Chapter 2 Design Properties of Materials

Only those problems requiring numerical data are shown.

2-14 𝑠𝑢 = 90 ksi (621 MPa); 𝑠𝑦 = 60 ksi (414 MPa); 25% Elongation [Appendix A-10]

Because % Elongation >5%, it is ductile.

2-15 1020 HR: 36% Elongation – Greater ductility [Appendix A-10]

1040 HR: 25% Elongation

2-16 SAE 1141 OQT 700: High sulfur alloy steel with 0.41% carbon, quenched in oil,

tempered at 700℉. [Appendix A-10]

2-17 Yes, AISI 1141 steel has: 𝑠𝑦 = 172 ksi @ OQT 700, 𝑠𝑦 = 129 ksi @ OQT 900

By interpolation, 𝑠𝑦 ≈ 150 ksi @ OQT 800. [Appendix A-10]

2-18 𝐸 = 30 × 106 psi (207 GPa) For all carbon and alloy steels. [Appendix A-10]

2-19 𝑊𝑡 = Density × Volume = (0.283 lb/in3)(1.0)(4.0)(14.5)in3 = 𝟏𝟔. 𝟒 𝐥𝐛

[Appendix A-10] Value of lbm = Value of lb force (Wt)

2-20 Volume = Area × Length =𝜋

4(50)2 × 250 = 4.909 × 105 mm3

Steel Bar: Mass =7680 kg

m3 ×4.909×105 mm3

1×

1 m3

(103 mm)3 = 3.77 kg [Appendix A-10]

𝑊𝑡 = 𝑚 ∙ 𝑔 = 3.77 kg ∙ 9.81 m/s2 = 36.98 kg ∙ m/s2 = 𝟑𝟔. 𝟗𝟖 𝐍

2-21 Magnesium would stretch more because it has a lower 𝐸.

𝐸𝑀𝑎𝑔 = 45 GPa; 𝐸𝑇𝑖 = 114 GPa; Ti is stiffer. [Appendix A-11]

2-23 Alloy of aluminum with silicon and magnesium. Heat treated to T6 temper.

2-24

[Appendix A-14]

2-29 𝑠𝑢𝑡 = 40 ksi; 𝑠𝑢𝑐 = 140 ksi [Appendix A-13]

2-31 Bending 𝜎𝑑 = 1450 psi; Tension 𝜎𝑑 = 850 psi; Compression 1000 psi Parallel to

grain, 385 psi Perpendicular to grain; Shear 𝜏𝑑 = 95 psi [Appendix A-15]

2-32 2000 to 7000 psi [Section 2-11]

𝑠𝑢 𝑠𝑦 𝐸 Density

6061-0 18 ksi 8 ksi 10 × 106 psi 0.10 lb/in3

6061-T4 35 ksi 21 ksi 10 × 106 psi 0.10 lb/in3

6061-T6 45 ksi 40 ksi 10 × 106 psi 0.10 lb/in3

2-44 Graphite fibers.

2-45 S-glass, quartz fibers, tungsten fibers coated with silicon carbide

2-51 Material Specific strength (in) Ratio to SAE 1020

Graphite/Epoxy (High Strength) 4.86×106 25.0

Aramid/Epoxy Composite 4.00×106 20.6

Boron/Epoxy Composite 3.60×106 18.5

Graphite/Epoxy (Ultra-high mod.) 2.76×106 14.2

Glass/Epoxy Composite 1.87×106 9.63

Titanium Ti-6Al-4V 1.00×106 5.15

SAE 5160 OQT 700 Steel 0.929×106 4.78

Aluminum 7075-T6 0.822×106 4.23

Aluminum 6061-T6 0.459×106 2.36

SAE 1020 HR Steel 0.194×106 1.00

2-52 Material Specific modulus (in) Ratio to SAE 1020

Graphite/Epoxy (Ultra-high mod.) 8.28×108 7.81

Boron/Epoxy Composite 4.00×108 3.77

Graphite/Epoxy (High Strength) 3.45×108 3.25

Aramid/Epoxy Composite 2.20×108 2.07

SAE 1020 HR Steel 1.06×108 1.00

SAE 5160 OQT 700 Steel 1.06×108 1.00

Titanium Ti-6Al-4V 1.03×108 0.97

Aluminum 6061-T6 1.02×108 0.96

Aluminum 7075-T6 0.99×108 0.93

Glass/Epoxy Composite 0.66×108 0.62

2-60 Vm = 1.0 – Vf = 1.0 – 0.60 = 0.40

2-61 See Equation (2-10)

2-62 See Equations (2-11), (2-12), (2-13), (2-14)

See Table 2-15 for data.

Use Equation (2-10):

See Table 2-15 for data.

Use Equation (2-10):

Use Equation (2-10): See Table 2-15 for data.

Solutions to Problems 2-66 to 2-77: Some data are approximated from Figure P2-66. The most accurate values are for ultimate strength (b.) and % elongation (f.). The elastic limit (d.) is estimated between the proportional limit (c.) and yield strength (a.). The modulus of elasticity (e.) is computed from [ stress / strain], the slope of the straight-

line part of each curve. Listed materials are found in Appendixes A-10 – A-14, matching su, sy, E, and % elongation.

2-66 a. sy = 73 ksi; Offset method 2-67 a. sy = 173 ksi; Yield point b. su = 83 ksi b. su = 187 ksi c. sp = 60 ksi c. sp = 162 ksi d. sel = 67 ksi d. sel = 168 ksi e. E = 10.0×106 psi e. E = 29.0×106 psi f. 11% elongation f. 15% elongation g. Ductile g. Ductile h. Aluminum h. Steel i. 7075-T6 i. SAE 4140 OQT 900 2-68 a. sy = 62 ksi; Offset method 2-69 a. sy = 49 ksi; Yield point b. su = 75 ksi b. su = 65 ksi c. sp = 50 ksi c. sp = 46 ksi d. sel = 56 ksi d. sel = 48 ksi e. E = 16.7×106 psi e. E = 26.5×106 psi f. 15% elongation f. 36% elongation g. Ductile g. Ductile h. Copper alloy h. Steel i. C54400 Bronze-Hard i. SAE 1020 CD

2-70 a. No yield strength-Brittle 2-71 a. sy = 53 ksi; Offset Method b. su = 55 ksi b. su = 59 ksi c. sp = 50 ksi c. sp = 31 ksi d. sel = 53 ksi d. sel = 42 ksi e. E = 20.0×106 psi e. E = 12.0×106 psi f. 0.5% elongation f. 5.0% elongation g. Brittle g. Borderline Ductile/Brittle h. Cast iron h. Zinc i. ASTM A48 Grade 60 i. Cast ZA-12 2-72 a. sy = 35 ksi; Yield point 2-73 a. sy = 19 ksi; Offset Method b. su = 57 ksi b. su = 40 ksi c. sp = 30 ksi c. sp = 14 ksi d. sel = 27 ksi d. sel = 17 ksi e. E = 26.0×106 psi e. E = 6.0×106 psi f. 21% elongation f. 5.0% elongation g. Ductile g. Borderline Ductile/Brittle h. Structural Steel h. Magnesium i. ASTM A36 i. ASTM AZ 63A-T6

2-74 a. sy = 155 ksi; Offset Method 2-75 a. sy = 40 ksi; Offset Method b. su = 170 ksi b. su = 45 ksi c. sp = 142 ksi c. sp = 30 ksi d. sel = 149 ksi d. sel = 35 ksi e. E = 16.5×106 psi e. E = 10.0×106 psi f. 8% elongation f. 17% elongation g. Ductile g. Ductile h. Titanium h. Aluminum i. 6Al-4V i. 6061-T6 2-76 a. sy = 80 ksi; Offset Method 2-77 a. sy = 80 ksi; Offset Method b. su = 90 ksi b. su = 95 ksi c. sp = 62 ksi c. sp = 55 ksi d. sel = 71 ksi d. sel = 68 ksi e. E = 26.0×106 psi e. E = 26.0×106 psi f. 15% elongation f. 2.0% elongation g. Ductile g. Brittle – Does not yield h. Stainless Steel h. Malleable Iron i. SAE 430 – Full hard i. ASTM A220 Grade 80002

Courtesy of CRC Press/Taylor & Francis Group

Figure 2–1 (See color insert.) Understanding the properties of a material is critical to achieving safe and effective designs. Test equipment, such as that shown here, is available to determine the performance of a wide variety of materials with regard to strength and deformation.

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Courtesy of CRC Press/Taylor & Francis Group

(a) (b)

Figure 2–2 (a) Universal testing machine for obtaining stress–strain data for materials. (Courtesy of Instron Corporation, Norwood, MA.) (b) A technician is installing a tensile test specimen in a holder that is installed in the instrument shown in part (a). The device attached to the specimen, called an extensometer, is used to continuously monitor elongation as the tensile load is increased during the test.

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Strain, in./in. or m/m

60

50

40

30

20

10

0

Tensilestrength

D

YieldpointC

B Elastic limit

400

350

300

250

200

150

100

50

0

Stre

ss, M

Pa

Stre

ss, k

si

A Proportional limit

Figure 2–3 Typical stress–strain curve for steel.

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Strain, in./in. or m/m

450

400

350

300

250

200

150

100

50

0.2% offsetε = 0.002

0

10

20

30

40

50

60

70 Yieldstrength

Tensilestrength

N

M

Stre

ss, M

Pa

Stre

ss, k

si

0

Figure 2–4 Typical stress–strain curve for aluminum.

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250

200

150

100

50

0

40

30

20

10

00.00070

0.0012

Strain, in./in. or m/m0.0200

SteelE= 30 × 106 psi (207 GPa)

TitaniumE= 16.5 × 106 psi (114 GPa)

AluminumE= 10 × 106 psi (69 GPa)

MagnesiumE= 6.5 × 106 psi (45 GPa)

Stre

ss, M

Pa

Stre

ss, k

si

0.0031

Figure 2–5 Modulus of elasticity for different metals.

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Gage length

Typically 2.00 in. or 50.0 mm(a)

(b)

Figure 2–6 Gage length for tensile test specimen: (a) gage length marked on a test specimen and (b) test specimen in a fixture used to mark gage length. (Courtesy of Tinius Olsen Testing Machine Co., Inc., Willow Grove, PA.)

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Gage marks

Gage lengthOriginal specimen

Broken specimen fitted back together

Total elongation

(usually 2.00 in.)L0

Lf

Lf – L0

L0× 100%

Lf – L0

% Elongation =

Figure 2–7 Measurement of percent elongation.

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Initial shape

Final shape

F

F

Axial strain =

Lateral strain =

Poisson’s ratio =

Lf –L0

Lf

hf – h0

hfL0

L0

h0

εa

= εa

–εL

= εL

h0

= v

Figure 2–8 Illustration of Poisson’s ratio for an element in tension.

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γ

τ

τ

τ

τ

Shearing strain

Figure 2–9 Shearing strain shown on a stress element.

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(a)

300

250

200

150

110

100

90

80

70

60

50

40

30

20

10

0

Brinell hardness number, HB

Rock

wel

l har

dnes

s num

ber,

HRB

or H

RC

App

roxi

mat

e te

nsile

stre

ngth

, sn,

ksi

0 100 200 300 400 500 600 700 800

100

50

0

HRB

HRC

Tensile strengthfor steels

(b)

Figure 2–10 Hardness tester and conversions: (a) Rockwell hardness tester and (b) hardness conversions and relations to tensile strength for steels. (Courtesy of Instron Corporation, Norwood, MA.)

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80°

Specimen 10 × 10 × 55 mm

Striking edgeof pendulum

0.8 mm radius

40 m

mNotch

Radius1 mm

Anvil

Anvil

(b)

28 m

m

8mm

0.66 mm radius75° 10°

5°

22 m

m

Specimen10 × 10 ×75 mm

Striking edgeof pendulum

Standardnotch

Vise

47 m

m

75 m

m

(a)

(d)(c)

Figure 2–11 Impact testing devices and equipment: (a) Izod test specimen and striker (side view), (b) Charpy test specimen and striker (top view), (c) pendulum-type impact tester, and (d) drop-type impact tester. (Courtesy of Instron Corporation, Norwood, MA.)

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Rupture

Constant slope

Secondary creep

Primary creep

Creepstrain

Initialstrain

00

Timet1

ε1

ε2

εr

∆ε ∆ε∆t ∆t

ε0

t2 tr

Tertiary creep

Strain rate = ε =

Figure 2–12 Typical creep behavior.

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Strain, %

Stre

ss, M

Pa

0

5

10

15

20

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0.1 h 1 h 100 h 5000 h

0

Figure 2–13 Example of stress versus strain as a function of time for nylon 66 plastic at 23°C (73°F). (Courtesy of DuPont Polymers, Wilmington, DE.)

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SAE

Carbon content

Alloy number—indicatesmajor alloying elements

SAE

0.20% carbon

Plain carbon steel

X X X X

1

SAE

0.40% carbon

Molybdenum and chromiumalloying elements

4 4

Examples

2 00

1 0

Figure 2–14 Steel designation system.

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200

2000

1750

1500

1250

1000

750

500

250

0

300

250

150

100

50

0

Stre

ngth

, MPa

Stre

ngth

, ksi

Tempering temperature, °F 400 600 800 1000 1200

Perc

ent e

long

atio

n

30%

20%

10%

0

Ultimatestrength

Yieldstrength

Percentelongation

Figure 2–15 Effect of tempering temperature on the strength and ductility of an alloy steel.

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Note:RT = room temperatureLC = lower critical temperatureUC = upper critical temperature

Time

Quenching

UC

LC

Temperingtemperature

Slow cooling

RT

Tem

pera

ture

Time

Slow cooling

UC

LC

RT

Tem

pera

ture

Time

Slow cooling

UC

LC

RT

Tem

pera

ture

Very slow coolingin furnace

Time

Slow cooling

UC

LC

RT

Tem

pera

ture

(a) (b)

(c) (d)

Figure 2–16 Heat treatments for steel: (a) quenching and tempering, (b) normalizing, (c) full annealing, and (d) stress-relief annealing.

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400

350

300

250

200

150

100

50

0

60

50

40

30

20

10

00.5 1.0 1.5 2.0 2.5

Ulti

mat

e st

reng

th, M

Pa

Ulti

mat

e st

reng

th, k

si

Grade 40 cast iron

�ickness of casting, in.

Figure 2–17 Strength versus thickness for Grade 40 gray cast iron.

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0

fc /2

fc

fc

Stre

ss

Strain0.001 0.002 0.003 0.004

A

Secant modulus line

Figure 2–18 Typical stress–strain curve for concrete.

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00

1000

2000

3000

4000

5000

5

0

10

15

20

25

30

35

Com

pres

sive

stre

ngth

, psi

Com

pres

sive

stre

ngth

, MPa

Strain0.001 0.002 0.003 0.004

4000

f c= 5000 psi

3000

2000

1000

Figure 2–19 Typical stress–strain curves for a variety of concrete grades.

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TM

FIGURE 2–20 Prosthetic that employs composite materials to achieve the desired performance.

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FIGURE 2–21 High-performance bicycle employing a composite frame and other structural components.

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Figure 2–22 Large composite wind turbine blade at the installation site.

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Corecell

Shear web:

Shell:

Priming:

Process CoatUV Gelcoat

Spar:

Carbon prepreg PVCellG-PETG-Balsa

Prepreg CoreInfusion Core

InfusionPrepreg

Glass prepreg

Infusion

Infusion

Prepreg

Prepreg

SPRINT

SPRINT

SPRINT IPTSPRINT

CorecellTM

Finishing/Repair:

Epoxy Gelcoat

Structural adhesive:

SP340LVSP340

Root:

RENUVO™

Figure 2–23 (See color insert.) Cut-away view of a large wind turbine blade showing the complexity and the role of composite materials in the generation of renewable energy.

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Figure 2–24 Fabrics and braided sleeves made from glass and carbon fibers used for composite materials. The products shown in Figures 2–20 through 2–23 are made with these filler materials. (Courtesy of A&P Technology, Cincinnati, OH.)

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Spec

i�c

sti�

ness

(×10

8 in

.)Sp

eci�

c st

reng

th (×

106

in.)

Aluminum7075-T6

TitaniumTi–6Al–4V

Glass/epoxy

Aramid/epoxy

MetalsComposites

8

7

6

5

4

3

2

1

0

8

7

6

5

4

3

2

1

0Steel

1020 HRSteel5160

OQT 700

Aluminum6061-T6

Graphite/epoxy

(ultrahighmodulus)

Graphite/epoxy

Boron/epoxy

Speci�c strength

Speci�c sti�ness

Figure 2–25 Comparison of specific strength and specific stiffness for selected materials.

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0 1 2 3 4 5 6 7 8Sp

eci�

c st

reng

th (×

106 in

.)

Speci�c modulus (×108 in.)

Graphite/epoxy composite

Glass/epoxy composite

Steel 1020 HRAluminum 6061-T6

Steel AISI 5160 OQT 700Aluminum 7075-T6

Aramid/epoxy composite

Titanium Ti–6Al–4V

1 2 3 4 5 6 7 80

5

4

3

2

1

0

5

4

3

2

1

0

Boron/epoxy composite

Graphite/epoxy compositeultrahigh modulus

Figure 2–26 Specific strength versus specific modulus for selected metals and composites.

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2

3

1

0°0°0°0°0°0°0°0°

Figure 2–27 Unidirectional composite showing direction of principal axes.

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0°

0°

90°

90°

+45°

+45°

–45°–45°

Figure 2–28 Multilayer laminated composite construction designed to produce quasi-isotropic properties.

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Failure of �ber

Fiber

Matrix

Stre

ss

Strain

suf

εuf

σm

Figure 2–29 Stress versus strain for fiber and matrix materials.

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Fiber

Composite

Matrix

Strain

Stre

ss

σf

σc

σm

εf = εc= εm

Figure 2–30 Relationship among stresses and strains for a composite and its fiber and matrix materials.

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CompositesSandwiches

HybridsSegmented structures

Lattices andfoams

SteelsCast ironsAl-alloysMetals

Cu-alloysZn-alloysTi-alloys

IsopreneNeoprene

Butyl rubberElastomers

Natural rubberSilicones

EVA

PE, PP, PET,PC, PS, PEEKPA (nylons)PolymersPolyestersPhenolicsEpoxies

AluminasSilicon carbides

CeramicsSilicon nitrides

Zirconias

Soda glassBorosilicate glass

GlassesSilica glass

Glass–ceramics

Figure 2–31 Classifications of materials. (Courtesy of Granta Design, Cambridge, U.K.)

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(a)

Composite outer skin

Composite inner skinFoam core

(b)

Glass/epoxy layerswith decorative surface

Honeycomb core

Glass/epoxy layer

Figure 2–32 Laminated panels with lightweight cores: (a) curved panel with foam core and composite skins and (b) flat panel with hon-eycomb core and composite skins.

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CeramicsMetals

Composites

Polymers andelastomers

Strength—density

Naturalmaterials

CFRP

GFRP

Rigid polymerfoams

Butylrubber

Zinc alloysLead alloys

Ti alloys

Ni alloysTungsten

alloys

Copperalloys

Tungstencarbide

Steels

Cork

Concrete

MTA, DA

Guidelines forminimum

mass design

Siliconeelastomers

PEEKPETPA

PCPMMAWood

|| grain

Woodgrain

Mg alloys

Al alloysSiC

Si3N4Al2O3

10 000

1 000

100

10

1

0.1

1010.10.010.01

Density, ρ, Mg/m3

Stre

ngth

, σf ,

MPa

Foams

Metals and polymers: yield strengthCeramics and glasses MORElastomers: tensile tear strengthComposites tensile failure

f2/3

Flexible polymerfoams

σf

σρρ f

1/2σρ

Figure 2–33 Strength versus density chart for materials selection. (Courtesy of Granta Design, Cambridge, U.K.)

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Metals

Polymers

Composites

Technicalceramics

Young’s modulus—density

Naturalmaterials

Rigid polymerfoams

Polyestor

Flexible polymerfoams

MTA, DA

100

10

1000

1

10−1

10−2

10−3

102 m/s

103 m/s

104 m/s

10−4

1010.10.01Density, ρ, Mg/m3

Youn

g’s m

odul

us, E

, GPa

Foams

Guidelines forminimum

mass design

CFRP

GFRP

Butylrubber

Zinc alloysLongitudinalwave speed

Lead alloys

Ti alloysNi alloys

Cu alloys

W alloysWC

Steels

ConcreteEpaxes

PEEKPET

PC

PTFE

Siliconeelastomers

Pc yureithane

PMMAPA

PSPPPE

Isoprene

EVA

Leather

Mg alloysGlass

Al alloys

SiCSi3N4B4C

Al2O3

Cork

E1/3

ρ

E1/2

ρ

Eρ

Wood|| grain

Woodgrain

Neoprene

Elastomers

Figure 2–34 Young’s modulus versus density chart for materials selection. (Courtesy of Granta Design, Cambridge, U.K.)

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