HYGRO-THERMALLY CURVAURE-STABLE LAMINATES WITH NON-STANDARD PLY - PDF document

18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS HYGRO-THERMALLY CURVAURE-STABLE LAMINATES WITH NON-STANDARD PLY ORIENTATIONS. C. B. York Aerospace Sciences, School of Engineering, University of Glasgow, Scotland, UK. (Christopher.York@Glasgow.ac.uk) Keywords : Thermally stable, Warp free, Coupled laminate configurations may be described as hygro-thermally curvature- 1 Abstract stable (HTCS) or warp-free. Stacking sequence configurations for hygro- The design of aero-elastic compliant rotor blades thermally curvature-stable (HTCS) laminates have with tailored Extension-Twisting coupling is a well- recently been identified in 9 classes of coupled known example laminate design concept that laminate with standard ply angle orientations +45, requires either specially curved tooling or HTCS − 45, 0 and 90°. All arise from the judicious re- properties in order to remain flat after high alignment of the principal material axis of laminate temperature curing. classes with Bending-Twisting and/or Bending- Winckler [3] is credited with being the first to Extension and Twisting-Shearing coupling; Off-axis discover a solution: an eight-ply HTSC material alignment of these parent classes gives rise configuration, developed by using the concept of to more complex combinations of mechanical bonding two (or more) symmetric cross-ply coupling behavior. However, for standard ply angle [ � / � / � / � ] T sub-laminates, where each sub- orientations +45, − 45, 0 and 90°, HTCS solutions laminate is counter-rotated by π /8, giving rise to the were found in only 8-, 12-, 16- and 20-ply laminates. laminate: [22.5/-67.5 2 /22.5/-22.5/67.5 2 /-22.5] T , This article considers non-standard ply angle which possesses Extension-Twisting and Shearing- orientations +60, − 60, 0 and 90°, which lead to Bending coupling. Winckler [3] recognized that the solutions in all ply number groupings for 10 plies symmetric cross-ply sub-laminate represents a and above, thus offering a possibility for tapered hygro-thermally curvature-stable configuration, warp-free laminate designs. which remains so after rotation and/or combining with additional sub-laminates through stacking or 2 Introduction. interlacing. Tailored composite laminates possessing complex Chen [4] used an optimisation procedure to mechanical couplings are beginning to find maximise the Extension-Twisting coupling of the application beyond the aerospace sector, with which laminate and investigated several different sub- they have been traditionally associated, and towards sequence forms to achieve this. All coupled new and emerging applications for which laminate results were based on 16-ply certification is less stringent and design rules have configurations, optimised for maximum mechanical not become entrenched and risk averse. Recent coupling compliance (b 16 ). The first configuration, research [1,2] has demonstrated that there is a vast based on the most general form: [ θ 1 / θ 2 /…../ θ 16 ] T and unexplored laminate design space containing gave the following optimum sequence: exotic forms of mechanical coupling not previously [14.62/16.21/-69.56/21.63/-66.34/-59.38/-55.98/- identified, which includes all interactions between 49.52/49.13/56.01/61.46/64.36/-21.3/69.04/-17.01/- Extension, Shearing, Bending and Twisting, and that 14.88] T a surprisingly broad range of these coupling Cross et al. [5] augmented the theoretical proofs of responses can be achieved without the undesirable Chen [4] for the necessary conditions for hygro- warping distortions that result from the high thermally curvature-stable coupled laminates, temperature curing process. Such laminate designs focussing also on maximising the mechanical coupling response, but now with the smallest

possible ply number groupings. A 5-ply anti- Bending and Shearing-Twisting; which is a parent symmetric configuration was derived: [76.3/- class for the majority of the forgoing solutions. 33.6/0/33.6/-76.3] T . The article also included The concept can be seen clearly from one of two numerical and experimental validation to assess the new 13-ply laminate solutions described later in the robustness of the designs due to ply orientation paper: [+ / − / � / − / � / + / � / + / − / � / � / � / � ] T , where errors. However, conclusions were drawn entirely + , − , � and � become +60, -60, 0 and 90 ° (or +30, - on the basis of the anti-symmetric 6-ply solution: 30, 90 and 0 ° ), i.e. [60/-60/0/-60/0/60/0/60/- [15/-75/-45] A . 60/0/90/90/0] T . Here, the first nine plies of the A number of subsequent articles have substantially stacking sequence represent a quasi-isotropic extended this work; the focus, however, remaining [60/-60/0/-60/0/60/0/60/-60] T , laminate: with almost entirely on maximising the mechanical Bending-Twisting coupling, but the addition of the compliance ( b 16 ) using free form rather than cross-ply sub-laminate [0/90/90/0] T to the outer standard ply orientations. Only the most recent surface, results in a hygro-thermally curvature stable work [6] has considered combined mechanical laminate, possessing Extension-Bending, Shearing- coupling, i.e. Extension-Twisting and Bending- Twisting and Bending-Twisting coupling when axis Twisting coupling behaviour at the laminate level. aligned. Weaver [7] developed a small number of laminate By contrast, the single 8-ply laminate solution: configurations containing repeating groups of four- [ + / � / − / � / − / � / + / � ] T , i.e. [60/0/-60/0/-60/90/60/0] T , ply symmetric sub-sequences with orthogonal which possesses Extension-Bending, Shearing- orientations which serve to validate a number of the Twisting and Bending-Twisting coupling, illustrates laminate forms proposed by Winckler [3]. The π /3 an example where the cross-ply and resulting configurations are repeated here for extensionally isotropic sub-sequences are interlaced completeness: [0/90/90/0/45/-45/-45/45] T , [90/0/0/ rather than added. Several 8-ply solutions were 90/60/-30/-30/60] T , [0/45/90/-45/90/-45/0/45] T , presented by Cross et al. [5], but in fact correspond [0/90/45/-45/90/0/-45/45] T , [90/45/-45/0/-45/45/0/- to the above sequence with off-axis rotation, reversal 45/45/90/45/-45] T , where the repeating 0/90/90/0 of the stacking sequence and sign switching. sub-laminate is rotated by 45 ° in the first solution, and by 90 ° and 60 ° , respectively, in the second. The 3 Development of hygro-thermally curvature- concept of sub-laminate ‘splicing’, proposed by Tsai stable (HTCS) laminates designs. [8], was also shown to be applicable to coupled The necessary conditions for hygro-thermally hygro-thermally curvature-stable laminates with curvature-stable behaviour can be found in repeating sub-laminate groupings, whereby an numerous articles [2,4,5,7,9], but are summarized underscore identifies the plies of one sub-laminate here in terms of the well-known lamination which have been ‘spliced’ or, more appropriately, parameters and the equivalent form of the ‘interlaced’ with another. extensional and coupling stiffness matrices, which Cross et al. [5] provide an important clue to vary with material axis alignment, β , as follows: discovering an entire range of non-standard ply β = m π /2 and π /8 + m π /2 ( m = 0, 1, 2, 3) orientations that are the basis for this study. Listed ⎡ A A 0 ⎤ are HTCS configurations developed in the absence 11 12 ⎢ ⎥ ξ 1 = ξ 2 = ξ 3 = 0; of repeating cross-ply sub-laminates assumed by A A 0 (1) ⎢ ⎥ 12 11 others [3,7]. Instead, solutions contain combinations ⎢ ⎥ 0 0 A ⎣ ⎦ 66 of π /3 extensionally isotropic and cross-ply sub- β = m π /2 ( m = 0, 1, 2, 3) sequences; the result being a transformation from ⎡ B - B 0 ⎤ uncoupled isotropic properties to coupled, but warp 11 11 ⎢ ⎥ ξ 5 = ξ 7 = ξ 8 = 0; free solutions. This transformation can be - B B 0 (2) ⎢ ⎥ 11 11 understood from the well-known fact that the ⎢ ⎥ 0 0 - B ⎣ ⎦ 11 addition of cross-plies to an otherwise uncoupled β = π /8 + m π /2 ( m = 0, 1, 2, 3) laminate renders the laminate coupled in Extension-