2-D Deformation Measurement by Digital Image Correlation (DIC)

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					                                                               2-D Deformation Measurement by Digital
                                                                       Image Correlation (DIC)
                                                    Contact: Jean-José Orteu (Jean-Jose.Orteu@enstimac.fr) – Laurent Robert (Laurent.Robert@enstimac.fr)


                                                                               Digital Image Correlation (DIC)
                                                                                      time t0           time t1                   time t2
    Purpose: Deformation measurement from a                                                                                                                The gray levels of image patches are
    sequence of images taken by a single camera                                                                                                            matched, assuming that they present
                                                                                                                                                           some similarity, by using Digital Image
• Full-field measurement                                                                                                                                   Correlation (DIC).
• Non-intrusive
                                                                                                                                                           The image correlation technique is
• Planar specimen only
                                                                                                                                                           efficient on textured objects. If the
• No out-of-plane motion                                                                                                                                   objects are not enough textured
                                                                                                                                                           naturally, it only takes a few seconds to
                                                                                                                                                           mark the surface of the object with a
                                                                                                                                                           random pattern of spray paint.

                                                                      The similarity of the image patches is computed using a correlation criterion (similarity score).


                                                                       The specimen is deformed: the correlation algorithm must also deform the correlation window
                                                                       (adaptive correlation window shape). The displacement transformation is modeled (parametric
                                                                       representation) and the parameters of the transformation are estimated using optimization algorithms
                  Specimen deformation
                                                                       (Levenberg-Marquardt).
         Time t                           Time t’




    To achieve sub-pixel accuracy the correlation algorithms use gray value interpolation:
    • Optimization algorithms require the criterion to be continuous over its parameter space
    • Images are discrete: we need to reconstruct the continuous information by means of
    interpolation
    • B-Splines are a good choice for that purpose

                                                                                                                                        Raw image                         B-spline interp.
                                                                                                                                                                Bi-linear B-spline interp.                   B-spline interp.
                                                                                                                                                                                                    Bi-cubic B-spline interp.


                                         “Punch” deformation                                                          The DIC technique gives the displacement field. The strain field
                                                                                                                      is computed by numerical derivation of the displacement field.
      Initial image       Deformed image
                                                                    Displacement field
y                                                              Ux                        Uy
                                                                                                                             Rotation motion
                                                                                                                                                                                      Displacement field
                                                                                                                                                                                Ux                          Uy

                                                                                                                        Initial                    Rotation
                                                                                                                       image                      10 degrees
                      x



                                                    Strain field (computed by numerical derivation)
                                                      ε xx                 ε
                                                                           yy                 xy    ε
                                                                                                                                                    Rotation
                                                                                                                       Area of
                                                                                                                                                   20 degrees
                                                                                                                       interest




                                                          Results obtained using Vic-2D® software                                                                        Results obtained using Vic-2D® software




                                                                                          Some applications

    Tensile test on an elastomer sample                                                                           Tensile test on a polymer (PEI) sample                     (results obtained using Vic-2D® software)




                                                                                                                                            Area of
                                                                                                                                            interest

                               Initial
                              image
                                                                                                                                                                        Ux                                     Uy
                                                                                                                                                                                    Displacement field




                                                                                                              Strain field        εxx                              εyy                                         εxy