Lab Course on Deformation and Fracture – Bauschinger Effect - Appendix

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Appendix: Overview over (some) hardening mechanisms 1. Imperfections in crystals Crystals are seldom perfect; typical imperfections are these:

Vacancies (a) and (b) foreign (solute) atoms (b) are point-defects (0-D). Dislocations (c) are 1-D (delimiting line of an extra half-plane of atoms). Grain boundaries (d) are 2-D.

Vacancies

(a)

Substitutionalsolute

Interstitialsolute

(b)

Dislocation Extra half-plane

Slipplane

(c)

Grain boundary

(d)

Lab Course on Deformation and Fracture – Bauschinger Effect - Appendix

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2. Dislocations Dislocations are defined by their Burgers vector b, which describes the closing error of the Burgers circuit: - if the Burgers vector is normal to the dislocation line: edge dislocation; - if the Burgers vector is parallel to the dislocation line: screw dislocation. In general, dislocations are of mixed character (curved).

S

S

Screw dislocation

line

Slipped area

Slip vector b

Slip plane

Extra half-plane

Edgedislocation

line

Slipped area

bSlip vector

(a)

Slip plane

Extra half-planeb

Slip vector

(b)

Slip plane

Lab Course on Deformation and Fracture – Bauschinger Effect - Appendix

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3. Movement of dislocations Dislocations are the predominant carriers of plastic deformation. This is because the movement of a dislocation requires the breaking of atomic bonds only along one single line (at a given time) instead of along an entire plane! Therefore plastic slip can operate at stresses far below the theoretical strength of the material!

Plastic slip operates by shear.

(a)

(b) (c) (d)

(e)

τ τ τ

b b

γ

Lab Course on Deformation and Fracture – Bauschinger Effect - Appendix

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4. Obstacles to dislocation motion Hardening of a metallic material is typically achieved by blocking the movement of dislocations, i.e. by introducing obstacles that will slow down or impede the movement of dislocations.

Such obstacles can be - solute atoms (foreign atoms that provide solution hardening); - hard particles (introduced by dispersion or—more often—by precipitation); - other dislocations (introduced by cold work); - and others (such as grain boundaries).

Example: Cu alloys

(a) Perfect lattice, resistance fi (b) Solution hardening, resistance fss

Solute atoms

Precipitate particle

(c) Precipitate hardening, resistance fppt

Forest dislocation(with slip step)

(d) Work hardening, resistance fwh

1 10 10020

50

100

200

500

1000

2000

Yield

stren

gth σ

y, ten

sion (

MPa)

Elongation εf (%)

Pure, softcopper

Copper–beryllium alloys

Work hardening

Brass, work hardened

Brass, soft

Pure copper, work hardened

Solution hardening

Precipitation hardening

Lab Course on Deformation and Fracture – Bauschinger Effect - Appendix

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5. Precipitation hardening A quite elegant way to introduce particles acting as obstacles to dislocation motion inside a metallic material is via precipitation (otherwise it is quite difficult to achieve a fine and homogeneous distribution of small particles). The method necessitates a good solubility of alloy elements within the base metal at elevated temperature, and a significant decrease of solubility towards lower temperature (cf. precipitation of air humidity in the form of dew or frost during a cold night). In alloys, a fine precipitation is achieved by quenching the alloy from elevated temperature (which leaves the solute atoms in supersaturated solution within the alloy), and by tempering at some intermediate temperature (where the diffusivity is high enough such that atoms diffuse and form precipitates). Also required is, of course, a good mechanical resistance of these precipitates.

Tem

pera

ture

, T

Time, t

TmSolid solutionregion

dt

dT

Cooling rate = dT/d t

Ts

Tm

TsTwo-phaseregion

Solutionize

Precipitation

Quench

Single- phasegrains

Two-phasegrains:

Precipitates+ matrix

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Lab Course on Deformation and Fracture – Bauschinger Effect - Appendix

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6. Some references M. F. Ashby, H. Shercliff, D. Cebon, Materials. Engineering, science, processing and design, Butterworth-Heinemann. W. D. Callister, Fundamentals of Materials Science and Engineering. An integrated approach, Wiley.