STRUCTURE AND STRENGTH OF METALS

Metals at a normal temperature are crystalline solids. The atoms in the crystals are located peri-odically and form a structure that represents a multitude of identical elements. If lines are drawn through the centers of atoms, these lines form a spatial lattice called crystal lattice. Metals and alloys used in engineering mostly have a cubic lattice. Figure 3.1a shows the elementary cube of the iron structure at a normal temperature. It is a body-centered cube (bcc) with atoms placed in the corners and in the center. The length of the cube side a = 2.86 Å, that is, 2.86·10⁻⁷ mm. (The unit Å is the Angström, a linear dimensional unit of convenient size for atomic-scale measurements.) If the metal is alloyed, not all the places in the cube are filled with the parent metal, but some of the places are taken by the alloying metal atoms. But this doesn’t change the following considerations.

Figure 3.1b shows a small part of a perfect crystal lattice. Application of load (Figure 3.1c) deforms the lattice, but the forces of atomic bonding resist the possible sliding of the atomic layers. When the external load ceases, the atomic forces restore the initial balanced condition of the lattice. It is clear that the external force can be big enough, so as to overcome the atomic bonding and to displace the atomic layers by one step of the lattice. But this assumes that the entire layer of atoms would be moved at once.

Calculations based on the strength of the atomic bonding show that the external force needed for this to take place would be greater than the real strength of the material by a factor of 100 and more.

Therefore, something must explain the disparity between theory and reality, and it is as follows.

Numerous investigations have disclosed that the reason for the degraded strength of materials (as compared to its theoretical value) is the imperfection of the crystal structure. Several kinds of imperfection are shown in Figure 3.2:

Vacancies (Figure 3.2a), where one atom is absent.

Interstitials (Figure 3.2b), where one atom has squeezed itself into the lattice.

Edge dislocations (Figure 3.2c), where an incomplete row of atoms is squeezed into the lattice (or, if you prefer to be more pessimistic, part of a row is missing).

Screw dislocations. (The last consist of a row of atoms turned relative to the parent lattice by a small angle; they have a 3-D form and therefore are more difficult for 2-D graphic presentation.) Of the reasons given previously, the greatest reduction of strength is due to dislocations.

Figure 3.3a shows an unloaded part of lattice with edge dislocation 1. Near the end of the dislocation the crystal lattice is distorted, and some of the atomic bonding forces (for example, between atom 2 (fully shaded) and atoms 3 and 4 (both are half-shaded) are weakened. When the load is applied

22 Machine Elements: Life and Design

FIGURE 3.1 Crystal cell and crystal lattice.

FIGURE 3.2 Crystal lattice imperfections.

FIGURE 3.3 Dislocation and its movement under load.

(c) (b)

(a)

Shear load

a

(a) (b) (c)

(a) (b) (c)

2

4 1 3

Slip plane

(d) (e)

Deformations and Stress Patterns in Machine Components 23 (Figure 3.3b), most of it is taken by the elastically displaced atomic rows, but, in addition, atom 2, which has been already moved from atom 3 toward atom 4, jumps from 3 to 4, so that the dislocation moves to the right as shown in Figure 3.3b. This jerking (stepwise) motion continues under load until the dislocation goes out of the crystal (Figure 3.3c to Figure 3.3e). Thus, when a dislocation exists, the force needed to displace the atomic rows by one atom spacing is quite small.

The plane of displacement is called sliding plane or slip plane.

The process of crystallization begins when the liquid metal is chilled somewhat below its melting temperature. In the liquid metal appear lots of nuclei of crystallization, and the neighboring atoms attach to them. The crystals grow until they meet the neighboring crystals. In the end of this process, which lasts several seconds, the metal passes into solid state in the form of a granular structure (see Figure 3.4). Because, in the nuclei centers, the orientation of the initial cubes was random, the same orientation remains in the grains of the solidified metal.

Figure 3.4 may give the impression that the quantity of the lattice cells in one grain is not so big. This impression is false. Let’s calculate. The dimensions of the grains in steel, for example, range from about 0.015 mm (extra-fine-grained steel) to 0.220 mm (extra-coarse-grained). If we take the finest grain, the quantity of the lattice cells in one row is given by

It is clear that the presentation of grains in Figure 3.4 exaggerates the size of the lattice cubes for illustration.

The quantity of lattice cubes in 1 mm³ is FIGURE 3.4 Crystals and grains in the metal structure.

0 015

2 86 10 5 24 10

7

. 4

. .

⋅ ₋ = ⋅

24 Machine Elements: Life and Design

Among this astronomical amount, there may be millions of dislocations and other defects initiated by alien atoms, free electrons, grain boundaries, internal stresses, etc. When an external load is applied, it induces stresses in the macrovolume of a part. These stresses have a certain pattern of direction and magnitude depending on the shape of the part, the kind of load, and the place of load application. In the microvolumes in which the direction of the stresses coincides with the direction of the slip planes of a grain, this grain may become plastically deformed by a very small amount, perhaps the magnitude of one atomic spacing (depending on the stress magnitude), owing to the movement of dislocations. Such “unlucky” crystals are always present, so metals with ideal elasticity don’t exist; after even a small load is applied, some structural changes occur immediately. This kind of submicrodeformation is related to such phenomena as energy loss in materials in the course of elastic deformation (so-called internal friction) and a time delay in deformation as compared to the applied load.

When the stress is big enough, the dislocations multiply, and at the yield stress, they multiply very intensively, causing plastic deformation of the metal. Lots of dislocations interfere with each other, and their motion is hindered. This results in strengthening of the metal due to plastic deformation.

Dislocations are generated under smaller stress as well. At a cyclic load, the dislocations are constantly generated owing to movement on the grain boundaries and because of other processes in the crystal lattice, including their self-multiplication. The moving dislocations pile up on the grain borders and may finally form a microcrack.

The description of the mechanism of plastic deformation and fatigue given previously is very much simplified. The dislocations can move not only straight in direction (horizontally), as shown in Figure 3.3, but they also can move around a closed polygon in the sliding plane and even vertically (changing the sliding plane). The dislocations can unite within the crystal and divide it into parts forming subgrains. The atomic-scale processes occurring in the metal under load are multifarious in nature and are not yet studied enough to be used in strength calculations. But this description shows that the metal is similar to living matter that feels the load applied and reacts to it by structural changes.

Thus, perfection of elasticity depends on the accuracy of measurements. But in practice, when we deal with macrostresses and macrodeformations, it is generally agreed (and it is accurate for most practical applications) that the metals are perfectly elastic until the stress reaches the yield point; then it begins to get plastically deformed in macrovolumes, and the part changes its shape.