Measurement of the components of plastic displacement gradients in three dimensions

Abstract

A method for non-destructive characterization of plastic deformation in bulk materials is presented. The method is based on X-ray absorption microtomography investigations using X-rays from a synchrotron source. The method can be applied to materials that contain marker particles, which have an atomic number significantly different from that of the matrix material. Data were acquired at the dedicated microtomography instrument at beamline BW2 at HASYLAB / DESY, for a cylindrical aluminium sample containing W particles with an average particle diameter of 7 µm. The minimum detectable size of the maker particles is 1-2 µm with the present spatial resolution at HASYLAB. The position (x,y,z) of all the detected marker particles within 1 mm 3 was determined as function of strain. The sample was deformed in stepwise compression along the axis of the cylinder. A tomographic scan was performed after each deformation step. After a series of image analysis steps to identify the centre of mass of individual particles and alignment of the successive tomographic reconstructions, the displacements of individual particles could be tracked as a function of external strain. The particle displacements are then used to identify local displacement gradient components, from which the local 3D plastic strain tensor can be determined. This allows us to map the strain components as a function of location inside a deforming metallic solid.

Microtomography using synchrotron radiation at DESY: current status and future developments

“…A few of these application are presented in this proceeding. 7,[12][13][14][15][16][17] Here the new technique of scanning microtomography to investigate samples larger than the field of view is demonstrated.…”

Recent advances in X-ray microtomography applied to materials

“…495 Movement of marker particles within metals or in unconsolidated powders can be used very effectively to map displacement fields in response to deformation. [496][497][498][499] Specimens of Al-1 vol.-%Ti (particle diameters between 1 and 10 mm) were imaged with synchrotron microCT at the 2 mm level, and displacement gradients for deformations up to 9?5% compression were quantified. 496,497 Bulk material flow has also been studied in friction stirred welds in Al using the particle technique and synchrotron microCT.…”

“…[496][497][498][499] Specimens of Al-1 vol.-%Ti (particle diameters between 1 and 10 mm) were imaged with synchrotron microCT at the 2 mm level, and displacement gradients for deformations up to 9?5% compression were quantified. 496,497 Bulk material flow has also been studied in friction stirred welds in Al using the particle technique and synchrotron microCT. 498 Closed die compaction and sintering of powders have long been used to fabricate metal and ceramic components, but constitutive models for loose powder behaviour under intense shear deformation need to be developed.…”

Tomographic analysis and FE-simulations of MMC-microstructures under load

“…[10][11][12] In the last years, different techniques have been implemented to study displacement and strain fields in the bulk of materials starting from tomograms. Nielsen et al 13 identified several particles in the tomograms at different load stages. In the gray scaled tomograms the gray-value-weighted centers of gravity of each particle were determined, which were used to calculate the displacement gradient tensor of each particle by a least-squares fit of the relative displacement of the eight nearest neighbor particles.…”