Abstract
Identifying local thickness information of fibrous or highly porous structures is challenging. The analysis of tomography data calls for computationally fast, robust and accurate algorithms. This work systematically investigates systematic errors in the thickness computation and the impact of observed deviations on the predicted mechanical properties using a set of 16 model structures with varying ligament shape and solid fraction. Strongly concave, cylindrical, and convex shaped ligaments organized in a diamond structure are analyzed. The predicted macroscopic mechanical properties represent a highly sensitive measure for systematic errors in the computed geometry. Therefore, the quality of proposed correction methods is assessed via FEM beam models that can be automatically generated from the measured data and allow an efficient prediction of the mechanical properties. The results show that low voxel resolutions can lead to an overprediction of up to 30% in the Young’s modulus. A model scanned with a resolution of 200 voxels per unit cell edge (8M voxels) reaches an accuracy of a few percent. Analyzing models of this resolution with the Euclidean distance transformation showed an underprediction of up to 20% for highly concave shapes whereas cylindrical and slightly convex shapes are determined at high accuracy. For the Thickness algorithm, the Young’s modulus and yield strength are overpredicted by up to 100% for highly concave ligament shapes. A proposed Smallest Ellipse approach corrects the Thickness data and reduces this error to 20%. It can be used as input for a further robust correction of the Thickness data using an artificial neural network. This approach is highly accurate with remnant errors in the predicted mechanical properties of only a few percent. Furthermore, the data from the FEM beam models are compared to results from FEM solid models providing deeper insights towards further developments on nodal corrections for FEM beam models. As expected, the FEM beam models show an increasing overprediction of the compliance with increasing solid fraction. As an unexpected result, the mechanical strength can however be underpredicted or overpredicted, depending on the ligament shape. Therefore, a nodal correction is needed that solves contradicting tasks in terms of stiffness and strength.
Highlights
Lacking a detailed morphological and topological description of the microstructure, the structure-property relationship of open-pore materials, such as metal foams, elastomeric foams, or Nanoporous gold (NPG) is commonly described by the GibsonAshby scaling law, in which the solid fraction is the most important parameter characterizing the materials morphology (Gibson and Ashby, 1997; Ashby et al, 2000)
Richert and Huber (2018) mathematically calculated the influence on the overestimated ligament diameters on the mechanical stiffness for single parabolic ligaments, showing an overestimation by up to a factor of 8. These results clearly show the significance of the error to be expected as function of the ligament geometry, but it is unclear how strong this effect is reflected in the macroscopic properties of a Representative Volume Element (RVE)
This study focuses on analyzing the influence of the Thickness and Euclidean distance transformation (EDT) algorithm on NPG-like RVEs, which are based on known geometries
Summary
Lacking a detailed morphological and topological description of the microstructure, the structure-property relationship of open-pore materials, such as metal foams, elastomeric foams, or Nanoporous gold (NPG) is commonly described by the GibsonAshby scaling law, in which the solid fraction is the most important parameter characterizing the materials morphology (Gibson and Ashby, 1997; Ashby et al, 2000). Hu et al (2016), Mangipudi et al (2016), and (Ziehmer et al, 2016) analyzed NPG samples of larger volumes, obtained from focused ion beam (FIB) sectioning and scanning electron microscope (SEM) imaging. By these thorough works, a systematic analysis of the NPG morphology in terms of ligament size distribution and connectivity density has become possible for the first time. Because the ligaments are of nanoscale dimension, these investigations are all based on high-resolution SEM images for which techniques for an automated image processing are an asset. Hu et al (2016) and Mangipudi et al (2016) use the 3D Biggest Sphere Thickness algorithm by Hildebrand and Rüegsegger (1997) for the estimating the ligament size distribution of 3D volumes
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