Laminate fibre wave defect – KDF evaluation

The positive side of using composite materials in Aerospace industry is the weight reduction. The drawback are the defects created on solid laminates, during manufacturing. Structure life and strength reduction, due to the defects, need to be accurately evaluated against the A/C airworthiness requirements.


Introduction
The approach, suggested in this paper, consists on using the Conformal Mapping for laminate defects topology modeling. Scope of this approach is to evaluate a KDF for Margin of Safety calculation as a ratio between defect configurations against the intact one. For most of defect scenario, the Conformal Mappings are available in literature. For each type of defect, it is possible to define fiber pattern, angle, derivative, thickness and length.

Figure 1. Solid laminate typical defect
This paper reports only a numerical methodology for stress-strain calculation of wavy ply configuration. Fiber and matrix strength check (not included on this paper) is performed in accordance with the applicable criteria and allowable for each type of ply, The KDF for each defect topology is then calculated as follows: For clarity, the analysis of intra-lamina shear and out-of-plane matrix stress due to wavy ply curvature are not reported on this paper.

Defect Configuration topology definition
The defect analysed is an embedded resin accumulation shown on Figure 2 The wavy ply profile is defined via complex variable function F(z) (see Ref. [2]). Note that "streamline" ( ) doesn't have physical meaning rather than representing the profile of the ply, consistently with the defect type: 1. A=1.0 2. Analytical formulation of wavy ply 3. Derivative values in each point of the plies 4. Ply thickness variation 5. Ply curvature 6. Ply length

Algorithm basic assumption
Defect analysed on this paper is shown on below   The static analysis of wavy configuration, is basically a modification of the ply stress calculated via Classical Laminate Theory (Ref. [1]) for intact configuration.
The following criteria apply (see Figure4).
1. Applied load F0 is constant in each section along X axis : F(x) = F0 2. Section(X) remain plane. 3. Wavy ply mechanical properties, are re-calculated in each section (X)as per fibre-resin mixture criteria due to thickness variation. 4. Ply stress in each section (X) depends on two geometric parameters : a. Derivative Y': defines the fibre orientation and the component along X axis.
b. Stiffness ratio" λ ": Wavy longer ply (Lw ) have a lower tension stiffness than intact ply ( L0 ) and consequently "attract" less load. Fibre stress calculated at point a), is therefore scaled down by a factor "λ". (subscript0, refer to CLT).

Algorithm: step-by-step definition
In this example, the laminate length is subdivided in 31 section.  One single section can be analysed independently from the others, once the following data are available: 1. CLT stress for intact configuration 2. Derivative Y'(i), λ(i) , t(i) , curvature R(i) from conformal mapping .

Analysis of section from 16 to 31
Because of symmetry, the results are reported, for clarity, only for section from 16 to 31. The calculation is performed per following parameters: 1. Segment-to-segment calculation is based on constant step (∆ = 0.2 mm).
Note: the "sharper" is the wave and the "shorter" is the assumed segment step ∆.

3DFEM analysis
The symmetric 3D FEM is set up with defect scenario "similar" to the one analysed on this paper. Both models show the same "trend" for fibre stress profile, in spite of substantial difference on laminate configuration and mechanical properties: (comment on Par. 5)

Shear load S0
This paragraph reports the analysis of laminate defect under shear load. A simplified numerical approach is presented to calculate the shear stress at each ply based on the deformation compatibility. Ply shear load (fxy=τ*t),is proportional to factor [d0*G] and inversely proportional to the ply length. Example of a 3DFEM model is added for algorithm explanation and evaluation.