Material property charts
策划书封面One way of displaying the span of the properties of engineering materials is as a bar-chart like that of Figure 4.1 for thermal conductivity. Each bar reprents a single material. The length of the bar shows the range of conductivity exhibited by that material in its various forms. The materials are gregated by class. Each class shows a characteristic range: metals have high conductivities; polymers have low; ceramics have a wide range, from low to high.
Much more information is displayed by an alternative way of plotting properties, illustrated in the schematic of Figure 4.2. Here, one property
(the modulus, E, in this ca) is plotted against another (the density, ) on logarithmic scales. The range of the axes is chon to include all materials, from the lightest, flimsiest foams to the stiffest, heaviest metals. It is then found that data for a given family of materials (e.g. polymers) cluster together on the chart. Data for one family can be enclod in a property-envelope, as Figure 4.2 shows. Within it lie bubbles enclosing class and sub-class. All this is simple enough—just a helpful way of plotting data. But by choosing the axes and scales appropriately, more
砂锅美食can be added. The speed of sound in a solid depends on E and ; the longitudinal wave speed v, for instance, is
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For a fixed value of v, this equation plots as a straight line of slope 1 on Figure 4.2. This allows us to add contours of constant wave velocity to the chart: they are the family of parallel diagonal lines, linking materials in which longitudinal waves travel with the same speed. And there is
more: design-optimizing parameters called material indices also plot as contours on to the charts.猪肉皮冻
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The material property charts
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The Modulus–Density chart
Figure 4.3 shows the full range of Young’s modulus, E, and density, , for engineering materials. Data for members of a particular family of material cluster together and can be enclod by an envelope (heavy line). The samefamily-envelopes appear on all the diagrams: they correspond to the main headings in Table 4.1.
The density of a solid depends on three factors: the atomic weight of its atoms or ions, their size, and the way they are packed. The spread of density comes mainly from that of atomic weight, ranging from 1 for hydrogen to 238 for uranium.
The moduli of most materials depend on two factors: bond stiffness, and the density of bonds per unit volume. A bond is like a spring: it has a spring constant, S (units: N/m). Young’s modulus, E, is roughly
where r0is the ‘‘atom size’’ (r03 is the mean atomic or ionic volume). The wide range of moduli is largely caud by the range of values of S. The covalent bond is stiff (S=20–200 N/m); the metallic and the ionic a little less so (S=15– 100 N/m). Diamond has a very high modulus becau the carbo
n atom is small (giving a high bond density) and its atoms are linked by very strong springs (S=200 N/m). Metals have high moduli becau clo-packing gives a high bond density and the bonds are strong, though not as strong as tho of diamond. Polymers contain both strong diamond-like covalent bonds and weak hydrogen or Van-der-Waals bonds (S=0.5–2 N/m); it is the weak bonds that stretch when the polymer is deformed, giving low moduli.
The chart shows that the modulus of engineering materials spans from 0.0001 GPa (low-density foams) to 1000 GPa (diamond); the density spans from less than 0.01 to 20Mg/m3. Ceramics as a family are very stiff, metals a little less so—but none have a modulus less than 10 GPa. Polymers, by contrast, all cluster between 0.8 and 8 GPa. To have a lower modulus than this the material must be either an elastomer or a foam. At the level of approximation of interest here (that required to reveal the relationship between the properties of materials class) we may approximate the shear modulus, G, by 3E/8 and the bulk modulus, K, by
E, for all materials except elastomers (for which G=E/3 and K E) allowing the chart to be ud for the also. The chart helps in the common problem of material lection for applications in which mass must be minimized.
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