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THE ANALYSIS OF FRACTURE SURFACES OF POROUS METAL MATERIALS USING AMT AND FRACTAL GEOMETRY METHODS

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Title: THE ANALYSIS OF FRACTURE SURFACES OF POROUS METAL MATERIALS USING AMT AND FRACTAL GEOMETRY METHODS


1
THE ANALYSIS OF FRACTURE SURFACES OF POROUS METAL
MATERIALS USING AMT AND FRACTAL GEOMETRY METHODS
  • Sergei Kucheryavski
  • Artem Govorov

Altai State University Barnaul, Russia
2
Ideal life
3
Deformation Structure of Porous Metals
Deformation stages (Optical microscope)
Fracture surfaces (Electronic microscope)
4
Known methods
  • Traditional methods
  • Classical statistics methods (i.e. Mean Absolute
    Deviation)
  • Textural features methods
  • Alternative methods
  • Fractal analysis
  • The AMT technique

5
Fractal geometry
  • Fractals
  • irregular, fragmented objects
  • self-similar objects
  • Fractal geometry methods
  • simulation complex objects like trees, clouds and
    so on
  • measure of self-similarity
  • quantitative description of irregular, complex
    structure fractal dimension Df

6
Housdorf dimension
7
Fractal dimension
N number of cells
8
Fractal dimension
  • Advantages
  • D can be considered as the measure of
    roughness, irregularity of surface
  • The results showed the dependencies between
    fractal dimension of fracture surfaces and their
    porosity were obtained
  • Disadvantages
  • Some time there is no chance to calculate D
  • It works bad with surfaces that have a small D
    (from 2 to 2.2)
  • It works bad with noised images

9
AMT Angle Measure Technique
  • Algorithm
  • Image is unfolded into 1D digitized line.
  • A number of points A are randomly chosen
    along the line.
  • For all scales S from 1 to N
  • Find points B and C points of intersection of
    circle with radius S and line
  • For each point A the Angle and Y-Difference are
    measured
  • For all measuring the Mean Angle (MA) and Mean Y
    Difference (MDY) are calculated.
  • The AMT-spectrum (dependencies of MA and MDY on
    scale S) is plotted.

10
AMT-Spectra example
11
AMT Features
  • AMT transform the 2D image into 1D spectra
    without losses the structure information
  • AMT can be used for data compression
  • AMT is highly sensitive
  • Using PCA or PLS for AMT-spectra one can analyze
    and classify the structures

12
Fractal Analysis vs. AMT
  1. Is there any correlations between fractal
    dimension of surfaces and their AMT-spectra?
  2. Is it possible to use AMT for noised images of
    surfaces?
  3. Apply the AMT to analyze the fracture surfaces of
    porous metals

13
Software
  • Fractal software simulation - C program
    (Diamond-Square Algorithm)
  • Fractal dimension calculations C program
    (Box-Counting Algorithm)
  • AMT-analysis MATLAB macros (Jun Huang,
    Telemark University College)
  • PCA-analysis The Unscrumbler

14
Simulated fractal surfaces
15
The results of PCA of AMT spectra
225 specimen with Df from 2.1 to 2.9
16
The results of PCA of AMT spectra
Outliers detection and scores w/o outliers
17
The results of PCA of AMT spectra
The result for specimen with D2.1 and 2.9
18
Conclusions
  • PCA-analysis of AMT-spectra of fractal surfaces
    allow to make a classification depending on
    fractal dimension
  • Scores plot shows that the clouds of samples
    with Dlt2.5 are overlapped
  • Score plot shows that the samples with greater D
    are arranged closely than others

19
Fractal analysis vs. AMT. Noised images
  • The real fracture surfaces is differ from
    simulated fractal surfaces first of all with
    presence of noise because of imperfection of
    devices, external influence and so on.
  • The task is to add the noise to simulated fractal
    surfaces and to compare fractal analysis and AMT
    results.

20
Simulated surfaces with Gauss noise
Original D 2.5 Calculated D 2.7
21
AMT results
- Noised Images
- w/o Noise
22
AMT-results
- Noised Images
- w/o Noise
23
Conclusions
  • Fractal analysis doesnt allow to classify noised
    images the calculated and initial fractal
    dimension are in not close agreement
  • PCA-results of AMT-spectra of noised images show
    that clouds of samples with equal D are more
    overlapped and stretched along PC1
  • In further investigations one can use the fractal
    dimension of surface as an additional variable in
    PCA analysis
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