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Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Chapter 3: Solid Materials
Iron is taken from the earth and copper is smelted from ore.Man puts an end to the darkness;he searches the farthest recesses for ore in the darkness.The Bible (Job 28:2-3)
Image: Iron flows from a blast furnace. Source: American Iron and Steel Institute.
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Ductile Tension Test Specimens
Figure 3.1 Ductile material from a standard tensile test apparatus. (a) Necking; (b) failure.
text reference: Figure 3.1, page 90
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Brittle Tension Test Specimen
Figure 3.2 Failure of a brittle material from a standard tesile test apparatus.
text reference: Figure 3.2, page 91
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Strength/Density Comparison
Figure 3.3 Strength/density for various materials.
text reference: Figure 3.3, page 94
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Fiber Reinforced Composite
Figure 3.4 Cross section of fiber reinforced composite material.
text reference: Figure 3.4, page 95
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Ductile - diagram
Figure 3.5 Stress-strain diagram for a ductile material.
text reference: Figure 3.5, , page 96
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Yield Strength Definition
Figure 3.6 Typical stress-strain behavior for ductile metal showing elastic and plastic deformations and yield strength Sy.
text reference: Figure 3.6, page 97
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Brittle and Ductile Metal Comparison
Figure 3.7 Typical tensile stress-strain diagrams for brittle and ductile metals loaded to fracture.
text reference: Figure 3.7, page 98
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Stress-Strain Diagram for a Ceramic
Figure 3.8 Stress-strain diagram for a ceramic in tension and in compression.
text reference: Figure 3.8, page 99
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Composite Bar
Figure 3.9 Bending strength of bar used in Example 3.6.
text reference: Figure 3.9, page 100
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Stress-Strain Diagram for Polymers
Figure 3.10 Stress-strain diagram for polymer below, at, and above its glass transition temperature Tg.
text reference: Figure 3.10, page 101
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Density of Various Materials
Figure 3.11 Density for various metals, polymers and ceramics at room temperature (20°C, 68°F) [From ESDU (1984)].
text reference: Figure 3.11, page 102
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Density for Various
Materials
Material Dens ity, kg/m3 lbm/in3
MetalsAluminum and its alloysa
Aluminum tinBabbitt, lead-based white metalBabbitt, tin-based white metalBrassesBronze, aluminumBronze, leadedBronze, phosphor (cast)b
Bronze, porousCopperCopper leadIron, castIron, porousIron, wroughtMagnesium alloysSteelsc
Zinc Alloys
2.7 x 103
3.1 x 103
10.1 x 103
7.4 x 103
8.6 x 103
7.5 x 103
8.9 x 103
8.7 x 103
6.4 x 103
8.9 x 103
9.5 x 103
7.4 x 103
6.1 x 103
7.8 x 103
1.8 x 103
7.8 x 103
6.7 x 103
0.0970.110.360.270.310.270.320.310.230.320.340.270.220.28
0.0650.280.24
PolymersAcetal (polyformaldehyde)Nylons (polyamides)Polyethylene, high densityPhenol formaldehydeRubber, naturald
Rubber, silicone
1.4 x 103
1.14 x 103
0.95 x 103
1.3 x 103
1.0 x 103
1.8 x 103
0.0510.0410.0340.0470.0360.065
CeramicsAlumina (Al2O3)Graphite, high strengthSilicon carbide (SiC)Silicon nitride (Si3N4)
3.9 x 103
1.7 x 103
2.9 x 103
3.2 x 103
0.140.0610.100.12
aStructural alloysbBar stock typically 8.8 x 103 kg/m3 (0.03lbm/in3.)cExcluding “refractory” steelsd“Mechanical” rubber
Table 3.1 Density for various metals, polymers, and ceramics at room temperature (20°C; 68°F). [From ESDU (1984)]
text reference: Table 3.1, page 103
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Elastic Modulus for Various Materials
Figure 3.12 Modulus of elasticity for various metals, polymers, and ceramics at room temperature (20°C, 68°F) [From ESDU (1984)].
text reference: Figure 3.12, page 105
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Elastic Modulus for Various Materials
Material Modulus of Elasticity, EGPa Mpsi
MetalsAluminumAluminum alloysa
Aluminum tinBabbitt, lead-based white metalBabbitt, tin-based white metalBrassesBronze, aluminumBronze, leadedBronze, phosphorBronze, porousCopperIron, grey castIron, malleable castIron, spheroidal graphiteb
Iron, porousIron, wroughtMagnesium alloysSteel, low alloysSteel, medium and high alloysSteel, stainlessc
Steel, high speedZinc alloysd
62706329521001179711060124109170159801704119620019321250
9.010.29.14.27.514.517.014.116.08.718.015.824.723.111.624.75.928.429.028.030.77.3
PolymersAcetal (polyformaldehyde)Nylons (polyamides)Polyethylene, high densityPhenol formaldehydee
Rubber, naturalf
2.71.90.97.0
0.004
0.390.280.131.02
0.0006Ceramics
Alumina (Al2O3)GraphiteCemented carbidesSilicon carbide (SiC)Silicon nitride (Si3N4)
39027450450314
56.63.965.365.345.5
aStructural alloysbFor bearingscPrecipitation-hardened alloys up to 211 Gpa (30 Mpsi).dSome alloys up to 96 Gpa (14 Mpsi).eFilledf2.5%-carbon-black “mechanical” rubber.
Figure 3.12 Modulus of elasticity for various metals, polymers, and ceramics at room temperature (20°C; 68°F). [From ESDU (1984)]
text reference: Table 3.2, page 106
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Poisson’s Ratio for Various Materials
Table 3.3 Poisson’s ratio for various metals, polymers, and ceramics at room temperature (20°C; 68°F). [From ESDU (1984)]
text reference: Table 3.3, page 107
Material Poisson’s ratio, Metals
Aluminum and its alloysa
Aluminum tinBabbitt, lead-based white metalBabbitt, tin-based white metalBrassesBronzeBronze, porousCopperCopper leadIron, castIron, porousIron, wroughtMagnesium alloysSteelsZinc alloys
0.33---------
0.330.330.220.33---
0.260.200.300.330.300.27
PolymersAcetal (polyformaldehyde)Nylons (polyamides)Polyethylene, high densityPhenol formaldehydee
Rubber
---0.400.35---
0.50Ceramics
Alumina (Al2O3)Graphite, high strengthCemented carbidesSilicon carbide (SiC)Silicon nitride (Si3N4)
0.28---
0.190.190.26
aStructural alloys
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Thermal Condictivity for Various Materials
Figure 3.13 Thermal conductivity for various metals, polymers, and ceramics at room temperature (20°C, 68°F). [From ESDU (1984)].
text reference: Figure 3.13, page 113
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Thermal Conductivity for Various Materials
Material Thermal Conductivity, K tW/m-°C Btu/ft-hr°F
MetalsAluminumAluminum alloys, casta
Aluminum alloys, siliconb
Aluminum alloys, wroughtc
Aluminum tinBabbitt, lead-based white metalBabbitt, tin-based white metalBrassesa
Bronze, aluminuma
Bronze, leadedBronze, phosphor (cast)d
Bronze, porousCoppera
Copper leadIron, grey castIron, spheroidal graphiteIron, porousIron, wroughtMagnesium alloysSteel, low alloyse
Steel, mediumSteel, stainlessf
Zinc alloys
2091461701511802456120504750301703050302870110353015110
120849887
100143269292729179817291716406420178.764
PolymersAcetal (polyformaldehyde)Nylons (polyamides)Polyethylene, high densityPhenol formaldehydee
Rubber, naturalf
0.240.250.5---1.6
0.140.140.29---
0.92Ceramics
Alumina (Al2O3)g
Graphite, high strengthSilicon carbide (SiC)Silicon nitride (Si3N4)
2512515---
14728.6---
aAt 100°CbAt 100°C (~150 W/m-°C at 25°C)c20 to 100°CdBar stock typically 69 W/m-°Ce20 to 200°CfTypically 22W/m-°C at 200°CgTypically 12W/m-°C at 400°C
Table 3.4 Thermal conductivity for various metals, polymers, and ceramics at room temperature (20°C; 68°F). [From ESDU(1984)]
text reference: Table 3.4, page 114
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Thermal Expansion Coefficient for
Various Materials
Figure 3.14 Linear thermal expansion coefficient for various metals, polymers, and ceramics applied over temperature range 20 to 200°C (68 to 392°F) [From ESDU (1984)].
text reference: Figure 3.14, page 115
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Linear Thermal Expansion
Coefficient for Various Materials
Material Linear Thermal ExpansionCoefficient, a
(°C) -1 (°F) -1
MetalsAluminumAluminum alloysa
Aluminum tinBabbitt, lead-based white metalBabbitt, tin-based white metalBrassesBronzesCopperCopper leadIron, castIron, porousIron, wroughtMagnesium alloysSteel, alloyb
Steel, stainlessSteel, high speedZinc alloys
23 x 10-6
24 x 10-6
24 x 10-6
20 x 10-6
23 x 10-6
19 x 10-6
18 x 10-6
18 x 10-6
18 x 10-6
11 x 10-6
12 x 10-6
12 x 10-6
27 x 10-6
11 x 10-6
17 x 10-6
11 x 10-6
27 x 10-6
12.8 x 10-6
13.3 x 10-6
13.3 x 10-6
11 x 10-6
13 x 10-6
10.6 x 10-6
10.0 x 10-6
10.0 x 10-6
10.0 x 10-6
6.1 x 10-6
6.7 x 10-6
6.7 x 10-6
15 x 10-6
6.1 x 10-6
9.5 x 10-6
6.1 x 10-6
15 x 10-6
PolymersThermoplasticsc
Thermosetsd
Acetal (polyformaldehyde)Nylons (polyamides)Polyethylene, high densityPhenol formaldehydee
Rubber, naturalf
Rubber, nitrileg
Rubber, silicone
(60-100) x 10-6(10-80) x 10-6
90 x 10-6
100 x 10-6
126 x 10-6
(25-40) x 10-6
(80-120) x 10-6
34 x 10-6
57 x 10-6
(33-56) x 10-6
(6-44) x 10-6
50 x 10-6
56 x 10-6
70 x 10-6
(14-22) x 10-6
(44-67) x 10-6
62 x 10-6
103 x 10-6
CeramicsAlumina (Al2O3)
h
Graphite, high strengthSilicon carbide (SiC)Silicon nitride (Si3N4)
5.0 x 10-6
1.4-4.0 x 10-6
4.3 x 10-6
3.2 x 10-6
2.8 x 10-6
0.8-2.2 x 10-6
2.4 x 10-6
1.8 x 10-6
aStructural alloysbCast alloys can be up to 15 x 10-6/(°C)cTypical bearing materialsd25 x 10-6(°C)-1 to 80 x 10-6(°C)-1 when reinforcedeMineral filledfFillers can reduce coefficientsgVaries with compositionh0 to 200°C
Table 3.5 Linear thermal expansion coefficient for various metals, polymers and ceramics at room temperature (20°C; 68°F). [From ESDU (1984)]
text reference: Table 3.5, page 116
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Specfic Heat Capacity for
Various Materials
Figure 3.15 Specific heat capacity for various metals, polymers, and ceramics at room temperature (20°C; 68°F) [From ESDU (1984)].
text reference: Figure 3.15, page 117
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Specific Heat Capacity for Various MaterialsMaterial Specific Heat Capacity, Cp
kJ/kg-°C Btu/lb°FMetals
Aluminum and its alloysAluminum tinBabbitt, lead-based white metalBabbitt, tin-based white metalBrassesBronzesCoppera
Copper leadIron, castIron, porousIron, wroughtMagnesium alloysSteelsb
Zinc alloys
0.90.960.150.210.390.380.380.320.420.460.461.00.450.4
0.220.23
0.0360.05
0.0930.0910.0910.0760.100.110.110.240.11
0.096Polymers
ThermoplasticsThermosetsRubber, natural
1.4---2.0
0.33---
0.48Ceramics
Alumina (Al2O3)h
GraphiteCemented CarbidesSilicon carbide (SiC)Silicon nitride (Si3N4)
---0.80.7------
---0.20.17------
aAluminum bronze up to 0.48 kJ/kg-°C (0.12 Btu/lbm-°F)bRising to 0.55 kJ/kg-°C (0.13 Btu/lbm-°F) at 200°C (392 °F)
Table 3.6 Specific heat capacity for various metals, polymer, and ceramics at room temperature (20°C; 68°F). [From ESDU (1984)]
text reference: Table 3.6, page 118
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Rigid Beam Assembly
Figure 3.16 Rigid beam assembly used in Example 3.12.
text reference: Figure 3.16, page 120
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Figure 3.17 Modulus of Elasticity plotted against density. The heavy envelopes enclose data for a given class of material. The diagonal contours show the longitudinal wave velocity. The guidelines of constant E/, E1/2/ , and E1/3/ allow selection of materials for minimum weight, deflection-limited design. [From Ashby (1992)].
text reference: Figure 3.17, page 122
Elastic Modulus vs.
Density
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Material ClassesClass Members Short nameEnginering alloys
(the metals and alloys ofengineering)
Aluminum alloysCopper alloysLead alloysMagnesium alloysMolybdenum alloysNickel alloysSteelsTin alloysTitanium alloysTungsten alloysZinc alloys
Al alloysCu alloysLead alloysMg alloysMo alloysNi alloysSteelsTin alloysTi alloysW alloysZn alloys
Engineering polymers(the thermoplastics andthermosets of engineering)
EpoxiesMelaminesPolycarbonatePolyesterPolyethylene, high densityPolyethylene, low densityPolyformaldehydePolymethylmethacrylatePolypropylenePolytetrafluoroethylenePolyvinyl chloride
EPMELPCPESTHDPELDPEPFPMMAPPPTFEPVC
Engineering ceramics(fine ceramics capable ofload-bearing application)
AluminaDiamondSialonsSilicon carbideSilicon nitrideZirconia
Al2O3CSialonsSiCSi3N4ZrO2
Table 3.7 Material classes and members and short names of each member. [From Ashby (1992)].
text reference: Table 3.7, page 123
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Material Classes (cont.)
Table 3.7 Material classes and members and short names of each member. [From Ashby (1992)].
Class Members Short nameEngineering composites
(the composites ofengineering practice) Adistinction is drawnbetween the properties of aply (uniply) and a laminate(laminates)
Carbon-fiber reinforcedpolymerGlass-fiber reinforcedpolymerKevlar-fiber reinforcedpolymer
CFRP
GFRP
KFRP
Porous ceramics(traditional ceramics,cements, rocks, andminerals
BrickCementCommon rocksConcretePorcelainPottery
BrickCementRocksConcretePclnPot
Glasses(ordinary silicate glass)
Borosilicate glassSoda glassSilica
B-glassNa-glassSiO2
WoodsSeparate clusters describeproperties parallel to thegrain and normal to it andwood products
AshBalsaFirOakPineWood products (ply, etc.)
AshBalsaFirOakPineWood products
Elastomers(natural and artificialrubbers)
Natural rubberHard butyl rubberPolyurethanesSilicone rubberSoft butyl rubber
RubberHard butylPUSiliconeSoft butyl
Polymer foams(foamed polymers ofengineering)
CorkPolyesterPolystyrenePolyurethane
CorkPESTPSPU
text reference: Table 3.7, page 123
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Strength vs. Density
Figure 3.18 Strength plotted against density (yield strength for metals and polymers, compressive strength for ceramics, tear strength for elastomers, and tensile strength for composites). The guidelines of S/, S2/3/, and S1/2/ allow selection of materials for minimum-weight, yield-limited design. [From Ashby (1992)].
text reference: Figure 3.18, page 125
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Elastic Modulus
vs. Strength
Figure 3.19 Modulus of elasticity plotted against strength. The design guidelines help with the selection of materials for such machine elements as springs, knife-edges, diaphragms, and hinges. [From Ashby (1992)].
text reference: Figure 3.19, page 127
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Wear Constant
vs. Limiting Pressure
Figure 3.20 Archard wear constant plotted against limiting pressure. [From Ashby (1992)].
text reference: Figure 3.20, page 129
Hamrock, Jacobson and Schmid©1998 McGraw-Hill
Elastic Modulus vs.
Cost x Density
Figure 3.21 Modulus of elasticity plotted against cost times density. The reference lines help with selection of materials for machine elements. [From Ashby (1992)].
text reference: Figure 3.21, page 131