M5

• causes plastic deformation

  Motion of a large number of dislocations
• Plastic deformation

  1. An edge dislocation moves in response to shear stress applied perpendicular to its line.

  2. Bonds incrementally broken and reformed with adjacent atoms
• Metals

  • Dislocation motions are easier
  • Non-directional bonding
  • Closed-packed directions for slip
• Covalent ceramics (Si, diamond)


  • Dislocation motions are harder
  • Directional (angular) bonding
• Ionic ceramics (NaCl)

  • Dislocation motions are also harder
  • Uniform bonding around ions
• Slip plane


  Preferred plane for dislocation motion
• Slip direction


  Preferred direction for dislocation motion
• Slip system


  Combination of slip plane and slip direction
• Slip systems for various crystal structures

  • FCC: 12
  • BCC: 24
  • HCP: 3
• Metals with FCC or BCC crystal structures have a relatively large number of slip systems and are quite ductile
• HCP crystals have few slip systems and are normally quite brittle
• Resolved shear stress


  Shear stress components that depend on the orientation of the slip plane and direction within the plane
• Critical resolved shear stress


  Minimum shear stress required to initiate slip on the most favorably-oriented slip system
• Slip on single crystals

  1. Shear stress components exist at all but parallel or perpendicular alignments to the stress direction

  2. Magnitudes depend on applied stress and orientation of slip plane and direction
• Slip will occur on the slip system where the resolved shear stress first exceeds the critical resolved shear stress
• BCC iron single crystal

  • Tensile stress along [010] direction
  • Resolved shear stress on (110) plane in [111] direction is 21.3 MPa
  • Applied tensile stress to initiate yielding is 73.4 MPa
• Polycrystalline materials

  • Crystallographic directions and planes are discontinuous across grain boundaries
  • Resolved shear stress changes from grain to grain
  • Grain with greatest resolved shear stress yields first (the crystal most favorably-oriented with the applied stress direction).
• Dislocation in Polycrystalline Materials

  • Polycrystalline metals are stronger than single crystals because slip is constrained to individual grains
  • It cannot deform unless the adjacent and less favorably oriented grain is capable of slip also
• Strengthening mechanisms

  Restrict or hinder dislocation motion to increase hardness and strength
• Strengthening techniques

  • Grain-size reduction
  • Solid-solution alloying
  • Strain hardening
• Strengthening by grain size reduction


  Adjacent grains usually have different crystallographic orientations, and a common grain boundary.

  1.Grain boundaries act as barriers to dislocation motion

  2. Slip must change direction to cross grain boundaries

  3. The boundary acts as a discontinuity in the slip planes
• Hall-Petch equation

  The yield strength varies with the grain size. Smaller grains have a greater total grain boundary area to impede dislocation motion.
• High-angle grain boundaries are more effective in interfering with slip than small-angle grain boundaries
• Solid-solution strengthening

  • Impurity atoms added substitutionally or interstitially strengthen the lattice
  • Overlapping stress fields from impurities create barriers to dislocation motion
• Moving a dislocation past an impurity increases the strain energy. The impurity acts as a pinning point.
• High-purity metals are almost always softer and weaker than alloys composed of the same base metal
• Solid-solution strengthening

  Impurity atoms are added substitutionally or interstitially to strengthen the lattice
• An extra half plane acts like a wedge


  Compressive stress (green) and tensile stress (red)
• A small substitutional atom

  Exerts tensile stress on the surrounding atoms
• A large substitutional atom

  Exerts compressive stress on the surrounding atoms
• Overlapping stress fields


  Produce a barrier to dislocation motion
• Moving a dislocation past an impurity

  Increases the strain energy
• The impurity


  Acts as a pinning point
• A large substitutional atom

  Exerts compressive stress on the edge dislocation
• The tensile stress


  Cancels the compressive stress
• Strain hardening

  Achieved by deforming the metal through working (work hardening)
• Cold working


  The temperature at which metals are worked is "cold" relative to its melting temperature
• Influence of cold work on stress-strain behaviour for a low-carbon steel

  Yield strength, tensile strength, and ductility versus percent cold work for steel, brass, and copper
• As the material is worked

  • More dislocations appear, dislocation density increases
  • The average distance separation between dislocations decreases
  • The dislocations exert repulsive forces upon each other, hindering its movement
• The net effect of dislocation increase and decreased separation

  Enhanced hardness and strength, at the expense of being more brittle