JEC COMPOSITES MAGAZINE - Issue #71 - March 2012 - 105

Fig. 3: Representative outputs of buckling modes of open-hole laminates (left) and natural frequency of tubular beam (right)

twisting are also likely to be present. We can demonstrate that laminates are the strongest and toughest when they are homogenized. This is achieved with 2 or 3 ply angles and thin-ply sub-laminates, and repeated 10 or more times. When a laminate is homogenized, the bending-shear coupling as expressed in [B] becomes zero, the normalized in-plane [A*] and normalized flexural [D*] become equal, and suddenly an asymmetric laminate is better than a symmetric one. The in-plane solution of i-MicMac is the same as the general solution when both in-plane and flexural loading are present. With these and other tools which are offered in our online Composites Design Workshop, many traditional design rules laid down 40 years ago can be challenged. Certainly laminates need not be symmetric and balanced. Ply angles should be continuous variables, not fixed. Homogenization is a feature worth exploring. Composite is not black aluminum. Uniaxial strength alone is not sufficient. Simple analysis tools offered here can promote safe and competitive use of composites. We have discovered that Chomarat’s unique thinply NCF can be made with 2 ply angles that can open up many exciting laminate design opportunities. Homogenization can be achieved in as few as 24-ply or 1.5 mm thick laminates. Edge delamination can be suppressed. A [0/25] bi-angle NCF layer is a worthwhile building block of laminates that can reduce weight and cost that the same time. n
More information: steve.tsai@mac.com Acknowledgment Our online workshop and supporting tools were the work of a global team of researchers and engineers, including Jose Daniel Dimiz Melo, Sung Ha, Jin Park, Yasushi Miyano, Melih Papila, Kim Parnell, Jeffrey Fong, TE Tay, Huhammad Ridha, and many students and postdocs. Jan Demone and her Abaqus professionals at Dassault Systèmes Simulia Corp. have also given us critical support.

each ply based on FPF and LPF. 3) Failure envelopes of the ultimate strength where ult = max (FPF, LPF). Inputs and outputs of MicMac/FEA are more extensive because it solves many boundary-value problems for FPF and LPF strengths as well as natural frequencies and critical buckling loads. Several case problems are ready to solve with the following pre-existing Abaqus/CAE models: 1) A tensile test coupon of any laminate with different clamped ends. 2) A cantilever circular tube subjected to different end load conditions.

3) A laminate with open circular hole subjected to combined stresses. 4) A laminate with open slotted hole subjected to combined stresses. Solutions of these problems give confidence to users of composites that purely empirical approaches can be improved with even elementary predictions of strength under combined stress that cannot be easily tested. After all, laminates in structures are subjected to combined stresses in nearly all loading cases. While in-plane behavior is a special case of general loading, bending and

Fig. 4: Predicted failure envelopes of open circular and slotted holes under bi-axial stress space using MicMac/FEA.

No71 March 2012

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JEC COMPOSITES MAGAZINE - Issue #71 - March 2012

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #71 - March 2012