Design of and with thin-ply non-crimp fabric as building blocks for composites

3.1 Conventional NCF building block

The typical and conventional NCF building block choices seem to be angle-ply, cross-ply, and/or combinations thereof, which all result in a balanced and/or orthotropic building block [e.g. (45/−45), (0/90), and (0/45/90/−45), respectively]. The balanced/orthotropic designs to start with are also useful for implementing the general design of an NCF building block. It is because one requires nominal ply data for the NCF design process, such as in CLT-based (classical lamination theory [34]) calculations/predictions on the mechanical behavior of the NCF building block. And the ply properties can be back-calculated from the data of a baseline, somewhat more traditional NCF configuration, which enables arguably more reliable coupon test data.

A UD ply may also be produced with the NCF machines by laying the fiber tows in parallel and stitching for the planar stability of the tows. This procedure, for instance, was reported for a carbon/epoxy material [25]. Although it was a direct method for obtaining the single ply data, the stitching and tow placement are not necessarily the best representation of an optimized multi-angle NCF production that may be the primary goal. Stabilizing a UD ply of the tows may require a nonwoven mat and/or somewhat heavier stitching than what may be the optimal and minimally intrusive stitching of a multi-angle/layer NCFs. Unlike in a single UD NCF ply, multi-angle plies assist each other in stabilizing the tows within themselves. Therefore, multi-angle NCFs, for instance an angle-ply balanced NCF of (±ϕ) fiber orientations and preferably with a shallow angle ϕ, may be used to make test coupons and back-calculate the UD equivalent ply data, as the associated stitching would be more representative.

The following approach for the back-calculation of the nominal ply properties can be incorporated: (i) prepare NCF-made laminates and characterize them for the laminate mechanical properties (E_xE_y, ν_xy, G_xy); (ii) suggest ranges for nominal UD ply parameters (E₁, E₂, ν_12,, G₁₂) and calculate the laminate stiffness parameters for the tested lay-ups using CLT; and (iii) compare with the available test data to determine the ply properties which result in the best correlated predictions. Figure 3 shows an illustration of the procedure. For the selected ranges of E₁ and E₂, predicted contour bands of different laminate properties capturing the associated experimental findings on the tested laminates can be overlapped. This enables one to zoom-in to the nominal ply property settings which can correlate all the test data reasonably well. This approach can also be adopted for the strength parameters by incorporating failure predictions, for instance by the Tsai-Wu failure criterion.

Figure 3:

Illustration of the approach to back-calculate nominal UD ply data due to available NCF-made laminate mechanical properties.

Contours represent estimated range of laminate longitudinal modulus, E_x transverse modulus E_y and Poisson’s ratio ν_xy as function of the ply moduli covering the experimental data of the laminates, say (A) laminate (±ϕ₁), and (B) laminate (0/±ϕ₂/0). Red cross indicates the selected ply moduli, E₁ and E₂ which best predicts the available test data of the laminates.

In the work of the Stanford Composite Design Group focusing on the thin-ply NCF, test coupons of C-ply™/epoxy were made available by using various manufacturing techniques [25], [26], [27]. The laminates tested were of (±12.5), (±22.5), (0/±25/0), and (0/±45/0) thin-ply NCF building blocks. Back-calculated nominal carbon fiber (0)-ply stiffness and strength parameters were reported in Refs. [28], [31], which are also included in the second column of Table 2.

With these nominal ply properties incorporated, the stiffness and strength parameters of two NCF sub-laminate families, namely (±ϕ) and (0/±ϕ/0), were predicted as a function of the off-axis fiber orientation angle ϕ via classical lamination theory and the micromechanics-based MicMac toolset [34], [35]. This exercise is simply equivalent to the design of the NCF building block. Figure 4 presents typical balanced/orthotropic-like (no extension-shear coupling) NCF design curves for sub-laminate stiffness and strength. They also include the test data from four coupons: sub-laminates by (±12.5), (±22.5), (0/±25/0), and (0/±45/0) NCFs [27].

Figure 4:

Basic stiffness and strength predictions for T700/Epoxy (±ϕ) and (0/±ϕ/0) C-ply™ laminates.

Test data from (±12.5), (±22.5), (0/±25/0), and (0/±45/0) type laminates [25], [26], [27].

3.2 Anisotropy in NCF building block: unconventional and intriguing for design

One of the features in NCFs, deserving emphasis is that the building block NCF can be designed to introduce anisotropy inherently [23], [24]. That is, a choice of the ply orientations can make a highly anisotropic building block NCF, such as (0/25), (0/45) orientations (shown in Figure 2B). Their stacks or repeats then translate into an anisotropic, homogenized laminate (as discussed in the next section). The anisotropy is typically due to the unbalanced off-axis fiber orientation ϕ along with the 0-degree ply forming the (0/ϕ) NCF. This building block results in shear-extension coupling. Figure 5 shows how shear-extension coupling is induced on homogenized laminates of an anisotropic (0/ϕ) NCF as opposed to a (0/ϕ/–ϕ) NCF building block, subject to the plane stress state of combined normal and shear stresses. When the applied stress state is uniaxial (σ_x≠0, σ_xy/σ_x=0), no shear, but an extensional normal strain, γ_xy/ε_x=0 results for the balanced NCF building block regardless of the off-axis ply angle ϕ (Figure 5A). In contrast, when the sub-laminate is unbalanced, the γ_xy/ε_x ratio is nonzero and depends on the off-axis ply angle ϕ due to the nonzero shear-extension stiffness coupling (Figure 5B). Figure 5B also indicates the stress ratio being positive or negative will result in differences in the absolute magnitude of the strain ratio, unlike in the sub-laminate of balanced off-axis plies. The in-plane extension-shear coupling due to anisotropy and associated strain dependence can be tailored by the design of the NCF that can translate into the laminate design for deformation, as discussed in the upcoming sections.

Figure 5:

Ratio of γ_xy : in-plane shear strain component and ε_x: extensional (on-axis) strain component as a result of applied shear-normal stresses.

Shear-extensional strain ratio for (A) (0/ϕ/−ϕ) balanced, orthotropic-like NCF; (B) (0/ϕ) anisotropic NCF.

One can also exemplify the potential benefit of the custom design NCF building block by comparing the most traditional quasi-isotropic [π/4=(0/45/90/−45)] design against shallow off-axis angle (ϕ) NCF configurations. Figure 6 provides Tsai-Wu failure surfaces under combined stress states. The contour plot was tailored so that the stress-states stand out, where the shallow angle designs are safer than the π/4 design. Considering the stress-ratios on the plot, these colored regions (corresponding to the failure surface towers) suggest that the shallow angle NCF designs are likely to outperform the π/4 design for highly slender structural problems.

Figure 6:

Comparison of Tsai-Wu failure surfaces for laminates of QI: (0/45/90/−45), (0/±25/0), and (0/25) stacks.

4.1 Asymmetry associated with the fixed sub-laminates of NCF

While symmetrical stacking sequences are often preferred in laminated composites, as noted in Table 1, not all NCF building blocks are suitable for creating overall symmetric laminates, unless their matching alternates for symmetry are also made available [e.g. (0/45) and (45/0) both to be available]. An NCF building block may not necessarily provide its own mirror image alone by simple lamination practices, such as flipping over and/or rotating by an angle unless the ply orientations are of cross-ply family, (0/90) or (45/−45), and π/4-quasi-isotropic (0/45/−45/90) (Table 3). A consequence of this intrinsic asymmetry is the nonzero extension-bending coupling matrix [B]. However, the effect of the asymmetry is also reduced as homogenization at the laminate level is increased by a sufficiently high number of repeats of the building block or sub-laminate. Figure 8A shows how the entities of the normalized extension-bending coupling stiffness matrix [B*] vanish as the number of repeats increase for sub-laminate π/4, suggesting the minimized effect of the asymmetry of the whole laminate.

Figure 8:

(A) Normalized extension-bending coupling stiffness matrix for π/4 sub-laminate repeated r times, [0/45/90/−45]_r.

(B) Diminishing effect of asymmetry on flexural strain to axial strain ratio under simple uni-axial stress, σ_x.

The number of the distinct fiber orientations within the NCF sub-laminate is also a factor in the homogenization at the laminate level. Among the bi-, tri- and quad-angle sub-laminates, a lower repeat of the building block or sub-laminate will be sufficient, when fewer angles or orientations are used within a building block. This can be demonstrated by the diminishing ratio of resulting bending/flexural (ε_flex) to in-plane (ε_in-plane) strains for the asymmetric stacks of bi-, tri-, and quad-angle sub-laminates, when the loading is extensional only (Figure 8B). That is, the symmetry and asymmetry of the lay-up may converge to the same overall deformation as the number of repeats ‘r’ is increased. This also suggests that simplicity of the basic building block results in minimized errors due to use of the homogenized or equivalent properties instead of the ply-by-ply values, the topic to be discussed in the next section.

4.2 Homogenized properties of thin-ply NCF building block and failure envelopes

The NCF building block or sub-laminate design curves in Figure 4 also represent fully homogenized laminate properties before the first ply failure (FPF). For general and multi-angle NCF sub-laminates, on the other hand, progressive failure may occur, calling attention to the last ply failure (LPF), as well as the FPF. Therefore, the prediction procedure of FPF is also followed for the homogenized LPF predictions, but incorporating an additional degradation scheme [34], which traditionally imposes an empirical degradation factor, d in the range of 0.1–0.2. For this present study, a factor d=0.2 was used on the matrix material properties and reflected here onto the matrix-dominating ply properties by using micromechanics relations [34], [35]. In contrast, the longitudinal-ply modulus was maintained at its “intact value”. The laminate strength parameters can be computed by applying the ply-by-ply Tsai-Wu criterion based analyses. Specifically, six basic uni-mode loading/stress state scenarios are considered, namely (σ_x, σ_y, σ_xy)=(1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1), and (0, 0, −1) corresponding to the laminate strength parameters X, Xʹ, Y, Yʹ, S and Sʹ, respectively. The representative stiffness and strength predictions for several thin-ply NCF building block designs of C-ply™/epoxy are given both for FPF and LPF in consecutive columns of Table 2. Such predictions shall be the essential data/parameters in designing NCF laminates and structures by analyses within the most commercial finite element software in which Tsai-Wu criterion is typicaly built-in.

4.3 Homogenized FPF and LPF envelopes

Another direct graphical way to assess the performance of the NCF designs is to study the failure surfaces or envelopes, which were also considered for the homogenized laminates. Following a common practice in the design cycle of laminated composites, the FPF and LPF envelope predictions can be performed using the ply-by-ply analyses. Alternatively, the use of homogenized equivalent strength parameters in LPF along with the FPF predictions is discussed here. The envelopes based on traditional Tsai-Wu criterion [34] are referred to as the homogenized envelopes [32]. If the repeat of a sub-laminate increases, the laminate characteristics normalized with respect to its thickness converge to those of a symmetric laminate. For instance, a quadratic failure envelope for a sub-laminate, say (ϕ₁/ϕ₂), and a homogenized laminate with its sufficiently large repeat ‘r’, [ϕ₁/ϕ₂]_r can be considered to be equivalent to the envelope of a simple symmetric laminate of [ϕ₁/ϕ₂]_s.

In order to compare the homogenized laminate failure envelopes with the ply-by-ply envelopes, the results for several sub-laminates of bi-, tri-, and quad- ply orientations are shown in Figure 9. The choice of the sub-laminates for comparison are: quasi-isotropic, orthotropic-like, and anisotropic building-blocks. Recalling the discussion in Figure 4, focus was specifically on the σ_x−σ_xy plane, where the bi-angle NCF can make the utmost impact. This is the stress plane, where highly loaded slender structures such as wind turbine blades and wing designs, can be improved for reduced weight, but increased strength. It should be noted that although homogenized envelopes require ply-by-ply analyses along with the anchor points, X, Xʹ, Y, Yʹ, S and Sʹ as in Table 2, once they are formed, the implementation in the design cycle can be performed as if a homogenous material [31] was used.

Figure 9:

Sub-laminate first ply (FPF) and last ply (LPF) failure envelopes (in MPa): ply-by-ply (-P) vs. homogenized (-H) (A) quasi-isotropic, (B) balanced and orthotropic-like (C) anisotropic.

The failure envelopes presented in Figure 9 suggest the following: (i) the degree of anisotropy does not adversely affect the accuracy of equivalent or homogenized laminate failure envelopes: they are all in very good agreement with the ply-by-ply analyses; (ii) the ply-by-ply LPF envelopes with discontinuity-like abrupt shape changes may be hard to implement in automated design cycles (in the case of equivalent or homogenized LPF envelopes, these models are also ellipsoids, similar to the FPF envelopes and well-behaved quadratic functions. They can easily be incorporated parametrically as constraints to avoid failure in the design optimization process.); and (iii) bi-angle NCF homogenized laminates with shallow off-axis plies do not have a significant FPF and LPF distinction, i.e. FPF (without an assumed/empirical degradation scheme) predominantly drives the design cycle.

5.1 Design for deformation

As any NCF ply arrangement is virtually possible, the sub-laminates are not necessarily orthotropic, but may also be anisotropic. For instance, a building block, bi-angle thin-ply NCF may reunite composite designers and practitioners with the anisotropy and associated benefits complemented by the one-axis lay-up advantage. One can homogenize the laminates and reduce the normalized in-plane/bending coupling to a great extent by the bi-angle thin-ply NCFs, while taking advantage of the bending-twisting coupling for the out-of-plane deflection control.

Slender load-bearing structures such as wings and wind turbine blades are subject to inevitable combined bending and twisting type loading and deformations. Unlike traditional quasi-isotropic laminates, anisotropic lay-ups under either one of the loadings result in the both types of deformation simultaneously due to the bending-twisting coupling.

The bending-twisting coupling due to anisotropy has been long recognized for its potential of controlling or designing the deformation counter effects on the loading types, usually referred to as passive aeroelastic tailoring in the field of aerostructures. The potential of the bi-angle NCF for such a tailoring approach can be shown on the simple laminated plate design (Figure 10) for suppressing one of the deformation modes despite combined loading. Figure 11A (left column) and Figure 11B (right column) show how an off-axis angle ϕ can be determined for zero tip deflection and zero tip rotation, respectively, when the anisotropic laminate [0/ϕ]_8S is subject to combined loading.

Figure 11:

Design of deflection and twisting of a cantilever flat anisotropic panel subject to combined twisting and bending moments, m_x and m_y, respectively.

Design vs. loading ratio (A) for zero central deflection with tip rotation; (B) for zero tip rotation with tip central deflection w_c.

5.2 Design optimization using homogenized laminate properties

Although design optimization of composite structures is a well-established field [37], [38], [39], [40], [41], [42], associated research continuously progresses. Novel strategies are demonstrated such as the use of lamination parameters as design variables while adapting the evolving manufacturing capabilities and practicability into the design [40], [41].

The form of the materials used in the composite structures may also be a decisive factor regarding the strategies. One supplementary aspect herein, for instance, is to tailor the design framework to the distinct and descriptive characteristics of NCF. Homogenized or dispersed collections of fiber orientations in the form of sub-laminates, which are intrinsic to NCF in composites, offer several advantages. Analyses for preliminary design can be carried out by adjusting to a building block approach which relies on the homogenized material properties and failure envelopes. Preliminary composite design may implement simplified analyses by replacing the composite laminates in the structural model as if they were constructed of equivalent homogenized material [40], [43]. Parnell and Tsai [33] reported use of the equivalent properties in finite element analyses of a typical stiffened panel problem. The approach can provide a design optimization framework five times faster, due to overall solution and memory reductions. In addressing the use of sub-laminates and their equivalent properties in the design of composite structures, Venkataraman et al. [44] have demonstrated that error due to equivalent properties may be as high as 20%, but can be reduced to 6% if the repeat of the sub-laminate is increased. They have also cautioned that their findings may not be applicable, when the lay-up is asymmetric, which is typically the case in this article.

One simplifying difference here, yet specific to NCF practices in analysis and design, is that the sub-laminate is formed from a single unit basic building block. This approach reduces the error in the bending stiffness matrix [D] and enables even an asymmetric overall lay-up, provided that the number of repeats is sufficient. Recall Figure 8B which showed how the ratio of bending to in-plane strains converges to zero, for asymmetric stacks of bi-, tri- and quad-angle sub-laminates, when the loading is extensional in nature only.

The process of sub-laminate-based analysis and design herein can be represented by Figure 7. The NCF sub-laminate is treated as a homogenous material with the associated homogenized/equivalent properties. Then homogenous thickness variables are assigned to the spatial domain(s) of the structure so that they can be optimized for the given problem. Once the optimal homogenized thickness profile is found for the structure, it can then be converted back to the sub-laminate stack.

Several isolated unit-load cases were first evaluated for deformation and stress fields computed from finite element analyses, using individual ply-data and NCF building block/sub-laminate properties within the ply-by-ply and homogenized laminate analyses, respectively. The lay-up was made-up of a stack of (0/25) sub-laminates with a repeat of 16, resulting in a total laminate thickness of 2 mm (32 thin plies of C-ply material). Table 4 summarizes the comparisons for the load cases and associated percentage errors due to use of the homogenized properties. In addition, Figure 12 shows how the tip displacement due to axial (in-plane) unit load deviates from the ply-by-ply analysis result (A), and when the homogenized properties are utilized (B). The latter results in zero lateral tip displacement, as the coupling stiffness matrix [B] is not incorporated, despite the asymmetry of the lay-up. The difference is negligible – 0.2 mm (as opposed to 900 mm length of the plate) for the unit load case, although it is directly proportional to the applied load. For the same problem, a stress field comparison is also presented in Figure 12. As reported in Table 4, the three in-plane stress components σ_x, σ_y, σ_xy were underestimated by 5%, 17% and 27%, respectively. However, it should be noted that the latter two stress components are the minor ones and an order of magnitude smaller than the axial stress. Furthermore, the Tsai-Wu failure criterion based strength ratio predictions differ by about 10%.

Figure 12:

Lay-up, (0/25)_16T – total 16 repeats of (0/25) NCF, Load case: p_x=1 N/mm, deformed shape and stress contours, σ_x.

(A) Ply-by-ply analysis; (B) homogenized laminate analysis (displacements are not scaled).

As for the distributed lateral (out-of-plane) load case, the tip displacements predicted by the two approaches are almost the same, where the difference is about 0.1%. The three in-plane stress components (σ_x, σ_y, σ_xy) are different by, 0.7%, 2.5% and 2.1%, respectively (Table 4).

Twisting and bending moment unit load cases were also studied, and their results are presented in Table 4. Deformed shape and the stress contours for the bending moment load case are presented in Figure 13. Furthermore, as an example of the combined loading, analysis by the homogenized laminate approach under axial load and twisting moment results in stresses and deformation, to within 5% of the results by the conventional ply-by-ply analysis. Comparisons of the displacement, stress fields, buckling loads, and strength ratio in Table 4 suggest that the homogenized (equivalent or effective) laminate properties within the course of the NCF sub-laminate/building block approach can be utilized for preliminary analysis and design efficiency.

Figure 13:

Lay-up, (0/25)_16T – total 16 repeats of (0/25) NCF, Load case: m_y=1 N, deformed shape and stress contours, σ_x.

(A) Ply-by-ply analysis; (B) homogenized laminate analysis (displacements are not scaled).

In order to demonstrate the expected accuracy along with the simplicity of sub-laminate building block/homogenized laminate based design optimization as summarized in Figure 7, the same flat plate problem subject to distributed transverse load p_z and twisting moment m_x was considered. Finite elements of the model were grouped as 15 longitudinal (along the x-axis) regions, each assigned to a homogenized thickness resulting in a total of 15 continuous design variables. The sub-laminate building block for the homogenized laminates was chosen as [0/25]. The minimum weight optimization problem was solved for a constrained maximum tip displacement, d_tip. Figure 14 shows the initial design and the optimal thickness profiles for two different load cases while the tip displacement constraint was fixed to 30 mm. The results are based on the homogenized laminate approach and require verification by the ply-by-ply analysis. Figure 15 presents the comparisons for the combined load case of p_z=1 N/mm and m_x=10 N, such that d_tip≤30 mm. The ply-by-ply analysis on the optimal thickness profile results in the tip displacement d_tip=32 mm, as opposed to 30 mm in the homogenized laminate analysis; an error of about 8%. The stress distributions were well captured, but the error may be as high as 6%. Note that the stress constraints were found to be inactive for this problem. The optimal solution of the homogenized laminate was driven by the tip displacement constraint. Despite the error in the tip displacement for this example problem, the homogenized laminate or sub-laminate building block based optimization approach is in general proposed to be an efficient and accurate preliminary sizing strategy.

Figure 14:

Optimization of clamped-free flat plate problem (Figure 10) subject to distributed lateral force p_z and distributed twisting moment, m_x for constrained tip displacement d_tip≤30 mm.

Minimum weight laminate thickness profiles by (0/25) sub-laminate: distribution of 15 discrete thickness variable zones and nominal smoothing fit.

Figure 15:

Deformation of the optimal laminate design subject to p_z=1 N/mm m_x=10 N.

(A) homogenized laminate analysis of the design optimization cycle; (B) posterior ply-by-ply analysis of the optimal profile due to Figure 14.