Arabian Journal for Science and Engineering https://doi.org/10.1007/s13369-018-3465-y RESEARCH ARTICLE - MECHANICAL ENGINEERING A New Approach to Modeling the Ductile Cast Iron Microstructure for a Finite Element Analysis Jesus A. Basurto-Hurtado 1 · G. I. Perez-Soto 2 · Roque A. Osornio-Rios 1 · Aurelio Dominguez-Gonzalez 2 · L. A. Morales-Hernandez 1 Received: 5 November 2017 / Accepted: 12 July 2018 © King Fahd University of Petroleum & Minerals 2018 Abstract In this article, a methodology for the generation of geometric models representing the microstructure of a ductile cast iron (DCI) is presented. This methodology is based on a series of image processing algorithms to extract the graphite nodules contours and the utilization of the Bezier curves to smooth the geometric models curves. For the contours obtained by the image processing stage and generated geometric models, the circularity is calculated using the circular shape factor index, in order to analyze the induced error through the discretization process by the image processing stage and the variation of the circularity as the design parameters of the geometric modeling change. On the other hand, the design parameters effect of the geometric models on the stress behavior in the microstructure, through a finite element analysis, is also analyzed. It is shown that as the Bezier curve degree increases, the circularity of the geometric models decreases, thus increasing the maximum stresses produced in the DCI microstructure. Further, it is also found that the number of interpolation points has a significant effect on the mechanical properties when the Bezier curves degrees are equal to 10 and 12 than for the lower degrees. Keywords Bezier curves · Geometric modeling · Finite element analysis · Circularity · Ductile cast iron · Image processing 1 Introduction Ductile cast irons (DCIs) are widely used in the automo- tive sector for the manufacture of cardan shafts, crankshafts and monoblocks due to the interesting combination of prop- erties such as high ductility, high mechanical strength, and good wear resistance. One way to improve the mechanical properties of these components is to increase their volume, but at the expense of increasing the weight and cost of the vehicle; additionally, the performance of the pieces could be reduced. Another alternative that has been recently used to optimize the mechanical properties is the modification of the microstructural properties of a ductile cast iron (DCI), as it has been demonstrated, nodular density, nodularity, graphite B L. A. Morales-Hernandez lamorales@hspdigital.org 1 CA Mecatronica, Facultad de Ingenieria, Universidad Autonoma de Queretaro (UAQ), Av. RioMoctezuma 249, Col. San Cayetano, 76807 San Juan del Rio, Queretaro, Mexico 2 Facultad de Ingenieria, Universidad Autonoma de Queretaro (UAQ), Cerro de las Campanas S/N, Col. Las Campanas, 76010 Santiago de Queretaro, Queretaro, Mexico percentage and spatial distribution have a direct influence on certain mechanical properties such as wear, elastic modu- lus, yield and tension strength, and fatigue behavior [1–6]. The mechanical properties of DCIs are especially dependent on the graphite shape, which according to the state of art it has been determined as spherical or semi-spherical [7,8]. Among all the different shape factors used to evaluate the shape of graphite, the most used in literature is the circular shape factor (CSF), as it is useful to measure the circular- ity of the graphite nodules. The CSF value is within a range of [0, 1], where 1 is reached only by a perfect circular nod- ule, DCIs have a CSF value that varies between 0.9 and 1 [9]. Recently, one of the techniques used to analyze the rela- tionship between microstructural and mechanical properties is the finite element method (FEM) [10,11]. The investiga- tions that have worked with FEM require the use of geometric models which are generated directly from the contours of the graphite nodules, which are obtained from the microscopic images, making them exposed to distortions due to geomet- ric discretization, and thus, affecting the DCIs circularity. In this regard, the abovementioned distortion could have a significant effect on the estimation of mechanical proper- ties. Therefore, it is necessary to develop a methodology that 123