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What is it? How to measure it? How to understand it?
The Bauschinger Effect:
C. W. Sinclair
Dept. Materials Engineering, The University of British Columbia, Vancouver Canada
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect
What is it?
How to measure it
How to understand it
Summary
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect
“ Pre-straining in any direction,
as defined by the principal axis of
the strain tensor, will introduce
an anisotropy for further
deformation in any other
direction. The intensity of this
prestrain-associated anisotropy is
at maximum when the direction
of further straining is opposite to
that of the prestrain.”
A. Abel, Historical Perspectives and
Some of the Main Features of the
Bauschinger Effect, Mater. Forum,
1987, 10, 11-26.
Johann Bauschinger (June 11, 1834 November 25, 1893)
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect
Bauschinger, J. Mittheilungen aus dem Mechanisch-Technischen
Laboratorium der K. Technischen Hochschule in Munichen, Heft 13
(Abschnitt 5) 1881, 31
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect
I
I
Classic example of
tension-compression
asymmetry
Several things to note:
I
I
I
Yield stress lowered on
reversal of strain
Direction of first straining
not important
Significant transient
before work hardening is
regained
High carbon steel: Sidebottom and Chang, 1952
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect
8
6
1. Tension
4
stress/modulus × 103
2. Compression
3. Mirror compression
2
0
-2
-4
-6
-8
-0.01
-0.005
0
0.01
0.015
0.02
strain
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect
8
6
1. Tension
4
stress/modulus × 103
2. Compression
3. Mirror compression
2
0
-2
-4
-6
-8
-0.01
-0.005
0
0.01
0.015
0.02
strain
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect
8
6
1. Tension
4
stress/modulus × 103
2. Compression
3. Mirror compression
2
0
-2
-4
-6
-8
-0.01
-0.005
0
0.01
0.015
0.02
strain
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect
8
stress/modulus × 103
6
1. Tension
4
2. Compression
3. Mirror compression
2
0
0
0.01
0.015
0.02
strain
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect
8
σF
stress/modulus × 103
6
kσR k
1. Tension
4
2. Compression
3. Mirror compression
2
0
0
0.01
0.015
0.02
strain
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Practical Consequences:
Bauschinger effect is of practical importance whenever strain path
reversals are expected:
Example 1: UOE Tube Forming
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Practical Consequences:
Bauschinger effect is of practical importance whenever strain path
reversals are expected:
or
When tension and compression co-exist
Example 2: Springback of sheet
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Theoretical Consequences:
The existance of the Bauschinger effect underlines our poor
understanding of the underlying physics of work hardening –
particular from a materials science perspective our ability to predict
a priori a Bauschinger effect is very poor
√
σ = σ0 + αµb ρ
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Sources
There are several sources which can give rise to a Bauschinger
effect:
I
Asymmetry of
plasticity (e.g.
twinning in HCP
materials)
I
Residual stresses
I
Macroscopic
non-uniform plasticity
I
Microstructure effects
(intrinsic)
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Sources
There are several sources which can give rise to a Bauschinger
effect:
8
Asymmetry of
plasticity (e.g.
twinning in HCP
materials)
I
Residual stresses
I
Macroscopic
non-uniform plasticity
I
Microstructure effects
(intrinsic)
6
kstressk/modulus × 104
I
4
2
(1)
0
(1)
0
0.5
1.0
cumulative strain × 103
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Sources
There are several sources which can give rise to a Bauschinger
effect:
8
Asymmetry of
plasticity (e.g.
twinning in HCP
materials)
I
Residual stresses
I
Macroscopic
non-uniform plasticity
I
Microstructure effects
(intrinsic)
6
kstressk/modulus × 104
I
4
(2)
2
(2)
(1)
0
(1)
0
0.5
1.0
cumulative strain × 103
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Sources
There are several sources which can give rise to a Bauschinger
effect:
8
(3)
Asymmetry of
plasticity (e.g.
twinning in HCP
materials)
I
Residual stresses
I
Macroscopic
non-uniform plasticity
I
Microstructure effects
(intrinsic)
6
kstressk/modulus × 104
I
4
(2)
(3)
2
(2)
(1)
0
(1)
0
0.5
1.0
cumulative strain × 103
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Sources
There are several sources which can give rise to a Bauschinger
effect:
8
(3)
Asymmetry of
plasticity (e.g.
twinning in HCP
materials)
I
Residual stresses
I
Macroscopic
non-uniform plasticity
I
Microstructure effects
(intrinsic)
6
kstressk/modulus × 104
I
4
(2)
(3)
2
(2)
(1)
0
(1)
0
0.5
1.0
cumulative strain × 103
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Sources
There are several sources which can give rise to a Bauschinger
effect:
8
Asymmetry of
plasticity (e.g.
twinning in HCP
materials)
I
Residual stresses
I
Macroscopic
non-uniform plasticity
I
Microstructure effects
(intrinsic)
6
kstressk/modulus × 104
I
4
2
(4)
0
0
(4)
0.5
1.0
cumulative strain × 103
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Sources
There are several sources which can give rise to a Bauschinger
effect:
8
Asymmetry of
plasticity (e.g.
twinning in HCP
materials)
I
Residual stresses
I
Macroscopic
non-uniform plasticity
I
Microstructure effects
(intrinsic)
6
kstressk/modulus × 104
I
(5)
4
2
(4)
(4)
(5)
0
0
0.5
1.0
cumulative strain × 103
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Sources
There are several sources which can give rise to a Bauschinger
effect:
8
(6)
Asymmetry of
plasticity (e.g.
twinning in HCP
materials)
I
Residual stresses
I
Macroscopic
non-uniform plasticity
I
Microstructure effects
(intrinsic)
6
kstressk/modulus × 104
I
(5)
4
2
(4)
(4)
(6)
0
0
0.5
(5)
1.0
cumulative strain × 103
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Sources
There are several sources which can give rise to a Bauschinger
effect:
I
Asymmetry of
plasticity (e.g.
twinning in HCP
materials)
I
Residual stresses
I
Macroscopic
non-uniform plasticity
I
Microstructure effects
(intrinsic)
Most Interest
Come back at 14h
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect
What is it?
How to measure it
How to understand it
Summary
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: How To Measure it
Uniaxial Tension + Compresssion:
I
Common problems
I
I
I
I
I
Alignment!
Strains in tension +
compression
(buckling)
Microstructure
alignment (fibres in
compression)
Complex for sheet
Need to check carefully
to know when you buckle
in compression i)
extensometry ii) image
correlation
* See: Pragnell, P B; Stobbs, W M; Withers, P J, Mater. Sci. Eng. A A159 (1992) pp. 51-63
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: How To Measure it
Uniaxial Tension + Compresssion:
I
Common problems
I
I
I
I
I
Alignment!
Strains in tension +
compression
(buckling)
Microstructure
alignment (fibres in
compression)
Complex for sheet
Need to check carefully
to know when you buckle
in compression i)
extensometry ii) image
correlation
* See: Pragnell, P B; Stobbs, W M; Withers, P J, Mater. Sci. Eng. A A159 (1992) pp. 51-63
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: How To Measure it
Uniaxial Tension + Compresssion:
I
Common problems
I
I
I
I
I
Alignment!
Strains in tension +
compression
(buckling)
Microstructure
alignment (fibres in
compression)
Complex for sheet
Need to check carefully
to know when you buckle
in compression i)
extensometry ii) image
correlation
* See: Pragnell, P B; Stobbs, W M; Withers, P J, Mater. Sci. Eng. A A159 (1992) pp. 51-63
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: How To Measure it
Shear - Reverse Shear:
I
I
Either torsion or simple
shear of sheet
Common problems
I
I
I
I
I
Uniformity of strain
Measurement of strain
Off-axis loading
Material evolution
with (large) strain
Other variations on shear
testing exist as well
O. Bouaziz, S. Allain and C. Scott, Scripta Mater., Scripta Materialia 58 (2008) 484487
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: How To Measure it
Bending:
I
Most complex
I
Closest to practice
Common problems
I
I
I
I
Can have an extrinsic
Bauschinger effect
Requires inverse analysis
Other methods typically
preferred from a materials
perspective
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: How To Measure it
Bending:
I
Most complex
I
Closest to practice
Common problems
I
I
I
I
Can have an extrinsic
Bauschinger effect
Requires inverse analysis
Other methods typically
preferred from a materials
perspective
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: How To Measure it
Complimentary Techniques
I
I
Bauschinger effect comes from stress inhomogeneity
Any technique able to capture stress re-distribution can give
insight
I
I
Kinematic vs. isotropic hardening behave differently
I
I
I
Diffraction (this afternoon)
Thermal stability (this afternoon)
Rate sensitivity (this afternoon)
Microstructure characterization
I
I
I
I
Second phase
Grain/twin boundaries
Dislocation arrangements
...
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect
What is it?
How to measure it
How to understand it
Summary
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
stress
tension
σp
σY 0.2%
σr
σr0
Ep
σf
∆σ
ǫB
Reversed
compression
Es
strain
0.2%
Stress Based Parameters:
Backstress/Bauschinger
Stress:
σB =
1
(σp − σr )
2
Bauschinger stress
parameter:
βσ =
σp − σr
σp
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
stress
tension
σp
σY 0.2%
σr
σr0
Ep
σf
∆σ
ǫB
Reversed
compression
Es
strain
Strain Based Parameters:
Bauschinger Strain: B ,
Total reverse strain at
σr = f σp
Bauschinger strain
parameter:
0.2%
β =
β
B
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
stress
tension
σp
σY 0.2%
σr
σr0
Ep
σf
∆σ
ǫB
Reversed
compression
Related to Energy:
Bauschinger Energy
Parameter:
Es
strain
βE =
ES
EP
0.2%
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
stress
tension
σp
σY 0.2%
σr
σr0
Ep
σf
∆σ
ǫB
Reversed
compression
Es
strain
Permanent Softening:
Mean internal stress:
hσi =
∆σ
1 0
=
σf − σr0
2
2
0.2%
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
I
Simple 2-element Masing
Model
8
I
I
σf
stress/modulus × 103
6
σ0
I
If one element remains
elastic → permanent
softening
I
magnitude of permanent
softening related to mean
internal stress
I
mean internal stress is the
difference between flow
stress and stress carried by
“matrix”
4
σr
∆σ = σf − σr
∆σ = 2 (σf − σ0 )
2
0
σf = σ0 + hσi
2 hσi = σf − σ0
hσi = 12 (σf − σr )
0
0.01
strain
0.015
Elastic, perfectly plastic
Iso-strain
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
I
Simple 2-element Masing
Model
I
I
Al-Al3 Ni in-situ composite
Lasalmon and Martin, Scripta Metall., 8 (1974) 377-382
Elastic, perfectly plastic
Iso-strain
I
If one element remains
elastic → permanent
softening
I
magnitude of permanent
softening related to mean
internal stress
I
mean internal stress is the
difference between flow
stress and stress carried by
“matrix”
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
I
Simple 2-element Masing
Model
8
I
I
σf
stress/modulus × 103
6
σ0
I
If one element remains
elastic → permanent
softening
I
magnitude of permanent
softening related to mean
internal stress
I
mean internal stress is the
difference between flow
stress and stress carried by
“matrix”
4
σr
∆σ = σf − σr
∆σ = 2 (σf − σ0 )
2
0
σf = σ0 + hσi
2 hσi = σf − σ0
hσi = 12 (σf − σr )
0
0.01
strain
0.015
Elastic, perfectly plastic
Iso-strain
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
I
Atkinson, Brown and Stobbs† proposed that the magnitude of
the permanent softening should be used to quantify the
Bauschinger effect since they are directly related to mean
internal stresses
I
Calibrated this through experiments on internally oxidized Cu
I
Eshelby model for load transfer to spherical oxides
I
Used results on x-ray diffraction measurements from Wilson
and Koonan‡ to justify model
† Atkinson, JD Brown, LM and Stobbs, WM. Philosophical Magazine 30(6):1247 - 1280, 1974.
‡ Wilson, DV and Koonan, YA. Acta Metallurgica 12(5):617 - 628, 1964.
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
Problem!
Proudhon et al. Philosophical Magazine 88 (2008) 621640 → AA6111
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
Problem!
I
I
Atkinson et al. were correct → under special conditions!
Very often do not observe permanent softening even when we
know we have large internal stresses!
I
Even the calibration used above was somewhat faulty given
that the data of Wilson and Koonan shows no permanent
softening!
I
If there is no elastically loading element then permanent
softening disappears (cf. Masing Model)
I
Pragnell et al.† experimentally verified reversal of internal
stresses and lack of permanent softening in MMCs
† Prangnell et al. Materials Science & Eng., 197A (1995)pp. 215-221
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
I
Typical solution – choose an (arbitrary) offset reverse strain
Magnitude of result strongly depends on offset selected
I Trends of ∆σ with forward strain appear to be similar in many cases
I
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
I
Typical solution – choose an (arbitrary) offset reverse strain
I
Magnitude of result strongly depends on offset selected
I
Trends of ∆σ with forward strain appear to be similar in many cases
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
I
Typical solution – choose an (arbitrary) offset reverse strain
I
Magnitude of result strongly depends on offset selected
I
Trends of ∆σ with forward strain appear to be similar in many cases
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect: Understanding it
I
There is a wealth of
information about the
distribution of stress in reverse
part of the flow curve
I
e.g. yield in reverse direction
corresponds to the yielding of
the softest element → tangent
at σr tells us the fraction of
“unyielded” material
I
Need to explore the shape of
the reverse part of the curve to
be able to predict the full
distribution of “backstresses”
or “internal stresses” within a
plastically deformed material!
UCL Lunch Seminar, Dec. 18 2009
The Bauschinger Effect
What is it?
How to measure it
How to understand it
Summary
UCL Lunch Seminar, Dec. 18 2009
Summary
I
Bauschinger test: Easy experiment to do... hard experiment
to do well!
I
Bauschinger test gives us a sort of “mechanical spectrometer”
I
“Classical” interpretations are important but have significant
problems when treating “real” materials
I
Even if we can’t predict it fully, can get a long way in some
materials (e.g. precipitation hardened materials)
I
Capturing the full shape of the ∆σ vs. r curve is of both
fundamental and practical importance!
UCL Lunch Seminar, Dec. 18 2009