Holographic-interferometric investigations of microdeformations in heterogeneous materials
by Dr.-Ing. Wolfgang Hintze
The determination by numerical simulation of mechanical field quantities such as deformations and stresses on the local level and taking the material microstructure into account, is a very active field of research. On the other side only few experimental results exist able to verify numerical results and to validate the underlying methodologies. In this work holographic-interferometric interference patterns are determined describing the three-dimensional microdisplacements of the surface of a notched cantilever bar of a microscopically heterogeneous steel. Sandwich holograms sensitized with ammonium-dichromate are used. The double exposured reflection-interferograms show the deformation state in form of interference fringe patterns together with the changes of the surface structure. The displacement field at the bottom of the notch for one load step was calculated with a finite-element program in the region of the two-phase structure, to compare it with the experimentally obtained.
The optical pathlength difference of the illuminating waves between two states results in a change of the interference phase difference Df. The displacement of point P to P' gives rise to a stationary intensity distribution:
I(P,P')=|E(P)+E(P')|2 = 2 Io(P)[1+cos(Df(P))]
To detect such an displacement, in this work two holograms are placed in a sandwich manner, whereas the upper plate is in a rest position and the other is fixed on the moving part of the specimen. The notched cantilever bar is stepwise loaded with a single force and at each step two dichromated gelatin holograms are recorded simultaneously. The first exposure is the reference state. After the load has been increased in one small step, the second exposure was taken. This state is the reference state for the following loadstep.
Figure 1. Sandwich arrangement
The two photographs in figure 2 show a pair of sandwich holograms of the 13-th load step, on both sides of a crack. The rupture behaviour is recognizable, on both sides (upper/lower hologram) of the visible crack the occuring displacements only exists in the surface of the specimen, because the fringes of the shown sandwich holograms are completely different. Several carbides must have been broken - some interrupted fringes indicate this -, whereas the rest of the observed displacement fields - because of their noninterrupted lines - indicate, that the interface between the matrix and the hard phases assumed to be bonded. The both fringe patterns are joined together in form of a fringe skeleton, performed by interactive manual fringe counting. This process is visualized in figure 3. The distance between two neighbouring skeleton lines is equal to the wavelength lambda = 488 nm.
Figure 4 shows on the left side a photograph of the visible broken carbides - immediately taken after the respective load step - and on the other side a photograph of the corresponding part of the reconstructed interferogram (lower plate 2). The crackpath and the simplified contours of the six broken carbides are marked. The magnification factor is 180. The numerical calculation also takes into account the remaining not marked carbides. In this work the experimentally obtained displacement fields are compared with a finite-element calculation of the displacements.
Figure 5. Microscopic model
The displacement field of the microstructure was calculated with the two-dimensional finite-element program CRACKAN. The numerical solution is obtained with a macroscopic model to simulate the bending test, and a microscopic model - shown in figure 5 -, which takes into account the presence of the two-phase structure in order to simulate the rupture mecanisms. The macroscopic model was calculated with the program IDEAS.
The comparison of the theoretically calculated micro-displacement fields with the experimentally obtained fields shows a fairly good agreement of the qualitative form of the fringes and the order of magnitude of the displacements. Nevertheless the numerical results differ from the fringes in the interferograms. As a matter of fact, the numerical values of the displacements are in local regions much more smaller than those experimentally obtained.