Context: Materials for transport applications
14-4-2016 2
• 3 credits
• Evaluation: o Oral exam
o Presentation
o Executive summary report
o Active contribution in seminars
• Compulsory readingo Davies, Materials for automotive bodies, Elsevier. 2003
o Yamagata, The science and technology of materials in automotiveengines, Woodhead Publishing. 2005
• Additional literatureo Banabic, Sheet Metal Forming Processes, Springer, 2010
o Illig, Thermoforming: a practical guide, Hanser Verlag, 2001
o Matthews & Rawling, Composite Materials, Elsevier, 1999
1 general aspects of
plasticity
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Strength and stiffness
• Stiffness
o Determined by composition and atom binding energy
• Strength
o Determined by
• Composition
• Microstructure
• Point defects (intersitial or substitutional atoms, vacancies)
• Dislocations
o Affected by
• Mechanical treatment (cold forming)
• Heat treatment (annealing, hardening, tempering …)
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Ductility
• Importance
o Forming
o Crash behavior
• Determined by
o Composition
o Microstructure
o Point defects (interstitial or substitutional atoms, vacancies)
o Dislocations
• Affected by
o Mechanical treatment (cold forming)
o Heat treatment (annealing, hardening, tempering …)
Plasticity: strain definitions
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• Engineering strain / technical strain / Cauchy strain
• True strain / logarithmic strain / Hencky strain
• Green strain
• Euler-Almansi strain
10
L
Le
lnln0
1
L
L
12
1
2
1 2
20
20
21
L
LLG
221
20
21 1
12
1
2
1
L
LLE
Stress definitions
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• Cauchy stress tensor
• Principal stresses
Plane stress condition
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• Principal stresses in plane stress condition
• Maximum and minimum shear stress
o In principal stress terms:
Tresca yield criterion (1864)
Hydrostatic and distortional stress
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• Hydrostatic:
o deforms the body (changes the volume)
o Does not cause plastic deformation
• Distortional stress component:
o distorts the body
o Plastic deformation
ijijij s
ij
Von Mises stress / octahedral stress
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• Invariants of the distortional stress tensor
• Von Mises stress
• Octahedral stress: 2222
3
2
3
1JIIIIIIIIIIIIoct
2222
32
1JIIIIIIIIIIIIVM
Huber-Mises-Hencky yield criterion
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• Yielding starts when J2 reaches a critical value
General
Principal stress
Plane stress
general
Plane stress
principal
Pure shear
uniaxial
22222 IIIIIIIIIIIIy
222IIIIIIy
231
223
212
21133
23322
22211
2 62 y
212
2222211
211
2 3 y
123 y
1 y
Graphic representation
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I
Compressiontest
Tensile test
Tensile testSphericalpressurevessel
Sphericalbathosphere
Torsion test
Torsion test
Compressiontest
Von Mises
Tresca
Uniaxial loading
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2 Forming processes
Shaping processes
Stretch forming – deep drawing
Defects in deep
drawing
Parameters influencing
formability
Example
3 formability of metals
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Formability definitions
• Work-hardening factor ‘n’
o Strengthening during plastic deformation
o Related to stretching
o Important for energy absorption and impact
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Importance of work hardening n
• Importance:
o Stretch forming
o Energy absorption
• Determined by microstructure;
dislocations, point defects :
o composition
o Heat treatment
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Formability definitions
• Anisotropy factor r
o Related to part thinning during deformation
lw
w
t
wr
Directional dependence of r
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Coefficient of normal anisotropy
• Depends on strain
4
2 90450
rrrrm
• Variation of normal anisotropy
• Responsible for earing
4
2 90450
rrrr
Planar anisotropy
Biaxial anisotropy coefficient
• Barlat Pöhland
o Flatwise compression ° Biaxial tensionRD
TDbr
Consequences of anisotropy
• Tresca and Von Mises criteria no longer valid
• More yield stresses needed
• Yield criterion for anisotropic materials: Hill1948
1222 212
213
223
221
213
232 NMLHGF
2
2
2
222
222
222
12
12
12
1112
1112
1112
TN
SM
RL
ZYXH
YZXG
XZYF
Hill 1990
b: yield stress in biaxial tension
: yield stress in pure shear
Further developments
• New criteria for the complex steel alloys for automotive
Experimental correlation
• Further reading: D. Banabic, Sheet Metal Forming Processes,
Springer, 2010
4 Determination of
formability
• Tensile tests
o n
o r
o Plasticity during necking
• Forming limit tests
o Punch stretching methods: Erichsen test, Hecker test
o Deep drawing methods: Swift test
o Forming limit methods: Nakazima test
Punch stretching methods
• Erichsen test
o Indentation depth (mm)
• Hecker test
Deep drawing methods
• Swift test
o Limit drawing ratio
LDR=𝐷𝑚𝑎𝑥
𝑑
Forming limit strain diagram
Nakazima test
• Forming test with varying boundary conditions
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Determination of deformability limits:
Hecker method• Deformation of a printed circular grid
o Largest strain 1
• Always positive
o Smallest strain 2
• Positive or negative
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Forming limit curve
n important
r important
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Influencing parameters
Other parameters
• Temperature
• Strain rate
• Punch curvature
• Pressure
• Dimensions of the grid
• …
Alternative measurement
method:
Digital Image Correlation
B. Van Mieghem et al. Digital image correlation for on-line wall
thickness measurements in thick gauge thermoforming. Key
Engineering Materials (2013)
In e
ver
y s
tep o
f th
e
pro
cess
Introduction – Digital Image Correlation
47
Time t
UndeformedTime t’
Deformed
Def
orm
atio
n
mat
rix
Corr
elat
ion
coef
fici
ent
DIC in forming - Challenges
48
• Strain > 100% is not exceptional when judging strain,
choice of strain definition is important
• Strain rate 0,01/s up to 10/s
• Speckle technique on sheet (low surface energy)
o Custom paint
o Spray/Print
• Forming temperature 100-300°C
• Big displacements in 3D
o Field of View
o Depth of Field
o Lighting
DIC in thermoforming
49
366 mm
59
mm
16
9 m
m
15
3 m
m
63
mm
197 mm
147 mm
Top view
Side view
75
mm
160 mm
13
4 m
m
Top view
Side view
Stress relaxation
Bubble inflation
DIC in thermoforming - Applications
50
• Full field in-situ thickness maps
• Influence of extrusion anisotropy
• Simulation optimisation
• Process optimisation
• ...
Applications – Full field thickness maps
51
• Symmetric products are not always symmetric in thickness
• Find cause by measuring in-situ during the process
Simulation
Thickness symmetry
DIC
Shape
symmetry
DIC
Thickness
asymmetry
Applications – Influence of extrusion
anisotropy
52
B. Van Mieghem et al. Impact assessment of extrusion anisotropy on quality of thermoformed products.
Composites Week @ Leuven and TEXCOMP-11 Conference (2013)
Final thickness distribution
Asymmetric thinning due to sag
Stress relaxation
53
Applications – Simulation optimisation
• Cross sectional thickness measurement
• What influences the thickness distribution
• Sheet mould contact
o Temperature dependent friction
o Heat transfer coefficient air/sheet
o Heat transfer coefficient mould
Applications – Simulation optimisation
54
Use of DIC to determine FLC
Example: steel
Effect of history and
crystallographic texture
on anisotropy
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Steel production
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Steel production 2
• Improvements for automotive:
o AK (Al-killed)
• Binding of Al with N: improved ageing resistance
• Pancake grains
o Vacuum degassing:
• Removal of all inclusions
• Low level of impurities
• Addition of Ti and Nb
- Binds C and N
• IF-steel (interstitial free)
• Ultradeep drawable steel
- Improved r-factor
• Complete ferritic matrix
- C content very low C < 0.0002%
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Production of steel slabs
• Continuous casting
• Ingots
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Sheet steel manufacturing
• Hot rolling to thickness of 3mm-1.6mm at 900-1200°C
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Sheet steel manufacturing
• Pickling with hydrochloric acido Removal of oxide skin
• Cold rolling to 0.5mm
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Effect of cold work on anisotropy
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Annealing
• batch
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Continuous Annealing (CAPL)
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Annealing differences
batch CAPL
Slow heating: 30 hours Rapid heating: 90 s
Slow cooling: 25 hours Fast cooling: 10 min
Coarse grain Finer grain
Stronger
Higher ductility
High r: 1.6-2.1 Low r 1.0-1.4
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skin pass
• 1% deformation after annealing
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Lüdersbanden
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Surface topography
• Importance of the surface topography
o Forming process
• Lubrication characteristics
o Paint quality
• Adhesion
• gloss
• Determined by the skin pass
High strength steels
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IF HSS
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• Vacuum degassedo Removal of C, N, O
o Reduced dent resistence
• Complete ferritic
• Alloyed with Mn, Si, P
• Further strengthening via bake hardening
Second generation AHSS
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TWIP
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• TWIP: twinning induced plasticity
• High Mn (17-24%)
• Fully austenitic at room temperature
• Cold forming causes twinning
o Fine sized austenite grains increased strength
• Expensive
TRIP > < TWIP
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Consequences
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Steel versus
aluminium
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Al alloys used in automotive
Comparison 5xxx and 6xxx
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5xxx 6xxx
Formability +++ ++
Corrosion resistance +++ ++
Heat resistance > 65°C Not good for >
% Mg
+++
Crash performance +++ +++
Surface quality Stretcher strain
markings
+++
Strength + +++
Effect heat treatment on strength decrease increase
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Deformability: tensile stress-strain curve
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Deformability: forming limit diagram
Спасибо