1 VALIDATION of CoDA SOFTWARE for COMPOSITES SYNTHESIS AND PRELIMINARY DESIGN (or GETTING COMPOSITES USED - PART 2 ) Graham D Sims and William R Broughton Composites Design Data and Methods, Centre for Materials Measurement and Technology, National Physical Laboratory, Teddington TW11 0LW UK. SUMMARY Successful composites applications are an optimisation of the geometry and the material properties that often only come together during the final forming process. Hence, it is important that the effect of altering each can easily be assessed by both material suppliers, engineering designers and end users. This can be undertaken using preliminary design procedures that can be used either to reduce the make and test process in a small or medium sized company or as a precursor to more detailed analysis such as FEA in a company that can afford more expensive (both software and staff) analysis facilities. In both cases, the aim of preliminary electronic back of the envelope calculations is to quickly identify combinations of materials and geometries that meet the end requirements with some confidence. For users to have confidence in the predictions, experimental validation is necessary. KEYWORDS: material synthesis, preliminary design, material formulation, validation, software. INTRODUCTION A major benefit of composites materials is that the variations allowed in fibre type, fibre format, fibre length, orientation, stacking sequence and resin type can provide potentially many materials tailored to individual applications. This material design advantage is, however, a potential Achilles heel for composites materials as even with the reduced number of test methods discussed elsewhere [1,2], it is not possible to obtain full property data on all potential materials. Hence, there is continuing interest in, and many examples of, software being developed for predicting the properties and performance of composites, and research continues on developing improved material models . It is of particular interest to assess what practical use can be made of currently available modelling and design procedures. If the procedures are to be used with confidence, it is important to validate them through comparison with experimental evidence and the results of alternative analyses. This has lead to a programme to,
2 validate predictive approaches for synthesis of composite materials properties validate preliminary design tools for composite panel and beam sub-components integrate the material synthesis function with the preliminary design tools These aspects are described in this paper with validation evidence given for each module and the integrated software. The modules considered are material layer synthesis, lay-up module, panel module and beam module. Further developments, such as a parametric design facility, design of bolted joints, creep and impact predictions are briefly discussed PRELIMINARY DESIGN REQUIREMENTS Design has progressed from a linear to a concurrent activity for established materials based on well developed material specifications and related properties. Composite materials design requires a higher level of integration as the material can also be designed and is often only fully formed during manufacture of the actual component. In addition, the anisotropy of composite materials demands that a larger database of properties is available. Fig. 1: Overlapping areas of design remit and adjacent QA requirements For composite materials, the designer sits at the focus of overlapping remits covering material, processing and performance, all of which must be understood to some degree (see Fig. 1). Between each of these areas are quality requirements to ensure that, for example, the starting materials are within their shelf-lives, the processing is correct and the final product is fit for purpose (eg. thermal analysis techniques, mechanical and ageing tests, NDT including ultrasonic C-scanning). Good progress has been made on the supporting infrastructure of test methods [1,2] in eliminating duplicate methods through international harmonisation and in preparing material specifications. However, the ability to vary the type and volume fraction of fibres, their orientation, etc. makes it
3 expensive to test all possible candidate materials. Hence, there is strong interest in predicting composite material properties with acceptable accuracy for preliminary design and for identifying new materials. It is beneficial to integrate the material property synthesis with preliminary design predictions as in the NPL produced CoDA (Composite Design Analysis) software to reflect the integration of material and product form that occurs in practice. Fibre properties Resin properties Synthesised Layer - 3D Properties Layer stacking sequence and orientation. Synthesised Laminate - Properties Parametric Studies Panel Design Beam Design Sandwich Panels Creep Impact Bonded Joints Bolted Joints Fig. 2: Flowchart showing lay-out of CoDA software CoDA uses fibre and matrix properties from integral databases in a synthesis module to generate the 3D properties of a layer of known fibre geometry and volume fraction. Layers are then laid-up using a laminate module to predict the laminate properties with layers of different type, different orientations and different thicknesses possible. The material properties, at the layer or laminate, level can be used in integrated design packages under different loading situations, including the CoDA panel and beam loading modules. The flow diagram in Fig. 2 outlines the structure of the software. The scope and validation of these modules are described in the following sections.
4 SYNTHESISER MODULE The synthesiser module enables the full three-dimensional properties of composite materials for individual laminae (ie. layers) to be generated. The analysis, based on micromechanics equations (eg. rule of mixtures or Tsai-Halpin formulations), are used to predict the behaviour of laminae as a function of the properties and volume fractions of the constituents (i.e. fibre and matrix). The CoDA micromechanics analysis includes equations for continuous and discontinuous aligned and random fibre-reinforced formats. The CoDA software is configured in a manner so that the input parameters (including fibre format) from the operator automatically define the formulations appropriate to the system being analysed. For discontinuous fibre-reinforced systems, the fibre length and diameter are used in the determination of some of the elastic and hygrothermal properties. The micromechanics analysis predicts the lamina mechanical properties (elastic constants and strengths) for longitudinal tension and compression, transverse tension and compression, and inplane shear loads. Thermal and moisture expansion coefficients are also predicted. A number of assumptions are made in the analysis: Matrix is homogeneous and isotropic. Fibres and matrix exhibit linear elastic behaviour. Fibres are uniform and regularly spaced. Fibres are perfectly aligned if unidirectional or perfectly random if random. Perfect interfacial bonding between fibre and matrix. A void free composite. Axial strains experienced by the fibres, matrix and composite are equal. Table 1: Comparison of in-plane properties for a CFRP material Calculated Measured Difference (%) density (kg/m³) E 11 (GPa) E 22 (GPa) G 12 (GPa) υ υ σ 11 (T) (MPa) σ 11 (C) (MPa) σ 22 (T) (MPa) σ 22 (C) (MPa) τ 12 (MPa) α 11 (/10 6 K) α22 (/10 6 K)
5 These synthesised properties can be used in the CoDA design modules or in other design packages, including finite element analysis (FEA). It is possible to input directly into the CoDA materials database measured properties, manufacturer s data and text book values. As these other data inputs are frequently incomplete, the synthesiser facility can generate the missing properties. In general, the micromechanics equations incorporated in the synthesiser module used to determine the in-plane and through-thickness laminae properties can be considered to provide satisfactory values for preliminary design purposes. The ability to predict the in-plane engineering properties for the different fibre formats, based on well characterised constituent properties, increases in the order Discontinuous random, Discontinuous aligned, Continuous random and Continuous aligned. The software includes correlation or reality functions based on the agreement obtained between these simple micro-mechanics predictions and experimentally determined values. An extensive validation programme on a wide range of generic composite materials (e.g. CSM and SMC) as both simple plaques and finished products, and for different processing routes (e.g. resin injection and press moulded) was undertaken. Table 1 compares predicted and experimental data for unidirectional carbon fibre-reinforced epoxy. Similarly, there is good agreement between predicted and experimental data for the through-thickness (T-T) properties for glass fibre-reinforced polyester CSM (Table 2), with the exception of the T-T tensile strength. Table 2: Through-thickness properties of CSM (*tensile failure) Property Predicted Measured E 33 (GPa) ν ν G 13 (GPa) G 23 (GPa) S T 33 (MPa) 40 9* S C 33 (MPa) S 13 (MPa) S 23 (MPa) As is to be expected, the degree of correlation between predicted and actual elastic constants is far better than that for the strength properties. Many of the correlation factors were equal to unity, especially for elastic properties. The worst correlation was found for the axial compression strength of composites composed of fully aligned continuous fibres, a situation where the models are too simplistic and the experimental results are most difficult to conduct. However, simple equations are preferred as they limit the input data required. For example, theories including fibre waviness need this parameter to be measured or predicted. Based on this experimental evidence, the correlation (or reality) factors were compiled, so that the micromechanics provide realistic, useable material property data (Table 3). These factors are applied automatically, unless otherwise de-selected by the user, ensuring that realistic, practical predictions are obtained.
6 Table 3: Derived Correlation Factors for In-plane Properties Property Unidirectional Random Continuous Discontinuous Continuous Discontinuous E E G ν ν T S T S C S C S τ VALIDATION OF LAYUP MODULE The lay-up module allows for the design of laminated panels of virtually any stacking sequence and predicts the effective principal elastic and hygrothermal properties and in-plane strengths in tension, compression and shear. Calculations are based on classical laminate analysis. Effects of residual stresses due to hygrothermal loading are taken into account. The Tsai-Wu tensor failure criterion is used to calculate layer strength. Individual laminae properties may either be synthesised using the CoDA micromechanics analysis or based on experimental data, which can be directly entered into the layer database by the operator. The assumptions on which the lamination theory is based are as follows: The laminate is considered quasi-homogeneous and anisotropic Each layer of the laminate is orthotropic and transversely isotropic. The laminate has the properties of a thin. Displacements are linear throughout the laminate thickness and continuous throughout the composite. The bond between two adjoining laminae in a laminate is assumed to be perfect. The authors concur with other researchers that the Tsai-Wu failure criterion, which is used in CoDA laminate analysis to predict strength, can be considered as essentially a curve fitting exercise. It is generally agreed that although this failure theory provides better agreement with experimental data than most other failure criteria, the theory will only indicate if ply failure occurs and will not provide information on the mode of failure (e.g. fibre breakage or matrix cracking). The authors are aware of the limitations of the Tsai-Wu failure criterion and recognise that further work is required to resolve this issue. Loss of layer integrity, which occurs when a layer fails, is modelled by a change in moduli according to whether the layer is continuous or discontinuous. For continuous reinforcement, all the elastic properties of a failed layer are set to zero with the exception of the longitudinal modulus, which remains unaltered in the failed layer. For a discontinuous layer that has failed, all elastic properties are assigned a zero value. The modelling assumes that the ply is degraded by transverse cracks resulting from matrix and/or interface failure prior to the final failure. Currently there is no simple, systematic method for assessing the reduction in ply properties as a result of ply failure, hence the approach adopted. It may be possible through an intensive testing
7 programme to obtain reasonable estimates of the derating factors, but this would probably be system dependent (see also ). First ply failure (FPF) analyses can be carried out with or without including residual stresses, depending on the judgement of the designer/user. Inclusion of residual stresses provides a more conservative and therefore safer design level for FPF. It is generally agreed that that there is no need to include residual stresses following FPF as their effects are relatively marginal and of secondary importance . The other concern relates to the temperature at which the onset of residual stresses occur. Contrary to a commonly held view, residual stresses do not develop within a laminate as soon as the material starts to cool down from the curing temperature. In fact, a stress-free temperature exists somewhere between the cure temperature and room temperature, and the temperature dependence of the material properties (stiffness and thermal expansion) is not included. Hence, calculated residual stresses tend to be much higher than those actually experienced. As with the material synthesiser, reasonable agreement can be obtained between the laminate analysis and experimental results as shown in the case study below for a pultrusion, which uses a laminate containing two fibre formats (eg. mat and unidirectional). VALIDATION OF PANEL MODULE The panel module assists in the design of panel structures, enabling the user to determine the stiffness and strength of circular and rectangular panels, sandwich panels and ribbed plate elements. Loading conditions considered include point, line and pressure. The software can also be used to predict stresses and deflections, and to determine critical material properties or geometric parameters. Validation tests were undertaken by loading panels in a wide range of conditions. Initially, experiments were undertaken on 44 different materials or different thicknesses using both unreinforced and reinforced (mainly short fibres) plastics. The work was extended to more highly reinforced materials . Table 4 shows the results for plates of varying anisotropy as given by the D 1 /D 2 and D 3 /D 2 ratios (where D 1 and D 2 are bending stiffness in perpendicular directions, and D 3 is related to the shear stiffness) of the panel defection parameter, α (ie. equivalent to comparing panel deflections). Table 4: Comparison of predicted and experimental plate parameter, α MATERIAL D 1 /D 2 D 3 /D 2 α Expt. α Calc Sheet moulding compound Chopped strand mat Glass-fibre/epoxy Cross-plied glass-fibre/epoxy Unid. glass-fibre/epoxy Unid. aramid-fibre/epoxy Unid. carbon-fibre/epoxy
8 A range of loading conditions were used representing the options available in the software. Edge conditions can be changed independently and for isotropic materials rib designs are included. An important feature is the correction due to large deflection behaviour. This geometrical factor becomes of increasing importance as the deflection of the plate increases and is considered important when the deflection is 0.5 times the plate thickness. Additional input parameters are needed to describe the plate response, which are not know in all cases. The effect is to increase the apparent stiffness of the panel reducing both the deflection and the stress in the panel. The data can be presented as a displaced mesh shape that gives a useful visual link with FEA analysis. Rapid visualisation of changes to the input parameters are possible. It takes a fraction of a second to run a new solution, for example, by replacing a clamped edge with a simply supported or free edge. VALIDATION OF BEAM MODULE The beam module, predicts strength, stress levels, stiffness and deflections for generic beam shapes, such as hollow, solid, box and channel designs as well as T and I sections. Loading conditions considered include flexural, torsion and mixed loading. Strength predictions include assessment of the relative likelihood of failure occurring by buckling or material fracture under both bending and shear stresses. The predictions were experimentally checked by a wide range of beam loading tests. Test were undertaken using different materials: a carbon-fibre/epoxy preimpregnate, a carbon-fibre/peek preimpregnate, a glass-fibre/polypropylene, a pultruded profile, a thermoformed GMT, an injection moulded channel of three aspect ratios(ie. channel width to depth). Pultrusions were used for the majority of the initial work to assess each loading condition because of their low cost and easy availability in the range of shapes and aspect ratios covered by the CoDA module. The software predicts section properties (eg flexural, shear and torsional stiffnesses) and the maximum capability of the beam section in shear or bending as controlled by the material failure stresses (tensile, compressive or shear) or, as appropriate, the buckling on compressive or shear loaded faces. These section properties are then applied to the actual loading case in flexure and/or torsion to predict beam stresses, displacements and failure modes. Validation of this module is shown within the following case study for a pultruded box profile. Additional results are given in Ref. 7.
9 PULTRUSION PROFILE CASE STUDY The properties were predicted for a 51 mm wide box section pultrusion from a knowledge of the layup and volume fractions involved, prior to loading to failure in three point flexure. As a thin-walled structure, it was necessary to consider buckling failure of the compression and shear faces, in addition to material fracture in tension, compression or shear. Table 5: Structure of wall of pultruded box profile Layer Position Fibre Format Volume Fraction Thickness Outer surface Swirled random mat 31 % 0.65 mm Centre Unidirectional roving 61 % 1.90 mm Inner surface Swirled random mat 31 % 0.65 mm Analysis of the construction of the wall of the box section found two layers of swirled mat sandwiching a layer of aligned roving as detailed in Table 5 (mean values shown). The overall wall thickness varied from 3.03 mm to 3.37 mm, with a mean of 3.2 mm. These values together with supplier s data for the constituent properties were used in CoDA to predict the wall material properties, as detailed in Table 6. Table 6: Comparison of CoDA predicted and experimental properties for pultrusion (* = non-standard specimens, = first ply/last ply failure) Property CoDA Predictions Expt. Mat Roving Combined Young s modulus, E 11 (GPa) Young s modulus,,e 22 (GPa) * Shear Modulus, G 12 (GPa) Possion s Ratio, v Possion s Ratio, v * thermal exp.1, E thermal exp.2, E Tension strength, σ 11 T (MPa) / Tension strength, σ 22 T(MPa) / * Compression strength, σ 11 C (MPa) / Compression strength, σ 22 C (MPa) * Shear strength, τ 12, (MPa) * The correlations for the laminate stiffness properties were acceptable, in view of the variation noted in the actual material itself and the use of miniature non-standard specimens for the transverse properties. The axial strengths measured were greater than the first failure stress predicted for failure of the mat layer and well below the stress predicted for final failure when no interaction between the layers is assumed. A 910 mm length of the pultrusion failed under three-point flexure loading by compressive face buckling, as predicted. The measured peak load of 7857 N compared well with the predicted value of 8411 N for the 3.2 mm mean thickness. The predicted failure load varied from 7200 N to 9783 N for the range of wall thickness, with the experimental result towards the lower end of this range as expected, highlighting the advantages of accurate wall thickness control.
10 A major advantage of CoDA is that having completed a panel or beam design any of the material synthesis or laminate formulation stages can be assessed by re-opening the appropriate material or lay-up Window and altering the conditions. Thus alternative solutions can be assessed virtually instantaneously. The design solutions themselves (eg. clamped vs simply supported edge) can also be re-assessed with the same rapidity. In some cases, the software can predict, say, ribbing geometries to meet the specified requirement. Additional modules planned or under development will consider other structural elements and also the inclusion of stress concentration features such as bolted fixings, flanges, holes and impact modelling. When data are experimentally measured, increased confidence can be obtained through the use of CoDA to check the values are close to those expected. Dubious data has been identified using this approach, in a subsequent exercise to confirm the correlation factors. FURTHER DEVELOPMENTS AND CONCLUSIONS A facility being developed in each module allows parametric studies to be undertaken at the material and structural design stage. For example, within the beam module any of the output parameters (eg. beam deflection, maximum bending moment) can be found as a function of any input material or geometry parameter. The analysis is undertaken between two values that may be in absolute units or as factors (eg. 0.5 to 2) of the initial design values with a user specified number of intermediate points. It is possible to determine optimum solutions (ie maximum or minimum values of the output parameter) using this approach. The parametric facility allows variations to be quickly studied. For instance, for the above pultrusion case study a wall thickness increase of ~3% raises the predicted failure load by ~10%, whereas a ~3 % increase in the axial Young's Modulus results only in a ~1 % increase in the failure load. These design tools are integrated into the PC Windows software CoDA, Composite Design Analysis, in order to provide validated predictive tools in an easily accessible and digestible manner. The integration of the synthesis of 3D properties with the response of structural elements such as beams and plates recognises the fundamental nature of composite materials manufacture and use, in that for most cases material and geometry are formed at the same time. CoDA is not limited to aerospace prepregs but considers mats and discontinuous systems. ACKNOWLEDGEMENTS The authors gratefully acknowledges the efforts and support of colleagues at NPL, members of Industrial Advisory Groups, industrial sponsor companies and the Materials Measurement programme at the DTI. REFERENCES 1. Sims G D, Standards will cut composites industry costs, Reinforced Plastics, pp (1998). 2. Sims G D, Harmonised standards arrive at last!, Proceedings of 4 th Composites: Testing and Standardisation Conference, Lisbon (1998). 3. L N McCartney, Prediction transverse crack formulation in cross-plied laminations Composites in Science and Technology, 58, pp (1999). 4. Tsai, S W, Composites Design, Think Composites, (1987). 5. Datoo, M H, Mechanics of Fibrous Composites, Elsevier Applied Science, (1991). 6. Johnson A F and Sims G D, Simplified Design Procedures for Composite Plates under Flexural Proceedings of 2 nd Intern. Conference. On Composite Structures, Paisley, (1983) 7. Broughton W R and Sims G D, Failure modes in beam structures, Proceedings of Deformation and Fracture of Composites, Surrey Univ. (1995).
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