Abstract
The aim of this article is to develop a methodology that is capable of generating micro-scale models of Ductile Cast Irons, which have the particular characteristic to preserve the smoothness of the graphite nodules contours that are lost by discretization errors when the contours are extracted using image processing. The proposed methodology uses image processing to extract the graphite nodule contours and a genetic algorithm-based optimization strategy to select the optimal degree of the Bézier curve that best approximate each graphite nodule contour. To validate the proposed methodology, a Finite Element Analysis (FEA) was carried out using models that were obtained through three methods: (a) using a fixed Bézier degree for all of the graphite nodule contours, (b) the present methodology, and (c) using a commercial software. The results were compared using the relative error of the equivalent stresses computed by the FEA, where the proposed methodology results were used as a reference. The present paper does not have the aim to define which models are the correct and which are not. However, in this paper, it has been shown that the errors generated in the discretization process should not be ignored when developing geometric models since they can produce relative errors of up to 35.9% when an estimation of the mechanical behavior is carried out.
Highlights
Ductile Cast Irons (DCIs) have become one of the most important materials when it is desired to manufacture mechanical components that will be exposed to low to moderate stress with complex and large shapes, due to their low production costs and their excellent castability [1]
The third section makes a comparison of the geometric behavior between the model developed with the proposed methodology, a set of models that are generated obtained with a fixed Bézier curve degree and a model obtained using a commercial software called img2CAD; in this same section, it is analyzed the CSFest and Er values that are obtained for the different models using a fixed Bézier curve degree, to demonstrate the effect that the different degrees on the circularity (CSF) of each nodule have; besides, it is shown that the optimal degree that is chosen by the methodology proposed for four particular nodules
The models that are generated are characterized by the smoothness in their curves with the objective of avoiding or mitigating the discretization errors produced when the graphite nodules contours are obtained using image processing, since the discretization process by which the graphite nodules contours are obtained, generates significant errors up to 35.9% in the estimation of the stresses that are produced in a simulation by means of a Finite Element Analysis (FEA)
Summary
Ductile Cast Irons (DCIs) have become one of the most important materials when it is desired to manufacture mechanical components that will be exposed to low to moderate stress with complex and large shapes, due to their low production costs and their excellent castability [1]. The microscale-models are usually obtained from the nodules contours of a DCI micrograph (Figure 1a) using image processing techniques, as shown, and from this data, the geometric models are generated, as it can be observed, in this figure the model was generated using commercial software called img2CAD (Img2CAD LLC., Cologne, Germany). As it can be seen, some regions of the contour of the model are completely straight due to the contour that is computed at the pixel level; besides, other sections have corners with angles of 45◦ and 90◦ , which can produce stress concentrators in a FEA. These geometric characteristics are a part of the errors that are produced by the discretization at the pixel level at the time of obtaining the contours through image processing
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