Multiscale finite element modeling of sheet molding compound (SMC) composite structure based on stochastic mesostructure reconstruction

Abstract Predicting the mechanical behavior of the chopped carbon fiber Sheet Molding Compound (SMC) due to spatial variations in local material properties is critical for the structural performance analysis but is computationally challenging. Such spatial variations are induced by the material flow in the compression molding process. In this work, a new multiscale SMC modeling framework and the associated computational techniques are developed to provide accurate and efficient predictions of SMC mechanical performance. The proposed multiscale modeling framework contains three modules. First, a stochastic algorithm for 3D chip-packing reconstruction is developed to efficiently generate the SMC mesoscale Representative Volume Element (RVE) model for Finite Element Analysis (FEA). A new fiber orientation tensor recovery function is embedded in the reconstruction algorithm to match reconstructions with the target characteristics of fiber orientation distribution. Second, a metamodeling module is established to improve the computational efficiency by creating the surrogates of mesoscale analyses. Third, the macroscale behaviors are predicted by an efficient multiscale model, in which the spatially varying material properties are obtained based on the local fiber orientation tensors. Our approach is validated through experiments at both meso- and macro-scales, such as tensile tests assisted by Digital Image Correlation (DIC) and mesostructure imaging.

[1]  J. Feder.  Random sequential adsorption , 1980 .

[2]  Tai Hun Kwon,et al.  Invariant-based optimal fitting closure approximation for the numerical prediction of flow-induced fiber orientation , 2002 .

[3]  B. Budiansky.  On the elastic moduli of some heterogeneous materials , 1965 .

[4]  G. Matheron,et al.  A Simple Substitute for Conditional Expectation : The Disjunctive Kriging , 1976 .

[5]  Wenlong Tian,et al.  Numerical evaluation of effective elastic properties of composites reinforced by spatially randomly distributed short fibers with certain aspect ratio , 2015 .

[6]  Kenneth E. Evans,et al.  The packing of thick fibres , 1989 .

[7]  N. Kikuchi,et al.  Preprocessing and postprocessing for materials based on the homogenization method with adaptive fini , 1990 .

[8]  David H. Allen,et al.  Multiscale Modeling and Simulation of Composite Materials and Structures , 2008 .

[9]  Y. Benveniste,et al.  A new approach to the application of Mori-Tanaka's theory in composite materials , 1987 .

[10]  C. Rudd,et al.  Characterisation of random carbon fibre composites from a directed fibre preforming process: The effect of tow filamentisation , 2007 .

[11]  Somnath Ghosh,et al.  Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model , 1996 .

[12]  A. Philipse,et al.  Random packings of spheres and spherocylinders simulated by mechanical contraction. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[14]  Yong-Taek Im,et al.  Numerical simulation of three-dimensional fiber orientation in short-fiber-reinforced injection-molded parts , 2002 .

[15]  Wilson K. S. Chiu,et al.  Determining the representative volume element size for three-dimensional microstructural material characterization. Part 1: Predictive models , 2015 .

[16]  Suresh G. Advani,et al.  The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites , 1987 .

[17]  Pedro P. Camanho,et al.  Generation of random distribution of fibres in long-fibre reinforced composites , 2008 .

[18]  Ulrich Gabbert,et al.  Numerical evaluation of effective material properties of randomly distributed short cylindrical fibre composites , 2007 .

[19]  Dominique Jeulin,et al.  Towards gigantic RVE sizes for 3D stochastic fibrous networks , 2014 .

[20]  N. Warrior,et al.  Three-dimensional numerical modelling of discontinuous fibre composite architectures , 2011 .

[21]  R. Chang,et al.  Accurate predictions of orientation dependent modulus in short‐fiber‐reinforced composite with experimental validation , 2018 .

[22]  C. L. Tucker,et al.  Orientation Behavior of Fibers in Concentrated Suspensions , 1984 .

[23]  Charles L. Tucker,et al.  Orthotropic closure approximations for flow-induced fiber orientation , 1995 .

[24]  Assimina A. Pelegri,et al.  Numerical generation of a random chopped fiber composite RVE and its elastic properties , 2008 .

[25]  C. Qian,et al.  3D geometric modelling of discontinuous fibre composites using a force-directed algorithm , 2017 .

[26]  Wenlong Tian,et al.  Representative volume element for composites reinforced by spatially randomly distributed discontinuous fibers and its applications , 2015 .

[27]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[28]  P. Hine,et al.  Orientation Averaging for Stiffness and Thermal Expansion of Short Fiber Composites , 2002 .

[29]  Xiang Ling,et al.  Numerical Simulation of Saturation Behavior of Physical Properties in Composites with Randomly Distributed Second-phase , 2005 .

[30]  Tai Hun Kwon,et al.  Improved model of orthotropic closure approximation for flow induced fiber orientation , 2001 .

[31]  R. Hill.  Elastic properties of reinforced solids: some theoretical principles , 1963 .

[32]  Anil K. Jain,et al.  Fingerprint Image Enhancement: Algorithm and Performance Evaluation , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  Mahesh Gupta,et al.  Fiber orientation and mechanical properties of short‐fiber‐reinforced injection‐molded composites: Simulated and experimental results , 1993 .

[34]  Assimina A. Pelegri,et al.  Numerical characterization of material elastic properties for random fiber composites , 2008 .

[35]  T. Miloh,et al.  A generalized self‐consistent method for the effective conductivity of composites with ellipsoidal inclusions and cracked bodies , 1988 .

[36]  A. J. Booker,et al.  A rigorous framework for optimization of expensive functions by surrogates , 1998 .

[37]  Assimina A. Pelegri,et al.  Analysis of 3D random chopped fiber reinforced composites using FEM and random sequential adsorption , 2008 .

[38]  Yi Pan.  Stiffness and progressive damage analysis on random chopped fiber composite using FEM , 2010 .

[39]  U. Gabbert,et al.  Evaluation of effective material properties of randomly distributed short cylindrical fiber composites using a numerical homogenization technique , 2007 .

[40]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[41]  G. P. Tandon,et al.  Average stress in the matrix and effective moduli of randomly oriented composites , 1986 .

[42]  Somnath Ghosh,et al.  Small deformation multi-scale analysis of heterogeneous materials with the Voronoi cell finite element model and homogenization theory , 1996 .

[43]  Hui Liu,et al.  Development of RVE-embedded solid elements model for predicting effective elastic constants of discontinuous fiber reinforced composites , 2016 .

[44]  Tungyang Chen,et al.  Mori-Tanaka Estimates of the Overall Elastic Moduli of Certain Composite Materials , 1992 .

[45]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[46]  Hongyi Xu,et al.  A generalized uncertainty propagation criterion from benchmark studies of microstructured material systems , 2013 .

[47]  Hongyi Xu,et al.  Modeling and Simulation of Compression Molding Process for Sheet Molding Compound (SMC) of Chopped Carbon Fiber Composites , 2017 .

[48]  Somnath Ghosh,et al.  Multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method , 1995 .

[49]  Somnath Ghosh,et al.  A Voronoi Cell Finite Element Model for Random Heterogeneous Media , 1994 .