Formation of three dimensional crack patterns

• Applicants: Dr.-Ing. Martin Hofmann; Professor Dr.-Ing. Wolfgang Tillmann
• Subject Area: Mechanical Properties of Metallic Materials and their Microstructural Origins ; Metallurgical, Thermal and Thermomechanical Treatment of Materials
• Term: from 2012 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 213158658

The aim of the project is a detailed understanding for the mechanisms of the formation of three dimensional (3D) crack patterns as a result of inhomogeneous shrinkage processes. During the 1st phase the method of fracture mechanical 3D bifurcation analysis based on a series expansion of the crack contour itself was developed successfully. This method now shall also be applied to cases with transient thermal shock loads at ceramics. Thereby both, the penetration depth of the cracks at overload cases and the residual strength can be predicted computationally. In addition, the impact on the crack propagation by internal stresses that develop during the thermal sputtering of insulation layers shall be examined. The drying procedure of ceramic precursor material in small tubes leads to star-shaped crack patterns. The mentioned bifurcation analysis shall be applied to investigate this phenomenon as well.For the first time, 3D crack patterns with curved crack surfaces were computed in the last period of the project. This calculation verified successfully that hexagonal cross sections in the columnar structures of basalt are energetically preferred during the process of development. In this simulation it is assumed that the crack front propagates in a direction at which the released energy is at a maximum. Now, the unexplained phenomenon of the oscillating crack surfaces of basalt columns shall be investigated using the same approach.In the experimental part of the project imaging techniques with significantly higher resolution shall be developed in order to improve the imaging of thermal shock cracks in ceramics. That way, cracks with small openings will become detectable. This methodical improvement aims at a quality of the measurement of crack spacings and crack depths that suffices for a verification of the expected results of the simulation. In order to map the cracks more clearly the techniques of computer laminography, serial sectioning technique with dye penetrant testing and tomographic microscopy are compared. Furthermore, instead of the formerly used ceramics with their tiny crack openings, now more suitable ceramics like for example porcelain or pottery shall be subjected to thermal shocks.Moreover, the software that processes the 3D images obtained by X-ray analyses techniques will be enhanced to detect the cracks more robust. For this purpose, the evaluation of each tomographic slice will incorporate the information in the adjacent tomographic slices. A software solution that tracks the column transitions occurring during the development of crack patterns is planned by which the transitions between several column arrangements are identified and their frequencies are quantified . In so doing, the analyses of experimentally obtained 3D images of crack patterns in ceramic systems and in dried starch-water-suspensions will contribute to the general understanding of the development of 3D crack patterns.

• DFG Programme: Research Grants
• Major Instrumentation: Digitaler Flachbilddetektor
• Instrumentation Group: 4020 Röntgenkameras für Feinstruktur und Topographie