Physical and Mechanical Properties w=modulus of elasticity AE FIGURE 1.1 Determination of modulus of elasticity force is released. the bar will not return to its sInce some permanent deformation has taken place. 1. 3 shows schemati ally an engineering stress-strain curve for an eformed metal. The lastic limit extends from the point of origin to the proportional limit, where departure from a linear relationship between stress and strain occurs. Since his point of departure is difficult to measure, a scheme was developed whereby a line is constructed parallel to the elastic line but is offset by a strain of 0.2% on the strain axis. The American Society for Testing and Materials(ASTM) specification E8-90 defines this offset. The point where the constructed line intersects the actual stress -strain curve is called the yield stress. The proportional limit is almost never used to define the yield stress. As the stress is increased, the slope of the curve depends on the plastic behavior of the metal being tested. for most metals the stress to maintain TABLE1.1 Typical Moduli at73°F/20°C Materia E×10°(psi) Aluminum alloy 10.3 Plain carbon ste Copper 16 Titanium 17 MARCEL DEKKER. INC 270 Madison Avenue. New York. New York 10016
Physical and Mechanical Properties 3 FIGURE 1.1 Determination of modulus of elasticity. TABLE 1.1 Typical Moduli at 73F/20C Material E 106 (psi) Aluminum alloys 10.3 Plain carbon steel 29 Copper 16 Titanium 17 force is released, the bar will not return to its original length or shape since some permanent deformation has taken place. Figure 1.3 shows schematically an engineering stress–strain curve for an easily deformed metal. The elastic limit extends from the point of origin to the proportional limit, where departure from a linear relationship between stress and strain occurs. Since this point of departure is difficult to measure, a scheme was developed whereby a line is constructed parallel to the elastic line but is offset by a strain of 0.2% on the strain axis. The American Society for Testing and Materials (ASTM) specification E8-90 defines this offset. The point where the constructed line intersects the actual stress–strain curve is called the yield stress. The proportional limit is almost never used to define the yield stress. As the stress is increased, the slope of the curve depends on the plastic behavior of the metal being tested. For most metals the stress to maintain
Chapter 1 10 5 1200 FIGURE 1.2 Youngs modulus versus temperature for some common metals plastic flow increases due to strain hardening. Therefore the stress must increase with increasing plastic strain and the curve rises to its maximum value-the ultimate tensile strength, or tensile strength C. Yield Strength Yield strength is the stress at which plastic deformation is fully developed n some portion of the material. Strain-aging types of metallic materials, such as annealed or normalized low-carbon steels, show a sudden transition from elastic to plastic behavior as the applied stress reaches a critical value This gives a true yield point, an observable physical phenomenon from which the stress can be determined quite accurately In other metals the transition is gradual. For these materials the yie strength is defined as the stress required to cause a predetermined amount of plastic strain, called the offset, as described under tensile strength and illustrated in Figure 1.3 In brittle materials, yielding does not really take place. On occasion alues of yield strength are listed for brittle materials like cast iron. That is the stress at some arbitrary amount of strain. This is a special case since the naterial has essentially no linear portion of the curve and fracture occurs at MARCEL DEKKER. INC 270 Madison Avenue. New York. New York 10016
4 Chapter 1 FIGURE 1.2 Young’s modulus versus temperature for some common metals. plastic flow increases due to strain hardening. Therefore the stress must increase with increasing plastic strain and the curve rises to its maximum value—the ultimate tensile strength, or tensile strength. C. Yield Strength Yield strength is the stress at which plastic deformation is fully developed in some portion of the material. Strain-aging types of metallic materials, such as annealed or normalized low-carbon steels, show a sudden transition from elastic to plastic behavior as the applied stress reaches a critical value. This gives a true yield point, an observable physical phenomenon from which the stress can be determined quite accurately. In other metals the transition is gradual. For these materials the yield strength is defined as the stress required to cause a predetermined amount of plastic strain, called the offset, as described under tensile strength and illustrated in Figure 1.3. In brittle materials, yielding does not really take place. On occasion values of yield strength are listed for brittle materials like cast iron. That is the stress at some arbitrary amount of strain. This is a special case since the material has essentially no linear portion of the curve and fracture occurs at
Physical and Mechanical Properties tensile strength 0.2% offset proportional slope = modulus 0.2 FIGURE 1. 3 Typical stress-strain curve for a ductile metal. very small strains. It does not yield in the conventially accepted meaning of the term D. Elongation Elongation is a measure of ductility, as measured by the percentage of elon- gation. Increasing the gauge length of a specimen will decrease the percent of elongation to fracture. This is because after the neck forms all subsequent deformation takes place in the vicinity of the neck. The behavior around the neck is the same regardless of the length of the specimen. Therefore in shorter gauge lengths, a larger fraction of the specimens length is deformin during the test In longer specimens, the portion away from the neck is not ontinuing to deform after the onset of necking, therefore a smaller e specimens length is contributing to the total deformation. Because of this it is necessary to compare percents of elongation of various metals with the same gauge length when comparing ductile E. Hardness The hardness test is the most utilized mechanical property test of all methods available. These tests do not require much time and are very informative MARCEL DEKKER. INC 270 Madison Avenue. New York. New York 10016
Physical and Mechanical Properties 5 FIGURE 1.3 Typical stress–strain curve for a ductile metal. very small strains. It does not yield in the conventially accepted meaning of the term. D. Elongation Elongation is a measure of ductility, as measured by the percentage of elongation. Increasing the gauge length of a specimen will decrease the percent of elongation to fracture. This is because after the neck forms all subsequent deformation takes place in the vicinity of the neck. The behavior around the neck is the same regardless of the length of the specimen. Therefore in shorter gauge lengths, a larger fraction of the specimen’s length is deforming during the test. In longer specimens, the portion away from the neck is not continuing to deform after the onset of necking, therefore a smaller percentage of the specimen’s length is contributing to the total deformation. Because of this it is necessary to compare percents of elongation of various metals with the same gauge length when comparing ductility. E. Hardness The hardness test is the most utilized mechanical property test of all methods available. These tests do not require much time and are very informative
Chapter 1 since hardness is related to strength. See Table 1.2. Hardness tests do not have the precision of other tests. Of the various hardness tests and hardness scales available they all have one thing in common-their hardness numbers ure relative. There is no such thing as an absolute hardness number as in yield strength, for example. The two most common tests used for metals are Rockwell and Brinell, with the former being the most popular. TABLE 1.2 Approximate Tensile Strength from Rockwell and Brinell Tests Tensile scale Tensile strength strength 10(psi) C A 980.7 5880.1 301 7654321 78.5 560 102 216 292 78.0 95 210 774 525 76.8 200 76.3 496 5075.9481 190 246 09876 4975.2 469 89 90 451 80 74.1442 868875.1176 73.6 432 45 73.1 421 169 208 72 409 82 165 194 4271.5390 81 654 62 182 171 3869.4 353 156 161 3668.4 152 674319 150 146 3266.3 301 147 138 8898 144 131 64.3 271 77 141 125 63.3258 明666 76 119 24624 237 110 060.5 7096 8 125 59 68 956 121 MARCEL DEKKER. INC 270 Madison Avenue. New York. New York 10016
6 Chapter 1 TABLE 1.2 Approximate Tensile Strength from Rockwell and Brinell Tests Tensile strength 103 (psi) Rockwell scale C A Brinell Tensile strength (psi) Rockwell scale B F Brinell 351 59 80.7 634 146 100 240 358 58 80.1 615 114 99 234 325 57 79.6 595 109 95 228 313 56 79 577 104 97 222 301 55 78.5 560 102 96 216 292 54 78.0 543 100 95 210 293 53 77.4 525 98 94 205 273 52 76.8 512 94 93 200 264 51 76.3 496 92 92 195 255 50 75.9 481 90 91 190 246 49 75.2 469 89 90 185 238 48 74.5 451 88 89 180 229 47 74.1 442 86 88 75.1 176 221 46 73.6 432 84 87 172 215 45 73.1 421 83 86 169 208 44 72.5 409 82 85 165 194 42 71.5 390 81 84 162 182 40 70.4 371 80 83 159 171 38 69.4 353 77 82 156 161 36 68.4 336 73 81 153 152 34 67.4 319 72 80 150 146 32 66.3 301 70 79 147 138 30 65.3 286 69 78 144 131 28 64.3 271 68 77 141 125 26 63.3 258 67 76 139 119 24 62.4 247 66 75 99.6 137 115 22 61.5 237 65 74 99.1 135 110 20 60.5 226 63 72 98.0 130 61 70 96.8 125 59 68 95.6 121 since hardness is related to strength. See Table 1.2. Hardness tests do not have the precision of other tests. Of the various hardness tests and hardness scales available they all have one thing in common—their hardness numbers are relative. There is no such thing as an absolute hardness number as in yield strength, for example. The two most common tests used for metals are Rockwell and Brinell, with the former being the most popular
Physical and Mechanical Properties The basic rockwell tester has a number of scales which consi various indenters used in combination with a variety of loads. The most common scales employ either a 1/16-in. diameter steel ball, a 1/8-in. di ameter ball. or a diamond indenter. Each indenter can be used with a load of 60, 100, or 150 kg, giving a total of nine common scales. The Rockwell tester measures the depth of indentation which is automatically converted a hardness number. The scale is arbitrary and very nonlinear The Rockwell C scale, 150 kg with the diamond pyramid indenter, and the Rockwell A scale, 60 kg with the diamond indenter, are normally used for steel and similarly hard alloys. Aluminum alloys are usually measured on the B scale, 100 kg with a 1/16-in. diamond sphere, while some copper alloys are measured on the k scale The Brinell hardness test measures the diameter of the indentation neration of a hardened steel or tung sten carbide ball that has been pressed into the surface under a specified load, usually 500 or 3000 kg. Other hardness tests that are used include the mohs scale, the vickers or diamond pyramid hardness(DPh), and the Knoop hardness test. As men- tioned previously the various hardness scales are not linear, however the DPH and Knoop scales are more linear than any other scale. For example a DPH value of 300 is probably close to three times the hardness of a material measured with a 100 DPh value The density of a metal is its mass per unit volume. The customary unit pounds per cubic foot G. Specific Gravity Specific gravity is the ratio of the density of the metal to the density of a reference material, usually water at a specified temperature and pressure Specific gravity is unitless H. Thermal Conductivity Thermal conductivity is the quantity of heat flow under steady state condi tions through unit area per unit temperature gradient in the direction per- dicular to the area The heat flow through a wall per unit of area is called the thermal flux, J, which is proportional to the thermal gradient, the proportionality constant being the thermal conductivity. The equation is MARCEL DEKKER. INC 270 Madison Avenue. New York. New York 10016
Physical and Mechanical Properties 7 The basic Rockwell tester has a number of scales which consist of various indenters used in combination with a variety of loads. The most common scales employ either a 1/16-in. diameter steel ball, a 1/8-in. diameter ball, or a diamond indenter. Each indenter can be used with a load of 60, 100, or 150 kg, giving a total of nine common scales. The Rockwell tester measures the depth of indentation which is automatically converted to a hardness number. The scale is arbitrary and very nonlinear. The Rockwell C scale, 150 kg with the diamond pyramid indenter, and the Rockwell A scale, 60 kg with the diamond indenter, are normally used for steel and similarly hard alloys. Aluminum alloys are usually measured on the B scale, 100 kg with a 1/16-in. diamond sphere, while some copper alloys are measured on the K scale. The Brinell hardness test measures the diameter of the indentation microscopically resulting from the penetration of a hardened steel or tungsten carbide ball that has been pressed into the surface under a specified load, usually 500 or 3000 kg. Other hardness tests that are used include the Mohs scale, the Vickers or diamond pyramid hardness (DPH), and the Knoop hardness test. As mentioned previously the various hardness scales are not linear, however the DPH and Knoop scales are more linear than any other scale. For example a DPH value of 300 is probably close to three times the hardness of a material measured with a 100 DPH value. F. Density The density of a metal is its mass per unit volume. The customary unit is pounds per cubic foot. G. Specific Gravity Specific gravity is the ratio of the density of the metal to the density of a reference material, usually water at a specified temperature and pressure. Specific gravity is unitless. H. Thermal Conductivity Thermal conductivity is the quantity of heat flow under steady state conditions through unit area per unit temperature gradient in the direction perpendicular to the area. The heat flow through a wall per unit of area is called the thermal flux, J, which is proportional to the thermal gradient, the proportionality constant being the thermal conductivity. The equation is