to the intensity of the incident light Io, is given by
(4.51)
Light that has entered a material can be reflected out due to scattering inside the material. If the amount of scattering is not too excessive, the material can appear translucent. Even the transmitted light can be scattered as it passes through the material, giving a transmitted beam that will spread out and appear blurred. Scattering occurs at the grain boundaries of polycrystalline materials, at fine pores within a material and at the interface between two phases of different refractive index. A dense homogeneous pore‐free glass lacks these microstructural features and, thus, suffers from little scattering.
Small changes in composition can lead to large changes in the color of a material as, for example, the formation of glasses with a variety of colors by the addition of less than ~1% by weight of a transition metal oxide to a composition that would normally form a transparent glass. Changes in the electronic energy levels of the transition metal ions give rise to selective absorption of light at certain frequency ranges in the visible region of the electromagnetic spectrum, and, thus, to different colors.
Lithium disilicate glass‐ceramics have become one of the most commonly used materials for dental restorations such as crowns and bridges (Chapter 7). The microstructure of these glass‐ceramics consists of fine lithium disilicate crystals within a glass matrix (Figure d). In addition to an attractive combination of mechanical properties, thermal conductivity, and chemical stability in the oral environment, lithium disilicate glass‐ceramic compositions have been designed to provide desirable optical properties such as color and fluorescence to match those of the existing tooth structure. This is achieved by adding small quantities of various transition metal oxides to the glass composition during its manufacturing process. In this way, the refractive index of the glass phase is made approximately equal to that of the crystals to reduce scattering of light at the enormous number of interfaces between the fine crystals and the glass matrix. A few of these metal ions and, if required, the use of additional metal ions, provide an additional benefit of esthetic appearance. They lead to the production of a wide range of desirable colors and fluorescence to match the existing tooth structure.
4.9 Concluding Remarks
In this chapter, we discussed how a three‐dimensional material responds to an applied physical stimulus such as a mechanical stress, an electric field, a magnetic field or an electromagnetic field (light). Overall, the response has its origins in the atomic structure (atomic bonding) of the material.
The physical properties of a material, such as strength, elastic modulus, electrical conductivity, magnetic susceptibility, thermal conductivity, and refractive index are controlled by its atomic structure and they can be modified by the microstructure of the material
An understanding of the mechanisms by which materials respond to an applied physical stimulus and how the properties of materials depend on their atomic bonding and microstructure is critical in designing and creating biomaterials with a desirable combination of properties for the intended application
Mechanical properties are among the most important physical properties for biomaterials that are subjected to mechanical stresses at some point or during their entire application. Consequently, designing biomaterials for mechanical reliability must take into account the inherent response of different types of materials to stresses.
As the applications of biomaterials normally involve a combination of physical properties, an understanding of other physical properties in addition to, or instead of mechanical properties, is desirable.
Problems
1 4.1 The figure below shows general stress–strain curves for different types of materials at room temperature:Which curve best represents the mechanical response of (i) alumina, (ii) high density polyethylene, (iii) polystyrene, (iv) stainless steel, and (v) titanium.Which curve represents the toughest material?Which curve represents the material with the lowest Young’s modulus?Explain your answers.
2 4.2 A cylindrical specimen of length 100 mm and diameter 10 mm is loaded in tension in a mechanical testing machine. Upon application of a force of 1000 N, the length increased to 100.5 mm. Determine the engineering (nominal) stress and strain in the specimen. If all the deformation occurred within the elastic region of its mechanical response, determine the Young’s modulus of the material.
3 4.3 Determine the stress on the femoral bone of average diameter 2.5 cm in a human when it is subjected to a compressive force equal to the weight of a human of mass 90 kg (~200 pounds). How does this stress compare with the tensile strength of human cortical bone?
4 4.4 The following data were obtained in tensile testing of an aluminum alloy specimen of gage length 50.8 mm and diameter 12.8 mm:Force (kN)Length (mm)050.808.950.8517.850.9035.651.0044.551.0553.451.1657.851.3162.352.0771.253.369.4 (fracture)54.2Plot the engineering stress–strain curveDetermine the Young’s modulus, yield strength (at an offset strain 0.2%), and the ultimate tensile strengthDetermine the engineering fracture strength and the true fracture strength, given that the diameter of the fractured specimen was 10.16 mm.
5 4.5 Define toughness and resilience. Draw a stress–strain curve for a ductile material and indicate how the toughness and resilience can be determined from it.
6 4.6 Explain why and how grain size influences the strength of metals. Give a relationship (name and equation) between strength and grain size, and define the terms in the equation.
7 4.7 Explain why a metal that has undergone mechanical fatigue often fails at stresses far smaller than those for a similar metal that has not. Is the fracture of a fatigued metal expected to be ductile or brittle in character?
8 4.8 Explain why a ceramic material such as Al2O3 commonly shows a compressive strength that is far higher than its flexural strength.
9 4.9 Discuss the most important properties that should be considered in designing metals, ceramics, and polymers for use as biomaterials in load‐bearing applications in vivo.
10 4.10 Explain the differences between diamagnetism, paramagnetism, ferromagnetism, and ferrimagnetism, and how these differences influence the applications of biomaterials.
11 4.11 Distinguish between phonons and photons. Explain how phonons influence the thermal conductivity of materials.
12 4.12 Metals typically have high electrical and thermal conductivities. On the other hand, diamond has a high thermal conductivity but is an electrical insulator. Explain.
13 4.13 Determine the number of unpaired electrons in the following atoms or ions: Cr, Al3+, Zn, Ni, O2−, Co2+.
14 4.14 Assuming that the magnetization of nickel results from its unpaired electrons only, calculate the saturation magnetization per kilogram of nickel which has a density of 8.9 g/cm3 and an FCC structure of unit cell length 0.352 nm.
References
1 Balint, R., Cassidy, N.J., and Cartmell, S.H. (2014). Conductive polymers: toward a smart biomaterial for tissue engineering. Acta Biomaterialia 10: 2341–2353.
2 Callister, W.D. (2007). Materials Science and Engineering: An Introduction, 7e.
