Dislocations, Slip, Texture, and Twinning — Study Materials Flashcards

Front

Dislocation

Back

A line defect in a crystal that separates slipped from unslipped regions on a plane. Dislocations enable plastic deformation at much lower stresses than ideal shear and are characterized by a Burgers vector $b$ and line direction $\xi$.

Front

Burgers vector

Back

A vector that quantifies the magnitude and direction of lattice distortion produced by a dislocation. It equals the closure failure of a loop taken around the dislocation and determines slip magnitude on a slip system.

Front

Peierls stress

Back

The critical resolved shear stress required to move a dislocation in a perfect crystal lattice. It depends strongly on core width, bond strength, temperature, and strain rate; higher for ceramics and covalent solids than for metals.

Front

Stacking fault energy

Back

Energy per unit area associated with a disruption in the normal stacking sequence of close-packed planes, denoted $\gamma_{sf}$. It controls partial dislocation separation, cross-slip ease, and influences work hardening.

Front

Ideal shear strength

Back

A theoretical shear stress required to shear an entire crystal plane simultaneously (no dislocations). It is on the order of $\tau_{theor}\sim \mu/2\pi$ and is much larger than observed yield strengths because real crystals contain dislocations.

Front

Frank–Read source

Back

A mechanism by which a pinned dislocation segment bows out under applied shear and generates a dislocation loop, multiplying dislocations. The critical stress to operate a source scales inversely with pin spacing $\ell$.

Front

Cross-slip

Back

A process where a screw dislocation changes its glide plane to bypass obstacles. Cross-slip is easier when stacking fault energy $\gamma_{sf}$ is large (smaller separation between partials) and at higher temperatures.

Front

Climb

Back

A dislocation motion mechanism where an edge dislocation moves out of its glide plane by absorbing or emitting vacancies. Climb is diffusion-controlled, favored at high temperature and enables bypass of obstacles that block glide.

Front

Partial dislocation

Back

A dislocation whose Burgers vector is a fraction of a full lattice translation; in FCC materials full dislocation $b_1$ can dissociate into partials $b_2$ and $b_3$ separated by a stacking fault. Partials influence cross-slip and stacking fault width.

Front

Stacking fault width

Back

The equilibrium separation $w_{sf}$ between partial dislocations; approximately $w_{sf}=\frac{\mu b_2 b_3}{2\pi\gamma_{sf}}$. A larger $\gamma_{sf}$ gives smaller $w_{sf}$ and promotes cross-slip.

Front

Schmid factor

Back

A geometric factor $S=\cos\lambda\cos\phi$ that relates applied tensile stress to resolved shear stress on a slip system. It predicts which slip system is most likely to activate under a given crystal orientation and load.

Front

Slip systems (FCC)

Back

In FCC crystals the dominant slip systems are {111} slip planes with $\langle110\rangle$ directions, giving 12 independent slip systems. These dense-packed planes and directions facilitate ductility in FCC metals.

Front

Slip systems (BCC/HCP)

Back

BCC commonly uses {110}/$\langle111\rangle$ (and {112}/{123} variants) while HCP favors basal {0001} and prism systems depending on $c/a$. HCP often lacks five independent slip systems, limiting polycrystal ductility.

Front

Texture

Back

A non-random distribution of crystallographic orientations in a polycrystalline material, quantified by pole figures. Texture affects anisotropic mechanical behavior such as sheet thinning and R-value in forming.

Front

Pole figure

Back

A stereographic map that shows the distribution of particular crystallographic directions or planes relative to sample coordinates. Pole figures are derived from diffraction and quantify texture strength and symmetry.

Front

Twinning

Back

A deformation mechanism where a region of the crystal is sheared to produce a mirror-image orientation across a twin plane. Twinning can accommodate strain when slip systems are insufficient and often produces serrated stress-strain behavior.

Front

R-value

Back

A measure of plastic anisotropy in sheet metal defined from strain components during uniaxial stretching; larger R-values indicate better resistance to thinning and improved formability in deep drawing.

Front

Dislocation density

Back

Total dislocation line length per unit volume, often denoted $\rho_{disl}$. Higher dislocation density increases strength via work hardening because dislocations impede each other.

Front

Obstacle types

Back

Features that impede dislocation motion include other dislocations, solute atoms, vacancies, grain boundaries, and precipitates. The dominant obstacles determine work hardening rate and mechanisms like pile-up, pinning, and Orowan looping.

Front

Temperature effects

Back

Increasing temperature generally lowers Peierls stress and increases dislocation mobility by thermal activation; conversely lowering temperature raises yield stress and may promote brittle behavior in some materials.