Plastic Deformation: Basics You Should Know

1. Basic concepts

1. Plastic deformation mode of single crystal at room temperature or low temperature:

  • Slip
  • Twining
  • Link

Diffusive deformation and grain boundary sliding and moving are mainly seen in high-temperature deformation (creep).

2. Stress strain curve

(1) Stretch Curve

Plastic Deformation: Basics You Should Know 1

(2) Compression curve

Plastic Deformation: Basics You Should Know 2

2. Plastic deformation of single crystal

1. Slip

Under the action of shear stress, a part of the crystal moves relative to another part along a certain crystal plane (slip plane) and a certain crystal direction (slip direction).

Plastic Deformation: Basics You Should Know 3

(1) Slip characteristics:

1. The lattice type of crystal remains unchanged after sliding;

2. The orientation of each part in the crystal remains unchanged;

3. The slip amount is an integral multiple of the atomic spacing in the slip direction;

4. After sliding, a series of steps appear on the crystal surface.

Plastic Deformation: Basics You Should Know 4
Plastic Deformation: Basics You Should Know 5

Schematic diagram of slip band formation

The crystal plane where slip occurs is called slip plane, which is usually the most closely arranged crystal plane of the crystal;

The direction of sliding is called slip direction, which is also the most densely arranged direction of crystals;

A slip plane and a slip direction on the plane form a slip system. It can be represented by {hkl}.

(2) Common metal slip system

Crystal structure


Slip plane

Slip direction


Al, Cu, Ag, Au, Ni





{110}, {112}, {123}


Mo, W((at 0.08-0.24Tm)









crystal structure


slip plane

slip direction















The slip plane and slip direction are usually the crystal plane and crystal direction with the most closely arranged atoms in the metal crystal.

This is because the crystal plane with the largest atomic density has the largest crystal plane spacing and the smallest lattice resistance, so it is easy to slip along these planes;

As for the direction with the maximum atomic density in the slip direction, the atomic spacing in the most closely packed direction is the shortest, that is, the dislocation b is the smallest.

Each slip system represents a spatial orientation that the crystal may take when sliding.

When other conditions are the same, the more slip systems in the crystal, the more spatial orientations that can be taken during the sliding process, the easier the sliding will be, and the better its plasticity will be.

(3) Critical shear stress of slip

Slip can only occur when the shear stress along the slip direction on the slip surface reaches a certain value.

The minimum shearing stress that can cause slip is called the critical shearing stress, which is expressed by τc.

Plastic Deformation: Basics You Should Know 6

Suppose that there is only one group of slip planes in the single crystal, the cross-sectional area of the sample is A, the axial tension is F, the angle between the normal line N and F of the slip plane is φ, the angle between the slip direction and F is λ, and the area of the slip plane is:

Plastic Deformation: Basics You Should Know 7

The tangential component of the external force on the slip surface along the slip direction is:

Plastic Deformation: Basics You Should Know 8

Shear stress of external force in slip direction:

Plastic Deformation: Basics You Should Know 9
Plastic Deformation: Basics You Should Know 10

When the shear stress in the slip system reaches its critical value and starts to slip, σ=σS, at this time τ=τc, so τc=σScosλcosφ.

cosλcosφ is called the orientation factor or Schmidt factor.

Schmidt’s law: the minimum shearing stress required for the sliding system to start is a constant independent of the external force orientation.

Uniaxial tension: when the external force is parallel (φ=90 °) or vertical to the slip plane( λ= At 90 °), the orientation factor is the smallest, σS is infinite, and slip is impossible.

At this time, the orientation is called hard orientation;

When the slip direction is in the plane composed of the external force and the normal of the slip plane, and φ=45 °, the orientation factor is the largest, σS is the smallest, and it is easy to slip. At this time, the orientation is called soft orientation.

(4) Rotation of crystal plane during sliding

When a single crystal slips, in addition to the relative displacement of the slip plane, the rotation of the crystal plane is also accompanied.

The originally deformed slip is the form b in the following figure.

Due to the limitation of the collet, it is impossible to move in the wrong way, which causes the rotation as shown in Fig. c.

Plastic Deformation: Basics You Should Know 11

When stretching, the crystal rotation force makes the slip system turn to the direction parallel to the force axis;

Plastic Deformation: Basics You Should Know 12

In compression, the rotational force of the crystal seeks to turn the slip system to the direction perpendicular to the force axis.

Because of the rotation of the crystal, the crystal plane that is conducive to sliding becomes the crystal plane that is not conducive to sliding after sliding to a certain extent;

However, the crystal plane that is not conducive to slip may turn to the direction that is conducive to slip and participate in slip.

Therefore, slip can be alternately carried out on different slip systems, resulting in uniform deformation of the crystal.

Plastic Deformation: Basics You Should Know 13

(5) Multi system slip: the slip of crystals occurs simultaneously or alternatively on two or more sets of slip planes, resulting in multi system slip.

Cross slip: The slip of a crystal along a common slip direction on two or more different slip planes.

Cross slip of screw dislocation: the process of screw dislocation transferring from one slip plane to another slip plane intersecting with it;

Double cross slip of screw dislocation: the process of screw dislocation turning back to the original slip surface after cross slip.

Slip surface traces:

Plastic Deformation: Basics You Should Know 14

a. Single slip: single direction slip band;

b. Multiple slip: cross slip bands;

c. Cross slip: Corrugated slip band.

(6) Dislocation mechanism of slip

Crystal sliding is not a rigid overall displacement of one part of the crystal relative to the other along the slip plane, but a gradual movement of dislocations on the slip plane.

When moving to the outer surface of the crystal, the crystal has a displacement of b along its slip plane.

① Crystal slip is carried out step by step by means of dislocation movement on the slip plane.

② The dislocation motion must first overcome the (P – N) force.

③ The dislocation motion also needs to overcome the interaction between dislocations, the pinning effect of cutting steps and twists on dislocations, and the air mass pinning of point defects.

2. Twins

Under the action of shear stress, a part of the crystal takes a certain crystal plane (twin plane) as the symmetry plane and a certain crystal direction (twin direction) to shear with another part.

Plastic Deformation: Basics You Should Know 15

Complete crystal twinning

(1) Characteristics of twins:

① The lattice type remains unchanged, but the crystal orientation changes, showing mirror symmetry;

② Twinning is a kind of uniform shear.

The displacement of each atomic plane is proportional to the distance between the atomic plane and the twin plane.

The relative displacement of its adjacent atomic planes is equal and less than one atomic spacing, that is, the shear variable at twinning is a fraction of the atomic spacing;

③ Twinning occurs under the action of shear stress, and usually occurs in the stress concentration zone caused by the blocked slip.

Therefore, the critical shear stress required by twinning is much larger than that during slip.

(2) Formation of twins

There are three main ways to form twins in crystals: one is through mechanical deformation, also known as deformation twins or mechanical twins. Its characteristics are usually lenticular or flaky;

The second is growth twins, which include twins formed in the gas state (such as vapor deposition), liquid state (liquid solidification) or solid for a long time;

The third is the twin formed in the recrystallization annealing of deformed metals, also known as annealing twin, which often crosses the whole grain with twin planes parallel to each other as the boundary, and is formed by the growth of stacking faults during recrystallization.

In fact, it should also belong to the growth twin, which is formed in the process of growing from the solid.

The growth of deformed twins can also be divided into two stages: nucleation and growth.

During crystal deformation, thin twinning, often called nucleation, first erupts at an extremely fast speed, and then widens the twin by expanding the twin boundary.

(3) The closely packed hexagonal metals with low symmetry and few slip systems, such as Cd, Zn, Mg, are prone to twinning deformation.

The main deformation mechanism of bcc structure metals and fcc structure metals with high fault energy, such as Cu(gSEF~80mJ×m-2) and Al(gSEF~170mJ×m-2), is slip.

Twinning may occur at low deformation temperature or high deformation rate.

Fcc metals and alloys with low stacking fault energy (gSEF~20mJm-2), such as silver, brass and austenitic stainless steel, are prone to twinning during deformation.

(4) The difference between slip and twinning:





1. Uniform section;

2. Along a certain crystal plane and crystal direction;

3. Do not change the structure.


Crystal orientation

No change (no reproducibility when observing the polished surface)

Change, and forming mirror symmetry (reproducible observation of polished surface)


Integer times of the atomic spacing in the slip direction; more

Less than the atomic spacing in the twin direction; less

Contribute to shaping

Very large; The total deformation is large.

Limited; The total deformation is small.

Racking stress

There is a certain critical shearing stress.

The critical shear stress required is much higher than the slip.

Deformation conditions

Generally, slip occurs first.

It occurs when sliding is difficult.

Deformation mechanism

Full dislocation motion results

Results of dislocation movement

(5) Link

For places where neither sliding nor twinning can be carried out, in order to adapt the shape of the crystal to the external force, when the external force exceeds a certain critical value, the crystal will have local bending, which is called kinking, as shown in Fig. 5.20.

Torsion is a kind of compatible deformation, which can cause stress relaxation and prevent crystal from fracture.

After kinking, the crystal orientation is no longer the same as the original orientation, which may make the slip system in this area in a favorable orientation and slip occurs.

Plastic Deformation: Basics You Should Know 16

Leave a Comment

Your email address will not be published. Required fields are marked *