Slip is the primary mechanism of plastic deformation in metals — the process by which dislocations move through the crystal lattice along specific slip planes in specific slip directions, producing permanent shape change without fracture. A slip system is a combination of one slip plane and one slip direction within it. The number, geometry, and energy of available slip systems directly determines a metal’s ductility, formability, and susceptibility to fracture — making slip system analysis fundamental to understanding all aspects of metallic mechanical behaviour.
KEY TAKEAWAYS
- FCC metals have 12 slip systems {111}⟨110⟩ on 4 close-packed planes — maximum number for cubic metals, giving excellent polycrystalline ductility.
- BCC metals have up to 48 possible slip systems but lack a true close-packed plane — pencil glide occurs on whichever plane is most stressed, giving temperature-sensitive ductility.
- HCP metals have only 3 easy basal slip systems {0001}⟨11̄20⟩ — insufficient for general polycrystalline deformation without non-basal slip.
- The Von Mises criterion: 5 independent slip systems required for homogeneous plastic deformation of polycrystals. FCC satisfies easily; pure HCP does not.
- Schmid’s Law: the slip system with the highest resolved shear stress activates first. Schmid factor m = cos(φ)·cos(λ); maximum m = 0.5 at 45° orientation.
- Stacking fault energy (SFE) controls whether cross-slip is possible: high SFE (Al) = easy cross-slip; low SFE (Cu, austenitic SS) = wide stacking faults, no cross-slip, high work hardening.
📷 IMAGE: FCC Slip System: {111} Slip Plane with ⟨110⟩ Directions
Illustration of an FCC slip system showing one {111} octahedral plane (shaded) with three ⟨110⟩ slip directions marked as arrows. Four such planes, each with three directions, give 12 independent slip systems in FCC metals — satisfying the Von Mises criterion for polycrystalline ductility.
Search terms: FCC slip system 111 plane 110 direction octahedral slip metallurgy diagram
Source:
https://en.wikipedia.org/wiki/Slip_(materials_science)
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Slip System Summary by Crystal Structure
| Structure | Slip Plane | Slip Direction | No. of Systems | Key Metals | Ductility |
|---|---|---|---|---|---|
| FCC | {111} — 4 planes | ⟨110⟩ — 3 per plane | 12 | γ-Fe, Al, Cu, Ni, Au | Excellent — no DBTT |
| BCC (primary) | {110} — 6 planes | ⟨111⟩ — 2 per plane | 12 | α-Fe, W, Mo, Cr | Good above DBTT; poor below |
| BCC (all planes) | {110}+{112}+{123} | ⟨111⟩ | Up to 48 | α-Fe at high T | Pencil glide on best-stressed plane |
| HCP (basal) | {0001} — 1 plane | ⟨11̄20⟩ — 3 | 3 | Mg, Zn (easy basal) | Poor — only 3 independent |
| HCP (prismatic) | {101̄0} — 3 planes | ⟨11̄20⟩ — 1 | 3 | Ti (important) | Enables ductility in Ti |
| HCP (pyramidal) | {101̄1} — 6 planes | ⟨11̄2̄3⟩ | 6 | Ti (⟨c+a⟩ slip) | Satisfies Von Mises |
Schmid’s Law — The Resolved Shear Stress
τ_RSS = σ × cos(φ) × cos(λ) = σ × m
where:
σ = applied tensile stress (MPa)
φ = angle between tensile axis and slip PLANE NORMAL
λ = angle between tensile axis and slip DIRECTION
m = Schmid factor = cos(φ)×cos(λ) [range: 0 to 0.5]
The slip system with highest m activates FIRST.
Yield occurs when: τ_RSS = τ_CRSS
∴ σ_y = τ_CRSS / m_max
Maximum m = 0.5 when φ = λ = 45° → lowest yield stress
Minimum m = 0 when φ or λ = 90° → no resolved shear stress → no slip possible
Why FCC Metals are More Ductile Than BCC and HCP
Three factors make FCC systematically more ductile:
- Close-packed 111 planes: FCC 111 planes have the highest possible atom density — widest interplanar spacing, weakest cross-plane bonding, lowest Peierls-Nabarro resistance to dislocation motion. Slip initiation is easy and consistent at all temperatures.
- 12 independent slip systems: Satisfies the Von Mises criterion (5 independent) with large margin. Any grain in a polycrystal can accommodate deformation in any direction. No geometrical constraint fracture.
- No ductile-to-brittle transition: FCC dislocation cores are wide (spread-out on the close-packed plane due to low stacking fault energy relative to BCC). The Peierls barrier is temperature-insensitive, so FCC metals remain ductile to cryogenic temperatures.
The consequence for engineering: FCC austenitic stainless steels (304, 316) and FCC aluminium alloys are specified for cryogenic service (LNG, liquid nitrogen, liquid helium) precisely because they have no DBTT. BCC ferritic stainless steels (430) and BCC carbon steels become brittle below their DBTT — which can be −50°C to +20°C for conventional structural grades.
Critical Resolved Shear Stress (CRSS) for Common Metals
| Metal | Crystal Structure | CRSS (MPa) | Notes |
|---|---|---|---|
| Pure iron (α-Fe) | BCC | ~50–150 (T-dependent) | Strong T-dependence below DBTT |
| Aluminium | FCC | ~0.5–1.0 | Very easy to deform — lowest CRSS |
| Copper | FCC | ~0.6–1.5 | Low CRSS but high work hardening rate (low SFE) |
| Nickel | FCC | ~6–12 | Higher than Al/Cu due to atomic size |
| Magnesium | HCP (basal) | ~0.5–1.0 | Easy basal slip but limited systems → premature fracture |
| Titanium (α) | HCP (prismatic) | ~50–100 | Prismatic slip essential; higher CRSS than basal |
| Zinc | HCP (basal) | ~0.2 | Strongly basal; very anisotropic |
📷 IMAGE: Comparison of Slip in BCC and FCC: Pencil Glide vs Octahedral Slip
Comparison of slip character in BCC and FCC metals. BCC metals exhibit pencil glide — dislocations can glide on any plane containing the [111] direction, choosing the most-stressed plane. FCC metals show well-defined octahedral slip confined to {111} planes. The difference explains why BCC metals show pencil-shaped slip traces in polished surface observations.
Search terms: BCC pencil glide slip FCC octahedral slip comparison ductility
Source:
https://en.wikipedia.org/wiki/Slip_(materials_science)#BCC_metals
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Frequently Asked Questions
Q: What determines which slip system activates first in a crystal?
A: The Schmid factor m = cos(φ)cos(λ) determines the resolved shear stress on each slip system for a given applied stress direction. The system with the highest Schmid factor (closest to m = 0.5) activates first — it requires the lowest applied stress to reach the CRSS. In a single crystal tensile test, the initial yield point is determined by a single slip system (the primary system). As the crystal rotates during deformation, other systems may reach their CRSS (multiple slip), leading to the onset of rapid work hardening. In polycrystals, multiple slip systems operate simultaneously in each grain from the beginning of plastic deformation.
Q: Why does stacking fault energy affect work hardening rate?
A: In FCC metals, extended dislocations consist of two partial dislocations separated by a stacking fault ribbon. The width of this ribbon is inversely proportional to the stacking fault energy (SFE). High SFE metals (Al: 140 mJ/m²) have narrow ribbons — partials easily recombine, enabling cross-slip and dislocation annihilation. These metals work-harden slowly and recovery occurs readily. Low SFE metals (Cu: 45 mJ/m²; austenitic SS: 15–50 mJ/m²) have wide ribbons — cross-slip is inhibited, dislocations accumulate in tangles and cell walls, and work-hardening is rapid. This is why copper and austenitic stainless steel achieve much higher ultimate-to-yield strength ratios than aluminium.
Q: How does texture affect yield strength in polycrystalline metals?
A: In a textured polycrystal (preferred crystallographic orientation), the average Schmid factor ⟨m⟩ across all grains is not random (random ≈ 0.32 = Taylor factor 3.06). A texture with grains oriented for hard slip (low m) — such as the {111}⟨110⟩ gamma fibre in deep-drawn BCC steel — gives higher yield strength in the thickness direction and better formability in the in-plane directions. The Taylor factor M (typically 2.5–3.5 for polycrystals, related to 1/⟨m⟩) converts the single-crystal CRSS to the polycrystal yield strength: σ_y = M × τ_CRSS. Texture control through cold rolling and annealing is how manufacturers achieve directional properties in sheet metals for automotive and packaging applications.
References
- Dieter, G.E., Mechanical Metallurgy. 3rd ed. McGraw-Hill, 1986.
- Hull, D. and Bacon, D.J., Introduction to Dislocations. 5th ed. Butterworth-Heinemann, 2011.
- Hosford, W.F., Mechanical Behavior of Materials. 2nd ed. Cambridge University Press, 2010.
Related: BCC FCC HCP Crystal Structures · Dislocations in Metals · Miller Indices
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