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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Mechanical properties

• Deformation is the response of a material to an
  applied force
• elasticity
• reversible
• instantaneous
• anelasticity
• reversible
• delayed
• plasticity
• permanent
• progressive
• fracture
• permanent
• brutal

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Classes of materials

• Typical behaviours
• 3 main classes of materials
• depending on the nature of atomic bondings

Ceramics
Polymers
Composites
Metals
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Ceramics

• glass, concrete,
• technical ceramics (Al2O3, diamond, SiC, WC,
  Si3N4,)
• ionic or covalent bondings (strong)
• cristalline or amorphous structure
• brittle behaviour (no plasticity before fracture)
• very high mechanical resistance
• excellent behaviour at high temperature
• corrosion resistant

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Polymers

• PE, PP, PMMA, PTE,
• intramolecular covalent bondings, intermolecular
  Van der Waals or hydrogen bondings (weak)
• cristalline or amorphous structure (T dependent)
• ductile behaviour
• low mechanical resistance
• poor behaviour at high temperature
• corrosion resistant

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Metals

• ¾ of the elements
• metallic bondings
• cohesion is achieved by the cloud of free
  electrons
• cristalline structure (except metallic glasses)
• ductile behaviour
• high mechanical resistance
• good behaviour at high temperature
• low corrosion resistance

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Lectures

• Lattice deformation
• Macroscopic behaviour of the polycrystal
• Effect of temperature and strain rate
• Failure
• many illustrations with Fe-Mn-C steels
• (my main research topic)

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Lectures

• Lattice deformation
• 1) Elasticity
• 2) Elastic limit plasticity
• 3) Tensile test on a single crystal
• Macroscopic behaviour of the polycrystal
• Effect of temperature and strain rate
• Failure

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Lattice deformation1) Elasticity
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Enthalpic vs entropic elasticity
metals, ceramics
polymers, elastomers
Initial state applied force F 0 length
L0 bonding enthalpy H0 entropy S0 k ln O0
current state applied force F elongation L gt L0
H gt H0 S S0
H H0 S k ln O lt S0
G H TS gt G0 H0 TS0
e lt 1
e ? 800
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Linear elasticity at small strains
r
F

• interatomic potential energy

• interaction force

• small elastic displacement

• macrooscopic scale

• Youngs modulus
• E tens to hundreds of GPa

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Compared Youngs Moduli

• at room temperature

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Anisotropy of elastic constants

• Metals have a cristalline structure
• E depends on the cristallographic tensile
  direction
• hexagonal 5 elastic constants required
• cubic 3
• polycristal with no texture (isotropic) 2
• Lamé parametres l, m

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Dependence on temperature

• E, µ decrease when T increases
• Except when a phase transition occurs
• e.g. elastic anomaly observed in Fe-22Mn-0.6C
• antiferro/paramagnetic transition at TNéel 50C

DMTA experiment
austenitic steels
TNéel

• E(20C) 160 GPa (190-200 GPa in other
  austenitic steels)

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Lattice deformation 2) Elastic limit -
plasticity
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Lattice friction

• Plasticity is achieved by glide under applied
  deviatoric stresses
• Theoretical critical shear stress
• tc ? 0.10 0.16 m ? 10 GPa
• measured 2 to 4 orders of magnitude lower
• Plasticity is achieved by dislocation glide
• Potential energy W ? Peierls stress tp at 0K
• Lattice friction tf lt tp at T ? 0K (thermal
  activation)

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Selection of slip systems

• along which cristallographic planes ?
• lowest lattice friction
• highest inter reticular distance
• i.e. dense planes
• in which cristallographic directions ?
• Burgers vectors of the dislocations with the
  lowest line energy ( µb2)
• directions of the smallest lattice vectors
• i.e. dense directions
• depends of the cristallographic structure of the
  metal
• main structures f.c.c., b.c.c., h.c.p.

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Slip systems in the f.c.c. structure

• Cu, Al, Ni, Pb, Au, Ag, g-Fe, a-brass
• compact planes 111, Burgers vectors a/2lt110gt
• tf 111 0.01 MPa ltlt tf ijk

4 x 3
12 slip systems
(24 if the sign is taken into account)
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Slip systems in the b.c.c. structure

• dense planes 110gt112gt123 Burgers vectors
  a/2lt111gt
• tf strongly depends on T

Mo, W, a-Fe, b-brass Mo, a-Fe K
6 x 2
12 x 1
24 x 1
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Slip systems in the h.c.p. structure

• depends on the compacity of the structure
• in many cases tf Basal tf 111 f.c.c.

basal B prismatic P 1st order
pyramidal p1 2nd order pyramidal p2
1 x 3
3 x 1
6 x 1
Cd, Zn B, p2, p1, P Mg B, p1, P Ti, Zr
P, B, p1
6 x 1
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Lattice deformation 3) Tensile test on a single
crystal
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Resolved shear stress Schmid factor

• Peach Köhler force on a dislocation under
  applied stress
• glide force fg tb
• Resolved shear stress on a glide system
• Fb F cos l
• Schmid factor
• m cos l cos f t m s
• de m dg
• m lt 0.5
• Activation of the slip systems with the highest m
• when t reaches the elastic limit tc

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Example in the f.c.c. structure
orientation for single slip
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Crystal rotation in single slip

• deformation is achieved by glide along the
  activated slip system
• induces a rotation of the crystal
• the tensile direction moves towards the slip
  direction
• the Schmid factor of the primary system decreases
• until a second system is activated (secondary or
  conjugate system)

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Crystal rotation in single slip
stereographic projection

• standard triangles
• 100 and 110 planes
• 24 equivalent regions
• F in 1 triangle
• ? 1 slip system
• single slip
• primary slip system
• F moves towards
• double slip
• conjugate slip system
• F moves towards

b.c.c. structure case of Fe
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Tensile test curve

• resolved shear vs primary glide
• hardening q dt/dg

multi slip
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Lattice strengthening

• elastic limit tc
• lattice friction tf
• low in pure Cu (f.c.c.)
• solid-solution hardening
• Dt K cn
• 1/3 lt n lt 2/3
• Dtinsertion gt Dtsubstitution
• Dtinsert. CC gt Dtinsert. CFC
• strain hardening
• softening in stage III
• annihilation of dislocations
• by cross slip r ?

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• Most materials polycrystals
• agregates of crystals with different orientations
• macroscopic mechanical properties

part I
part II