Continuous Fiber Angle Topology Optimization for Polymer Composite Deposition Additive Manufacturing Applications

Mechanical properties of parts produced with polymer deposition additive manufacturing (AM) depend on the print bead direction, particularly when short carbon-fiber reinforcement is added to the polymer feedstock. This offers a unique opportunity in the design of these structures since the AM print path can potentially be defined in a direction that takes advantage of the enhanced stiffness gained in the bead and, therefore, fiber direction. This paper presents a topology optimization approach for continuous fiber angle optimization (CFAO), which computes the best layout and orientation of fiber reinforcement for AM structures. Statically loaded structures are designed for minimum compliance where the adjoint variable method is used to compute design derivatives, and a sensitivity filter is employed to reduce the checkerboard effect. The nature of the layer-by-layer approach in AM is given special consideration in the algorithm presented. Examples are provided to demonstrate the applicability of the method in both two and three dimensions. The solution to our two dimensional problem is then printed with a fused filament fabrication (FFF) desktop printer using the material distribution results and a simple infill method which approximates the optimal fiber angle results using a contour-parallel deposition strategy. Mechanical stiffness testing of the printed parts shows improved results as compared to structures designed without accounting for the direction of the composite structure. Results show that the mechanical properties of the final FFF carbon fiber/polymer composite printed parts are greatly influenced by the print direction, and optimized material orientation tends to align with the imposed force direction to minimize the compliance.

[1]  V. Sundararajan,et al.  Topology optimization for additive manufacturing of customized meso-structures using homogenization and parametric smoothing functions , 2010 .

[2]  D. Baird,et al.  Thermoplastic composites reinforced with long fiber thermotropic liquid crystalline polymers for fused deposition modeling , 1998 .

[3]  L. Fambri,et al.  Fused deposition modelling with ABS–graphene nanocomposites , 2016 .

[4]  H. P. Mlejnek,et al.  Some aspects of the genesis of structures , 1992 .

[5]  D. Tortorelli,et al.  Design sensitivity analysis: Overview and review , 1994 .

[6]  K. Lozano,et al.  Nanofiber-reinforced polymers prepared by fused deposition modeling , 2003 .

[7]  D. Smith,et al.  TOPOLOGY OPTIMIZATION FOR 3 D MATERIAL DISTRIBUTION AND ORIENTATION IN ADDITIVE MANUFACTURING , 2017 .

[8]  Randall F. Lind,et al.  The Economics of Big Area Addtiive Manufacturing , 2016 .

[9]  Guo Ping Li,et al.  Topology Optimization of Orthotropic Material Structure , 2008 .

[10]  Nathan K. Spinnie.  Large scale fused deposition modeling : the effect of process parameters on bead geometry. , 2016 .

[11]  O. Sigmund.  Morphology-based black and white filters for topology optimization , 2007 .

[12]  Andres Tovar,et al.  An efficient 3D topology optimization code written in Matlab , 2014 .

[13]  L. Kollár,et al.  Mechanics of Composite Structures , 2003 .

[14]  Douglas E. Smith,et al.  Rheology Effects on Predicted Fiber Orientation and Elastic Properties in Large Scale Polymer Composite Additive Manufacturing , 2018 .

[15]  Christopher B. Williams,et al.  Multiple-Material Topology Optimization of Compliant Mechanisms Created Via PolyJet Three-Dimensional Printing , 2014 .

[16]  Oded Amir,et al.  Topology optimization for additive manufacturing: Accounting for overhang limitations using a virtual skeleton , 2017 .

[17]  Ole Sigmund,et al.  A 99 line topology optimization code written in Matlab , 2001 .

[18]  Ren-Jye Yang,et al.  Optimal topology design using linear programming , 1994 .

[19]  P. Wright,et al.  Anisotropic material properties of fused deposition modeling ABS , 2002 .

[20]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[21]  N. Kikuchi,et al.  A homogenization method for shape and topology optimization , 1991 .

[22]  W. Cong,et al.  Additive manufacturing of carbon fiber reinforced thermoplastic composites using fused deposition modeling , 2015 .

[23]  Douglas E. Smith,et al.  Effects of extrudate swell and nozzle geometry on fiber orientation in Fused Filament Fabrication nozzle flow , 2016 .

[24]  Erik Lund,et al.  Discrete material optimization of general composite shell structures , 2005 .

[25]  R. Wicker,et al.  Fracture Surface Analysis of 3D-Printed Tensile Specimens of Novel ABS-Based Materials , 2014, Journal of Failure Analysis and Prevention.

[26]  Constance W. Ziemian,et al.  Anisotropic Mechanical Properties of ABS Parts Fabricated by Fused Deposition Modelling , 2012 .

[27]  Douglas E. Smith,et al.  Anisotropic mechanical properties of oriented carbon fiber filled polymer composites produced with fused filament fabrication , 2017 .

[28]  D. C. Guell,et al.  Flow-Induced Alignment in Composite Materials , 1997 .

[29]  E. Barbero.  Introduction to Composite Materials Design , 1998 .

[30]  Zafer Gürdal,et al.  Combined topology and fiber path design of composite layers using cellular automata , 2005 .

[31]  L. Love,et al.  Highly oriented carbon fiber–polymer composites via additive manufacturing , 2014 .

[32]  Wei Xu,et al.  Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A review. , 2016, Biomaterials.

[33]  Yaoyao Fiona Zhao,et al.  Bidirectional Evolutionary Structural Optimization (BESO) based design method for lattice structure to be fabricated by additive manufacturing , 2015, Comput. Aided Des..

[34]  L. Love,et al.  The importance of carbon fiber to polymer additive manufacturing , 2014 .

[35]  K. Huebner.  The finite element method for engineers , 1975 .

[36]  T. Shi,et al.  Optimization of composite structures with continuous spatial variation of fiber angle through Shepard interpolation , 2017 .

[37]  Erik Lund,et al.  Optimization formulations for the maximum nonlinear buckling load of composite structures , 2011 .

[38]  Robert Hoglund,et al.  CONTINUOUS FIBER ANGLE TOPOLOGY OPTIMIZATION FOR POLYMER FUSED FILLAMENT FABRICATION , 2016 .

[39]  Michaël Bruyneel,et al.  Composite structures optimization using sequential convex programming , 2000 .

[40]  Delin Jiang.  Three dimensional topology optimization with orthotropic material orientation design for additive manufacturing structures. , 2017 .

[41]  N. Kikuchi,et al.  General topology optimization method with continuous and discrete orientation design using isoparametric projection , 2015 .

[42]  Matthijs Langelaar,et al.  Topology optimization of 3D self-supporting structures for additive manufacturing , 2016 .

[43]  W. Zhong,et al.  Short fiber reinforced composites for fused deposition modeling , 2001 .

[44]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[45]  Douglas E. Smith,et al.  NON-ISOTROPIC MATERIAL DISTRIBUTION TOPOLOGY OPTIMIZATION FOR FUSED DEPOSITION MODELING PRODUCTS , 2015 .

[46]  Y. Xie,et al.  A simple evolutionary procedure for structural optimization , 1993 .

[47]  Nam Soo Kim,et al.  Thermo-mechanical Characterization of Metal/Polymer Composite Filaments and Printing Parameter Study for Fused Deposition Modeling in the 3D Printing Process , 2015, Journal of Electronic Materials.

[48]  Lonnie J. Love,et al.  Utility of Big Area Additive Manufacturing (BAAM) For The Rapid Manufacture of Customized Electric Vehicles , 2015 .

[49]  M. Zhou,et al.  The COC algorithm, Part II: Topological, geometrical and generalized shape optimization , 1991 .

[50]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[51]  Albert C. To,et al.  Efficient Design-Optimization of Variable-Density Hexagonal Cellular Structure by Additive Manufacturing: Theory and Validation , 2015 .

[52]  Anders Clausen,et al.  Efficient topology optimization in MATLAB using 88 lines of code , 2011 .

[53]  Agnes Bagsik,et al.  MECHANICAL PROPERTIES OF FUSED DEPOSITION MODELING PARTS MANUFACTURED WITH ULTEM*9085 , 2011 .