# Mechanisms of Origin and Classification of Out-of-Plane Fiber Waviness in Composite Materials—A Review

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## Abstract

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## 1. Introduction

## 2. Definition of Terms

## 3. Parameters

_{max}is considered to have the greatest impact on the mechanical properties. Important influencing parameters such as maximum deviation of the fiber orientation from the original orientation, as well as the laminate thickness [12], have received little attention in previous investigations. The wave pattern is typically represented mathematically as sinusoidal waves [13,14]. El-Hajjar and Petersen [15] used a Gaussian function to capture the bell curve of wavy plies, which was found to better represent the wave geometry. Nevertheless, there are a few more parameters that can influence the mechanical behavior and thus have to be considered. Results in [16] show that the position of wavy layers in the cross-section of a laminate also has a significant influence on the strength reduction. A more outward position of wavy layer leads to a greater decrease in strength, since the layers on the edge of the laminate are supported only one-sided and; therefore, fail earlier.

## 4. Occurrence of Fiber Waviness

#### 4.1. Mechanical Loading and Behavior of Dry and Impregnated Fiber Reinforcements

#### 4.1.1. Basic Material Behavior

#### 4.1.2. Mechanical Deformation of Layers Due to Manual Handling of Preforms, Moving Sliders, and Closing Tools

#### 4.2. Path Length Differences

#### 4.2.1. Micro/Meso Scale Deformation at the Material Level

#### 4.2.2. Global Deformation on Structural Level at Double Curved and Joggled Geometries

_{R}, which act in opposite direction to the material flow as the material is drawn into the cavity. Since the material cannot stretch in fiber direction due to virtually inextensible fibers, the fibers have to move from the outer edges of the sheet towards the center causing tensile stresses in fiber direction. According to Friedrich et al. [44], the decrease in area when moving towards the apex of the dome section simultaneously leads to compressive hoop stresses in the bisecting direction of the reinforcements which are resolved in out-of-plane buckles appearing in the direction away from the fibers. Dependent on the mold geometry inter-ply slip, inter-ply rotation and transverse matrix flow are necessary in order to form a component without instabilities such as out-of-plane buckling.

#### 4.2.3. Steering

#### 4.2.4. Consolidation in Corner Areas, External Radii, Stepped, or Tapered Laminates

#### 4.3. Non-Uniform Pressure Distribution

#### 4.3.1. Co-Bonding (or Pre-Cured Parts in LCM Process)

#### 4.3.2. Telegraphing Effect of Face Sheets at Honeycomb Core

#### 4.3.3. Welding Spots

#### 4.3.4. Ply and Vacuum Bag Bridging

#### 4.4. Interaction between Tool–Ply and Ply–Ply

#### 4.4.1. Inter-Ply Slippage

#### 4.4.2. CTE Mismatch

#### 4.5. Lay-Up Sequence

#### 4.5.1. Gaps and Overlaps

#### 4.5.2. Ply Drops in Tapered Laminates

#### 4.6. Textile Architecture

#### 4.6.1. Inherent Undulations in Woven and Braided Fabrics

#### 4.6.2. Shear Locking Angle of Woven Fabrics

#### 4.6.3. Stitches in Non-Crimped Fabrics

#### 4.6.4. Stitches in Dry Fiber Placements

#### 4.7. Foreign Objects

#### 4.7.1. Intended Foreign Objects (e.g., Optical Sensors, Pins, Inserts)

#### 4.7.2. Unintended Foreign Objects (e.g., Foils, Blades, etc.)

#### 4.8. Flow-Induced Waviness

#### 4.8.1. Fiber Wash-Out

#### 4.8.2. Hydraulic Effects (Squeezing, Transverse Flow)

#### 4.9. Cure-Induced Waviness

#### 4.9.1. Volumetric Shrinkage

#### 4.9.2. Large Temperature Gradient in Thick Laminates

#### 4.10. Unique Characteristics of Fabrication Processes

#### 4.10.1. Filament Winding

#### 4.10.2. Pultrusion

## 5. Classification Scheme

#### 5.1. Number and Distribution of Waves

#### 5.2. Traditional Differentiation of Wave Types—Constant or Changing Wave Amplitude

#### 5.3. Phase Characteristics of the Wave Form

#### 5.4. Visibility

#### 5.5. Dimensional Characteristics

#### 5.6. Continuity of Layers/Laminate

#### 5.7. Portion and Position of the Wavy Region in the Laminate

#### 5.8. Phase Characteristics of the Material

#### 5.9. Influence of t/A Ratio

#### 5.10. Geometric Position of the Wavy Region in the Part

## 6. Examples for Waviness Classification

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**General definition of deviations from the intended fiber orientation (i.e., wave/wrinkle, fold, undulation, and misalignment).

**Figure 2.**Parameters influencing the mechanical properties (e.g., amplitude A, wavelength L, laminate thickness t, maximum fiber misalignment angle θ

_{max}, layup, and the position of wavy layers within the laminate).

**Figure 3.**Wrinkling in compression of a woven reinforcement strip with different bending stiffness (from left to right 1, 10, 10

^{2}, 10

^{3}N mm

^{−1}) [19]. Reprinted from Phil. Trans. R. Soc. A, Vol. 374, Modelling the development of defects during composite reinforcements and prepreg forming, page 5, (2016), with permission from The Royal Society Publishing.

**Figure 4.**Wrinkling of initially planar unidirectional (UD) ply due to shear buckling in off-axis tensile test.

**Figure 5.**Path length differences between the edges of tows on the surface of a hemisphere/a double curved surface; adapted from [1].

**Figure 6.**Force analysis in 3D stamp forming, modified from [44].

**Figure 7.**Spar geometry with a flange recess area [28]. Reprinted from Composites: Part A, Vol. 50, An experimental study of mechanisms behind wrinkle development during forming of composite laminates, page 56, (2013), with permission from Elsevier.

**Figure 8.**Overview of tow steering defects leading to out-of-plane fiber waviness [52]. Reprinted from Composites: Part B, Vol. 43, The engineering aspects of automated prepreg layup: History, present and future, page 1005, (2012), with permission from Elsevier.

**Figure 11.**(

**a**) Representation of the book-end effect, created when a laminate is consolidated unconstrained over a corner radius and slippage occurs; (

**b**) constrained consolidation due to high shear resistance leading to fiber waviness; (

**c**) book-end resulting from forming process illustrating the termination angle θ.

**Figure 12.**Example of co-bonding of a pre-cured stringer onto wet face layers leading to fiber waviness due to non-uniform consolidation pressure distribution.

**Figure 13.**(

**a**) Telegraphing effect of thin layers on top of a honeycomb core; (

**b**) waviness in tool side face layers due to non-uniform consolidation pressure.

**Figure 14.**Illustration of a horn locally welding the laminate stack leading to fiber waviness due to uneven pressure distributions.

**Figure 16.**Vacuum bag bridging leading to low compaction pressure in the corner area, fiber waviness, and increased void growth.

**Figure 18.**Formation of wrinkles as a result of deformation rate, adapted from [87].

**Figure 19.**Possible manufacturing effects leading to fiber waviness in ply runout (tapered) regions, modified from [1].

**Figure 20.**Shear force vs. shear angle plot of a picture frame test showing shear locking (trellis effect) with resulting increased load and out-of-plane movement in form of wrinkling.

**Figure 21.**Schematic illustration of fiber waviness induced by zig-zag stitches in tailored fiber placement (TFP) process; adapted from [60].

**Figure 22.**Schematic illustration of waviness induced by foreign objects (e.g., optical sensors, pins, inserts) or inherent to NCFs due to stitching yarns. This kind of waviness can be, dependent on the orientation of the embedded object, in-plane and out-of-plane.

**Figure 23.**Optical fibers embedded parallel to the orientation of the reinforcement fibers can avoid fiber waviness as long as the diameter is small or the thickness of the composite layer is thick enough.

**Figure 27.**Random (stochastic distributed) waviness in pultrusion direction due to insufficient tow tension.

**Table 1.**Variation of minimum steering radius with slit-tape width for a 102 mm track width [50].

Slit-Tape Width | Typical Minimum Steering Radius |
---|---|

3.175 mm 1/8″ | 635.0 mm 25″ |

6.350 mm 1/4″ | 1778 mm 70″ |

12.70 mm 1/2″ | 8890 mm 350″ |

Material | Coefficient of Thermal Expansion [10^{−6}/°C] | |
---|---|---|

CFR-Epoxy—UD longitudinal | 0.3 | [92,93] |

CFR-Epoxy—UD transverse | 35 | [92,93] |

CFR-PEEK—UD longitudinal | 0.4 (23–143 °C)—solid state 0 (143–343 °C)—rubbery region | [94] |

CFR-PEEK—UD transverse | 30 (23–143 °C)—solid state 80 (143–343 °C)—rubbery region | [94] |

CFR-PEEK—quasi isotropic | 2.9 (23–143 °C)—solid state 7 (143–343 °C)—rubbery region | [94] |

Neat epoxy resin | 55–76 | [92,95,96] |

Carbon fiber—longitudinal | −0.4–−0.75 (High strength—high modulus fibers) | [80,96] |

Carbon fiber—transverse | 8 | [96] |

Glass fiber | 5 | [80,95] |

Aluminum | 12–25 | [80,97] |

Steel | 7–12 | [80,92] |

Example of Fiber Waviness | Number and Distribution (Single, Stochastic or In-Phase Distributed) | Through-Thickness Wave Form (Uniform vs. Graded) | Phase Characteristics of the Wave Form (Iso-Phase, Random-Phase) | Visibility (Embedded, Hump, Indention, Wave) | Dimensional Characteristics (2D, 3D) | Continuity of Layers/Laminate (Continuous, Non-Continuous) | Position (Centered, Outer Plies, Whole Laminate) | Phase Characteristics (Microscopic, Macroscopic) | Level of Influence (Material, Structure) | Geometric Position (Flat or Slightly Curved Areas, Complex Geometries) |
---|---|---|---|---|---|---|---|---|---|---|

Single | Uniform | Iso-phase | Wave | 2D | Continuous | Whole laminate | Microscopic | Structural | Flat | |

Single | Graded | Iso-phase | Embedded | 2D | Continuous | Whole laminate | Microscopic | Material | Flat | |

[162] | Stochastic distributed | Graded | Random-phase | Embedded | 3D | Non-continuous | Whole laminate | Microscopic | Material | T-joint |

[11] | Single | Graded | Iso-phase | Hump | 2D | Continuous | Whole laminate | Macroscopic | Material | Flat |

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**MDPI and ACS Style**

Thor, M.; Sause, M.G.R.; Hinterhölzl, R.M.
Mechanisms of Origin and Classification of Out-of-Plane Fiber Waviness in Composite Materials—A Review. *J. Compos. Sci.* **2020**, *4*, 130.
https://doi.org/10.3390/jcs4030130

**AMA Style**

Thor M, Sause MGR, Hinterhölzl RM.
Mechanisms of Origin and Classification of Out-of-Plane Fiber Waviness in Composite Materials—A Review. *Journal of Composites Science*. 2020; 4(3):130.
https://doi.org/10.3390/jcs4030130

**Chicago/Turabian Style**

Thor, Michael, Markus G. R. Sause, and Roland M. Hinterhölzl.
2020. "Mechanisms of Origin and Classification of Out-of-Plane Fiber Waviness in Composite Materials—A Review" *Journal of Composites Science* 4, no. 3: 130.
https://doi.org/10.3390/jcs4030130