride (PVDC) (Atactic)
-18
Polybutylene (PB)
-25
Polyvinyl fluoride
-20
Polyvinylidene fluoride (PVDF)
-35
Ionomer
-45
Polyacetal, polyoxymethylene (POM)
-50
Poly-ethylene oxide (PEOX)
-56
Poly-isobutylene
-70
cis – Poly-isoprene
-73
Polybutadiene (Syndiotactic)
-90
Polybutadiene (Isotactic)
-90
Polydimethylsiloxane (Silicone Rubber)
-123
Copolymers and Blends
Acrylonitrile-butadiene-styrene (ABS)
80-125
Polyacetal - polyethylene
~40
Fluoropolymer - ETFE
~20
Fluoropolymer - FEP
11
Fluoropolymer - ECTFE
~0
Polyethylene vinyl acetate (EVA)
-42
Poly chloroprene (chloroprene rubber or neoprene)
-50
High-Density Polyethylene (HDPE)
-90
Low-Density Polyethylene (LDPE)
-110
Polytetrafluoroethylene (PTFE)
-97
705
535-625
530-550
300
290
220
212
212
190
185
155
135
113
35
35
15
0
0
-13
-5
-31
-49
-58
-69
-95
-100
-130
-130
-190
~640
a
a
265
334
317
a
240
220-627
121
285
265
265
220
105
45
175
175
175
128
200
156
90-96
181
66
128
28
154
120
-54
~1185
a
a
510
635
600
a
465
428-513
415
545
510
510
428
220
115
347
347
347
262
390
313
194-205
358
151
260
80
310
250
-65
176-257
~104
~68
52
~32
-44
-60
-130
-165
-140
190
175
270
275
245
65-90
80
137
115
327
374
347
518
527
473
149-194
175
279
240
620
a = these polymers normally exist at least 95% non-crystalline
Adapted from Polymer Engineering Principles (Progelhof and Throne)
5|Page
A Tabulation of Diffusion Data
Diffusing
Species
Host Metal
D 0 (m 2 /s)
Cb
α – Fe (BCC)a
1.1 × 10−6
87.4
Cc
γ – Fe (FCC)a
2.3 × 10−5
148
Nb
Nc
α – Fe (BCC)a
γ – Fe (FCC)a
5.0 × 10−7
9.1 × 10−5
77
168
Fec
α – Fe (BCC)a
2.8 × 10−4
251
Fec
γ – Fe (FCC)a
5.0 × 10−5
284
Cud
Alc
Mgc
Znc
Mod
Nid
Cu
Al
Mg
Zn
Mo
Ni
2.5 × 10−5
2.3 × 10−4
1.5 × 10−4
1.5 × 10−5
1.8 × 10−4
1.9 × 10−4
200
144
136
94
461
285
Activation Energy
Q d (kJ/m ol)
Calculated Value
T(°C)
D(m 2 /s)
Interstitial Diffusion
500
900
900
1100
500
500
1.4 × 10−12
1.4 × 10−10
5.9× 10−12
5.3 × 10−11
3.1 × 10−12
4.0 × 10−16
500
900
900
1100
500
500
500
500
500
500
3.0 × 10−21
1.8 × 10−15
1.1 × 10−17
7.7 × 10−16
7.5 × 10−19
4.2 × 10−14
9.6× 10−14
6.6 × 10−12
1.2 × 10−35
1.0 × 10−23
500
500
500
500
500
500
4.0 × 10−18
8.7 × 10−13
4.2 × 10−14
1.9 × 10−13
1.3 × 10−22
5.4 × 10−20
Self-Diffusion
Znc
Cu
Zn
Al
Al
Ni
Cu
Cuc
Cuc
Mgc
Cuc
Nid
Interdiffusion (Vacancy)
189
2.4 × 10−5
2.1 × 10−4
6.5 × 10−5
1.2 × 10−4
2.7 × 10−5
1.9 × 10−4
124
136
130
256
230
Tabulation of Error Function Values
z
0
0.025
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
erf(z)
0
0.0282
0.0564
0.1125
0.1680
0.2227
0.2763
0.3286
0.3794
0.4284
0.4755
0.5205
z
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.0
1.1
1.2
erf(z)
0.5633
0.6039
0.6420
0.6778
0.7112
0.7421
0.7707
0.7970
0.8209
0.8427
0.8802
0.9103
z
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.2
2.4
2.6
2.8
erf(z)
0.9340
0.9523
0.9661
0.9763
0.9838
0.9891
0.9928
0.9953
0.9981
0.9993
0.9998
0.9999
Adapted from Callister & Rethwisch 9e.
6|Page
Room-Temperature Yield Strength and Plane Strain Fracture
Toughness Data for Selected Engineering Materials
Aluminum alloya
(7075-T651)
Aluminum alloya
(2024-T3)
Titanium alloya
(Ti-6Al-4V)
Alloy steela
(4340 tempered @ 260°C)
Alloy steela
(4340 tempered @ 425°C)
Yield Strength
MPa
ksi
Metals
495
72
KIc
𝑴𝑷𝒂√𝒎
𝒌𝒔𝒊√𝒊𝒏.
24
22
345
50
44
40
910
132
55
50
1640
238
50.0
45.8
1420
206
87.4
80.0
—
—
—
0.2-1.4
0.7-0.8
2.7-5.0
0.18-1.27
0.64-0.73
2.5-4.6
25.0-69.0
3.63-10.0
0.7-1.1
0.64-1.0
53.8-73.1
7.8-10.6
0.7-1.6
0.64-1.5
62.1
9.0
2.2
2.0
Ceramics
Concrete
Soda-lime glass
Aluminum oxide
—
—
—
Polymers
Polystyrene
(PS)
Poly(methyl methacrylate)
(PMMA)
Polycarbonate
(PC)
Adapted from Callister & Rethwisch 9e.
Figure 2: Hardness vs. Tensile Strength –
Low Alloy Cast Steels Regardless of Heat Treatment.
Source Book on Industrial Alloy and Engineering Data
7|Page
S – N Curves
Figure 3 : S – N Curves for various Materials
S-590 Alloy – Rupture Lifetimes
Figure 4: Stress vs. Rupture Lifetime
Figure 5: Stress vs. Steady-State Creep Rate
Adapted from Callister & Rethwisch 9e.
8|Page
S – N Curve for 1040 Steel
Figure 6: Normalized and
Tempered
Figure 7: Full Annealed
Curves for Various Steels
Figure 8: S – N Curves for Normalized
and Tempered Steels
Figure 9: Endurance Limit vs.
Tensile Strength
Source Book on Industrial Alloy and Engineering Data 1978
9|Page
Figure 10: Iron Carbon Diagram
Adapted from Callister & Rethwisch 9e.
10 | P a g e
Figure 11: A2 Steel Rockwell Hardness vs. Tempering Temperature
Figure 12: Cast – Low Alloy Steels tested at 40℃
Source Book on Industrial Alloy and Engineering Data 1978
11 | P a g e
Characteristics of Several Fiber-Reinforcement Materials
Material
Specific
Gravity
Tensile
Strength GPa
(106 psi)
Specific
Strength
(GPa)
Modulus of Elasticity
GPa (106 psi)
Specific
Modulus (GPa)
700
(100)
350-380
(50-55)
700-1500
(100-220)
480
(70)
318
Whiskers
Graphite
2.2
Silicon nitride
3.2
Aluminum oxide
4.0
Silicon carbide
3.2
Aluminum oxide
3.95
Aramid (Kevlar 49)
1.44
Carbona
1.78-2.15
E-glass
2.58
Boron
2.57
Silicon carbide
3.0
UHMWPE
(Spectra 900)
0.97
Molybdenum
10.2
Tungsten
19.3
20
(3)
5-7
(0.75-1.0)
10-20
(1-3)
20
(3)
9.1
1.56-2.2
2.5-5.0
6.25
Fibers
1.38
0.35
(0.2)
3.6-4.1
2.5-2.85
(0.525-0.600)
1.5-4.8
0.70-2.70
(0.22-0.70)
3.45
1.34
(0.5)
3.6
1.40
(0.52)
3.9
1.30
(0.57)
2.6
2.68
(0.38)
Metallic Wires
(0.35)
2.2
0.22
(0.32)
2.89
0.15
(0.42)
379
(55)
131
(19)
228-724
(32-100)
72.5
(10.5)
400
(60)
400
(60)
117
109-118
175-375
150
96
91
106-407
28.1
156
133
121
(17)
(30)
324
(47)
407
(59)
31.8
21.1
Adapted from Callister & Rethwisch 9e.
12 | P a g e
Time – Temperature – Transformation Diagrams
Figure 13: Carbon Steels: 1080
13 | P a g e
Time – Temperature – Transformation Diagrams
Figure 14: Carbon Steels: 1050
Figure 15: Manganese Steels: 1335
Source Book on Industrial Alloy and Engineering Data 1978
14 | P a g e
Figure 16: Chromium Steels: 5140
Figure 17: Vanadium Steels: 6150
Source Book on Industrial Alloy and Engineering Data 1978
15 | P a g e
Figure 18: Nickel – Chromium Steels: 3140
Figure 19: Nickel – Chromium Molybdenum Steels: 9440
Source Book on Industrial Alloy and Engineering Data 1978
16 | P a g e
Figure 20: Carbon – Molybdenum Steels: 4037
Figure 21: Chromium – Molybdenum Steels: 4140
Source Book on Industrial Alloy and Engineering Data 1978
17 | P a g e
Figure 22: 4140 Effect of Mass
Figure 23: 4140 Tempering Temperatures
Source Book on Industrial Alloy and Engineering Data 1978
18 | P a g e
Galvanic Series
The Standard emf Series
Increasingly Inert
(Cathodic)
Increasingly Active
(Anodic)
Au3+ + 3e− → Au
O2 + 4H+ + 4e− → 2H2O
Pt2+ + 2e− → Pt
Ag+ + e− → Ag
Fe3+ + e− → Fe2+
O2 + 2H2O + 4e− → 4(OH−)
Cu2+ + 2e− → Cu
2H+ + 2e− → H2
Pb2+ + 2e− → Pb
Sn2+ + 2e− → Sn
Ni2+ + 2e− → Ni
Co2+ + 2e− → Co
Cd2+ + 2e− → Cd
Fe2+ + 2e− → Fe
Cr3+ + 3e− → Cr
Zn2+ + 2e− → Zn
Al3+ + 3e− → Al
Mg2+ + 2e− → Mg
Na+ + e− → Na
K+ + e − → K
+1.420
+1.229
∼+1.2
+0.800
+0.771
+0.401
+0.340
0.000
−0.126
−0.136
−0.250
−0.277
−0.403
−0.440
−0.744
−0.763
−1.662
−2.363
−2.714
−2.924
Adapted from Callister & Rethwisch 9e.
Galvanic Series: Adapted from Callister & Rethwisch 9e. and Uhlig, Revie,
Corrosion and Corrosion Control 1985.
Increasingly Inert
(Cathodic)
Increasingly Active
(Anodic)
Platinum
Gold
Graphite
18 – 8 Stainless Steel, type 316 (passive)
18 – 8 Stainless Steel, type 304 (passive)
Titanium
70Ni – 30Cu (Monel)
Inconel 600 (76Ni – 16Cr – 7Fe) (passive)
Nickel (passive)
88Cu – Zn – 6.5Sn – 1.5Pb (Composition M – Bronze)
88Cu – Zn – 10Sn (Composition G – Bronze)
70Cu – 30Ni
5 Zn – 20Ni, Balc. Cu (Ambrac)
Silicon Bronze
Copper
Red Brass
Aluminum Bronze
Yellow Brass
76 Ni – Cr7Fe (Inconel 600) (active)
Nickel (active)
Naval Brass
Manganese Bronze
Muntz Metal
Tin
Lead
18 – 8, 3% Mo Stainless Steel, type 316 (active)
18 – 8 Stainless Steel, type 304 (active)
50 – 50 Lead – Tin Solder
13% Chromium Stainless Steel, type 410 (active)
Ni – Resist
Cast Iron
Wrought Iron
Mild Steel
Aluminum 2024T
Aluminum 2017T
Alclad Aluminum
Aluminum 6053T
Aluminum 1100
Aluminum 3003
Aluminum 3004
Aluminum 5052H
Zinc
Magnesium and Magnesium Alloys
Magnesium
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