Five useful charts

Five material property charts guide materials selection to minimize mass, total embodied energy, and thermal losses using the indices of Tables 8.3

The Modulus-Density chart: the one for stiffness at minimum weight.

and 8.4. They are five of a much larger collection that can be found in the texts listed under Further Reading at the end of this chapter.

■ The Modulus-Density chart (see Figure 8.11). The modulus E of engineering materials spans seven decades,[35] from 0.0001 GPa to nearly 1000 GPa; the density p spans a factor of 2000, from less than 0.01 to 20 Mg/m[36] [37]. Members of each family cluster together and can be enclosed in envelopes, each of which occupies a characteristic part of the chart. The members of the ceramics and metals families have high moduli and densities; none have a modulus less than 10 GPa or a density less than 1.7 Mg/m3. Polymers, by contrast, all have moduli below 10 GPa and densities that are lower than those of any metal or ceramic; most are close to 1 Mg/m3. Elastomers have roughly the same density as other polymers, but their moduli are lower by a
further factor of 100 or more. Materials with a lower density than polymers are porous; these include manmade foams and natural cellular structures such as wood and cork.

The three indices for lightweight, stiffness-limited design in Table 8.3 can be plotted onto this chart. The "Guidelines" show the slope associated with each.

■ The Strength-Density chart (see Figure 8.12). The range of the yield strength ay or elastic limit ael of engineering materials, like that of the modulus, spans about six decades: from less than 0.01 MPa for foams, used in packaging and energy-absorbing systems, to 104 MPa for diamond, exploited in diamond tooling for machining and polishing. Members of each family again cluster together and can be enclosed in envelopes.

Comparison with the modulus-density chart (Figure 8.11) reveals some marked differences. The modulus of a solid is a well-defined quan­tity with a narrow range of values. The yield strength is not. The strength range for a given class of metals, such as stainless steels, can span a factor

of 10 or more, depending on its state of work hardening and heat treat­ment. Polymers cluster together with strengths between 10 and 100 MPa. The composites CFRP and GFRP have strengths that lie between those of polymers and ceramics, as one might expect, since they are mixtures of the two.

The three indices for lightweight, strength-limited design in Table 8.3 can be plotted onto this chart. The guidelines show the slope associated with each.

■ The Modulus-Embodied Energy and Strength-Embodied Energy charts (see Figures 8.13 and 8.14). The two charts just described guide design to minimizing mass. If the objective becomes minimizing the energy embodied in the material of the product, we need equivalent charts for these.

The Strength-Embodied Energy chart: the one for strength at minimum embodied energy.

Figure 8.13 shows modulus E plotted against Hmp; the guidelines give the slopes for three of the most common performance indices for stiffness – limited design at minimum embodied energy. Figure 8.14 shows strength ay plotted against Hmp; again, the guidelines give the slopes for strength – limited design at minimum embodied energy. They are used in exactly the same way as the E-p and ay-p charts for minimum mass design.

■ The Thermal Conductivity-Thermal Diffusivity chart

(see Figure 8.15). Thermal conductivity, A, is the material property that governs the flow of heat, q (W/m2), in a steady temperature gradient dT/dx:

dT

q = – AdT (8.10)

dx


The thermal diffusivity, a (m2/s), is the property that determines how quickly heat diffuses into a material. It is related to the conductivity:

a = A – (8.11)

Cp p

where pCp is the specific heat per unit mass (J/kg. K). The contours show the volumetric specific heat pCp, equal to the ratio of the two, А/a. The data spans almost five decades in А and a. Solid materials are strung out along the line

meaning that the heat capacity per unit volume, pCp is almost constant for all solids, something to remember for later. As a general rule, then,

A = 3 x 106 a

(A in W/m. K and a in m[38]/s). Some materials deviate from this rule: they have lower-than-average volumetric heat capacity. The largest deviations are shown by porous solids: foams, low-density firebrick, woods, and the like. Because of their low density, they contain fewer atoms per unit volume and, averaged over the volume of the structure, pCp is low. The result is that, although foams have low conductivities (and are widely used for insulation because of this), their thermal diffasivities are not necessarily low. This means that they don’t transmit much heat, but they do change temperature quickly.