We discuss the relevance of methods of graph theory for the study of damage in simple model materials described by the random fuse model. While such methods are not commonly used when dealing with regular random lattices, which mimic disordered but statistically homogeneous materials, they become relevant in materials with microstructures that exhibit complex multi-scale patterns. We specifically address the case of hierarchical materials, whose failure, due to an uncommon fracture mode, is not well described in terms of either damage percolation or crack nucleation-and-growth. We show that in these systems, incipient failure is accompanied by an increase in eigenvector localization and a drop in topological dimension. We propose these two novel indicators as possible candidates to monitor a system in the approach to failure. As such, they provide alternatives to monitoring changes in the precursory avalanche activity, which is often invoked as a candidate for failure prediction in materials which exhibit critical-like behavior at failure, but may not work in the context of hierarchical materials which exhibit scale-free avalanche statistics even very far from the critical load. For such anomalous systems, our novel indicators prove more effective in the analysis of digital image correlation data from experiments, as well as from large-scale numerical simulations.
The spectral dimension is a generalization of the Euclidean dimension and quantifies the propensity of a network to transmit and diffuse information. We show that, in hierarchical-modular network models of the brain, dynamics are anomalously slow and the spectral dimension is not defined. Inspired by Anderson localization in quantum systems, we relate the localization of neural activityessential to embed brain functionality -to the network spectrum and to the existence of an anomalous "Lifshitz dimension". In a broader context, our results help shedding light on the relationship between structure and function in biological information-processing complex networks.
Electron beam powder bed fusion (PBF-EB) of Ni-base superalloys such as CMSX-4 is a demanding process. Using conventional PBF-EB machines, process observation is done by mounting optical camera systems on viewing windows at the top of the build chamber. However, the concomitant metallization blocks optical observation methods with increasing build time. Therefore, build quality evaluation is normally done after the process utilizing visual inspection or subsequent metallurgical analysis. In this work, CMSX-4 is processed using a freely programmable PBF-EB machine with an electron optical (ELO) imaging system. It consists of a four-segment ELO detector and in-house developed imaging software. The ELO system works reliably for almost 30 h of build time and allows a layerwise monitoring of the build area. A comparison of in-situ ELO monitoring and the sample surfaces shows remarkable accordance. Furthermore, ELO imaging is applied to exemplarily document surface cracking over long build times. Therefore, the present study successfully demonstrates the application of ELO imaging for improved process control under the demanding test conditions of Ni-base superalloys.
X-ray-computed tomography (CT) is today’s gold standard for the non-destructive evaluation of internal component defects such as cracks and porosity. Using automated standardized evaluation algorithms, an analysis can be performed without knowledge of the shape, location, or size of the defects. Both the measurement and the evaluation are based on the fact that the component has no internal structures or cavities. However, additive manufacturing (AM) and hybrid subtractive procedures offer the possibility of integrating internal structures directly during the building process. The examination of powder bed fusion (PBF) samples made of Ti64 and PA12 showed that the standardized evaluation methods were not able to identify internal structures correctly. Different evaluation methods for the CT-measured values were analyzed and recommendations on a procedure for measuring internal structures are given.
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