section epub:type=”chapter”> This chapter examines the ways of increasing the resistance to motion of a dislocation. Bulk engineering materials, however, are aggregates of many crystals or grains. To understand the plasticity of such an aggregate, the interaction of individual crystals with each other has to be examined. This allows to calculate the polycrystal yield strength—the quantity that enters engineering design. The chapter starts with a brief discussion of strengthening mechanisms. Most crystals have a certain intrinsic strength caused by the bonds between the atoms that have to be broken and reformed as the dislocation moves. A good way of hardening a metal is simply to make it impure. Impurities go into solution in a solid metal. A good example is the addition of zinc (Zn) to copper (Cu) to make the alloy called brass. If an impurity is dissolved in a metal or ceramic at a high temperature and the alloy is cooled to room temperature, the impurity may precipitate as small particles. The chapter concludes with a discussion of the dislocation yield strength. We showed in the last chapter that. In this chapter, we examine ways of increasing the resistance to motion of a dislocation—which determines the dislocation yield strength of a single isolated crystal of a metal or ceramic. Bulk engineering materials, however, are aggregates of many crystals, or grains. To understand the plasticity of such an aggregate, we also have to examine how the individual crystals interact with each other. This lets us calculate the polycrystal yield strength—the quantity that enters engineering design. A crystal yields when the force τb (per unit length) exceeds f, the resistance (force per unit length) opposing the motion of a dislocation. Using Equation (10.2) we can now define the dislocation yield strength Most crystals have a certain intrinsic strength, caused by the bonds between the atoms which have to be broken and reformed as the dislocation moves. Covalent bonding, particularly, gives a very large intrinsic lattice resistance, fi per unit length of dislocation. It is this that causes the enormous strength and hardness of diamond, and the carbides, oxides, nitrides, and silicates that are used for abrasives and cutting tools. But pure metals are very soft: they have a very low lattice resistance. Then it is useful to increase f by solid solution strengthening, by precipitate or dispersion strengthening, or by work-hardening, or by any combination of the three. Remember, however, that there is an upper limit to the yield strength: it can never exceed the ideal strength. In practice, only a few materials have strengths that even approach it. A good way of hardening a metal is simply to make it impure. Impurities go into solution in a solid metal just as sugar dissolves in coffee. A good example is the addition of zinc (Zn) to copper (Cu) to make the alloy called brass. The zinc atoms replace copper atoms to form a random substitutional solid solution. At room temperature Cu will dissolve up to 30% Zn in this way. The Zn atoms are bigger than the Cu atoms, and, in squeezing into the Cu structure, generate stresses. These stresses “roughen” the slip plane, making it harder for dislocations to move; they increase the resistance f, and thereby increase the dislocation yield strength, τy (Equation (11.1)). If the contribution to f given by the solid solution is fss then τy is increased by fss/b. In a solid solution of concentration C, the spacing of dissolved atoms on the slip plane varies as C–1/2; and the smaller the spacing, the “rougher” is the slip plane. As a result, τy increases parabolically (i.e., as C1/2) with solute concentration (Figure 11.1). Single-phase brass, bronze, and stainless steels, as well as many other metallic alloys, derive their strength in this way. If an impurity is dissolved in a metal or ceramic at a high temperature, and the alloy is cooled to room temperature, the impurity may precipitate as small particles, much as sugar will crystallize from a saturated solution when it is cooled. An alloy of Al containing 4% Cu (“Duralumin”) treated in this way gives small, closely spaced precipitates of the hard compound CuAl2. Most steels are strengthened by precipitates of carbides. Small particles can be introduced into metals or ceramics in other ways. The most obvious is to mix a dispersoid (such as an oxide) into a powdered metal (aluminum and lead are both treated in this way), and then compact and sinter the mixed powders. Either approach distributes small, hard particles in the path of a moving dislocation. Figure 11.2 shows how they obstruct its motion. The stress τ has to push the dislocation between the obstacles. It is like blowing up a balloon in a bird cage: a very large pressure is needed to bulge the balloon between the bars, though once a large enough bulge is formed, it can easily expand further. The critical configuration is the semicircular one (Figure 11.2(c)): here the force τbL on one segment is just balanced by the force 2T due to the line tension, acting on either side of the bulge. The dislocation escapes (and yielding occurs) when
Strengthening and Plasticity of Polycrystals
Publisher Summary
11.1 Introduction
11.2 Strengthening Mechanisms
11.3 Solid Solution Hardening
11.4 Precipitate and Dispersion Strengthening
