PLASTIC DEFORMATION OF POLYCRYSTALLINE MATERIALS

Deformation and slip in polycrystalline materials is somewhat more complex. Because of the random crystallographic orientations of the numerous grains, the direction of slip varies from one grain to another. For each, dislocation motion occurs along the slip system that has the most favorable orientation, as defined above. This is exemplified by a photomicrograph of a polycrystalline copper specimen that has been plastically deformed (figure 7.10); before deformation the surface was polished. Slip lines are visible, and it appears that two slip systems operated for most of the grains, as avidenced by two sets of parallel yet intersecting sets of lines. Furthermore, variation in grain orientation is indicated by the difference in alignment of the slip lines for the several grains.

Gross plastic deformation of a polycrystalline specimen corresponds to the comparable distortion of the individual grains by means of slip. During deformation, mechanical integrity and coherency are maintained along the grain boundaries; that is, the grain boundaries usually do not come apart or open up. As a consequence, each individual grain is constrained, to some degree, in the shape it may assume by its neighboring grains. The manner in which grain distort as a result of gross plastic deformation is indicated in figure 7.11. befor deformation the grains are equiaxed, or have approximately the same dimension in all directions. For this particular deformation, the grains become elongated along the direction in which the specimen was extended.

Polycrystalline metals are stronger than their sinle-crystal equivalents, which means that greater stresses are required to initiate slip and the attendant yielding. This is, to a large degree, also a result of geometrical constraints that are imposed on the grains during deformation. Even though a single grain may be favorably oriented with the applied stress for slip, it cannot deform until the adjacent and less favorably oriented grains are capable of slip also; this requires a higher applied stress level.

DEFORMATION BY TWINNING

In addition to slip, plastic deformation in some metallic materials can occur by the deformation of mechanical twins, or twinning. The concept of a twin was introduced in section 4.5; that is, a shear force can produce atomic displacements such that on one side of a plane (the twin boundary), atoms are located in mirror image positions of atoms on the other side. The manner in which this is accomplished is demonstrated in figure 7.12. here, open circles represent atoms that did not move, and dashed and solid circles represent original and final positions, respectively, of atoms within the twinned region. As may be noted in this figure, the displacement magnitude within the twin region (indicated by arrows) is proportional to the distance from the twin plane. Furthermore, twinning occurs on a definite crystallographic plane and in specific direction that depend on crystal structure. For example, for BCC metals, the twwin plane and direction are (112) and (111), respectively.

Slip and twinning deformations are compared in figure 7.13 for a single crystal which is subjected to a shear stress T. Slip ledges are shown in figure &.13a, the formation of which were described in section 7.5; for twinning, the shear deformation homogeneous (figure &.13b). These two process differ from one another is several respects. First of all, for slip, the crystallographic orientation above and below the slip plane is the same both before and after the deformation; whereas for twinning, there will be reorientation across the twin plane. In addition, slip occurs in distinct atomic spacing multiples, whereas the atomic displacement for twinning is less than the interatomic separation.

Mechanical twinning occurs in metals that have BCC and HCP crystal structures, at low temperatures, and at high rates of loading (shock loading), condition under which the slip process is restricted; that is, there are few operable slip systems. The amount of bulk plastic deformation from twinning is normally small relative to that resulting from slip. However, the real importance of twinning lies with the accompanying crystallographic reorientations; twinning may place new slip systems in orientations that are favorabel relative to the stress axis such that the slip process can now take place

MECHANISMS OF STRENGTHENING IN METALS

Metallurgical and materials engineers are often called on to design alloys having high strenghts yet some ductility and toughness; ordinarily, ductility is sacrificed when an alloy is strengthened. Several hardening techniques are at the disposal of an engineer, and frequently alloy selection depends on the capacity of a material to be tailored with the mechanical characteristics required for a particular application

Important to the understanding of strengthening mechanisms is the relation between dislocation motion and mechanical behavior of metals. Because macroscopics plastic deformation corresponds to the motion of large numbers of dislocation, the ability of a metal to plastically deform depends on the ability of dislocations to move. Since hardness and strength (both yield and tensile) are related to the ease with which plastic deformation can be made to occur, by reducinbg the mobility of dislocation, the mechanical strength may be enhanced; that is greater mechanical forces will required to initiate plastic deformation. In contrast, the more unconstrained the dislocation motion, the greater the facility with which a metal may deform, and the softer and weaker it becomes. Virtually all strengthening techniques rely on this simple principe: restricting or hindering dislocation motion renders a material harder and stronger.

The present discussion is confined to strengthening mechanism for single-phase metals, by grain size reduction, solid-solution alloying, and strain hardening. Deformation and strengthening of multiphase alloys are more complicated, involving concepts yet to be discussed.

STRENGTHENING BY GRAIN SIZE REDUCTION

The size of the grains, or average grain diameter, in a polycristalline metal influences the mechanical properties. Adjacent grains normally have different crystallographic orientations and, of course, a common grain boundary, as indicated in figure 7.14. during plastic deeformation, slip or dislocation motion must take place across this common boundary. Say, from grain A to grain B in figure 7.14. the grain boundary acts as a barrier to dislocation motion for two reasons:

1.       Since the two grains are different orientations,  adislocation passing into grain B will have to change its direction of motion; this becomes more difficult as the crystallographic misorientation increases.

2.       The atomic disoreder within a grain boundary region will result in a discontinuity of slip planes from one grain int to the order.

It shuld be mentioned that, for high-angle grain boundaries, it may not be the case that dislocations traverse grain boundaries during deformation;rather, a stress concentration ahead of a slip plane in one grain may active sources of new dislocations in an adjacent grain.

A fine-grained material (one that has small grains) is harder and stronger than one that is coarse grained, since the former has a greater total grain boundary area to impede dislocation motion. For many materials, the yield strength oy varies with grain size according to

In this expression, termed the hall-petch equation, d is the average grain diameter, and o and k are constants for a particular material. Figure 7.15. demonstrates the yield strength dependence on grain size for brass alloy. Grain size may be regulated by the rate of solidification from the liquid phase, and also by plastic deformation followed by an appropriate heat treatment, as discussed in section 7.13.

It should also be mentioned that grain size reduction improves not only strength, but also the thoughness of many alloys.

Small-angle grain boundaries (section 4.5) are not effective in interfering with the slip process because of the slight crystallographic misalignment across the boundary. On the other hand, twin boundaries (section 4.5) will effectively block slip and increase the strength of the material. Boundaries between two different phases are also impediments to movements of dislocations; this is important in the strengthening of more complex alloys. The sizes and shapes of the constituent phases significantly affect the mechanical properties of multiphase alloys; these are the topics of discussion in section 10.7, 10.8, and 17,1.

SOLID-SOLUTION STRENGTHENING

Another technique to strengthen and harden metals is alloying with impurity atoms that go into either substitutional or interstitial solid solution. Accordingly, this is called solid-solution strengthening. High-purity metals are almost always softer and weaker than alloys composed of the same base metal. Increasing the concentration of the impurity results in an attendant increase in tensile and yield strengths, as indicated in figures 7.16a and 7.16b for nickel in copper; the dependence of ductility on nickel concentration is presented in figure 7.16c.

Alloys are stronger than pure metals because impurity atoms that go into solid solution ordinarily impose lattice strains on the surrounding host atoms. Lattice strain field interactions between dislocations and these impurity atoms result, and, consequently, dislocation movement is restricted. For example, an impurity atom that is smaller than a host atom for which it substitutes exerts tensile strains on the surrounding crystal lattice, as ilustrated in figure 7.17a. conversely, a larger substitutional atom imposes compressive strains in its vicinity (figure 7.18a). these solute atoms tend to segregate around dislocations in a away so as to reduce the overall strain energy, that is, to cancel some of the strain in the lattice surrounding a dislocation. To accomplish this, a smaller impurity atom is located where its tensile strain will partially nullify some of the dislocation’s compressive strain. For the edge dislocation in figure 7.17b, this would be adjacent to the dislocation line and above the slip plane. A larger impurity atom would be situated as in figure 7.18b.

The resistance to slip is greater when impurity atoms are present because the overall lattice strain must increase if a dislocation is torn away from them. Furthermore, the same lattice strain interactions (figures 7.17b and 7.18b) will exist between impurity atoms and dislocations that are in motion during plastic deformation. Thus, a greater apllied stress is necessary to first initiate and then continue plastic deformation for solid-solution alloys, as opposed to pure metals; this is evidenced by the enhancement of strength and hardness.

STRAIN HARDENING

Strain hardening is the phenomenon whereby a ductile metal becomes harder and stronger as it is plastically deformed. Sometimes it is also called work hardening, or, because the temperature at which deformation takes place is “cold” relative to the absolute melting temperature of the metal, cold working. Most metal strain harden at room temperature.

It is sometimes convenient to express the degree of plastic deformation as percent cold work rather than as strain. Percent cold work (%CW) is defined as

Where A0 is the original area of the cross section that experiences deformation, and Ad is the area after deformation.

Figures 7.19a and 7.19b demonstrate how steel, brass, and copper increase in yield and tensile strength with increasing cold work. The price for this enhancement of hardness and strength is in the ductility of the metal. This is shown in figure 7.19c, in which the ductility, in percent elongation, experiences a reduction with increasing percent cold work for the same three alloys. The influence of cold work on the stress—strain behavior of a steel is vividly portrayed in figure 7.20.

Strain hardening is demonstrated in a stress—strain diagram presented earlier (figure 6.16). initially, the metal with yield strength () is plastically deformed to point D. The stress is released, then reapllied with a resultant new yield strength, (). The metal has thus become stronger during the process because (), is greater than ().

The strain hardening phenomenon is explained on the basis of dislocation—dislocation strain field interactions similiar to those discussed in section 7.3. the dislocation density in a metal increases with deformation or cold work, due to dislocation multiplication or the formation of new dislocations, as noted previously. Consequently, the average distance of separation between dislocation decreases—the dislocations are positioned closer together. On the average, dislocation—dislocation strain interactions are repulsive. The net result is that motion of a dislocation is hindered by the presence of other dislocations. As the dislocation density increases, this resistence to dislocation motion by other dislocations becomes more pronounced. Thus, imposed stress necessary to deform a metal increases with increasing cold work.

Strain hardening is often utilized commercially to enhance the mechanical properties of metals during fabrication procedures. The effects of strain hardening may be removed by an annealing heat treatment, as discussed in section 11.2.

In passing, for the mathematical expression relating true stress and strain, Equation 6.18, the parameter n is called the strain hardening exponent, which is a measure of the ability of a metal to strain harden; the larger its magnitude, the greater the strain hardening for a given amount of plastic strain.