Digital volume correlation: Three-dimensional strain mapping using X-ray tomography

A three-dimensional extension of two-dimensional digital image correlation has been developed. The technique uses digital image volumes generated through high-resolution X-ray tomography of samples with microarchitectural detail, such as the trabecular bone tissue found within the skeleton. Image texture within the material is used for displacement field measurement by subvolume tracking. Strain fields are calculated from the displacement fields by gradient estimation techniques. Estimates of measurement precision were developed through correlation of repeat unloaded data sets for a simple sum-of-squares displacement-only correlation formulation. Displacement vector component errors were normally distributed, with a standard deviation of 0.035 voxels (1.22 μm). Strain tensor component errors were also normally distributed, with a standard deviation of approximately 0.0003. The method was applied to two samples taken from the thigh bone near the knee. Strains were effectively measured in both the elastic and postyield regimes of material behavior, and the spatial patterns showed clear relationships to the sample microarchitectures.