310 Surface strain mapping

The strain field on the surface of a metallic foam resulting from thermome-chanical loading can be measured using a technique known as surface strain mapping. The surfaces of cellular metals are irregular, with the cell membranes appearing as peaks and troughs, allowing in-situ optical imaging to be used to provide a map of surface deformation. Commercial surface displacement analysis equipment and software (SDA) are available from Instron (1997). The SDA software performs an image correlation analysis by comparing pairs of digital images captured during the loading history. The images are divided into sub-images, which provide an array of analysis sites across the surface. Displacement vectors from these sites are found by using 2D-Fast Fourier Transform (FFT) comparisons of consecutive pairs of sub-images.

The method requires surface imaging, for which a commercial video camera with a CCD array of 640 x 480 or 1024 x 1528 pixels is adequate, preferably with a wide-aperture lens (F/1.4) and fiber-optic light source. Since cellular metals exhibit non-uniform, heterogeneous deformation, the field of view should be optimized such that each unit cell can be mapped to approximately 50 pixels in each direction. The analysis can be carried out by applying FFTs to a 32-pixel square array of sub-images, centered at nodal points eight pixels apart, such that the deformation of each unit cell is represented by at least four nodal points in each direction.

The method relies on the recognition of surface pattern. The foam surface can be imaged directly, relying on the irregular pattern of surface cell-edges for matching between consecutive frames. Alternatively, a pre-stretched latex film sprayed with black and white emulsion to give a random pattern can be bonded to the surface. During loading, the film follows the cell shape changes without delamination. While the latex film method is more accurate, direct imaging of the surface provides essentially the same continuum deformation field, and is preferred because of its simplicity.

Deformation histories for the Alporas material are visualized as false color plots of components of strain in the plane of the surface (Figure 3.9). Maps of the incremental distortion at loadings between the start of the non-linear response and the onset of the plateau reveal that localized deformation bands initiate at the onset of non-linearity having width about one cell diameter. Within each band, there are cell-sized regions that exhibit strain levels about

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Figure 3.9 Distortional strain maps for incremental loading : Top row: incremental distortion at various load levels. Middle row: maps of accumulated distortion at various load levels along the deformation history. Bottom row: incremental distortion at various unloading levels

Figure 3.9 Distortional strain maps for incremental loading : Top row: incremental distortion at various load levels. Middle row: maps of accumulated distortion at various load levels along the deformation history. Bottom row: incremental distortion at various unloading levels

an order of magnitude larger than the applied strain. Outside the bands, the average strains are small and within the elastic range. The principal strains reveal that the flow vectors are primarily in the loading direction, normal to the band plane, indicative of a crushing mode of deformation. The cumulative distortions exhibit similar effects over the same strain range.

As an example or the information contained in surface strain maps, consider the following features of Figure 3.9:

1. Strain is non-uniform, as seen in the top set of images. Bands form at the onset of non-linearity (site A) and then become essentially inactive. Upon further straining new bands develop. Some originate at previously formed bands, while others appear in spatially disconnected regions of the gage area.

2. Deformation starts at stress levels far below general yield. Plasticity is evident in the second set of images at stresses as low as 0.45 of the plateau stress.

3. Some of the strain is reversible. The bands in the bottom sequence of images show reverse straining as the sample is unloaded.

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