Predictive Modeling of Composite Materials & Structures: State-of-the-Art Solutions and Future Challenges.

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1 Predictive Modeling of Composite Materials & Structures: State-of-the-Art Solutions and Future Challenges. Roger A. Assaker Short Abstract Computer Aided Engineering has been used for many years to reduce the time and cost of vehicle design and manufacturing. The majority of the CAE processes, tools and even engineering mindset have been optimized and mainly targeted toward homogeneous and anisotropic materials like steel. This paper will discuss the opportunities and challenges of using emerging multi-scale modeling technology, tools and processes, with state-of-the-art CAE tools, to better understand and to optimize the usage of high performance light-weight materials for Greener and more efficient vehicles. Extended Abstract One of the many challenges facing the automotive industry is the need to develop greener vehicles with a minimal CO 2 footprint while improving the vehicle safety, quality, performance and value for money! The reduction in CO 2 emissions can be achieved thanks to more efficient powertrains, hybrid technology or electrical vehicles all combined with light-weight structures. The optimal use of high performance composite materials is the key enabler of light-weight vehicles. Composite materials as used here cover a large variety of multi-phase materials where a matrix phase is reinforced by one or more inclusion phases like fibers and/or other fillers. Composites used here include: - Chopped fiber composites where a thermoset or a thermoplastic matrix is reinforced by short or long fibers; - Continuous fiber composites with Unidirectional or Woven layers; - Honeycomb sandwich panels; - Nano-filled material, etc. These materials and the automotive parts made from these materials are processed using: - Molding technologies: injection, compression, Injection/Compression, RTM; - Draping or Automatic fiber placement;

2 - Forming, etc. The Figure below illustrates the fact that the micro-structure (e.g. the distribution, length and orientation of fibers) of a composite material is influenced by the processing conditions that the material and the part using the material have seen. This microstructure will influence the physical properties of the material and the final performance of the part and the automotive vehicle using this part. Material Processing Moulding: Injection, Compression,... Drapage, AFP,... Material Microsturcure Chopped fibers Continuous fibers: UD/Woven Nano,... Material Chracteristics Mechanical Thermal Electric,... Part/Vehicle Performance Ref: The injection molding machine image is created by Brendan Rockey under licensed under the Creative Commons Attribution 3.0 License Figure 1: From the material processing to the end performance of the automotive part. The material processing induces the material microstructure that will govern the material properties that will in turn influence the end performance of the automotive part. A typical composite material or part has predominant fiber orientations that will carry the load. The orientations are imposed, like in the case of draped UD or woven composites, or induced by the material flow, like it is the case of injection molded thermoplastic reinforced with short or long fibers. In addition to the fiber orientation, the fibers or other type of filler shape, length and content will also be influenced, to different degrees, by the material processing conditions. The typical behavior of such composites is illustrated in Figure 2. The mechanical behavior is usually: - Nonlinear; - Anisotropic (i.e. different behavior in the direction of the fiber and in the direction transverse to the fiber) - Strain-rate dependent (i.e. stiffer at high strain rate) With complex damage, failure and fatigue characteristics.

3 Figure 2. stress-strain curves in the flow and cross-flow directions (Left courtesy of Solvay). Stress-strain curves at different strain rates and different orientation with respect to the main flow direction (Right Courtesy of Rhodia) The actual behavior of the material (i.e. nonlinearity, degree of anisotropy, failure, etc.) will vary along and across the thickness of a part as illustrate in Figure 3. Figure 3. This figure illustrates the variation of fiber orientation along a technical front end carrier made of glass fiber reinforced polypropylene. The material nonlinearity and the degree of anisotropy can strongly vary in the plane or across the thickness of a part as a function of the local fiber orientation, length and content. Part courtesy of Renault. The change of the microstructure is induced by the processing conditions and can have a strong influence on the part performance as illustrated in Figure 4.

4 Figure 4. This figure illustrates the influence of the processing conditions (i.e. gate location) on the end performance (i.e. Failure Force) of a structured beam subject to an impact. The graph shows that: the actually measured force at break (gray curve) is influenced by the gate location and is higher when the beam is injected along the longitudinal direction (bottom case). Ignoring the actual fiber orientation in the beam will disregard the influence of the processing condition on the part performance (blue curve). Using micromechanical approaches to take the actual local fiber orientation into account we lead to the correct response and will discriminate between the two structural performances (red curves). Courtesy of Rhodia. The automotive design process relies heavily on advanced CAE to reduce the time to market and the development cost of new vehicles. State-of-the-art CAE tools are being used to design the parts and the entire vehicle for static and dynamic responses, for aerodynamics, for acoustics and many other performances. CAE software are also used for designing the tools, like molds and dies, needed to manufacture those parts. CAE software have been developed and mostly used to accurately model the behavior of homogeneous isotropic materials like steel and many other metallic materials. In the area of composites, CAE tools have been mainly developed to deal with linear UD or woven laminate composites as used in the Aerospace industry. The classical laminate theory is widely used to model this type of composites. The classical laminate theory is quite limited when dealing with more advanced nonlinear effects and not able to deal with the many other sorts of composites (i.e. General mutliphase materials) like chopped fibers with non-fixed orientation. To deal with such complex composites, Engineers tend to approximate them like a black Aluminum or black steel and use familiar concepts and methods inherited from homogeneous isotropic metal

5 analyses. The actual local anisotropic behavior is thus smeared and scaled down from the measured behavior. These analyses methods are not predictive and the results are at best approximate leaded to non-optimal material usage and non-optimal part design. Figure 5 illustrate the different results obtained with linear and nonlinear stress-strain response as measured or scaled down by a factor (a non-predictive fit parameter that is determined to fit, a posteriori, the experimental measurement). The only predictive solution and the one that gives the best correlation with the experimental response is the one using multi-scale modeling techniques to take into account the influence of material microstructure on the material and part response (denoted as DIGIMAT solution) Figure 5. Force vs Deflection of an automotive roof system part. The results of the analyses performed with different material definitions are illustrated: (Red) Phenomenological linear isotropic elastic approximation of the measured material behavior; (Purple) Phenomenological elasto-plastic isotropic approximation of the measured material data; (blue) The same as the red but where the measured module was scaled down by a factor of 60% (a non-predictive fit parameter). (continuous black) the nonlinear anisotropic material response is computed as a function of the local fiber orientation (DIGIMAT); (dotted black) experimental measurement. Courtesy of Ticona (Ref. DIGIMAT Users Meeting 2009).

6 After a brief discussion of: - the need of the automotive industry to reduce the CO 2 emissions of new vehicles; - The variety of the composite materials that can be used to achieve this goal; - The value of CAE in the automotive design process; - The limitation of the classical phenomenological material models and classical laminate theory to accurately model the behavior of large variety of multi-phase material that are being used; This paper will focus on introducing nonlinear multi-scale modeling technology and tools. A new paradigm for modeling multi-phase materials and the structures in which they are used. The mutli-scale modeling process as discussed here, integrates micromechanics at the material level, with Finite Element Analysis (FEA) at the structural level. The multi-scale modeling process is illustrated below and consists of replacing the phenomenological material models by micromechanical models taking explicitly into account: - The nonlinear behavior of each-constituent of the composite: the matrix and reinforcement phase(s); - The microstructure of the composite described by: o Filler weight or volume fraction o Filler shape like the fiber length o Filler orientation that can be fixed or described by a distribution. Figure 6. (Left) Phenomenological material model used in the classical FEA process. modeling process with micromechanical modeling of the material micro-structure. (Right) multi-scale

7 At the material level one can either use semi-analytical Eshelby-based homogenization methods like Mori-Tanaka or direct FEA modeling of a Representative Volume Element (RVE) of the material. The pros and cons of each methods are summarized in Figure 7. Figure 7. (Left) Semi-analytical mean field homogenization process. (Right) FE based homogenization using FEA to model material RVEs. In the reminder of the paper we will concentrate on injection molded plastics with chopped fibers. The same concepts apply for other type of composites using different processing technologies. Micromechanical models (Mean Filed (MF) homogenization and Finite Element (FE) based homogenization) and their interfaces to injection molding simulation software are industrially available in material modeling platforms (e.g. DIGIMAT). Micromechanical software are used to model small material specimens and are used by the material experts to understand, engineer and optimize the material behavior. The micromechanical model of the material can then be made available to the part analyst and designed that will use it for a predictive accurate modeling of the material within the actual part. This model will notably take into account the material processing history like the fiber orientation in a part as induced by the molding process (e.g. injection molded thermoplastics) or draping process (e.g. draping of UD or woven plies).

8 Figure 8. Micro-mechanics and multi-scale modeling tools as used, in combination of major injection molding and structural FEA tools, to understand and engineer the behavior or reinforced plastic materials and parts. The advanced mutli-scale modeling process described above is fully integrated within the existing CAE processes and tools like illustrated below. Figure 9. Mapping of the nonlinear fully-coupled multi-scale in the pre and post processes of major FEA software like Ansys Workbench and Abaqus/CAE. In summary, the multi-scale modeling approach discussed in this paper provide the technology, the tools and the modeling processes to enable material and structural engineers to understand and optimize the behavior of composite materials and structures

9 and to bridge the gap between the material processing and the end performance of the composite structure via the material microstructure. The use of composites is increasing to cover new functions that have been traditionally reserved for metals (e.g. Structural parts). Some of the new functionalities will require a more accurate modeling of complex microstructures (e.g. long and entangled fibers) or more advanced performance (e.g. creep at high temperatures and fatigue). These topics constitute the new challenges for the industrial multi-scale research community.

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