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

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

• Sergei Kucheryavski
• Artem Govorov

Altai State University Barnaul, Russia
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Ideal life
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Deformation Structure of Porous Metals
Deformation stages (Optical microscope)
Fracture surfaces (Electronic microscope)
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Known methods

• Traditional methods
• Classical statistics methods (i.e. Mean Absolute
  Deviation)
• Textural features methods
• Alternative methods
• Fractal analysis
• The AMT technique

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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

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Housdorf dimension
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Fractal dimension
N number of cells
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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

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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.

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AMT-Spectra example
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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

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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

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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

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Simulated fractal surfaces
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The results of PCA of AMT spectra
225 specimen with Df from 2.1 to 2.9
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The results of PCA of AMT spectra
Outliers detection and scores w/o outliers
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The results of PCA of AMT spectra
The result for specimen with D2.1 and 2.9
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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

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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.

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Simulated surfaces with Gauss noise
Original D 2.5 Calculated D 2.7
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AMT results
- Noised Images
- w/o Noise
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AMT-results
- Noised Images
- w/o Noise
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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