Plastic deformation of a single crystal occurs either by

(c) Slip or by (b) Twinning.

But slip is far more common a mechanism. Although the crystal may be subjected to other stresses; both slip and twinning occur by pure shearing stresses.

1   Deformation by Slip

— Slip is that mechanism of deformation wherein one part of the crystal moves, glides or slips over another part along certain planes known as slip planes (or glide planes).

A slip plane is a crystallographic plane in which, either the slip is likely to take place or in which slip has (already) taken place.

Generally, the slip plane is the plane of greatest atomic density and the slip direction is the closest packed direction within the slip plane.

— In metals with h.c.p. structures (such as Zn and Mg), there is only one set of slip planes at room temperature and that is (0001), the basal planes.

The slip direction is along any of the diagonals [2110], [l2T0] and [1150] (Fig. 54.8).

The most encountered slip systems (i.e., slip planes and slip direc-tions).

Structure                       Slip plane                        Slip direction

FCC                                   (111)                                         <110>

BCC                                  (110)                                         <111>

HCP                                 (0001)                                    <1120>

— The usual slip planes in metals having f.c.c. structure (e.g., Al, Cu, Ni, etc.) are the close packed {111} planes of which there are 4 equivalent sets. Each plane possesses 3 < 110 > directions and thus there are (4×3) = 12 slip systems whereas there are only 3 in h.c.p. structure.

— In metals having b.c.c. structure (e.g., a iron) the slip planes are {110}, {112} and {123}, depending upon the temperature. The slip directions are < 111 >.

— If there are more than one set of slip planes, the slip starts on the set along which there is the maximum shear stress.

— Slip results in visible step on the surface of the crystal (Fig. 54.9). The distance moved during slip (as the slip step) is in whole number increments of the unit spacing between the atoms.

— The results of slip in a polycrystalline mass of metal may be observed under a microscope. The direction of the slip planes is indicated in such a piece of metal after deformation by the presence of slip bands which form on the surface of metal (Fig. 54.10).

Slip bands are parallel in a single crystal but differ in orientation from one crystal to another. A single visible slip band is about 40 atoms thick and approximately 400 atoms high.

2  Critical Resolved Shear Stress for Slip

— All metals of similar crystal structure slip on the same crystal-lographic planes and in the same crystallographic directions. Slip occurs when the shear stress resolved along these planes reaches a certain value — the critical resolved shear stress. This is a property of the material and does not depend upon the structure. The value of the critical resolved shear stress depends on composition and temperature.

— Besides being a function of critical stress, the force required to produce slip also depends upon the

(i)  Angle between the slip plane and the direction of force (<p is the angle between the direction of force and the normal to slip plane):

(ii)  Angle, A, between the slip direction and the direction of force (Refer Fig. 54.11).

— From the elementary know­ledge of Strength of Materials, it is known that even if a specimen is subject­ed to tensile or compressive stresses, the material fails due to the induced shear stresses along the shear plane.

Consider Fig. 54.11, where A is the cross-sectional area perpendi­cular to the direction of the tensile force F.

The area of the slip plane inclined at the angle <p will be/l/cos <p and the component of the axial load acting in the slip plane in the slip direction is F cos A. Therefore the critical resolved shear stress is given by

σs= Fcosλ/(A/cosΦ) = (F/A)cosΦcosλ

Equation (i) is also known as Schmid’s Law.

 

Slip always beings when the shear stress across the slip plane reaches os, value; a change in the shape of specimen occurs, parts of specimen are

displaced relative to each other along one or more planes (Fig. 54.9) known as slip planes. In other words, blocks of crystalline material apparently slide over their neighbours in certain planes and along certain directions (as described earlier). The displacement of blocks of material along slip planes has been likened to the sliding of a pack of cards over one another.

— From equation (i), for Φ = λ = 45°

σs = (F/A)cosΦcosλ = (F/A)cos45cos45

σs = (F/A) . 1/√2 . 1/√2 = F/2A = σt/2

σs = σt/2                  …(ii)

Slip occurs with the minimum axial force when both X and <p are 45°. Under these conditions it can be seen from equation (ii) that as is equal to one-half the axial stress (at).

The resolved shear stress is less in relation to the axial stress for any other crystal orientation, dropping to zero as either A or <p approaches 90°.

— The magnitude of the critical resolved shear stress of a crystal is determined by the interaction of its population of dislocations with each other and with defects such as vacancies, interstitials and impurity atoms (refer Chapter 37).

— The value of critical shear stresses of the principal slip systems at (20°C) for some metals are given in Table 54.1.

MetalstructureSlip systemCritical resolvedshear stress
Slip planeSlip-direction
Copperf.c.c{111}<110>5
Aluminiumf.c.c{111}<110>8
Ironb.c.c{110}<111>280
Molybdenumb.c.c{110}<111>730
Magnesiumh.c.p{0001}<1120>4.5
cobalth.c.p{0001}<1120>67.5

3  Mechanism of Slip (Dislocation Theory)                                       ,

—                Earlier it was thought that slip occurs by the simultaneous gliding of a complete block of atoms over another.

This, however, requires that the shearing force must have the same value over all points of the slip plane. The vibrations of the atoms and the difficulties of applying a uniformly distributed force make this condition unattainable.

Thus this concept was discarded.

—                The modern concept of the mechanism of slip is that the slip occurs step by step by the movement of so called dislocations within the crystal.

Consider a wrinkled (decoration) paper. If it is tried to smooth out all the wrinkles by stretching the paper by holding from its two ends, quite possible, paper may tear out (because tensile force necessary to cause the whole sheet of paper to slide to eliminate wrinkles would be great enough to tear the paper). Instead, gentle coaxing of the wrinkles individually with a brush or cloth leads to their successful elimination, causing them to glide and get removed from the paper. It is thought that the movement of dislocations on a slip plane in a metallic crystal probably follows a similar pattern or procedure.

— Dislocations are imperfections or distorted regions in otherwise perfect crystals and the step-by-step movement of dislocations explains why the force required to produce slip is of the order of 1000 times less than the theoretical, assuming simultaneous slip over a whole system.

— Considering that mechanism of slip involves dislocation move­ment, the direction in which the critical shear stress is least is the direction with the shortest Burgers Vector, i.e., the shortest displacement distance and the greatest atomic density.

In that direction, the force required to move a dislocation is the least, because the force F is a function of the product of the shear modules G and the square of the Burgers vector b:

F =  f(G,b2)    …(iii)

— Slip originates at a definite point, where a dislocation, (i.e., imper­fection or defect in a crystal) exists and proceeds by movement of the dislocation in the given plane of the crystal due to shear stresses. A dislocation results in a surface step or slip band.

— It has been proved that in real single (metal) crystals, slip starts under a shear stress, at least two orders of magnitude lower than the values of 1.5 E (Modulus of Elasticity) calculated for a perfect crystal.

— The dislocation theory is the only one which explains from a single point of view the slip phenomenon and the various experi­mental facts about strength (referred above) and work hardening. The basic ideas are that local slipping takes place, starting at points of high stress concentration and being helped by thermal fluctuations of the atoms.

— The mechanism of slip involves a translatory motion along the sliding planes and rotation of the specimen with respect to the axis of loading (Fig. 54.12).

Thus the angle between the axis of the tensile force and the slip planes changes during stretching of the specimen. The more slip takes place, the more acute are the angles of slip planes.