Strengthening mechanisms in
aluminium alloys
1.
2.
3.
4.
5.
6.
Solid solution strengthening
Precipitation hardening (age hardening)
Precipitation strengthening
Grain size effect
Transition metals addition (dispersoids, Zener Drag)
Work hardening
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
1. Solid solution strengthening
MSc Eng Honorata Kazimierczak
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Solid solution strengthening
→ type of alloying that can be used to improve the strength of a pure metal.
The technique works by adding atoms of one element (the alloying element)
to the crystalline lattice of another element (the base metal).
Strategy for strengthening:
→ Make dislocations hard to move
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Solid solution strengthening
→ Impurity atoms generate stress by distorting the lattice
→ This stress can produce a barrier to dislocation motion
smaller substitutional impurity
larger substitutional impurity
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Solid solution strengthening mechanism in aluminium alloys
→ Alloy elements, such as Mg, Mn and Cu can 'pin' dislocations,
thereby strengthening the material.
→Solute atoms are barrier for dislocation
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Solid solution strengthening mechanism in aluminium alloys
→ Alloy elements, such as Mg, Mn and Cu can 'pin' dislocations,
thereby strengthening the material.
→Solute atoms are barrier for dislocation
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Solid solution strengthening mechanism in aluminium alloys
→ Alloy elements, such as Mg, Mn and Cu can 'pin' dislocations,
thereby strengthening the material.
→Solute atoms are barrier for dislocation
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Solid solution strengthening mechanism in aluminium alloys
→ Alloy elements, such as Mg, Mn and Cu can 'pin' dislocations,
thereby strengthening the material.
→Solute atoms are barrier for dislocation
For successful strengthening, alloy additions must satisfy 2 criteria:
→high solid solubility;
→atomic misfit to create local compressive or tensile strains.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Magnesium is most likely to be used as a solid solution
strengthener because:
→ the atomic misfit of Mg is quite high at 13%
→ it also has a high solid solubility in Al.
→ The principal alloys that are strengthened by
alloying elements in solid solution are those
in the aluminium-magnesium (5xxx) series,
ranging from 0,5 to 6 wt% Mg.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Potency of alloying Elements
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Potency of alloying Elements
Three final points are worthy of note:
• In addition to atomic misfit and solubility, other factors, such as
electronegativity can also affect the overall effectiveness of alloying elements
on solution hardening.
• As a strengthening mechanism, solid solution strengthening is effective at all
temperatures - indeed the solubility increases with temperature. This means
that alloys such as 5xxx (Al-Mg) are more difficult to process at higher
temperatures.
• The degree of solid solution strengthening is NOT dependent on process
history, simply on composition. This is not true of other hardening
mechanisms.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
2. Precipitation hardening
(age hardening)
MSc Eng Katarzyna Stan
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Aluminium
soft metal, insufficient strength for most engineering
applications
has to be strengthened
The strongest aluminium alloys
(2xxx, 6xxx and 7xxx)
are produced by precipitation (age) hardening.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Precipitation hardening – strengthening by precipitation of fine particles
of a second phase from a supersaturated solid solution. Another name for
this process is „Age Hardening” – because some metals form precipitates
at room temperature over time.
Saturated α
CuAl2
Room temperature microstructures in Al-4%Cu alloy.
Slow cooling
Age hardening
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Basic requirement: Alloy contains soluble alloying elements, but their solid
solubility decrease with decreasing temperature.
Precipitation Hardening Steps
600
α +L
α
T
400
α+β
200
A
Solution treatment at a relatively
high temperature within the single
phase region to dissolve the alloying
elements.
Rapid cooling or quenching (usually at
room temperature), to obtain a supersaturated solid solution (solid solution in
non-equilibrium state) of these elements
in aluminium
B%
Ageing - controlled decomposition of
the saturated solid solution to form
finely dispersed precipitate, usually
by ageing for convenient times at
one and sometimes two
intermediate temperatures.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Solution heat
treatment
single phase solid
solution
Ageing
Quench
supersaturated
solid solution
www.substech.com
TM
After
ageing
TF
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Precipitation Sequences
Guinier-Preston (GP) zones
Coherent with matrix, ordered, solute-rich clusters of atoms which often form on one
or more atomic planes – formation influenced by the presence of excess vacancies
retained in the matrix by quenching,
Depending on the system they are disc, rod or spherical shaped
Intermediate precipitate
Larger than a GP zone, only partly coherent with the matrix. Usually composition
and crystal structure differ only slightly from those of the equilibrium precipitate.
May be nucleated from, or at, the sites of stable GP zones. This phase nucleates
also heterogeneously at lattice defects such as dislocations.
Equilibrium precipitate
Formation of the equilibrium precipitate involves complete loss of coherency with
the parent lattice. It forms only at relatively high ageing temperatures and because it
is coarsely dispersed, little hardening results.
Maximum hardening normally occurs when there is present a critical
dispersion of GP zones, or an intermediate precipitate, or a
combination of both.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Precipitation Sequences
http://www.eaa.net/eaa/education/TALAT
TEM micrographs of an Al-4wt%Cu alloy after increasing heat treatment
times, showing (a) GP zones, (b) GP zones and Θ’ precipitates and (c) Θ’ and
Θ precipitates
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Ageing time in hours
‘Overageing’ – at a sufficiently elevated
temperature hardness usually
increases to a maximum and then
decreases
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
http://www.eaa.net/eaa/education/TALAT
Artificial ageing- because the diffusion
coefficient is strongly dependent on the
temperature, precipitation from
supersaturated solution is much faster at
elevated temperatures. Such process is
called artificial aging It takes usually a
time from several hours to one day
Hardness or strength
Natural ageing - the aging is conducted at
the room temperature and may continue
almost indefinitely, the rate of change
becomes extremely slow after months or
years
3. Precipitation strengthening
MSc Eng Piotr Bobrowski
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Mechanisms of precipitation strengthening
Precipitation strengthening results from inhibition of dislocation mobility
by interaction with internal strain zones and precipitates.
Mechanisms:
- coherent strain field
- chemical hardening
-dispersion hardening
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Coherency strain hardening
Interaction of internal strain fields caused by precipitates
and dislocation line.
Fine spacing
Ideal spacing
Coarse spacing
τ
t
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Chemical hardening
Increase in stress required to force
a dislocation movement through
a coherent precipitate
- increase in precipitate-matrix interfacial area
- creation of antiphase boundaries
- change in separation distance between
dislocations due to difference of stacking fault
energy
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Dispersion hardening
Dislocations can not cut through an incoherent precipitates and it has to by-pass it
Cross slip
Dislocation climbing
Dislocation bending
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Orowan effect
 Gb  1  D 
  2
  ln 
 4 1  v    r0 
Dislocation bending
v – Poissons ratio
G – shear modulus
b – Burgers vector
λ – interparticle spacing
D – particle planar diameter
r0 – dislocation radius
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
The ageing curve
Solute hardening
Coherency strain
Chemical hardening
Dispersion hardening
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
4. Grain size effect
MSc Eng Marta Gajewska
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Grain boundary effect
The grain boundary acts as a barrier to dislocation
motion for two reasons:
• dislocation passing into grain B will have to
change its direction of motion (more difficult as
the crystallographic misorientation increases)
• atomic disorder within a grain boundary region
will result in a discontinuity of slip planes from
one grain into the other
For high-angle grain boundaries dislocations tend to “pile up” (or back up) at grain boundaries rather than traverse grain
boundaries during deformation. These pile-ups introduce stress concentrations ahead of their slip planes, which generate new
dislocations in adjacent grains.
Fine-grained material has a greater total grain boundary area to impede dislocation motion
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Hall-Petch equation
σy = σ0 + kyd-1/2
d – is the average grain diameter
σ0 – intrinsic yield stress
ky – constant for a particular material
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Grain refinement advantages
The grain refinement offers:
• improved mechanical properties,
• consistent properties after heat treatment,
• uniform properties after extrusion,
• improved machinability,
• reduced chemical segregation and porosity,
• increased density.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Grain refinement methods
• During solidification of the molten metal:
- addition of trace elements
inoculation
- addition of borides, carbides, intermetallic compounds etc.
- use of ultrasonic treatment or electromagnetic field
-introduction of fine gas bubbles …
• During thermomechanical treatments involving recovery and recrystallization of the deformed
material
• During severe plastic deformation using processes such as equichannel angular processing (ECAP),
hydrostatic extrusion and roll bonding
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Grain refinement by inoculation
Inoculation is the addition of solid particles (or trace elements) – grain refiners - to
a metallic melt to act as nucleation catalysts for the formation of fine equiaxed,
rather than columnar, Al grains.
The requirements of an inoculant, so it could act as an effective nucleating site are:
• it should have a melting point higher than the alloy being solidified
• it should be able to initiate freezing at very small undercooling
• a sufficient number of nucleating particles should be uniformly distributed
• nucleating particles should be larger than a critical size, which depends on
the undercooling of the melt
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
5. Transition metals addition
(dispersoids, Zener Drag)
MSc Eng Jagoda Poplewska
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Periodic table
of elements with Al, main alloying elements in Al-alloys
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Periodic table
of elements with Al, main alloying elements in Al-alloys
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Grain growth
Grain size as a function of
annealing temperature (alloys
after ECAP, route Bc)
S. Lee, A. Utsunomiya, H. Akamatsu, M. Furukawa, Z. Horita, K.
Neishi, T.G. Langdon; Influence of scandium and zirconium on
grain stability and superplastic ductilities in ultrafine-grained Al–
Mg alloys, Acta Materialia 50 (2002) 553–564
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Grain growth
Grain size as a function of
annealing temperature (alloys
after ECAP, route Bc)
Vickers hardness measurements of
alloys after cold rolling (z=60%) and
annealing for 1h in different
temperatures
S. Lee, A. Utsunomiya, H. Akamatsu, M. Furukawa, Z. Horita, K.
Neishi, T.G. Langdon; Influence of scandium and zirconium on
grain stability and superplastic ductilities in ultrafine-grained Al–
Mg alloys, Acta Materialia 50 (2002) 553–564
L.Lityńska-Dobrzyńska; Rola cyrkonu i skandu
w procesach tworzenia struktur metastabilnych
w stopach Al.-Mg-Si-Cu, IMIM PAN, Kraków 2009
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Grain growth
Precipitate growth in
Al-0.25wt.%Sc
during a 1 h anneal
M.J. Jones, F.J. Humphreys; Interaction of recrystallization and
precipitation: The effect of Al3Sc on the recrystallization behaviour of
deformed aluminium, Acta Materialia 51 (2003) 2149–2159
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Grain growth
M.J. Jones, F.J. Humphreys; Interaction of recrystallization and
precipitation: The effect of Al3Sc on the recrystallization behaviour of
deformed aluminium, Acta Materialia 51 (2003) 2149–2159
Recrystallization temperature (50%
recrystallization) of cold-rolled sheets of
binary alloys of Al–Mn, Al–Cr, Al–Zr, and
Al – Sc systems as a function of the
content of transition metal (AE)
V. V. Zakharov; Effect of scandium on the strcture
and properties of aluminium alloys, Metal Science
and Heat Treatment, Vol. 45, Nos. 7 – 8, 2003
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Zener drag
A dispersion of particles will exert a retarding force or pressure on a low angle or high angle
grain boundary and this may have a profound effect on the processes of recovery, recrystallization
and grain growth. The effect is known as Zener drag after the original analysis by Zener which was
published by Smith (1948). The magnitude of this interaction depends the nature of the particle
and interface, and the shape, size, spacing and volume fraction of the particles.
The interaction between a grain boundary and a spherical particle (incoherent)
If the boundary meets the particle at an angle
β the restraining force on the boundary is:
The maximum restraining effect (FS) is obtained
when β =45°, so:
γ - energy
It should be noted that when a boundary intersects a particle, the particle effectively removes
a region of boundary equal to the intersection area and thus the energy of the system is lowered,
and boundaries are therefore attracted to particles.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Zener drag
The interaction between a coherent particle
and a high angle grain boundary
(a) The boundary by-passes the particle;
(b) The boundary halts at the particles;
If a high angle grain boundary moves past a coherent
particle then the particle will generally lose coherence
during the passage of the boundary. As the energy of the
incoherent interface is greater than that of the original
coherent interface, energy is required to cause this
transformation, and this energy must be supplied by the
moving boundary.
Therefore coherent particles will be more effective in
pinning boundaries than will incoherent particles.
The drag force from single particle is given by:
FC is a maximum when Θ=α/2 and α=0, giving:
Thus coherent particles are twice as effective in pinning a grain boundary as incoherent particles of the same size
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Zener drag
Interaction of particles with
(a) a rigid planar boundary
(b) a flexible boundary
For a volume fraction FV of randomly distributed spherical particles of radius r, the number of
particles per unit volume (NV) is given by:
The Zener pinning pressure exerted by the particles on unit area of the boundary:
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Interaction of particles with grain boundary
Backscattered electron SEM
micrograph showing heterogeneous
precipitation in 0.12wt.%Sc
annealed 5 m at 380°C
M.J. Jones, F.J. Humphreys; Interaction of recrystallization and
precipitation: The effect of Al3Sc on the recrystallization behaviour of
deformed aluminium, Acta Materialia 51 (2003) 2149–2159
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Interaction of particles with grain boundary
Backscattered electron SEM
micrograph showing
heterogeneous
precipitation in 0.12wt.%Sc
annealed 5 m at 380°C
M.J. Jones, F.J. Humphreys; Interaction of recrystallization and
precipitation: The effect of Al3Sc on the recrystallization behaviour of
deformed aluminium, Acta Materialia 51 (2003) 2149–2159
Transmission electron micrograph showing
migration of a high angle boundary through
a dispersion of semi-coherent particles in
Al-0.25wt.%Sc annealed 5 m at 575 °C.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
6. Work hardening
MSc Eng Grażyna Kulesza
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Work hardening

Wrought alloys that do not respond to age hardening (e.g. 1xxx, 3xxx, 5xxx) are usually strengthened
by strain hardening. This generally involves cold-working at ambient temperatures, at which the
multiplication of dislocations occurs at a faster rate than they are annihilated by dynamic recovery.

The strain field surrounding a dislocation in the aluminium lattice can be sufficiently large to inhibit
the passage of other dislocations gliding on intersecting slip planes.

A stress must therefore be applied in addition to the lattice friction stress in order for dislocations to
intersect.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
Initially the material deform elastically –
i.e. strain is proportional to stress.
The gradient of the slope is the Youngs
Modulus, E

E

Above the yield stress, the material starts
to deform plastically.
If the load is removed, the material will
show some permanent deformation.
Dislocations multiply rapidly and their
strain fields interact.
This stage corresponds to the ultimate
tensile stress (UTS). Strain localises so
that a „neck” starts to form on the
test piece.
Final failure occurs when the reduced
cross section can no longer support the
load.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

Commercial purity (CP) aluminium, such as EN AW-1050 has a low solute content and therefore
relatively low strength when annealed.

This can be increased to some extent by strain hardening. Note however that the rate of work
hardening is quite low.
At 1% strain the dislocation density is quite low
and individual dislocations are easily resolved
At 5% strain the dislocation density is increasing
At 20% strain the dislocation density has increased further.
However the dislocations have now undergone dynamic recovery –
they have arranged into cell walls (or sub boundaries) in order to
minimise the total strain energy. The crystal between these subboundaries is relatively free of dislocations
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

By introducing 5% Mg into solid solution, the proof stress, work hardening rate and thus Rm(UTS)
can be significantly increased.

From the stress-strain curve, it is clear that the effects of solid solution hardening and strain
hardening are more than additive, as can be seen by comparing with the curve for
99.5% Al.
Elastic limit
Solute pinning of dislocation sources raises yield stress compared to Al
Strain without load increase in number of dislocations unpinned
from their solute atmospheres.
Onset of serrated yielding – Lüders line propagation.
Serrated flow continues to maximum engineering stress.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

TEM microstructure at different strains.
At 5% strain, the dislocation density is still quite low
and individual dislocations are easily resolved.
At 20% strain, dense ‘forests’ of dislocations have formed.
The high alloy content reduces the tendency for dislocations to form
cell walls (c.f. the purer EN AW-1050)
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim

In comparison with 99.5% Al, the Mg solute allows very little dynamic recovery at room
temperature, thus preventing dislocation rearrangement into a cell structure.

Of course, since recovery is a thermally activated process, a cell structure can be produced in Al5%Mg by deforming at a higher temperature, e.g. at 400 °C.
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim
References
http://www.matsceng.ohio-state.edu/mse205/lectures/chapter7/index_chap7.htm
Joseph R. Davis „Aluminum and aluminum alloys”, J. R. Davis & Associates, ASM International. Handbook Committee
Ian Polmear „Light Alloys-From Traditional Alloys to Nanocrystals” Elsevier 2006
http://aluminium.matter.org.uk
www.eaa.net/eaa/education/TALAT/
„High performance materials in aerospace”, ed. By Harvey M. Flower, Published by Chapman and Hall, London 1995
„Aluminum properties and physical metallurgy”, edited by John E. Hatch, American Society for Metals, Metals Park, Ohio,1984
A. L. Greer „Grain refinement of alloys by inoculation of melts” Phil. Trans. R. Soc. Lond., A 2003 361, 479-495
P. Moldovan and G. Popescu „The Grain Refinement of 6063 Aluminum Using Al-5Ti-1B and Al-3Ti-0.15C Grain Refiners”,
JOM, 2004, 59-61
T.R. Ramachandran, P.K. Sharma and K. Balasubramanian, „Grain Refinement of Light Alloys”, 68th WFC - World Foundry
Congress, 7th - 10th February, 2008, 189-193
B. S. Murty, S. A. Kori, and M. Chakraborty „Grain refinement of aluminium and its alloys by heterogeneous nucleation and
alloying”, International Materials Reviews 2002 Vol. 47 No. 1, 3-29
William D. Callister Jr., David G. Rethwisch „ Materials Science and Engineering”, John Wiley & Sons, 2010, 212-215
S. Lee, A. Utsunomiya, H. Akamatsu, M. Furukawa, Z. Horita, K. Neishi, T.G. Langdon ”Influence of scandium and zirconium
on grain stability and superplastic ductilities in ultrafine-grained Al–Mg alloys” Acta Materialia 50 (2002) 553–564
L.Lityńska-Dobrzyńska „Rola cyrkonu i skandu w procesach tworzenia struktur metastabilnych w stopach Al-Mg-Si-Cu” IMIM
PAN, Kraków 2009
V. V. Zakharov „Effect of scandium on the strcture and properties of aluminium alloys”, Metal Science and Heat Treatment, Vol.
45, Nos. 7 – 8, 2003;
M.J. Jones, F.J. Humphreys „Interaction of recrystallization and precipitation: The effect of Al3Sc on the recrystallization
behaviour of deformed aluminium” Acta Materialia 51 (2003) 2149–2159
F.J. Humphreys, M. Hatherly „Recrystallization and Related Annealing Phenomena” PERGAMON 2002
Kun Yu, Songrui Li, Wenxian Li „Recrystallization Behavior; Recrystallization Behaviour in an Al.-Cu-Mg-Fe-Ni Alloy with Trace
Scandium and Zirconium”, Materials Transactions, JIM, Vol. 41, No. 2, (2000) 358-361
G. Gottstein, L.S. Shvindlerman „Grain Boundary Migration in Metals” CRC Press, 2010
Interdyscyplinarne studia doktoranckie z zakresu inżynierii materiałowej z wykładowym językiem angielskim