MSE 2001 Chapter 5: Linear, Planar, and Volume Defects

Vocabulary-style flashcards covering linear, planar, and volume defects, including dislocations, slip systems, and strengthening mechanisms in metals.

Slip System

Characterized by a slip plane normal, a slip direction, and a slip vector (a lattice vector in the slip direction).

Slip Planes

The most densely packed lattice planes in a crystal structure.

Slip Directions

The most densely packed lattice directions in a crystal structure.

Resolved Shear Stress ($\tau_R$)

The driving force for slip resulting from tensile stress, calculated as $\tau_R = \sigma \cos(\phi) \cos(\theta)$, where $\phi$ is the angle between force and the normal to the sheared plane, and $\theta$ is the angle between force and the slip direction.

Critical Resolved Shear Stress ($\tau_{cr}$)

The specific value of resolved shear stress at which plastic deformation occurs within a crystal.

Edge Dislocation

A linear defect characterized by an extra row of atoms where the dislocation line is perpendicular to the Burgers vector.

Screw Dislocation

A linear defect where the dislocation line is parallel to the Burgers vector and the lattice is distorted in a spiral manner.

Mixed Dislocation

A curved dislocation line that contains both edge and screw components on mutually perpendicular surfaces.

Burgers Vector ($b$)

A vector representing the mismatch of one lattice vector remaining when a closed circuit is made around a dislocation.

Dislocation Glide

The process by which a dislocation moves through a crystal lattice under applied shear stress.

Dislocation Climb

A motion perpendicular to the glide plane that occurs only if matter is added or removed, typically via vacancy diffusion.

Climb Velocity ($v_c$)

The rate of dislocation climb, proportional to the self-diffusion rate and expressed as $v_c \propto \sigma^N \exp\left(-\frac{E_{SD}}{kT}\right)$.

Dislocation Density

The total length of dislocation lines per unit volume, measured in units of $m^{-2}$.

Flow Stress

The stress required to cause plastic deformation or maintain dislocation motion, which increases as the amount of defects increases.

Solute Drag

A strengthening phenomenon where dislocations become trapped at the core of solute atoms (such as $C$ in $Fe$), making them difficult to move.

Intrinsic Stacking Fault

A planar defect in a lattice (such as FCC) where the normal stacking sequence of planes is interrupted.

Tilt Boundary

A low-angle grain boundary formed by an ordered arrangement of edge dislocations.

Twist Boundary

A low-angle grain boundary formed by screw dislocations.

Twin Boundary

A planar defect where the crystal structure is reflected across a mirror plane, creating a matrix and twin region.

Frank-Read Source

A mechanism responsible for dislocation multiplication during plastic deformation.

Hall-Petch Equation

An equation relating yield strength to grain diameter: $\sigma_0 = \sigma_s + B D_g^{-1/2}$, where $\sigma_0$ is the yield strength of polycrystalline material and $D_g$ is the grain diameter.

Strain Hardening (Work Hardening)

A strengthening mechanism resulting from the interaction and accumulation of dislocations, where flow stress is given by $\tau_{flow} = \tau_i + k \sqrt{\rho_{dis}}$.

Precipitation Hardening

A strengthening mechanism where the interaction of dislocations with second-phase particles or precipitates hinders their motion.

Total Shear Strength ($\tau_y$)

The combined strength of a material calculated as $\tau_y = \tau_i + \tau_{ss} + \tau_o + \tau_{wh} + \tau_{gr}$, representing intrinsic, solid solution, obstacle, work hardening, and grain boundary contributions.