Plastic deformation occurs by the following modes: 1. Slip 2. Twinning 3. Kink.
Mode # 1. Slip:
The surface of a crystalline solid which has been polished, Fig. 6.14 (a) and then plastically deformed, generally gets covered with one or, more sets of parallel lines, Fig. 6.14 (c). At high magnifications, these ‘slip lines’ are found to be steps on the surface [6.14 (b)] formed by sliding of blocks of crystal over one another along certain slip planes due to externally applied stress.
This parallel movement of two neighbouring crystal regions relative to each other across some plane, or planes is called slip, Fig. 6.15. This process resembles the motion of playing cards when force is applied on one side of a deck of cards, Fig. 6.15 (c) & (d). A view from right side shows steps as straight slip lines.
ADVERTISEMENTS:
Atoms in a metal move an integral number of atomic distances along the slip plane to result in producing a step. Each step appears as a line called slip line. Slip does not occur on just one plane but over small regions of parallel planes to result in a number of slip lines, together called slip band, Fig. 6.14 (b).
Optical microscope cannot resolve a single slip line, but a number of slip bands together appear as a slip line. If the surface is repolished after slip has occurred, the steps get removed and slip lines cannot be seen. If the polished surface is etched with proper etchant, there appears to be no difference in the etching characteristics.
Thus, the orientation of atoms, of all parts of the crystal, remains the same before and after the slip. Slip lines, are straight in FCC and HCP metals but are extremely wavy in BCC metals, as these are not produced by slip on single plane. As plastic deformation is continued, new slip lines are created, and earlier plane is made more resistant to shear as a result of process of slip.
As a single crystal remains a single crystal after the plastic deformation, and as all the slip lines occur in parallel sets with-in each grain, Fig. 6.14 (c) of polycrystalline material, slip must be occurring in same set of parallel planes, and in the same direction. It has been experimentally confirmed that the process of slip occurs on well-defined crystallographic planes and in definite crystallographic directions.
ADVERTISEMENTS:
These are called slip planes and slip directions respectively. The combination of a particular slip plane and a direction lying in the plane along which slip occurs is known as a ‘slip system’. Generally, the slip plane is the plane of greatest atomic density and the slip direction is the closest-packed direction in that plane.
This does not mean that slip cannot occur in a given crystal on planes other than the most closely packed planes. Fig. 6.16 illustrates that the closest-packed planes are also the most widely separated planes (X1 > X2 > X3). Thus, the interatomic bonds across the slip plane are relatively weak.
Consequently, the resistance to slip is generally less for these planes than for any other set of planes. The dislocations move more easily along these planes of widest-spacing because the lattice distortion due to the movement of the dislocation is small. Table 6.3 gives interplaner distance, interatomic spacing of some planes including the closest-packed plane in some common crystal systems.
The slip direction in a crystal has been seen to be almost exclusively a close-packed direction in which atoms touch each other in a straight line. The tendency of the slip to occur in close-packed direction is stronger than the tendency of slip to occur on the closest-packed plane.
Fig. 6.17 (a) illustrates two directions, one which is close-packed and the other which is not close-packed in a simple cubic lattice. A dislocation which has moved out through the crystal by shearing it in the close-packed direction sheared the upper half of the lattice to the right by ‘a’, which is the closest interatomic distance, which is also the Burgers vector of the dislocation, Fig. 6.17 (b).
Another shear in the arbitrarily chosen non-close-packed direction requires the movement of a dislocation of burgers vector, x (the distance between atom centres in this direction) resulting in the shape of crystal as illustrated in Fig. 6.17 (c). As x = 1.414 a, the dislocation corresponding to the shear in the close-packed direction, thus has the smallest Burger’s vector.
ADVERTISEMENTS:
According to Frank’s rule, the strain energy of a dislocation is directly proportional to the square of its Burgers’ vector. A dislocation with the smallest Burgers vector, and thus, with the smallest strain energy moves through the crystal more smoothly, causing the least distortion in the crystal structure, and requiring least outside stress. This accounts for the fact that slip direction is almost exclusively the close-packed-direction.
Slip Systems:
A combination of a slip plane and one of its close-packed directions defines a slip system. For example, Fig. 6.18 (a) shows a closest-packed plane (in the plane of paper of the book), having in it three closest-packed directions illustrating thus, three slip systems.
ADVERTISEMENTS:
On the basis of the requirements that the slip plane should be the densest plane, and the slip direction should be the closest-packed direction, the common crystal systems have the following slip systems:
Face-Centred Cubic Crystals:
FCC metals have {111} <110> family of slip systems as {111} is the family of closest-packed planes, also called octahedral planes, and <110> is the family of closest-packed directions in them. Since there are four possible {111} planes, namely, (111), (1̅11), (11̅1) and (111̅), and each plane contains three <110> slip directions as illustrated in Fig. 6.18 (a) for (111) plane. Thus, there are 12 possible slip systems.
BCC metals have four close-packed directions, the <111> directions. BCC structure is not a close-packed structure, and thus, there is no closest-packed plane like the octahedral planes {111} in FCC lattice. Thus, BCC metals lack truly close-packed planes. The slip lines have a wavy appearance.
In BCC metals, slip occurs predominantly on the {110} <111> slip systems as {110} planes have highest atomic density. There are six such planes in {110} family, and each has two directions <111> resulting in 12 such slip systems. Fig. 6.19 (a) illustrates one such plane (011) and two directions in it [111̅] and [1̅11̅].
The wavy appearance of slip lines is apparently due to simultaneous slip on other two similar possible systems (less common)- {211} <111> and {321} <111>, Fig. 6.19 (b) & (c). The <111> direction is common to these slip planes. Screw dislocations can easily cross-slip from one type of plane to another resulting in irregular wavy slip lines.
There is no definite single slip plane, but slip direction is always <111> direction in one of these three families of planes. Thus, in total, there are 48 slip systems in BCC crystals. The absence of a truly close-packed plane requires higher shearing stresses to cause slip in BCC metals.
Hexagonal Close-Packed Crystals:
In HCP metals, the number of slip-systems is very limited. The only plane having high atomic density is the basal plane, (0001) as illustrated in Fig. 6.17 and 6.20 (a). The three axes <1120> are the close-packed directions lying in the basal plane. As there is one basal plane per unit cell, and it has three slip directions, HCP crystals have three slip-systems as illustrated in Fig. 6.20 (a).
In HCP crystals, other slip systems having prismatic planes {101̅0} become operative particularly at high temperatures. The possibility of other slip systems becoming operative depends on the c/a ratio of the metal. It controls the packing densities and spacings of the non-basal planes.
For ideal packing of solid spheres in HCP crystals, c/a = 1.632. However, this ideal ratio does not occur in any HCP metal. Table 6.4 illustrates c/a ratio of some HCP metals. When c/a ratio is more than 1.632, there is preference for slip on basal-plane slip-system, <112̅0> (0001) such as in Zn, Cd, Mg. When c/a ratio is low, (0001) plane looses the distinction of being the plane of highest atomic density.
The prismatic planes {101̅0} and pyramidal planes {101̅1} become operative, but in each case the slip direction is <112̅0>. The limited number of slip systems is the cause of the plasticity to be extremely orientation dependent, .and also for low ductilities of HCP metals.
Some metals show additional operative slip systems when deformed plastically at increasing temperatures. Aluminium shows {110} planes at high temperature, Magnesium shows additional slip plane, {101̅1}, the pyramidal plane above 225°C. Titanium also shows {101̅0} and {101̅1} planes but in each case, the slip direction is the same. This fact explains why magnesium alloys can be more severely deformed at slightly elevated temperatures called warm working than at room temperature (cold working).
Mechanism of Slip:
Slip is the process of translation of one plane of atoms over another by an externally applied stress far smaller than the theoretical shear strength of that crystal. The mechanism of slip of the crystal is the motion of dislocations through the crystal. This concept is valid, as learnt in chapter on defects in crystals, that-
(i) The motion of a dislocation through a crystal lattice requires a stress far smaller than the theoretical shear stress, and
(ii) The movement of the dislocation produces a step at the free surface to account for the slip line.
(iii) The Peierls-Nabarro stress is the shear stress required to move a dislocation through a crystal lattice in a particular direction and is given by-
where, a is the distance between the planes, and b is the distance between atoms in the slip direction. The stress to move a dislocation, is low if ‘b’, the burgers vector is smallest and ‘a’ is large (at least a > b). For ‘b’, to be minimum, the slip direction should be a close-packed direction and for ‘a’ to be large, the atomic planes should be widest apart, i.e., the densest-packed plane. And slip does occur like that.
Critical Resolved Shear Stress (Schmid’s Law):
A polycrystalline metal deforms plastically when its yield stress is attained. Slip in a single crystal on its slip plane too begins only after the applied stress has reached a certain minimum value. This is called the critical resolved shear stress. It is the stress to move a large number of dislocations to produce a macroscopically measurable strain. Table 6.6 gives critical resolved shear stress of some common metals.
Generally, the crystal specimens are tested in tension. But the plastic deformation, i.e., the slip occurs by shear on definite slip systems. The resolved component of the applied stress on the operating slip plane and along the slip direction becomes important to cause deformation.
It has been found that slip can be initiated only when this resolved shear stress exceeds or becomes critical, i.e., attains the value called ‘critical resolved shear stress, CRSS. The component of stress normal to the slip plane does not influence slip. For example, in a single crystal of FCC metal, slip occurs on {111} planes along <110> directions in that plane.
The force that causes this slip to occur is not the tensile force but is a shear force on {111}
<110> slip systems. Thus, tensile force must be resolved on (111) planes along the <110> directions. Slip occurs first on that slip system having highest resolved shear stress, when this value exceeds the critical resolved shear stress of the metal.
Consider a single crystal under a tensile force F (Fig. 6.21). The angle between the normal to the slip plane and the tensile axis be ɸ. The angle between the slip direction and the tensile axis is θ. If A is the cross-sectional area of the specimen, then, the area of the slip plane inclined at an angle ɸ is A/cos ɸ. The component of the axial force F acting along the slip direction is F cos θ. Hence, the resolved shear stress is given by,
Thus, the tensile stress at which slip starts in a crystal depends on the relative orientation of the stress axis with respect to the slip plane and the slip direction. It is evident from equation (6.45) that all slip systems in a crystal will not have the same resolved shear stress for a given tensile stress along an axis.
As the applied tensile stress is increased from zero, the deformation will be initiated first on that slip system for which the resolved shear stress is maximum and thus, attains the critical value first.
The term in parenthesis of equation (6.45) is often called as Schmid factor. This equation also illustrates that the resolved shear stress of any slip system is proportional to its Schmid factor. For any given ɸ, the maximum Schmid factor occurs for 0 = 90 – ɸ. Hence, the maximum Schmid factor occurs at the maximum of the function, cos (90 – ɸ) cos ɸ, and is obtained at ɸ = 45°.
Thus, the maximum resolved shear stress is obtained up a plane at 45° from the tensile axis, i.e., when θ = ɸ = 45°. Then, the maximum possible value of the Schmid factor is 1/2 i.e. for all other combinations of these two angles, the resolved shear stress is smaller than one-half of the yield stress in tension.
Fig. 6.22 illustrates that yield stress varies with cos θ cos ɸ, but critical resolved shear stress remains constant.
In the following two limiting cases, the process of slip cannot occur at all-
(i) If the slip plane becomes more nearly perpendicular to the tensile axis, i.e., then angle θ = 90°, and as cos 90° = 0, the resolved shear stress is zero, irrespective of the magnitude of the tensile load. Actually, in such a situation, the applied stress has a greater tendency to pull the atoms apart than to slide them. The pulling apart of atoms by breaking their bonds needs very high stress.
(ii) If the tensile stress axis lies in the slip plane, then, angle ɸ = 90°, and the resolved shear stress on the slip plane is again zero. Physically, it is because, the area of the slip plane, A/cos ɸ, is correspondingly very large.
As the shear stress leads to the plastic deformation, the mechanical behaviour exhibited by a material depends on the nature of stress being applied during deformation. For example, a ductile metal can be made to show brittle fracture, without undergoing plastic deformation, when put in a state of hydrostatic or triaxial tension.
Under these conditions, the resolved shear stress on any plane is zero. The material, thus, does not undergo plastic deformation, and fails by brittle fracture. On the other hand, a material showing its brittle nature in a tensile test, can exhibit ductility if tested under conditions of high shear stresses and low tensile stresses.
Extrusion process resembles closely to a system of hydrostatic pressure, and thus, a common brittle material may exhibit some ductility when extruded. If a HCP single crystal has its basal plane perpendicular to the tensile axis, then the shear stress is zero to exhibit brittle behaviour in tensile test, can show ductile behaviour if the crystal is given a bend test.
Problem 1:
Prove that direction [101̅], [1̅10] & [01̅1] lie in (111) plane.
Solution:
To prove it, if hu + kv + Iw = 0, then that direction lies in the plane. Thus,
For [101̅] → (1) (1) + (1) (0) + (1) (-1) -1-1=0
[1̅10] → (1) (-1) + (1) (1) + (1) (0) = -1 + 1=0
[01̅1] → (1) (0) + (1) (-1) + (1) (1) = -1 + 1=0
Problem 2:
The critical resolved shear stress of perfect crystal of copper is 4 x 105 N/m2. Determine the amount of stress to he applied in tension along [11̅0] axis of the copper crystal to make it slip on (11̅1̅) [01̅1] slip system.
Solution:
The angle between tensile axis [11̅0] and normal to (11̅1̅) is:
(in cubic system, the normal to a plane has same indices, i.e., here it is [11̅1̅])
Factors Effecting Critical Resolved Shear Stress (CRSS):
The critical resolved shear stress, CRSS, of crystals of a metal at a temperature is remarkably constant of the same composition and microstructure.
The factors effecting the CRSS are:
1. Nature of Metal:
CRSS varies widely from material to material (Table 6.6). If CRSS of a metal is high, the applied stress, σ is high, and thus metal has high strength. As FCC metals have close-packed planes with 12 slip systems, CRSS is low, 0.35 to 0.7 MPa.
Thus, FCC metals have low yield strengths. BCC metals have no truly close-packed plane. Dislocations must move on non-closed-packed-planes, such as {110}, {112} and {123} planes. BCC metals have high strengths as CRSS may be 70 MPa. HCP metal like Zn, having c/a ratio greater than 1.633, CRSS is low, but metals with low c/a ratio, CRSS is equal to, or greater than BCC metals.
2. Purity of Metal:
In general, purer the metal crystal, lower is the critical resolved shear stress. For example, as the purity of the silver crystal changes from 99.999% to 99.93%, its critical resolved shear stress is raised by a factor more than three.
3. Temperature:
The critical resolved shear stress increases with the decrease in temperature. This effect has been seen to be less pronounced in FCC metals, but more in non-FCC structures. In latter metals, the rates of increase generally become greater at lower temperatures.
Thus, the three laws of governing the slip behaviour of a metal are:
1. The slip direction is almost always the closest-packed direction in crystals.
2. The slip usually occurs on the most densely-packed plane. The slip plane is more variable than is the slip direction.
3. Of the available slip systems, slip occurs on that slip system for which the resolved shear stress is highest, and takes place when it becomes critical.
In a tensile test, the plastic deformation of the single crystal occurs by slip on certain planes in particular direction. The grips of the cross-head of the tensile machine, which hold the specimen, must remain in a line during elongation of the specimen.
This does not permit free deformation by uniform glide on every slip plane, but instead the central portion of the crystal changes its orientation. The rotation occurs of both the slip plane and the slip direction into the axis of tension.
FCC crystals have uniformly spread 12 slip systems and thus, there is a wide choice of the slip systems, {111} <110>. On stress application, the choice of the initial operative slip system, called the primary slip system, depends on the orientation of the crystal relative to the tensile-stress axis, but is the one which has highest ‘Schmid factor’.
As the slip occurs on one of these 12 slip systems, for example (111) [101), the slip plane rotates away from its position of maximum resolved shear stress, the shear stress becomes equal to this value on another system (the, conjugate system). (1̅ 1̅ 1) [101]. At this point, slip occurs on two slip-systems simultaneously to cause ‘the duplex-slip’, or ‘multiple-slip’.
As the conjugate slip occurs, it is indicated by another set of intersecting slip lines under the
microscope. As the multiple slip occurs the specimen necks down and fractures. The duplex slip interrupts the free rotation of the slip system.
Thus, in a single crystal of FCC, multiple slip produces lower ductility at fracture as compared to a HCP single crystal, where the easy glide (mono-slip system operative) on only a single slip system continues uninterrupted to ultimately cause fracture (no necking). Deformation by duplex slip results in a high degree of strain- hardening because of interaction between dislocations on two intersecting slip systems as illustrated in Fig. 6.24.
In FCC crystals, because of 12 slip systems, the critical resolved shear stress may be achieved on more than one slip system, i.e., multiple-slip may be operative right from the beginning, or it becomes operative soon after some deformation on the primary slip system depending on the orientation of the crystal. In crystals of lower symmetry such as HCP crystals, a change in slip system may not be possible, and thus, angles θ and ɸ of the equation (6.45) are important in them for the slip to occur even on mono-slip system.
Mode # 2. Twinning (Mechanical Twinning):
Twinning may occur by mechanical deformation-called mechanical twinning or twinning, or by annealing after plastic deformation- called annealing twinning.
Mechanical twinning is explained here:
After slip, twinning is the important mode by which a crystal deforms; and alike slip, the process of twinning also consists of shear on definite planes in specified directions in each crystal structure as given in table 6.7.
In twinning, the atoms slide layer by layer to take up an orientation that is related to the orientation of the untwined region in a definite and symmetrical way, so that the twinned region of the crystal is a mirror image of the untwined region.
This is illustrated in Fig. 6.25. Fig. 6.25 (a) illustrates (110) plane of FCC crystal. If a shear stress is applied as illustrated, the crystal twins about the twinning plane. This crystallographic plane of reflection or symmetry is called the twin plane, which is also the boundary between twinned and untwined regions.
It is represented here by a line being perpendicular to the plane of the paper. Under the action of the shear stress, atoms on one side of the twin plane have moved so that the lattice forms a mirror image across the twin plane. Unlike slip, the shear movements in twinning are only a fraction of the interatomic spacing and the shear is uniformly distributed over a volume rather than being localised on a number of distinct planes during slip.
The extent of total movement for an atom from its original position is proportional to its distance from the twinning plane. Each atom moves relative to its neighbour by the same vector. This is a cooperative motion since all atoms in the twinned region move through the same vector relative to their neighbour. In Fig. 6.25 (b), open circles represent atoms which have not twinned, whereas the solid circles represent the final positions of the atoms in the twinned region.
Unlike the slip, a twinned region has difference in orientation of atoms as compared to the untwined region, Fig. 6.25 (b), and thus, can be visible after etching under the microscope due to their different etching characteristics.
During twin formation, thin lamellae forms very quickly almost at a rate equal to the speed of the sound, which then widens with the increasing stress by the steady movement of the twin interface. New twins may form in bursts, and are sometimes accompanied by a sharp audible click such as heard and called ‘tin cry’ (cry due to twinning). Twins in iron are seen as Neumann bands. Twins do not extend beyond a grain boundary.
As the atoms actually move very small distances to produce a twin image, the amount of gross deformation produced by twinning is small. Twinning plays an important role in the deformation of HCP metals as slip can occur only on the basal planes in many of these metals, although the amount of the shear (twinning produces) is small.
The significance of twinning during plastic deformation is not because of the amount of strain produced by it, but the reoriented lattice in the twinned region may have new slip systems in a favourable orientation on which resolved shear stress may become critical, and thus, additional slip may take place. As only a small fraction of the volume gets twinned, the amount of total deformation is less. Thus, HCP metals possess much lesser ductility than FCC metals.
HCP metals have commonly (101̅2) twinning plane and [101̅ 1̅] twinning direction. Twinning can cause compression, or extension along the c-axis depending on the c/a ratio of the metal. Zn and Cd, having c/a ratio greater than √3, twin to cause compression along c-axis. The twinning shear is zero when c/a = √3, but metals with c/a ratio less than get twinned in tension along c-axis.
Twinning is not the dominant deformation mode in metals which possess many slip systems. Several factors determine whether the deformation occurs by twinning, as most metals show a general reluctance to twin as the stress for twinning generally tends to be large (than for slip).
Consequently twinning occurs under conditions when the yield stress for slip is high for reasons:
(i) The process of slip which generally occurs preferably must be impeded for some reasons, for example: because of geometrical factors of the crystal.
(ii) Slip systems are restricted.
(iii) Some factor increases the CRSS, so that twinning stress is lower than the stress for slip. This is the reason of occurrence of twinning at low temperatures, or high strain rates in BCC and FCC metals,
(iv) The stress must be such that twinning process tends to accommodate the stress.
Copper shows twins by tensile deformation at 4°K, and by shock-loading, though FCC metals are not ordinarily considered to deform by twinning. Non-cubic crystals, Bi, Sb, and Sn show large portion of twinning deformation.
It has been seen that usually slip occurs first in most crystals, but once the flow stress increases for some reasons, such as strain-hardening, then twin nuclei are created by means of the very high stress-concentration, which exists at dislocation pile-ups.
Twins, once formed may themselves act as barriers to produce dislocation pile-ups, and thus, nucleate further the twins. Interestingly, it has been seen that indenting the specimen during the tensile test even with a sharp pin, when the stress is still lower, can artificially nucleate twins.
Since, the formation of twins involves the formation of extended stacking fault, a lowering of stacking-fault energy favours twinning at lower stresses as observed by solid solution alloying in FCC metals (copper alloys). Even the solid solution alloys of BCC metals readily twin at room temperature (Nb-V) because the increased lattice frictional stress reduces cross-slip, and thus helps to nucleate twins.
Dislocation Mechanism of Twinning:
Mechanical twinning, alike the slip, is thought to occur by a dislocation mechanism, but by the motion of partial dislocations, and not the unit dislocations. Consider the process of twinning in a FCC crystal. The stacking of closest-packed (111) planes is symbolically represented as ABCABC….
Suppose twinning occurs now such that one of the ‘C’ planes is the twin-plane, Fig. 6.26. The stacking sequence on twinning should resemble. Fig. 6.26 (b), i.e., about ‘C’ there is a mirror image CAB C BAC. This can be accomplished by movement of a partial dislocation on each of a set of parallel crystallographic planes as illustrated in Fig. 6.27.
Consider a partial dislocation on each of the atomic planes above the twin plane. The nature of the partial dislocation on each plane is identical. Successive movement of partial dislocations is shown in sequence in Fig. 6.27 (b) to (d). This result in the desired stacking as illustrated in Fig. 6.26 (b).
Clearly the movement of partial (twinning) dislocation on each plane can accomplish twinning developed homogeneously through successive planes of the lattice. This can also be alternatively obtained by the movement of a single partial dislocation successively from plane to plane-called the ‘pole-mechanism’ as illustrated in Fig. 6.28.
In pole mechanism, a single partial dislocation moves successively from plane to plane via a spiral ramp. The pole dislocation must have a screw component of such a nature that one of its partials can lie entirely in a possible twinning plane. The partial dislocation of such a nature is the ‘mobile partial dislocation’, Fig. 6.28.
The twinning dislocation (mobile partial) can sweep around the pole dislocation and trace out the helical ramp illustrated. The volume of the metal traversed in this manner is changed into twinned orientation relative to the perfect lattice. Thus, one partial dislocation will have moved across each of the planes in succession to create twinned region.
There are mainly two types of twins:
(i) Mechanical or Deformation Twins:
Mechanical twins are generally produced in HCP or BCC metals under conditions of shock loading and low temperatures. FCC metals are ordinarily not considered to deform by mechanical twinning.
(ii) Annealing Twins:
Annealing twins are commonly produced in FCC metals such as Cu, brass, austenitic stainless steel etc. These are obtained during annealing heat treatment after cold working.
Difference between Slip and Twinning:
1. Orientation:
The orientation of atoms above and below the slip plane is the same alter slip deformation, whereas twinning produces an orientation difference across the twin-plane.
2. Mirror-Image:
Atoms in the twinned portion move to orient themselves to produce mirror image of the original lattice, whereas, it does not happen in slip.
3. The appearance of slip lines on the surface of slipped metal shows that the deformation is inhomogeneous, with extensive slip occurring on certain planes, while the planes flying between them remain practically undeformed, but twinning is a cooperative motion since all the atoms move through the same vector relative to their neighbour, i.e., twinning is a uniform homogeneous deformation.
4. The direction of slip may be either positive or negative, but the direction of shear in twinning is limited to that which produces the mirror image.
5. Slip usually occurs in discrete multiples of the atomic spacing but in twinning, atoms move only a fraction of the interatomic distance, which is proportional to its distance from the twin-plane.
6. Slip produces thin slip lines but twins are seen as bands.
7. The shear stress for twinning is normally higher than for slip.
8. Twinning occurs in micro-seconds, but there is a time lag for slip.
9. Higher stress is required to propagate slip than to start it, but higher stress is needed to nucleate a twin than to propagate it.
10. Slip is a slower process at low temperatures, whereas the rate of formation of twins may be extremely high even at low temperatures.
11. CRSS for slip increases sharply with the fall of temperature, whereas there is little difference in the twinning stress.
Mode # 3. Kink Formation:
Fig. 6.23 (c) illustrates that two end-portions of the crystal restrain the neighbouring areas of the single crystal from slipping in the normal method. Apart from extra rotation of the crystal, bending occurs at the ends. This is local heterogeneous deformation. The geometrical effects of large strains can also influence the mode of deformation particularly in HCP or other crystals having few slip systems.
Deformation of polycrystalline materials show greater tendencies to heterogeneous deformation due to restraints imposed by the grain boundaries, surface irregularities, or other in homogeneities. Kink or also called accommodation kink is an example of inhomogeneous deformation.
Suppose an HCP crystal (Orowan Cadmium Crystal) is loaded in compression in the orientation illustrated in Fig. 6.29 (a), i.e., the basal planes are parallel to the crystal axis. As cos ɸ = 0 (in equation 6.45), the resolved shear stress on the (0001) slip planes is zero, and thus, deformation by slip mode cannot occur.
The crystal deforms-called kinks-as illustrated in Fig. 6.29 (b) by a localised-region of the crystal suddenly bending into a tilted position with a sudden shortening of crystal. This behaviour is called kinking or buckling. The crystal kinks if two arrays of dislocations cause local bending as illustrated.
Two important results of kink formation are:
(i) The crystal decreases its length and thus accommodates the applied stress. Kinks are thus also called accommodation kinks.
(ii) Kinked region has different orientation now. Some slip system may become operative as the resolved shear stress may become critical. Thus, the process of slip can occur now in the new orientation of kinked region. Fig. 6.25 illustrates that even twin formation causes similar change in orientation as also illustrated in 6.29 (c). The restraints imposed by the grips in testing machine, at the ends of the crystal produces accommodation kink-bands at atleast on one side of the twin, as illustrated in 6.29 (d). Kinks form when bending occurs at the ends as illustrated in Fig. 6.23 (c). Deformation kinks have been seen in both FCC and BCC metals. 