Materials for Biomedical Engineering. Mohamed N. Rahaman

23). The production of excessive wear particles between the articulating surfaces in these implants, such as between the CoCr ball and ultrahigh molecular weight polyethylene (UHMWPE) liner in a hip implant, leads to a severe foreign body response that invariably causes implant failure (Chapter 18).

4.3 Effect of Microstructure on Mechanical Properties

      The microstructure of a material controls its mechanical properties and other physical properties (Chapter 3). Microstructural parameters that have a major influence on mechanical properties are

       Porosity, the volume fraction of pores in the material, as well as their distribution within the material and their shape

       Grain size, relevant to metals and ceramics

       Presence of microstructural flaws such as microcracks and pores, often introduced accidentally during fabrication of the material, particularly relevant to brittle materials.

      4.3.1 Effect of Porosity

Porosity has a strong effect in reducing the elastic modulus (Figure 4.13) and the strength of materials. Introduction of porosity into metals and ceramics is a well‐known approach to bring their high strength and elastic modulus closer to those of bone. A variety of equations, theoretical and empirical, has been proposed to account for the effect of porosity on elastic modulus and strength. A popular equation based on a combination of simplicity and accuracy is

(4.33)

where, E is the Young’s modulus, E_o is the Young’s modulus at zero porosity, P is the porosity and b is parameter that depends on the shape and distribution of the pores in the material. Commonly, b is determined empirically from a fit of the experimental data for E versus P. For example, a good fit of Eq. (4.33) to the data shown in Figure 4.13 for a titanium alloy is obtained using E_o = 80 GPa and b = 4.7. Equation (4.33) often provides a good fit to data for P values up to ~25–40%. For higher porosity, one modification gives

(4.34)

where, b′ is a parameter determined from fitting the experimental data. Relationships similar in form to Eqs. (4.33) and (4.34) are often used to empirically describe the decrease in strength with porosity.

Figure 4.13 Data for the Young’s modulus as a function of porosity for a titanium specimen. The data points are fitted by a smooth curve.

      4.3.2 Effect of Grain Size

The yield stress of ductile metals is observed to increase with decreasing grain size (Figure 4.14), according to the well‐known Hall–Petch equation, given by

(4.35)

where, σ_y is the yield stress, σ_o is the yield stress for the easiest slip system in a single crystal, and G is the grain size of the polycrystalline metal. Thus, reduction of grain size provides a powerful method to enhance the yield stress of metals (Chapter 6). Equation (4.35) can be derived theoretically by assuming that dislocations pile up at the grain boundaries that provide obstacles to dislocation motion. As the grain size decreases, the number of boundaries per unit volume increases, providing a larger number of obstacles.

Figure 4.14 The influence of grain size on the yield strength of a 70Cu–30Zn brass alloy.

      Source: From Callister (2007) / with permission of John Wiley & Sons.

      The effect of grain size on the strength of brittle ceramics is more complicated than that for ductile metals. This is because the strength of brittle materials is strongly influenced by the presence of flaws such as microcracks, particularly those at their surface (Section 4.4.2). For ceramics composed of grains of size smaller than ~10–20 μm, the flaw size is often larger than the grain size and, consequently, the strength of these ceramics should be independent of the grain size. However, data for ceramics often do show an increase in average strength with decreasing grain size below 10–20 μm. Although there is a wide scatter in the data due to various degrees of surface finish of the specimens prior to testing, the average flexural strength of alumina, the most widely studied ceramic, shows an increase from ~400 MPa to ~600 MPa with a decrease in grain size from 10 to 1 μm (Wachtman et al. 2009).

4.4 Designing with Ductile and Brittle Materials

      An understanding of mechanical property principles is important in designing materials for use in biomedical applications and engineering applications as well. These principles are particularly important in applications where the biomaterial is subjected to a significant stress, such as fracture fixation plates, total joint replacement, healing of large defects in the long bones of the human limbs and dental restorations such as crowns and bridges.

      4.4.1 Designing with Metals

      A common requirement in the design of some biomaterials is that their shape and dimensions should remain constant. For ductile metals and alloys, this means that while plastic deformation might occur locally at a few specific points, such as the vicinity of a microvoid, it should not spread throughout the entire material. Consequently, the highest stress that the metal is subjected to should be less than its measured yield stress. As the fracture of ductile metals is considerably less sensitive to the presence of microstructural flaws such as pores and microcracks when compared to brittle ceramics, the average value of their measured yield stress is a useful design property.

      4.4.2 Designing with Ceramics

The design requirements for ceramics are often more complex than those for metals. These requirements should be recognized because brittle fracture of an implant in vivo is a serious complication. In general, the measured strength of a number