Basics of mechanical properties of metals

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Basics of mechanical properties of metals

• Jean-Philippe Chateau
• Ecole des Mines de Nancy
• Institut Jean Lamour

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Lectures

• Lattice deformation
• Macroscopic behaviour
• 1) Tensile test
• 2) Polycrystal
• 3) Alternative deformation mechanisms
• Effect of temperature and strain rate
• Failiure

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Macroscopic behaviour1) Tensile test
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Engineering stress-strain curve

• measure the force (simple)
• measure the elongation (not so easy)

Fe-22Mn-0.6C at 400C
applied force (N)
engineering stress s (MPa)
fracture
S0 4.4 mm2 L0 24.3 mm
elongation DL (mm)
engineering strain e ()
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Mechanical characteristics

• stiffness
• Youngs modulus E
• resistance
• yield stress sy, R0.2
• ultimate tensile strength su Fmax/S0
• ductility
• elongation to fracture eF
• area reduction q
• SF measured in the fractured zone

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Typical behaviours

• metals

annealed copper
annealed mild steel

• ceramics, glass

• elastomers, polymers

elastic
elastic
rubber
polypropylene
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Compared mechanical characteristics

• eF ? when sy, su ?
• metals
• best compromise

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True stress-strain curve

• true stress
• plastic deformation occurs by glide
• no volume change

• true strain
• the actual gauge length L increases

• Uniform strain eu
• strain at maximum load (N)
• Fracture strain
• stress strain law s f(e)
• to be used in FEM simulations
• and not s f(e) !

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Empirical laws

• Hollomons law
• strain hardening coefficient
• Ludwiks law
• Swifts law

sy
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Necking

• strain localisation at maximum load
• at Fmax
• volume conservation
• Considères criterion
• q s stress increase due to hardening higher
  than stress increase due to local section
  reduction
• q

or
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Strain localisation
Localised or diffuse necking

• Fe-22Mn-0.6C
• at different temperatures
• grain size 2.5 µm
• high elongation due to high
• hardening rate
• Annealed Mild steel
• dislocations pinned by carbon atoms
• immediate softening at yield point
• Lüders bands

strain hardening rate n
line n e
true strain
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Macroscopic behaviour 2) Polycristal
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Microscopic vs macroscopic yield stress

• microscopic yield stress
• deformation of grains with the maximum resolved
  shear stress
• ? 1 slip sytem / m 0.5
• dislocations are blocked at the grain boundaries
• small deformation
• not measurable by the tensile test
• macroscopic stress
• deformation extends to all the grains
• sy measured by the tensile test

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Relation between sy and tc ?

• Sachs formulation
• no texture random orientation of grains
• deformation mainly achieved by the primary system
  in each grain
• average Schmid factor on primary systems
• Von Mises condition
• ep 6 components (symmetrical)
• constant volume Tr(ep) 0
• 5 degrees of freedom 5 slip systems
• Taylor formulation
• energetic criterion to select the 5 slip systems

f.c.c. metals
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Influence of the grain boundaries

• Sachs and Taylor
• poor correlation with experiment
• pure polycristalline Cu sy tens of MPa tc 1 MPa
• polycrystals do not behave like
• a group of isolated crystals
• strain incompatibilities at
• the grain boundaries
• Hall Petch law A

predeformed pure Cu
A MSachs tc
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Macroscopic behaviour 3) Alternative
deformation mechanisms
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Intergranular glide
tg

• Grain boundaries have their own resistance
• sIG 2 tg
• Intragranular deformation
• If sIG
• deformation is achieved by grain boundary gliding
• Limit of the Hall Petch law
• HP not valid for small grain sizes (µm)
• superplastic behaviour (eu 1)

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Mechanical twinning

• Twin
• crystal with a symmetry relation with the host
  lattice

• f.c.c.
• achieved by glide of Shockley partial
  dislocations on parallel 111 planes
• twinning systems 111

• b.c.c.
• twin plane 112
• twin direction

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Mechanical twinning

• twins produce a permanent glide
• f.c.c., b.c.c.
• h.c.p.
• participates to plastic deformation
• h.c.p.
• Von Mises condition 5 slip systems required to
  achieve a given deformation
• Zn, Sn mainly basal glide 3 slip systems, only
  1 plane
• f.c.c.
• low stacking fault energy
• dislocations largely dissociated
• Shockley partials can move individually to
  achieve the glide
• b.c.c.
• dislocation glide is difficult
• at low temperature

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TWIP effect
400ºC, SFE 90 mJ/m2

• Twinning Induced Palsticity
• Fe-22Mn-0.6C
• metastable f.c.c. structure
• low stacking fault energy increasing with T
• increasing volume fraction of mocrotwins along
  with deformation

25ºC, SFE 20 mJ/m2
disloca-tions twins
thermochemical model of the SFE
disloca-tions
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TWIP effect

• twin boundaries are strong obstacles
• twin boundary grain boundary
• decrease of the mean free path of the
• dislocations
• dynamical Hall Petch effect
• very high hardening rate
• elongation 50 UTS 1 GPa

1600
Emboutis à chaud
1400
Multiphasés
1200
1000
tensile strength (MPa)
TWIP
TRIP
800
Dual Phase
600
Rephosphoré, BH
400
HSLA
Extra-Doux
200
0
0
10
20
30
40
50
60
elongation ()
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TRIP effect
-196ºC, SFE 7 mJ/m2

• Tansformation Induced Palsticity
• Fe-22Mn-0.6C
• metastable f.c.c. structure
• e-martensite (h.c.p.) more stable at low
  temperature
• achieved by glide of Shockley partials
• every 2 111 planes
• same effect as TWIP effect

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Shape memory and pseudo elasticity

• phase transformation
• cooling austenite ? martensite between MS and
  MF
• heating martensite ? austenite between AS and
  AF
• MF
• hysteresis due to the creation of heterophase
  interfaces
• displacive transformation
• the transformation temperatures increase with the
  applied stress
• Ni-Ti
• Cu-Al-Ni
• Cu-Al-Zn
• Fe-Mn-Si-C

shape memory
pseudo elasticity
reversible strain up to 10
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• Plastic deformation
• thermally activated mechanisms
• Part III influence of the loading conditions
• temperature
• strain rate

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