Dislocation Mechanics, Strengthening and Heat Treatment of Metals
Dislocation Types and Partial Dislocations
1. Dislocation types
Partial dislocations — FCC
Frank’s rule → Combination: b1 + b2 → b3. Dissociation: b1 → b2 + b3.
Shockley partials → Energetically favorable when b1^2 + … (b^2 = a^2(u^2 + v^2 + w^2)).
They create stacking faults in FCC (ABCABC) which locally transform the stacking toward HCP (ABABAB).
Sessile dislocations →
- Immobile; Burgers vector b is not in the fault plane.
- Only move by diffusion (climb) and are unlikely to move at low temperature.
I) Frank sessile dislocation loop: collapse of a cavity on (111); other planes collapse to fit HCP locally.
II) Lomer–Cottrell barrier: intersecting extended dislocations; two Shockley partials that attract and intersect. Both act as strong obstacles to glide.
Glissile dislocations →
- Glide freely on the slip plane.
- Includes perfect dislocations and Shockley partials.
Forces between dislocations → Opposite sign on the same slip plane: attract (perfect crystal). Same sign on the same slip plane: repel.
Dislocation Mechanics and Interactions
Dislocation mechanics
Cross slip → A screw dislocation has the freedom to move onto a cross-slip plane. The plane contains the dislocation line and the Burgers vector.
Climb → An edge dislocation glides in its slip plane (line and b vector). By vacancy diffusion it can move to a parallel plane (climb).
Intersection → When dislocations intersect other dislocations producing sharp kinks or jogs in the line.
Kink: Happens in the dislocation line and remains in the slip plane.
Jog: Moves the dislocation out of the slip plane.
Critical intersection → Screw–screw interactions can produce jogs with edge character in both screws. The only way for the screw to bypass the jog is by climb; this is non-conservative and produces vacancies.
Other intersections → Jogs can move with the dislocation under the right conditions.
Frank–Read sources → Dislocation segments bow out, form loops, and generate continuous dislocation sources (spiraling/annihilating segments).
Pile-ups → Dislocations accumulate on slip planes against barriers, increasing local stress concentration.
Strengthening Mechanisms in Metals
2. Strengthening mechanisms
Plastic deformation mechanisms → Plastic deformation occurs by the movement of dislocations. Strength and toughness of metals are related to microstructure:
- Plastic deformation in single crystals is the movement of dislocations by slip and by twinning.
- Crystal structure determines the number and type of slip systems and Burgers vectors.
- Grains in polycrystals do not deform identically because of constraining effects from surrounding grains.
Strengthening mechanisms → Make dislocation motion more difficult. Main mechanisms include:
Grain boundary strengthening
I) Grain boundary strengthening →
- Grains with different orientations force dislocations to change direction.
- Orientation changes across grain boundaries create discontinuities in slip planes and impede dislocation motion.
Solid solution strengthening
II) Solid solution strengthening → Introducing solute atoms breaks lattice periodicity and creates stress/strain fields that interact with dislocations. Interaction mechanisms include elastic, modulus, long-range/short-range, stacking fault energy modification, and electrical effects.
Particle strengthening (precipitates and dispersions)
Fine particles → Small second-phase particles act as obstacles distributed in the matrix:
- Coherent particles — dislocations can cut particles at higher stress levels if particles remain coherent and not too hard.
- Incoherent particles — dislocations bypass by Orowan looping; dislocations move by sharp changes in line shape.
- Dispersion — typically incoherent; dislocations loop around particles.
- Precipitation — often coherent initially; interactions depend on coherence and particle hardness.
Strain hardening and cold working
Strain hardening → A ductile metal becomes harder and stronger as it is plastically deformed due to increased dislocation density and interactions.
Cold working → Dimensional reduction and plastic deformation increase dislocation density and produce strengthening. Cold work produces internal stress fields, sessile dislocations, and jogs.
Annealing
Annealing → Heat treatment to partially or fully restore properties after cold work:
- Recovery: Atomic diffusion relieves internal energy and recovers some physical properties (e.g., electrical resistivity may be reduced) without major grain changes.
- Recrystallization: Formation and growth of strain-free new grains; eliminates effects of strain hardening.
- Grain growth: At high temperature for long times, large grains grow at the expense of small grains (undesirable for strength).
Phase Transformations and Heat Treatment of Steels
3. Phase transformations and heat treatments
Heat treatments
- Tempering → Martensite (M) is often too brittle and has high internal stresses. Tempering reduces internal stress and hardness to achieve a softer, more ductile state.
- Martempering → Cool steel until just above the martensite start temperature (M_s), hold until temperature equalizes, then cool through M to form martensite, followed by tempering.
- Austempering → Cool rapidly to the bainite (B) region and hold isothermally to form bainite (aiming for a bainitic structure rather than martensite).
Austenitizing → Heat steel above A3 to transform ferrite/pearlite to austenite (gamma, γ). This process homogenizes carbon by diffusion as the new γ phase consumes previous phases and carbon diffuses more uniformly.
How: Heat to the desired austenitizing temperature to homogenize carbon and dissolve precipitates; the new γ grains nucleate and grow.
Objective: Control austenite grain size. Fine austenite grains are desirable for improved mechanical properties. Excessive temperature or long soak times cause grain growth (undesirable).
Hardness, Microstructure and Etching
Hardness and microstructure
Chemical etching reveals microstructure: for plain (unalloyed) steels one can observe phases such as pearlite (P), ferrite/alpha (α, grains), and martensite (M). For alloyed steels, martensite and other constituents will appear differently depending on alloying and etch conditions.
Common hardness tests:
- Rockwell — e.g., HRC (C scale) uses a diamond cone indenter for hard materials; ball indenters are used for softer materials/scales.
- Brinell — reported as HBW, typical format: load (kgf), indenter diameter (mm), dwell time (s). Example notation: 143 HBW, 10 mm diameter, 500 kgf load, 10 s dwell. Brinell can be damaging to very small or heterogeneous samples.
- Vickers — pyramidal indenter suitable for most materials; reported as HV with load indicated (e.g., 191 HV20 means 191 Vickers with a 20 kgf load).
Microscopy and Thermal Conductivity
Microscopy
Electron beam interactions with the sample:
- Backscattered electrons (BSE): Provide compositional/atomic number contrast (heavier elements appear brighter) and some topographic information.
- Secondary electrons (SE): Provide surface topography information (fine surface detail, edges and pits appear pronounced).
- Transmitted electrons (TEM): Transmit through thin samples to reveal internal structure and crystallography.
Detector signals: BSE tends to highlight regions with higher average atomic number (appear “mountainous” or bright); SE highlights surface features (edges, holes, fine topography).
Thermal conductivity: k = α * c_p * ρ, where α is thermal diffusivity, c_p is specific heat capacity, and ρ is density.
Tensile Testing and Impact (Charpy)
Tensile and impact behavior
Tension (tensile testing) and impact tests measure different aspects of mechanical response. Impact events generate stress waves; specimen displacement during dynamic loading depends on the characteristic period of the event.
Charpy impact → Measures energy absorbed during fracture. Low absorbed energy indicates brittleness (e.g., < 25 J can indicate brittle behavior under certain conditions); high absorbed energy indicates ductility.
Fracture surface appearance:
- Brittle fracture: smooth, shiny surface.
- Ductile fracture: presence of voids and dimples; surface appears matte and rough.
Tensile test parameters:
- Engineering strain: ε_eng = ΔL / L0.
- Engineering strain rate: dot{ε}_eng = (ΔL / L0) / Δt = v / L0.
- Given a target velocity v = dot{ε}_eng * L0. Example from notes: v = 1.8 mm/min (used as a test crosshead speed for a particular specimen and strain rate).
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