4D mapping of internal mechanical quantities

Fig. 1 Number of grains and pores in aluminum. The values are the numbers contained in an X-ray CT specimen of a standard volume.

@X-ray CT visualizes all microstructures larger than the resolution within the field. We proposed to determine the physical displacements of all microstructure characteristics by 4D observation, and map the internal mechanical quantities(Review paper 1). We have so far mapped displacement, distortion, and the driving force of crack propagation (link). In combination with the grain boundary visualization technologies described in gHigh-resolution imagingh (link), we have successfully developed a technology for tracing in 4D the crystal grain deformation behavior within materials (Paper 5,6). As an example, distortion mapping is described below. If the number of microstructure characteristics to be visualized is sufficiently large, Delaunay division can be applied to divide the space into three-dimensional spaces that do not overlap, by using given point groups. Because the displacement is known for all apices, the distortion of the tetrahedron and its internal distortion can be determined. At present, this is the only method for experimentally measuring mechanical quantities such as distortion at high densities inside opaque materials. Metals have several tens to several hundreds of thousands of characteristics per 1 mm3, as shown in Fig. 1, and thus a sufficiently large density of characteristics.


Fig. 2 Conceptual diagram of microstructure tracking. The 3D/4D distributions of mechanical quantities, such as distortion, stress, and the driving force of crack propagation, are determined by tracking all grains and pores while heating and subjecting to plasticity processing, loading from outside, etc., and measuring their physical displacements.

@Key 4D image analysis technologies are those that can correctly track a vast number of characteristics under any disturbance (loading, high temperatures, etc.). We have developed and implemented a host of tracking methods, including matching parameters, which are based on the volume, surface area and the center of gravity of the characteristics(Paper 1); a spring model for solving the matching in areas where characteristics are coagulated(Paper 1);a method for predicting orbits based on displacements in previous phases; and a method that uses the radial basis function, which predicts orbits by determining local displacement fields from specific kinds of characteristic(Paper 3).


Fig. 3 Conceptual diagram of matching parameters and spring model

@The methods are schematically illustrated in Figs. 3 and 4. Today, almost 100% of characteristics are correctly tracked, enabling high-density and high-precision mapping.

Fig. 4 Conceptual diagram of local displacement measurement by the radial basis function method


Fig. 5 Measured internal distortion and its distribution in Al-Mg alloy under unconfined compression

@Figure 5 is one of the results of the first-ever 4D mapping of local distortion distribution of metal during the rolling process(Paper 3). Even under simple unconfined compression, the local distribution of distortion was very complex, and there were regions where the distortion was tensile (yellow). This was caused by the mismatching of crystal orientation between adjacent crystal grains. Local disappearance behaviors of pores can also be quantitatively explained by local distortion distribution.


Fig. 6 Comparison between 4D-equivalent strain measurement by X-ray CT (left) and image-based simulation (only crack shapes considered) of the same cross section

@Figure 6 shows an example of cracked materials (Paper 2,4). The calculation results of image-based simulation (microstructure disregarded) are also shown in the figure, in which the crack shape was used as the boundary condition. Although it was simple Mode I loading, the distortion field at the tip of the crack was asymmetrical below and above the crack (Fig. 6 (right)), and was highly inhomogeneous due to the non-uniform distribution of grains (Fig. 6(left)). This is quite different from what is predicted by fracture mechanics.

Review paper

  1. H. Toda, M. Kobayashi, Y. Suzuki, A. Takeuchi, K. Uesugi, 3Dฅ4D Materials Science: Its Current State and Prospects, Hihakaikensa, Vol.58CNo.10C2009C433-438
  2. H. Toda, M. Sato, H. Okuda, M. Kobayashi, Observation and analysis of materials with synchrotron radiation, Keikinzoku Vol.61, No.1, 2011

Research paper

  1. M. Kobayashi, H. Toda, Y. Kawai, T. Ohgaki, K. Uesugi, D.S. Wilkinson, T. Kobayashi, Y. Aoki, M. Nakazawa, High-density three-dimensional mapping of internal strain by tracking microstructural features, Acta Materialia, Vol.56, Issue 10, 2008, 2167-2181
  2. L. Qian, H. Toda, K. Uesugi, M. Kobayashi and T. Kobayashi, Direct observation and image-based simulation of three-dimensional tortuous crack evolution inside opaque materials, Physical Review Letters, Vol.100, No.11, 2008, 115505
  3. H. Toda, K. Minami, K. Koyama, K. Ichitani, M. Kobayashi, K. Uesugi, Y. Suzuki, Healing behavior of preexisting hydrogen micropores, in aluminum alloys during plastic deformation, Acta Materialia, Vol.57, 2009, 4391-4403
  4. H. Zhang, H. Toda, P.C. Qu, Y. Sakaguchi, M. Kobayashi, K. Uesugi, Y. Suzuki, Three-dimensional fatigue crack growth behavior in an aluminum alloy investigated with in situ high-resolution synchrotron X-ray microtomography, Acta Materialia, Vol.57, No.11, 2009, 3287-3300
  5. H. Toda, Y. Okawa, M. Kobayashi, K. Uesugi and Y. Suzuki, Acta Materialia, to be submitted.
  6. H. Toda, D. LeClere, Y. Okawa, M. Kobayashi, K. Uesugi and Y. Suzuki, Acta Materialia, to be submitted.