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A Comprehensive Explanation of Compression Strength Differences Between Various CFRP Materials: Micro-Meso Model, Predictions, Parameter Studies

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A Comprehensive Explanation of Compression Strength Differences Between Various CFRP Materials: Micro-Meso Model, Predictions, Parameter Studies Composites: Part A 40 (2009) 376–387 Contents lists available at ScienceDirect Composites: Part A journal homepage: www.elsevier.com/locate/compositesa A comprehensive explanation of compression strength differences between various CFRP materials: Micro-meso model, predictions, parameter studies S. Pansart a,*,1, M. Sinapius a,b, U. Gabbert b a German Aerospace Center, Institute of Composite Structures and Adaptive Systems, Lilienthalplatz 7, 38108 Braunschweig, Germany b University of Magdeburg, Department of Mechanical Engineering, Computational Mechanics, Universitätsplatz 2, 39106 Magdeburg, Germany article info abstract Article history: The present work proposes a model to predict the compression strength of CFRP as a function of various Received 26 August 2008 material characteristics: fiber properties and volume content, non-linear matrix properties, interface Received in revised form 7 December 2008 properties, residual strains, fiber misalignment, ply waviness, and interlaminar properties. For this, a Accepted 2 January 2009 three-step FE-based approach is developed considering (i) fiber microbuckling, (ii) wavy ply mesobuck- ling, and (iii) the mutual influence of these two. This approach is then applied to investigate the relative contribution of the mentioned material characteristics on compression strength deficits of NCF (Non- Keywords: crimp Fabric) CFRP with respect to prepreg, in order to identify ways to improve NCF performance. A. Fabrics/textiles Ó 2009 Elsevier Ltd. All rights reserved. B. Mechanical properties C. Finite Element Analysis (FEA) 1. Introduction microbuckling, forming the basis for a large variety of models introducing the aspects of matrix non-linearity, misalignment, Compared to classical prepreg technology, liquid composite and others. Theories describing compression failure in terms of molding technologies, in combination with non-crimp fabric kink band formation were developed in parallel (as e.g., in (NCF) dry fiber semi-finished products, offer the opportunity of [10,11]). Some of these theories treat microbuckling and kinking manufacturing more complex and less expensive carbon-fiber as two different mechanisms leading to compression failure, and reinforced plastic (CFRP) components for civil aircraft primary some treat microbuckling as the mechanism that triggers kinking. structures. However, it has been frequently observed that NCF- In addition, there are theories that describe compression failure on based CFRP has lower strength properties than comparable prepreg the geometrical scale of wavy laminae (plies) rather than on the systems, especially (amongst others) in terms of compression microscopic scale, by considering ply instability (as e.g., in [12]), strength [1–3]. Consequently, an effort is necessary to improve or stiffness degradations due to fiber mis-orientation (as e.g., in the mechanical performance of NCF-based CFRP. In this context, [13]). And finally, some approaches have been proposed investigat- the present work has the objective to improve the understanding ing the interaction between microscopic features and the ply mor- of the reasons for the observed performance differences between phology (as e.g., in [14,15]). NCF and prepreg: which are the NCF material’s characteristics A detailed discussion of these different theories and models, causing its compression strength deficit? and more, is available in [16]. They lead to different conclusions A vast theoretical background on compression failure in CFRP is regarding the relative importance of the factors that influence available in the open literature. In their review, Schultheisz and compression failure. Some have been designed to investigate more Waas [4,5] summarize the major aspects. Failure occurs mainly the matrix properties aspect, and some more the fiber orientation due to microbuckling of fibers, and due to the formation of kink aspect; some to investigate more the microscopic mechanisms, bands (localized damaged areas in which adjacent fibers are ro- some more the mesoscopic ply waviness, and some their interac- tated to the point of fiber failure). The controlling material charac- tion; and some to investigate additional aspects such as the influ- teristics are non-linear matrix properties, and the presence of fiber ence of fiber stiffness, fiber diameter, fiber-matrix interface misalignment and ply waviness (as described e.g., in [6–8]). In properties, or residual strains. None of the available approaches, 1960, Rosen [9] came up with a very basic description of fiber though, has been developed in order to deliver an unbiased estima- tion of the relative influence of all these various parameters simul- taneously. Therefore, in order to address the above-mentioned * Corresponding author. question regarding the NCF compression strength deficit, a new, E-mail addresses: [email protected] (S. Pansart), [email protected] (M. Sinapius), [email protected] (U. Gabbert). holistic approach has been developed and used to provide answers 1 Present address: Airbus, 316 route de Bayonne, 31060 Toulouse, France. to the given question. The present work contains a presentation of 1359-835X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2009.01.004 S. Pansart et al. / Composites: Part A 40 (2009) 376–387 377 the theoretical development of the modeling approach, and of the ure in fibrous composite materials, with the goal of obtaining a cu model predictions and effects of parameter variations allowing for prediction for the compression strength r11 of a single UD ply as studying the NCF compression strength deficit. a function of various material characteristics. First, the microbuck- ling stress rcrit of a small portion of the composite is analyzed as a 2. Model development function of the local misalignment angle a0, using an FE model. The result is the imperfection sensitivity function rcritða0Þ, which is va- For the regarded materials (both NCF and prepreg), the micro- lid for the small material portion where, according to the assumed scopic morphology of a UD ply is idealized as follows (Fig. 1). (i) It idealized microscopic material morphology, the fibers are all mis- is always possible to define a nominal overall 0°-direction of the aligned by the same a0. In a second step, in order to obtain a pre- cu ply; in an unloaded ply, the angle between the local fiber direction diction for r11, the function rcritða0Þ is combined with the and the nominal 0°-direction is then called the initial local fiber mis- stochastic distribution of misalignment angles of a UD ply, using alignment angle a0 (for the moment, a0 is defined only for the 1-2- a continuum damage model. plane, although obviously, fibers do deviate in the 3-direction from The geometry of the FE model (Fig. 1) represents one single the nominal 0°-direction, which will be accounted for in a later step). sine-shaped fiber, embedded in the matrix (similar as in [17]). (ii) The variation of a0 can be described as being nearly continuous The FE model height h is adjusted to a value corresponding to for all regarded material systems, i.e., adjacent fibers are almost par- the shortest distance between two fibers in an idealized 3-dimen- allel to each other, and orientation changes occur smoothly (usually, sional hexagonal fiber packing for a given fiber volume content V f . only very few single fibers deviate from this idealization, exhibiting For a given fiber diameter df ; h comes from the geometrical relation abrupt, discontinuous orientation changes); the stochastic a0-distri- (Fig. 4) bution, therefore, can be described in a continuous manner by the 2 rffiffiffiffiffiffiffiffiffiffi p d circular fiber area 4ffiffi f p df cumulative frequency function Fða0Þ. And (iii), all observed disorien- V f ¼ ¼ p ) h ¼ pffiffiffiffiffiffi Á pffiffiffiffiffiffi ð1Þ hexagonal unit cell area 3 2 V tations are comparatively small, with only an insignificant portion of 2 h 12 f fibers at an a above, say, 6°. 0 This is based on the assumption that fiber microbuckling is con- The mesoscopic structure of a local portion of the composite trolled by the lateral stiffness in direction I, and not by the lateral (Fig. 2) is idealized by describing the ply waviness morphology in stiffness in direction II, because – thinking of these two directions the x–z-plane, specified by the waviness angle b (the angle be- as configurations with stiffnesses in parallel configuration – the rel- tween the x–y-plane and the ply at the regarded location) and evant one for determining lateral fiber deflection behavior should the half wavelength L. be, approximately, the configuration with maximum stiffness, thus These two sets of morphology idealization (microscale and direction I. Note that Balacó de Morais [18] has found a similar con- mesoscale) form the basis for the hierarchical structure of the clusion. The FE model is realized through a PCL (Patran Command model (Fig. 3). The model consists of three different elements (or Language) session file for MSC.Patran, which allows for the auto- sub-models): a fiber microbuckling (FMB) model, a ply mesobuck- mated generation and post-processing of an MSC.Marc non-linear ling (PMB) model, and a combined FMB–PMB model accounting for static structural analysis with varying model geometry and constit- the interaction between the two former ones. A detailed descrip- uent material properties parameters. A plane stress quadrilateral tion of these sub-models follows in the next three sections. element (MSC.Marc type 114) is used. After convergence studies, the mesh density has been adjusted so that the matrix region con- 2.1. Fiber microbuckling (FMB) model sists of three rows of elements, and the model length has been set to approximately 50 times the fiber diameter. The boundary condi- The FMB sub-model consists of two steps for describing fiber tions at the upper and lower edge are defined to represent an infi- microbuckling as the underlying mechanism of compression fail- nite array of adjacent fibers. For this, the two edges are constrained to retain the same shape throughout loading (similar as in [19])by n2 ref2 n1 ref1 ui À ui ¼ ui À ui for i ¼ 1; 2 ð2Þ where n1 and n2 is any pair of nodes facing each other on edge 1 and edge 2, respectively (Fig.
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