Wavelet analysis is used for describing heterogeneous deformation in different scales. Slip step height experimental measurements of monocrystalline alloy specimens subjected to compression are considered. The experimental data are subjected to discrete wavelet transform and the spatial distribution of deformation in different scales (resolutions) is calculated. At the finer scale the wavelet analyzed data are identical to the experimental measurements, while at the coarser scale the profile predicted by the wavelet analysis resembles the shear band solution profile provided by gradient theory in agreement with experimental observations. The different data sets provided by wavelet analysis are used to train a neural network in order to predict the spatial distribution of strain at resolutions higher than those possible by the available experimental probes. In addition, applications of wavelet analysis to interpret size effect data in torsion and bending at the micron scale are examined by deriving scale-dependent constitutive equations which are used for this purpose.

Issue Section:
Technical Papers
Keywords:
plasticity, hardness, indentation, slip, plastic flow, hardening, recovery, dislocation density, elastic deformation, kinematics, torsion, compressive strength, bending
Topics:
Deformation, Wavelets, Artificial neural networks, Torsion, Plasticity
1.
Konstantinidis, A, 2000, “Applications of Wavelets and Neural Networks Theory on the Mechanical Behavior of Materials,” Ph.D. thesis, Aristotle University of Thessaloniki, Thessaloniki, Hellas (in Greek).
2.
Engelke
,
C.
, and
Neuha¨user
,
H.
,
1995
, “
Static and Dynamic Strain Ageing in D03-Ordered Fe3Al,
”
Scr. Metall. Mater.
,
33
, pp.
1109
–
1115
.
3.
Brinck
,
A.
,
Engelke
,
C.
, and
Neuha¨user
,
H.
,
1997
, “
On the Temperature Dependence of Slip Inhomogeneity in Fe3Al,
”
Mater. Sci. Eng., A
,
234–236
, pp.
418
–
421
.
4.
Brinck
,
A.
,
Engelke
,
C.
,
Neuha¨user
,
H.
,
Mole´nat
,
G.
,
Ro¨sner
,
H.
,
Langmaack
,
E.
, and
Nembach
,
E.
,
1998
, “
Dislocation Processes in Fe3Al Investigated by Transmission Electron, Scanning Force and Optical Microscopy
,”
Mater. Sci. Eng., A
,
258
, pp.
32
–
36
.
5.
Brinck
,
A.
,
Engelke
,
C.
, and
Neuha¨user
,
H.
,
1998
, “
Quantitative AFM Investigation of Slip Line Structure in Fe3Al Single Crystals After Deformation at Various Temperatures
,”
Mater. Sci. Eng., A
,
258
, pp.
37
–
41
.
6.
Daubechies, I., 1992, Ten Lectures on Wavelets, SIAM Press, Philadelphia, USA.
7.
Aifantis
,
E. C.
,
1984
, “
On the Microstructural Origin of Certain Inelastic Models
,”
ASME J. Eng. Mater. Technol.
,
106
, pp.
326
–
330
.
8.
Aifantis
,
E. C.
,
1987
, “
The Physics of Plastic Deformation
,”
Int. J. Plast.
3
, pp.
211
–
247
.
9.
Zbib
,
H. M.
, and
Aifantis
,
E. C.
,
1988
, “
On the Localization and Postlocalization Behavior of Plastic Deformation-I: On the Initiation of Shear Bands
,”
Res. Mech.
,
23
, pp.
261
–
277
.
10.
Zbib
,
H. M.
, and
Aifantis
,
E. C.
,
1988
, “
On the Localization and Postlocalization Behavior of Plastic Deformation-II: On the Evolution and Thickness of Shear Bands
,”
Res. Mech.
,
23
, pp.
279
–
292
.
11.
Zbib
,
H. M.
, and
Aifantis
,
E. C.
,
1988
, “
On the Localization and Postlocalization Behavior of Plastic Deformation-III: On the Structure and Velocity of the Portevin-Le Chatelier Bands
,”
Res. Mech.
,
23
, pp.
293
–
305
.
12.
Zbib
,
H. M.
, and
Aifantis
,
E. C.
,
1988
, “
On the Structure and Width of Shear Bands
,”
Scr. Metall.
,
22
, pp.
703
–
708
.
13.
More, J. J., 1995, “The Levenberg-Marquardt Algorithm: Implementation and Theory,” Numerical Analysis, Lecture Notes in Mathematics, G. A. Watson, ed., Springer-Verlag, Heidelberg, Vol. 630, pp. 105–116.
14.
Fleck
,
N. A.
,
Muller
,
G. M.
,
Ashby
,
M. F.
, and
Hutchinson
,
J. W.
,
1994
, “
Strain Gradient Plasticity: Theory and Experiment
,”
Acta Metall. Mater.
,
42
, pp.
475
–
487
.
15.
Tsagrakis, I., 2001, “The Role of Gradients in Elasticity and Plasticity. Analytical and Numerical Applications,” Ph.D. thesis, Aristotle University of Thessaloniki, Thessaloniki, Hellas (in Greek).
16.
Sto¨lken
,
J. S.
, and
Evans
,
A. G.
,
1998
, “
A Microbend Test Method for Measuring the Plasticity Length Scale
,”
Acta Mater.
,
14
, pp.
5109
–
5115
.
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