JEC COMPOSITES MAGAZINE - Issue #68 Special JEC Asia - October 2011 - 72

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bi-angle NCF

First and last ply failure predictions by homogenized strength parameters
It is a common practice to predict not only the first, but also the last ply failures (FPF and LPF) in design cycle of laminated composites. As the name implies the predictions are traditionally performed using ply-by-ply analyses. Alternatively we explore here the use of homogenized equivalent strength parameters in LPF as well as FPF predictions, as our thin ply NCF material can make homogenized laminate concept much more practical and attractive in design.
Table 1: Ply and laminate parameters for FPF and LPF analyses. Example provided for thin ply bi-angle (0/25) NCF building block. (stiffness and strength data are in GPa and MPa, respectively) FPF stiffness and strength parameters Laminate Stiffness [4] Laminate Strength [4] X= 718 X’= 666 Y= 71 Y’= 221 S=209 S’=101 LPF stiffness and strength parameters Degraded Ply Stiffness [3], [4] E11= 110 E22= 1.87 ν12= 0.06 G12= 1.0 Degraded Laminate Stiffness [4] E°11_LPF= 63.5 E°22_LPF= 5.0 ν°12_LPF= 0.6 G°12_LPF= 6.6 Laminate Strength [4] XLPF= 862 X’LPF= 745 YLPF= 71 Y’LPF= 221 SLPF= 209 S’LPF= 112

STEPHEN W. TSAI, PROFESSOR RESEARCH EMERITUS, MELIH PAPILA*, VISITING PROFESSOR, DEPARTMENT OF AERONAUTICS & ASTRONAUTICS, STANFORD UNIVERSITY *ASSOCIATE PROFESSOR, ADVANCED COMPOSITES AND POLYMER PROCESSING LABORATORY (AC2PL), SABANCI UNIVERSITY

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e are also showing in the companion articles herein this issue, use of homogenized laminate strength parameters can be an advantegaous alternative for preliminary design cycle (Parnell and Tsai[1]). The procedure with the homogenized parameters and FPF approach are summarized in the article by Tsai and Papila[2]. It incorporates Tsai-Wu quadratic failure criterion[3-4]. The FPF envelopes by the homogenized parameters were shown to match very well with the plyby-ply analyses based failure envelopes. The same procedure can be followed also for the homogenized LPF predictions as the laminate parameters are updated for LPF. That is, the LPF parameters are obtained by repeating the strength predictions, but with the degraded ply material properties. The degradation scheme traditionaly impose a degradation factor, d in the range of 0.1-0.2 (0.2 was used in this article) on the matrix material properties and reflected here onto the matrix dominating ply properties using the micromechanics relations[3], [4].

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jec composites magazine / No68 October 2011
Ply Stiffness E11= 110 E22= 7.4 ν12= 0.3 G12= 4.2

Whereas the longitudinal ply modulus is kept at its intact value. Table 1 summarizes the FPF and LPF parameters and show the specific values for the thin ply bi-angle (0/25) NCF by Chomarat. Laminate stiffness parameters for FPF and LPF are computed as homogenized equivalent properties of the whole laminate based on the corresponding ply stiffness data, as intact or degraded, respectively. The laminate strength parameters (XLPF, X’LPF, YLPF, Y’LPF, SLPF, S’LPF) are the strength predictions computed by the ply-by-ply analysis under basic loading scenarios. Note that although homogenized LPF envelopes require ply-by-ply analyses to get these anchor points for the failure envelopes, once

they are formed the implementation in the design cycle can be performed as if we have a homogenous material[1]. In order to compare the homogenized laminate LPF envelopes with the ply-byply envelopes, we are presenting the results for several sublaminates of bi-, three- and four ply orientations in Figures 1-3. The choices of the sublaminates make the comparisons as such quasi-isotropic (Figure 1), orthotropic (Figure 2) and anisotropic (Figure 3) LPF envelopes can be explored. We specifically focus on the 16 plane where our bi-angle NCF can make the utmost impact. This is also the stress plane where highly loaded slender structures such as wind turbine blades and wing designs can be improved for

E°11= 70.3 E°22= 8 ν°12= 0.5 G°12= 8
JEC COMPOSITES MAGAZINE - Issue #68 Special JEC Asia - October 2011

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