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, as well as grain boundary sliding and movement, are primarily observed in high-temperature deformations such as creep.

2. Stress strain curve

(1) Stretch Curve

(2) Compression curve

2. Plastic deformation of single crystal

1. Slip

When subjected to shear stress, a crystal undergoes movement along a specific crystal plane (known as a slip plane) and a specific crystal direction (known as a slip direction).

Slip characteristics:

• The lattice structure of the crystal remains unchanged during sliding.
• The orientation of each portion within the crystal remains unaltered.
• The amount of slip is a multiple of the atomic spacing in the slip direction.
• Following sliding, a series of steps become visible on the surface of the crystal.

Schematic diagram of slip band formation

The crystal plane where sliding occurs is known as the slip plane, and it is typically the most closely packed plane within the crystal.

The direction of movement during sliding is called the slip direction, which is also typically the most densely packed direction within the crystal.

A slip plane and a slip direction together form a slip system, which can be represented by {hkl}.

(2) Common metal slip system

The slip plane and slip direction typically refer to the crystal plane and crystal direction with the most closely arranged atoms in the metal crystal.

This is because the crystal plane with the highest atomic density has the largest crystal plane spacing and the smallest lattice resistance, making it easier for the material to slip along these planes.

Similarly, the direction with the highest atomic density in the slip direction has the shortest atomic spacing, resulting in the smallest dislocation b.

Each slip system represents a spatial orientation that the crystal may adopt while sliding.

Assuming other conditions remain constant, the greater the number of slip systems in the crystal, the more spatial orientations the material can take during the sliding process, resulting in better plasticity and easier sliding.

(3) Critical shear stress of slip

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

The minimum shearing stress required to cause slip is known as the critical shearing stress, which is denoted by τ_c.

Assuming there is only one group of slip planes in a single crystal, the sample has a cross-sectional area of A, an axial tension of F, the angle between the normal line N of the slip plane and F is φ, and the angle between the slip direction and F is λ. The area of the slip plane is given by:

The component of the external force that acts tangentially on the slip surface in the direction of slip is:

The shear stress of the external force in the direction of slip is:

When the shear stress in the slip system reaches its critical value and starts to slip, σ = σ_S. At this point, the corresponding value of τ is τ_c, where τc = σScosλcosφ. The term cosλcosφ is known as the orientation factor or Schmidt factor.

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

Under uniaxial tension, if the external force is parallel (φ=90°) or vertical to the slip plane (λ=90°), the orientation factor is the smallest, σ_S is infinite, and slip is impossible. This orientation is referred to as the hard orientation.

When the slip direction is in the plane formed by the external force and the normal of the slip plane, and φ=45°, the orientation factor is the largest, σ_S is the smallest, and it is easy to slip. This orientation is referred to as the soft orientation.

(4) Rotation of crystal plane during sliding

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

The initially deformed slip takes the form of ‘b’ in the following figure.

However, due to the limitations of the collet, it is impossible to move in the wrong way, which results in the rotation depicted in Fig. ‘c’.

During stretching, the rotational force of the crystal causes the slip system to turn in the direction parallel to the force axis.

During compression, the rotational force of the crystal attempts to turn the slip system perpendicular to the force axis.

Due to the crystal’s rotation, the plane that was initially favorable for sliding may become unfavorable after a certain extent of sliding.

However, the plane that was initially unfavorable for slipping may rotate towards a favorable direction and participate in the slip process.

As a result, slip can occur alternatively on different slip systems, leading to a uniform deformation of the crystal.

(5) Multisystem slip refers to the simultaneous or alternate slip of crystals on two or more sets of slip planes.

Cross-slip is a phenomenon where a crystal moves along a common direction on two or more distinct slip planes.

When a screw dislocation undergoes cross-slip, it transfers from one slip plane to another that intersects with it.

In the case of double cross-slip of a screw dislocation, the dislocation returns to its original slip surface after undergoing cross-slip.

Slip surface traces:

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

As the crystal moves toward its outer surface, it experiences a displacement of b along its slip plane.

① Crystal slipping occurs step-by-step through the movement of dislocations on the slip plane.

② The motion of dislocations must first overcome the (P-N) force.

③ Additionally, the motion of dislocations must overcome interactions between dislocations, the pinning effect of cutting steps and twists on dislocations, and the air mass pinning of point defects.

2. Twins

Under the influence of shear stress, a crystal can adopt a specific crystal plane (known as the twin plane) as its symmetry plane and a particular crystal direction (known as the twin direction) to shear with another part of the crystal.

Complete crystal twinning

(1) Characteristics of twins:

• The lattice type remains unchanged, but the crystal orientation changes, exhibiting mirror symmetry.
• Twinning is a type of uniform shear, where the displacement of each atomic plane is proportional to the distance between the atomic plane and the twin plane. The relative displacement of adjacent atomic planes is equal and less than one atomic spacing. In other words, the shear variable at twinning is a fraction of the atomic spacing.
• Twinning occurs under the influence of shear stress and typically happens in the stress concentration zone caused by blocked slip. Therefore, the critical shear stress required for twinning is significantly greater than that required during slip.

(2) Formation of twins

There are three main ways in which twins can form in crystals. The first way is through mechanical deformation, also known as deformation twins or mechanical twins. These twins are typically lenticular or flaky in shape.

The second way is through growth twins, which can occur in the gas state (such as during vapor deposition), liquid state (during liquid solidification), or in the solid state over a long period of time.

The third way is through twins formed during the recrystallization annealing of deformed metals, also known as annealing twins. These twins often cross the entire grain with twin planes parallel to each other, forming as a result of the growth of stacking faults during recrystallization.

In fact, annealing twins can also be considered a type of growth twin, as they form during the process of growing from a solid.

The growth of deformed twins can be divided into two stages: nucleation and growth. During crystal deformation, thin twinning – also known as nucleation – initially occurs at an extremely fast rate, 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（g_SEF~80mJ×m^-2） and Al（g_SEF~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 （g_SEF~20mJm^-2）, such as silver, brass and austenitic stainless steel, are prone to twinning during deformation.

(4) The difference between slip and twinning:

(5) Link

In situations where neither sliding nor twinning can be employed, crystals can adapt to external forces by undergoing local bending when the external force exceeds a certain critical value. This deformation is referred to as kinking, as shown in Figure 5.20.

Torsion is a type of deformation that is compatible with the crystal structure. It can induce stress relaxation and prevent the crystal from fracturing.

Following kinking, the crystal orientation is altered from its original orientation, which may create a favorable orientation for the slip system in that area, leading to the occurrence of slip.