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Principles of Modeling Textile Composites

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Issues Textile composites are not monolithic Mechanical characterization is not complete High degree of heterogeneity More variation in modulus than strength

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Modelling Approach Must have understanding of ultimate objective Stiffness or strength? Ideal or real geometry? Computational cost…

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Application of Models Component Design Process Design Unit Cell Modelling Material Characterization Material Variations Component Testing Reliability Structural Analysis

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Modelling Needs Correct kinematics Reasonable assumptions Correct properties Correlation between experiment and predictions

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Kinematics Satisfy External Boundary Conditions Satisfy Internal Boundary Conditions Continuity of displacements Continuity of strains or stresses as appropriate

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Assumptions Fiber-resin interface - bonding Isostrain, Isostress, ??? Small deformation Plastic deformation in matrix?

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Properties Fiber or yarn properties? Twisted yarns? Crimp Interaction of yarns at cross-overs Effect of yarn size

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Coarse Characterization Homogeneous Heterogeneous Mosaic

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Homogeneous "Smearing Method" Don't identify individual phases Only concerned with point correlations of phases Model typically insensitive to geometric parameters

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Heterogeneous Finite Element Methods Strictly distinguish yarns from matrix Sensitive to geometry

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Mosaic Separate structure into blocks Each block contains homogeneous material Between blocks is heterogeneous

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Homogeneous History Rules of mixtures Modified Matrix Method (XYZ) Stiffness Averaging (FGM) Compliance Averaging Property Blending

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Homogeneous Philosophy Fiber Properties Matrix Properties Micromechanics Unidirectional Properties Ply/yarn orientation Transformation Combine layersComposite stiffness matrix Unidirectional Properties Layer properties

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Modified Matrix Method Developed by Tarnopolskii to model XYZ type structures. The Z yarns are accounted by developing a “modified matrix” which consists of resin and Z yarns. The X and Y yarns are then treated as laminates where the unidirectional properties are calculated using the orthotropic modified matrix

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FGM The FGM Method is a variation on the stiffness averaging method developed by Kregers and Teters. Unidirectional stiffness matrices are developed based on the overall part fiber volume fraction The fabric is subdivided into piecewise linear elements Transformation matrices are developed for each element and corresponding stiffness matrices calculated (similar to laminate theory) Element stiffness matrices are combined iso-stress

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Comparison test Two types of XYZ weaves were fabricated and tested Glass/epoxy Different amounts of Z yarns in the two systems

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Homogeneous Results

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Variations on Homogeneity 0153045 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 FGM Kregers MMM E 11 as a function of Weave Angle

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Homogeneous Advantages Calculations are quick Model insensitive to geometry Good predictions of elastic properties Simple failure criteria can be applied Output is constitutive law

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Homogeneous Disadvantages No way to account for interface/interphase Cannot track damage progression Cannot account for size, edges, local defects, etc.

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Homogenization for Reliability Evaluate the distribution of elastic properties based on the material variations in a unit cell Apply stiffness averaging method in a Monte Carlo simulation Applicable to stochastic structural analysis

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Heterogeneous History Stick models (frames and trusses) "Mosaic" model (semi-heterogeneous) Full 3-D Modelling 2-D "Modal" analysis

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Heterogeneous Types Finite Element Models Stick Models

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FEA Example Whitcombe - Plain weave X Y Z 0.50.40.30.20.1 0.7 0.8 0.9 1.0 1.1 1.2 1.3 Ex Ez Gxy Gyz Waviness Ratio Normalized Modulus

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Stick Example X Y Z Matrix Member Fiber Member

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Stick Comparison 0 20 40 60 80 Stress (ksi) 00.511.522.53 Strain Carbon/Epoxy 3-D Braid, No Axial EXPFCMFGM 0 25 50 75 100 Stress (ksi) 00.250.50.751 Strain Carbon/Epoxy 3-D Braids, 50% Axial ExpFGMFCM

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Heterogeneous Advantages Output is structural analysis Can be used to track damage progression Complex failure criteria can be incorporated Pedagogical

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Heterogeneous Disadvantages Highly geometry sensitive Large number of degrees of freedom Hard to mesh Output is structural analysis

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Mosaic History "Sugar cube" method (Foye) GINA (Gowayed) SEDAF-sugar cube (Bogdanovich)

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Mosaic Types "Sugar Cube" By Sub-volume

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Mosaic Advantages Can provide partial heterogeneity Not very geometry sensitive Can be used for material property or structural analysis purposes Partial damage tracking

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Mosaic Disadvantages Does not fully represent geometry Partial damage tracking More degrees of freedom than homogenization

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Sensitivity to Material Modelling SEDAF Mosaic approach 3-D Weave, transverse bending Plain weave, axial tension Use material smart solution algorithm Solution is sensitive to material description

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Mechanical Property Predictions to model the structural response it is necessary to describe the mechanical properties of the material. The simplest form is to treat as homogenous medium with anisotropic properties. This is termed homogenization of the material. If the volume of material to be homogenized is small compared to the structural component, this approach seems reasonable. In the case of textile reinforced materials, the RVE is typically quite large, on the order of cm in some cases. It may not be reasonable to consider the RVE as representing the response of the material Special analytical tools need to be developed to understand the local response within the RVE.

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Homogenization of Properties Analytical techniques have been developed to predict the elastic properties of textile composite RVE's. averaging mechanical properties of the constituent materials, Bolotin (1966), Nosarev (1967), Tarnopol'skii et al. (1967), and Sendeckyj (1970), Roze and Zhigun (1970), Kregers and Melbardis (1978), Kregers and Teters (1979), Chou et al. (1986), Ishikawa and Chou (1982), Jortner (1984), Whyte (1986), Ko et al. (1987), Ko and Pastore (1989), Howarth (1991), Jaranson et al. (1993), Singletary (1994), Pochiraju et al. (1993) property predictions based upon detailed geometric descriptions of the reinforcement, and Foye (1991), Gowayed (1992), Bogdanovich et al. (1993), Carter et al. (1995). finite element methods treating matrix and fiber as discrete components. Kabelka (1984), Woo and Whitcomb (1993), Sankar and Marrey (1993), Yoshino and Ohtsuka (1982), Whitcomb (1989), Dasgupta et al. (1992), Naik and Ganesh (1992), Lene and Paumelle (1992), Blacketter et al. (1993) and Glaesgen et al. (1996), Hill et al. (1994), Naik (1994)

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Non-RVE Considerations The size of the RVE is relatively large compared to test specimens and some actual structures. The application of RVE based analysis may not be appropriate Even experimental data can be effected by this assumption The strain gage used in tensile testing usually covers only a few RVEs of the textile, and sometimes even less than 1.

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Moiré Interferometry Field on Axially Loaded Braided Composite

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Measurements of Elastic Properties If the measurement system does not contain a large number of RVEs, then the measurements do not reflect a true average value. The location of the gage will affect the measured values. Some of the perceived high variation in tensile modulus may be due to the relationship between strain gage and RVE size.

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Elastic Modulus vs. Gage Area for Braided and 3D Woven Composites

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Location of Test Cell with Respect to Unit Cells in a Triaxial Braid

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Predicted Tensile Moduli for 60 ° Triaxial Braid AS-4/ Epoxy Test Cell with y 1 = b and x 1 = 4.1a

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Predicted and Experimental Tensile Modulus of a Triaxially Braided AS-4/ Epoxy Composite with 45° Braid Angle and 12% Longitudinal Yarns

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Predicted and Experimental Tensile Modulus of a Triaxially Braided AS- 4/Epoxy Composite with 45° Braid Angle and 46% Longitudinal Yarns

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Predicted and Experimental Tensile Modulus of a Triaxially Braided AS-4/ Epoxy Composite with 70° Braid Angle and 46% Longitudinal Yarns

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Physical Limitations Current cost of production. modifications to machines are needed for shaping capabilities, capital cost is applied to a few prototypes, the unit cost is tremendous (no economy of scale) Processing difficulties. infiltration at high pressure, and thermal effects during curing. frequently results in internal yarn geometry distortions. elastic and strength properties have high variation. thermal effects can result in local disbonds from yarns. One approach that seems promising is the use of cold cure systems such as e- beam curing to reduce the temperature of cure and thus reduce the effect of different coefficients of thermal expansion between the fiber and resin.

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Analytical Shortcomings Analytical techniques are still not adequate to satisfy structural analysts planning to apply these materials to load bearing structures. Some “variation” in elastic performance is expected due to a non-integer number of RVE's. the design allowables for the materials are greatly reduced, frequently making them appear unsuitable for structural application due to the perception of high weight penalty. It is possible to account for this behavior even with simple tools such as stiffness averaging if the non-RVE element is modeled.

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Failure Analysis Understanding of failure initiation and growth is still required. Greater resolution of the internal stress state is needed than that for establishing homogenized elastic constants. Failure modes are poorly understood. These modes are associated with local curvature and distortion of the yarns at crossover points, and cracking between yarn bundles (inter- bundle cracking). Transverse cracking and fiber failure within the yarns (intra-bundle cracking) are also a function of the complex stress state inherent in a textile. An important issue is how curvature and inter-bundle cracking affect compression by reducing the stability of the yarn.

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