This dataset corresponds to a series of phase-enhanced tomographic images recorded during a monotonic mechanical tensile test with a polymer material. Tomographic measurements were performed at the PSICHE beamline, SOLEIL synchrotron. The reconstructed voxel size is 1.3 µm. The reconstruction was performed with pyHST (filtered back-projection) using the paganin filter with a propagation distance of 15 pixels. Each tomography measurement consists of 1000 radiographs of 1024×2048 pixels acquired over 180°. The binary reconstructed volumes are therefore 1024×2048×2048 voxels encoded with a dynamic range of 32 bits (floating-point). The 44 measurements taken during the mechanical test represent a volume of 700 GB. The reduction strategy used is based on a thresholding of the specimen in each volume and a zeroing of the voxels outside the sample. In the preserved voxels, the binary representation of each value is truncated to have a precision of the order of the experimental uncertainties: the insignificant least significant bits are replaced by 0s which, combined with a transposition of the order of the bits just before compression (bit shuffling), makes it possible to drastically increase the compressibility of the data. The data is arranged in an HDF5 container using block access with on-the-fly compression/decompression. The total size of the dataset is thus reduced with a reduction ratio of 16:1 using Zstandard level 1. The mask used as well as even smaller volumes (pixel binning 2×2 and 4×4, dynamic range reduction on 4 or 8 bits) are added to allow fast access to very small data if needed, in the same fashion as the thumbnail used in some 2D image formats. The footprint of the reduced version as described is 47 GB. The format is self-described and contains additional metadata.