Journal of Energy and Power Technology (JEPT) is an international peer-reviewed Open Access journal published quarterly online by LIDSEN Publishing Inc. This periodical is dedicated to providing a unique, peer-reviewed, multi-disciplinary platform for researchers, scientists and engineers in academia, research institutions, government agencies and industry. The journal is also of interest to technology developers, planners, policy makers and technical, economic and policy advisers to present their research results and findings.

JEPT focuses on all aspects of energy and power. It publishes original research and review articles and also publishes Survey, Comments, Perspectives, Reviews, News & Views, Tutorial and Discussion Papers from experts in these fields to promote intuitive understanding of the state-of-the-art and technology trends. 

Main research areas include (but are not limited to):
Renewable energies (e.g. geothermal, solar, wind, hydro, tidal, wave, biomass) and grid connection impact
Energy harvesting devices
Energy storage
Hybrid/combined/integrated energy systems for multi-generation
Hydrogen energy 
Fuel cells
Nuclear energy
Energy economics and finance
Energy policy
Energy and environment
Energy conversion, conservation and management
Smart energy system

Power Generation - Conventional and Renewable
Power System Management
Power Transmission and Distribution
Smart Grid Technologies
Micro- and nano-energy systems and technologies
Power electronic
Biofuels and alternatives
High voltage and pulse power
Organic and inorganic photovoltaics
Batteries and supercapacitors

Rapid publication: manuscripts are peer-reviewed and a first decision provided to authors approximately 4.3 weeks after submission; acceptance to publication is undertaken in 6 days (median values for papers published in this journal in the first half of 2020, 1-2 days of FREE language polishing time is also included in this period).

Free Publication in 2020
Current Issue: 2020  Archive: 2019
Open Access Original Research
Computational Micromechanics for the Optimization of Compression Strength of Unidirectional Carbon Fiber Composites for Use in Wind Turbine Blades

Ryan J. Clarke , David A. Miller †, *

Composites Research Group , Montana State University, Bozeman, MT, 59715, USA

† These authors contributed equally to this work.

Correspondence: David A. Miller

Academic Editor: Andrés Elías Feijóo Lorenzo

Special Issue: Offshore Wind Farms

Received: April 15, 2020 | Accepted: June 03, 2020 | Published: June 09, 2020

Journal of Energy and Power Technology 2020, Volume 2, Issue 2, doi:10.21926/jept.2002010

Recommended citation: Clarke RJ, Miller DA. Computational Micromechanics for the Optimization of Compression Strength of Unidirectional Carbon Fiber Composites for Use in Wind Turbine Blades. Journal of Energy and Power Technology 2020;2(2):18; doi:10.21926/jept.2002010.

© 2020 by the authors. This is an open access article distributed under the conditions of the Creative Commons by Attribution License, which permits unrestricted use, distribution, and reproduction in any medium or format, provided the original work is correctly cited.


As wind turbine blades grow longer, new design parameters gain additional importance such as blade weight, tip deflection and material cost. These parameters require designers to relook at carbon fiber as a potential design solution. However, the composite materials in wind turbine blades are subjected to significant compressive loading, and the compressive strength of carbon fiber reinforced polymer (CFRP) composites is much lower than its tensile strength. This reduction in compression strength is due to a change in failure mode from that seen in tensile loading. The aim of this study is to investigate three factors that affect the compressive failure response of CFRP composites. These factors include fiber defect severity, volume fraction, and multiaxial loading.

Compressive strength was shown to have decaying sensitivity with increasing fiber misalignment. Decreasing the volume fraction not only decreased the compressive strength but also increased the compressive failure strain. In addition, adding in-plane shear loads proved detrimental to the compressive load-carrying capacity of a composite structure. This research showed minimizing fiber misalignment in manufacturing processes is only beneficial for high tolerance processes. Decreasing volume fraction could be beneficial for highly flexible structures. Finally, the results demonstrated the need to minimize multiaxial loading for optimal composite compressive response.


Carbon fiber; computational micromechanics; wind turbine rotors

1. Introduction

The economic viability of offshore wind energy is largely dependent on the size and lifetime of the wind rotors [1]. Larger turbines mean that less are needed for the same energy production, thereby reducing installation costs. This trend in increasing turbine size is expected to continue for the foreseeable future to maintain wind energy’s cost competitiveness and keep up with global energy demand. As wind turbines continue to grow in size, the weight of the rotor and the wind loads experienced by the rotors grow at an ever-increasing rate [2]. With increasing rotor size the structural performance requirements become more difficult to achieve. To maintain acceptable levels of structural performance needed for a service lifetime of 20 years or more, either structural geometry or the materials of the wind turbine rotor can be modified. One solution to this problem that is already being implemented by the wind industry is to replace the traditional materials, Glass Fiber-Reinforced Polymer Composites (GFRP), with stronger and stiffer materials, such as Carbon Fiber-Reinforced Composites (CFRP) [3] in specific areas of the rotor.

CFRP composites offer a variety of advantages over GFRP including high specific tensile strength, high specific stiffness, and resistance to environmental effects like corrosion [4]. However, a limiting design factor in structures made from CFRP is the relatively low compressive strength capabilities compared to their tensile strength. Studies on unidirectional (UD) CFRP composites have shown a decrease in strength from tensile to compressive of up to 70% [5]. One reason there is such a significant reduction in strength between tensile and compressive loading is due to the change in failure modes [6,7]. In tension a UD CFRP composite fails primarily in fiber rupture which is governed primarily by the ultimate strength of the fiber used. In compression a UD CFRP composite can fail in a variety of modes, such as fiber micro-buckling, fiber crushing, fiber kinking, and matrix cracking and splitting. Of these failure modes, fiber kinking is considered the most dominant final failure mechanism in CFRP materials. Fiber kinking is a localized shear deformation of the matrix accompanied by eventual fiber fracture and is sometimes considered to be a final consequence of micro-buckling.

While there is a great deal of information and work on optimal design methodologies for tensile strength of CFRP composites, there lacks proper guidelines of optimal design and manufacture for the compressive strength of CFRP composites. This is especially problematic for wind rotor design, where composite structures see equal amounts tensile and compressive loading. In this study a Finite Element (FE) micromechanical model was used to study factors that influence fiber kinking as a compressive failure mechanism in UD CFRP composites. FE analysis offers an advantage over experimental work because of its ability to quickly iterate design changes that would be difficult to control in an experimental setting like fiber misalignment. It is also often difficult to identify the effect different changes could have on the compressive failure response in experimental work due to the inherent scatter involved.

Kyriakides [8] was one of the first researchers to use micro-mechanical FE models to study fiber kinking of a UD fiber-reinforced polymer composite. Kyriakides model consisted of a 2-D array of alternating fiber matrix layers with the with the matrix being modeled with elasto-plastic behavior using J2 flow theory. Defects were introduced into the model with initial fiber misalignment and the model underwent a compressive load to initiate kink-band formation. Gutkin et al. [9] also used a 2-D micro-mechanical model but employed Periodic Boundary Conditions (PBCs) to improve computational efficiency by approximating the composite structure implicitly with a repeating unit cell (RUC). One problem with using a 2-D RUC is the ambiguity of volume fraction of the composite. Recently, Naya et al. [10] studied the influence of environmental effects on the compressive failure response of CFRP composites using a 3-D RUC model with applied PBCs.

The objective of this study was to examine the influence of three different design and manufacturing factors have on the compressive failure of UD CFRP composites. The three factors varied were fiber misalignment severity, fiber volume fraction, and multiaxial loading. To accomplish the objective of this study, a 3-D RUC micro-mechanical FE model was developed to identify the trends and influences these factors have on CFRP compression failure.

2. Model Development

2.1 Model Geometry

A base-line single fiber RUC was used for the analyses of this study. The base model consisted of a single circular fiber embedded in a square matrix. This RUC geometry represents a square packing structure of the composite. The dimensions of the RUC were h = 10 , and L = 675 . The dimensions of the fiber were selected to maintain a volume fraction of 34%. The basic geometric features of the model can be seen below in Figure 1. The length of the RUC model has been shown to be important to the buckling response of composite micromechanics models. If the model is too short the model will predict an overly conservative estimate for composite compressive strength as well as not be able to capture all aspects of kink-band formation [9]. However, the model should not be too long to maintain computational efficiency.

Gutkin et al. [9] and Barulich et al. [11] both conducted parametric studies on their FE models and found that fiber kinking results converge approximately at a critical half wavelength corresponding to 75 times the fiber diameter used. Subsequent experimental results from Sun et al. [12] were in good agreement with the above-mentioned parametric studies and found that the critical wavelength associated with kink band failure were on the order of 50-75 times the fiber diameter for CFRP composites.

From the results of the studies by Gutkin, Barulich, and Sun et al., the length L of the model analyzed, which corresponds to the half wavelength of the fiber, was determined to be approximately 100 times the diameter of the fiber, or 675 µm. The length of 675 µm was determined to maintain a conservative estimate of the critical half wavelength. By increasing the model past this length the critical buckling load does not change and only increases computational time [9].

Click to view original image

Figure 1 Basic geometry definition of RUC.

2.2 Boundary Conditions and Loads

Key aspects to any micromechanical analysis are the boundary conditions and loads applied to the model. For the RUC models used in this study the basic boundary conditions and loads remained the same and are illustrated below in Figure 2.

Click to view original image

Figure 2 Location of Boundary Conditions and applied loads on the Micro-mechanical FE RUC model.

In Figure 2 the number indicates the boundary condition or load corresponding to:

Rear face of RUC: no z-displacement, pinned condition in x and y
Lateral faces of RUC: PBCs applied
Front face of RUC: Incremental compressive displacement in the negative z-direction

The compressive displacement was applied as an incremental displacement to all nodes on the front z-face. Displacement control was used instead of load control for convergence purposes. The rear z-face of the RUC model was constrained from movement in the z-direction and one node in the middle of the fiber was constrained in the x- and y-directions to prevent free body motion. Finally, PBCs were applied to the lateral faces of the RUC model to approximate an infinite periodic array in both the x- and y-directions. The PBCs were applied using Equations (1) and (2).

$${\rm u}_{\rm i}^{}(0,{\rm y})={\rm u}_{{\rm i'}}({\rm h,y})+{\rm U}_{\rm x}\tag{1}$$ $${\rm u}_{\rm j}^{}({\rm x},0)={\rm u}_{{\rm j'}}({\rm x,h})+{\rm U}_{\rm y}\tag{2}$$

Where Ux and Uy are macroscopic strains that account for transverse expansion of the RUC model under load, u is the displacements of nodes, and denote the ith pair of nodes on opposing x-faces and j and j’ denote the jth pair of nodes on opposing y-faces.

2.3 Material Model

Carbon fiber and epoxy properties were used to simulate the fiber and matrix materials, respectively, with the elastic values used shown in Table 1. The fiber is assumed to be linear elastic and isotropic. Since fiber kinking by its definition is an inelastic phenomenon of the matrix, the matrix must be modeled as an elasto-plastic material.

Table 1 Elastic properties of fiber and matrix material used [13].

The inelastic region of the matrix was modeled with a Von Mises Yield Criterion, sometimes referred to as J2 flow theory. Since in fiber kinking the polymer matrix deforms primarily in shear, the experimental shear stress-strain curve of Hexion Epikote MGS RIMR 135/Epicure MGS RIMH 1366 was used to calibrate the plasticity model in ABAQUS CAE (Figure 3). The shear stress-strain curve was first converted to an equivalent Von Mises stress and strain using the pure shear simplification of the Von Mises Yield Criterion. The resulting equivalent stress-strain curve was then used to calibrate the matrix plasticity model in ABAQUS. Since there is a limit to how far the experimental shear stress-strain curve was tested, the model strains at a constant stress after 4% strain.

Click to view original image

Figure 3 Experimental shear stress-strain curve of Hexion Epikote MGS RIMR 135/Epicure MGS RIMH 1366 used to calibrate matrix plasticity model [13].

2.4 Baseline Model Modifications

To explore the effects of fiber misalignment, volume fraction and multiaxial loading on the compressive response of a UD FRP composite, modifications were made to the base model described previously in sections 2.1-2.3.

2.4.1 Fiber Misalignment Severity

Fiber misalignment was incorporated into the geometry by extruding the RUCs along the fiber direction as a half -wavelength sinusoidal spline to simulate a defect in the composite [14]. The z-axis was aligned with the fiber direction and the spline is described by Equation (3), Where A is the amplitude of the imperfection, and is the wavelength of the imperfection.

$${\rm y}=A\cos(\frac{\pi {\rm z}}{L})\tag{3}$$

The misalignment angle of the initial imperfection can then be obtained by Equation (4).

$$\tan(\alpha_0^{})=\frac{\pi {\rm z}}{L}\tag{4}$$

Simulations were run at five different misalignment angles: 1°, 2°, 3°, 4°, and 5°. The curves that represent these misalignments are shown in Figure 4. The implementation of the fiber misalignment into the RUC model can be seen below in Figure 5 .

Click to view original image

Figure 4 Five half-sine wave curves that the baseline model is extruded along to represent varying degrees of fiber misalignment.

Click to view original image

Figure 5 Example of a 4° fiber misalignment incorporated into the baseline RUC model.

2.4.2 Varying Volume Fraction

The micromechanical method used in this study was a first order method. In first order methods, absolute size is not accounted for in the solution and only ratios e.g., volume fraction, has any affect. To examine the effect that volume fraction has on compressive strength, the square matrix dimensions of the RUC are changed while maintaining the absolute size of the fiber cross-section to generate volume fractions of approximately 24%, 30%, 34%, and 40%, as shown below in Figure 6.

Click to view original image

Figure 6 The four RUC faces with dimensions used to represent the volume fraction: 24%, 30%, 34%, 40%.

2.4.3 Applied In-Plane Shear Stress

Composite materials experience complex mechanical loadings, including in-plane shear stress along with compressive stress. To accurately simulate these types of loading conditions in the model developed in this study, the loads were applied in two separate steps in ABAQUS CAE. In the first step the shear stress was applied as a shear displacement on the front face nodes (item 3 in Figure 2). The shear displacements were calibrated to accurately represent three shear stress levels: 10 MPa, 20 MPa, and 30 MPa. In the second step, the compressive stress is applied as an incremental displacement to the front face.

2.5 Mesh

All FE models were meshed with 3-D 8-node fully integrated iso-parametric linear brick elements (C3D8). The in-plane mesh size is set such that 10 elements along the edge length of the RUC and six elements through the thickness of the fiber (Figure 7). The lateral length of the baseline model was meshed with 135 elements which corresponds to an element length of 5 , or an element aspect ratio of 5.

Click to view original image

Figure 7 Meshed baseline RUC model.

2.6 Solver and Post-Processing

To solve the compression step of the non-linear RUC model the Modified-Riks algorithm in ABAQUS CAE was used to account for the potential snap-through and snap-back behavior. To solve for the compressive response of the composite as a whole, the macroscopic stress and strain of the RUC must be determined. Homogenization theory states that the macroscopic stress is equal to the average normal traction at the base of the RUC. To obtain the macroscopic stress, the sum of the reaction forces in the z-direction of all the nodes on the bottom face were selected and divided by the cross-sectional area of the RUC as shown in Equation (7). The macroscopic strain was computed from a logarithmic formula shown in Equation (6) where is the average z-displacement of all nodes on the top face of the model, and L is total length of the model [14].

$$\bar{\sigma}=\frac{\Sigma F_{nodes}}{Area}\tag{5}$$ $$\bar{\varepsilon}=\ln(1+\frac{\delta}{L})\tag{6}$$

2.7 Model Validation

Rosen and Dow determined via an energy method approach that the analytic expression for the in-phase shear mode buckling strength of an elastic ‘perfect’ fiber reinforced composite structure was equal to the composite in-plane shear modulus of the composite [15,16].


To validate the PBCs in the FE model, the baseline RUC model was used without initial fiber misalignment. An Eigenvalue buckling analysis was then performed in ABAQUS with 3 different values of fiber Young’s modulus to determine a range of linear elastic buckling strength predicted by the FE model. These values were then compared against the theoretical in-plane shear modulus, determined by the Cylindrical Assemblage Model, Equation (8)[4].


The FE model was in good agreement with the analytical predictions as shown in Table 2. The difference between the FE model and analytical expression decreased with increasing fiber modulus. This is because the assumption of a high fiber modulus to matrix modulus ratio becomes more accurate.

Table 2 Comparison of numerical vs. analytical theoretical compressive strengths for different fiber property inputs.

3. Results

For the first section of results, the baseline RUC model was modified to examine the effects of fiber misalignment on composite compressive strength. In the next two sections, fiber misalignment is coupled with changing volume fraction and additional in-plane shear stress respectively. The results of this study are presented in terms of stress (MPa) and strain (%). Failure of the composite is deemed to occur at the bifurcation point in the equilibrium paths of the simulated RUC. Therefore, composite compressive strengths are taken as the maximum stress reached before bifurcation of the equilibrium path.

3.1 Effect of Fiber Misalignment

The equilibrium paths for the different misalignment angles are shown below in Figure 8. At low fiber misalignment the initial stress-strain response is highly linear with a sharp drop in stress at the bifurcation point. As the misalignment becomes larger the initial stress-strain response becomes more nonlinear and the drop between peak stress and the post-failure residual stress. The RUC model showed a significant reduction in compressive strength with increasing fiber misalignment with a reduction in strength between 1° and 5° misalignment of 62%. The strains at maximum stress were also significantly reduced at increasing fiber misalignment with a 51% reduction between 1° and 5° misalignment. The equilibrium paths in shown in Figure 8 exhibit significant snap back behavior, this is an computational effect from the Riks algorithm used and not necessarily indicative of real physical behavior.

Click to view original image

Figure 8 Equilibrium paths of the RUC of fiber kinking for five initial misalignment angle imperfections.

Figure 9 shows the composite compressive strength has decaying sensitivity with increasing initial fiber misalignment. There is high-imperfection sensitivity for strength at low misalignment angles that quickly becomes less sensitive at larger misalignment angles. For example, there was a 30% reduction in maximum strength for the RUC model between 1° and 2° misalignment. The reduction in maximum strength between 4° and 5° misalignment for the RUC model was 17%. Which indicates a quick transition from a primarily fiber dominated response at low misalignment angles to a matrix shear dominated response at larger misalignment angles.

Click to view original image

Figure 9 Compressive strength sensitivity curve for the RUC at the five different initial misalignment angles.

3.2 Effect of Varying Volume Fraction

Misalignment angles were varied to investigate the relationships between volume fraction, fiber defect severity, and compressive strength. As can be seen in Figure 10, composite compressive strength has decreasing sensitivity to fiber misalignment angle as the misalignment angle becomes larger. This trend of decreasing sensitivity to fiber misalignment remains the same across all volume fractions. Contrasting the relationship of compressive strength to fiber misalignment, the compressive strength linearly increases as the volume fraction increases, this trend also remains the same as fiber misalignment angle increases.

Click to view original image

Figure 10 Compressive strength sensitivity surface plot showing the relationship between composite compressive strength, fiber volume fraction, and initial fiber misalignment angle.

Table 3 RUC compressive strength values at varying misalignment angles and volume factions.

The goal of this study was to illustrate general trends and the overall effect different factors have on compressive strength. To do this it is helpful to look at the percent reduction from the most severe cases of fiber misalignment or volume fraction to the least. The fiber misalignment angle has been shown to have a strong adverse effect on the compressive strength at all volume fractions as can be seen in Table 3. The RUC model has an average reduction in strength of 61.2% across all volume fractions when increasing the fiber misalignment angle from 1° to 5°. The percent strength reduction at increasingly larger volume fractions becomes greater although this effect is minimal. To illustrate this the RUC with a volume fraction of 24% had a strength reduction of 59.0% from 1° misalignment to 5° misalignment and the RUC with a volume fraction of 40% had a strength reduction of 63.3% between the same misalignment angles.

Decreasing the fiber volume fraction by 16% has a relatively small effect on compressive strength reduction of the composite compared to increasing fiber misalignment (Table 3). The largest strength reduction from decreasing fiber volume fraction occurs at the lower fiber misalignment angles, with a strength reduction of 18.3% at 1° initial fiber misalignment (Table 3). The sensitivity to decreasing fiber volume fraction is significantly decreased at larger fiber misalignment angles with a strength reduction of 8.8% at 5° initial fiber misalignment.

Figure 11 shows a surface plot of the relationship between compressive failure strain, fiber misalignment angle, and fiber volume fraction. The compressive failure strain exhibits an opposite trend to the compressive strength at varying fiber volume fractions with an increase in compressive failure strain at lower volume fractions. However, the effect of fiber misalignment is still the same with a significant decrease in failure strain at larger misalignment angles and a decreasing sensitivity to increasing misalignment angles at larger misalignment angles.

Click to view original image

Figure 11 Compressive failure strain sensitivity surface plot showing the relationship between composite compressive failure strain, fiber volume fraction, and initial fiber misalignment angle.

Table 4 RUC compressive failure strain values at varying misalignment angles and volume factions.

The compressive failure strain exhibits similar trends as the compressive strength. The average percent reduction in strength across all fiber volume fractions simulated was 51.0%. The RUC model showed similar reductions in strength across varying fiber volume fractions. The largest failure strain reduction was at a volume fraction of 40% with a 53.4% reduction in failure strain from 1° misalignment to 5° misalignment.

Unlike the compressive strength, which was insensitive to changes in fiber volume fraction, the compressive failure strain increased after the volume fraction was decreased by 16%. The failure strain increased an average of 43.5% across all fiber misalignment angles simulated when the volume fraction was decreased from 40% to 24% (Table 4). The increase in failure strain from decreasing volume fraction was magnified at larger misalignment angles with the failure strain increasing by 51.4% at 5° misalignment when the fiber volume fraction was decreased from 40% to 24%. One explanation for the increase in failure strain at lower volume fractions is that the fibers are spaced farther apart from one another. When the fibers rotate under compressive loading, the fibers that are farther apart from each other induce a smaller shear strain on the matrix which delays ultimate failure.

3.3 Effect of Shear Loading

To determine the effect multiaxial loading has on compressive strength of a UD CFRP composite the combination of in-plane shear loading with compressive loading was examined along with variable fiber defect geometry. The relationship between compressive strength and fiber misalignment angle continues to show decaying sensitivity as fiber misalignment angle becomes larger, as seen in previous results (Figure 12). The relationship between compressive strength and applied in-plane shear stress shows a linear with a similar drop in compressive strength from 0 MPa shear stress to 10 MPa shear stress, as there would be between 10 MPa and 20 MPa across all misalignment angles (Table 5).

Click to view original image

Figure 12 Compressive strength sensitivity surface plot showing the relationship between composite compressive strength, applied in-plane shear stress, and initial fiber misalignment angle.

Table 5 RUC compressive strength values at varying misalignment angles and applied in-plane shear stress.

Across all shear stress levels, the RUC model showed an average reduction in strength of 57.3%. The reduction in strength was consistent across varying applied in-plane shear stresses. At an applied in-plane shear stress of 0 MPa the strength was reduced 61.8% when the initial fiber misalignment angle was increased from 1° to 5°. At an applied in-plane shear stress of 30 MPa the strength was reduced 51.6% when the initial fiber misalignment angle was increased from 1° to 5°.

In-plane shear stress had a detrimental effect on the composite’s compressive strength with an average compressive strength reduction across all fiber misalignments of 73.4% for a change in in-plane shear stress from 0 MPa to 30 MPa (Table 5). Increasing the fiber misalignment angle did not have a large effect on the strength reduction due to in-plane shear stress, with the relative strength reduction remaining mostly constant across all shear stress values.

Figure 13 shows a surface plot of the interaction between composite compressive failure strain, fiber misalignment angle, and applied in-plane shear stress. Figure 13 shows the same general trends between fiber misalignment and applied in-plane shear stress as the above compression strength plot. There is a negative linear relationship between increasing in-plane shear stress and compressive failure strain and the same relationship between fiber misalignment angle and compressive failure strain as seen before in this study.

Click to view original image

Figure 13 Compressive failure strain sensitivity surface plot showing the relationship between composite compressive failure strain, applied in-plane shear stress, and initial fiber misalignment angle.

Table 6 RUC compressive failure strain values at varying misalignment angles and applied in-plane shear stress.

At low applied in-plane shear stress the percent reduction in compressive failure strain (Table 5) is similar to reduction in compressive strength (Table 6) from low fiber misalignment to large fiber misalignment as shown by the 50.6% reduction in failure strain from 1° to 5° misalignment at an in-plane shear stress of 0 MPa. However, as the applied in-plane shear stress increases, the effect that the increased fiber misalignment has on the compressive failure strain is lessened considerably. In comparison, at an in-plane shear stress of 30 MPa increasing fiber misalignment from 1° to 5° reduces the compressive failure strain by only 6.6% for the circular fiber (Table 6).

In-plane shear stress had a detrimental effect on the composite’s compressive failure strain. From 0 MPa to 30 MPa (Table 6), failure strains were reduced by 71.9%. These reductions were similar to the compressive strength reductions in Table 5. Unlike the compressive strength, increasing the fiber misalignment angle had a large effect on the failure strain reduction due to in-plane shear stress, with the relative failure strain reduction decreasing from 71.9% at 1° misalignment to 46.9% at 5° misalignment.

4. Discussion

The results from varying fiber defect geometry indicate a decaying sensitivity of CFRP compressive strength to increasing fiber misalignment angle. This means that there is potential for great improvements in the compressive response of a composite structure if the manufacturing processes tolerances have the potential to be very high (i.e. +/- 1°), such as in pre-impregnated fiber composites, pultrusion, and autoclave processes. However, there is not much to be gained in incremental improvements if the manufacturing method can only maintain a tolerance within multiple degrees, such as in Vacuum Assisted Resin Transfer Molding (VARTM) processes. In the context of wind blade manufacturing, the largest gains to performance would be made by using a pultrusion process for the spar caps instead of the traditional VARTM process to insure that low fiber misalignment exists in a structurally significant area.

There was a decrease in ultimate compressive strength with a decrease in volume fraction. An unexpected result was the significant increase in compressive failure strain with a decrease in volume fraction. This could be an important design consideration for large scale flexible structures such as some of the concept designs found in the Big Adaptative Rotor (BAR) project report [17]. The increased flexibility of a wind turbine rotor decreases the operational loads experienced by the structure, so strain at failure becomes more important than overall composite compressive strength. Results from varying volume fraction in these simulations suggest that a lower volume fraction composite could offer benefits over the traditional composite design methodology that “a higher volume fraction is better” for these types of structure.

Multiaxial loading via a combination of shear and compression loading was shown to have a detrimental effect on the compressive strength properties of a UD CFRP composite. The addition of a relatively small shear load can decrease the compressive load carrying capacity of a composite structure by over 50%. Shear stress should be minimized in composite structures that expect to carry large compressive loads i.e. wind blades. This is an issue in modern turbines were the size of the turbine means shear stresses due to gravitational loads begin to become significant.

The results discussed above show trends that must be considered in the design methodology to optimize compressive strength of composite structures. There is a decreasing benefit to ensuring high fiber alignment. Lower fiber volume fraction may have benefits for highly flexible composite structures. Shear stress should be minimized in design for optimal compressive strength properties.


The authors would like to express their gratitude towards Ariel Lusty at Montana State University for her editing of this manuscript. Dr. Erick Johnson, and Dr. Ladean McKittrick are acknowledged for their advice on finite element modelling. Finally, thanks to Dr. Douglas Cairns for his knowledge and advise on composites use in wind energy.

Author Contributions

The authors contributed equally to this work.


This work was funded through the Wind Energy Technologies Office at Sandia National Laboratories.

Competing Interests

The authors have declared that no competing interests exist.


  1. Veers PS, Ashwill TD, Sutherland HJ, Laird DL, Lobitz DW, Griffin DA, et al. Trends in the design, manufacture and evaluation of wind turbine blades. Wind Energ. 2003; 6: 245-259 [CrossRef]
  2. Jorgensen JB. Adhesive joints in wind blades. Lyngby: Denmark Technical University; 2017.
  3. Ennis BL, Kelley CL, Naughton BT, Norris RE, Das S, Lee D, et al. Optimized carbon fiber composites in wind turbine blade design. Albuquerque NM: Sandia National Laboratories; 2019; SAND2019-14173. [CrossRef]
  4. Barbero EJ. Introduction to composite materials design. 2nd ed. Boca Rotan: CRC Press, 2010.
  5. Kaddour AS, Hinton MJ. Input data for test cases used in benchmarking triaxial failure theories of composites. J Compos Mater. 2012; 46: 2295-2312 [CrossRef]
  6. Schultheisz CR, Waas AM. Compressive failure of composites, part I: Testing and micromechanical theories. Prog Aerosp Sci. 1996; 32: 43-78 [CrossRef]
  7. Waas AM, Schultheisz CR. Compressive failure of composites, part II: Experimental studies. Prog Aerosp Sci. 1996; 32: 1-42 [CrossRef]
  8. Kyriakides S, Arseculeratne E, Perry EJ, Liechti KM. On the compressive failure of fiber reinforced composites. Int J Solids Struct. 1995; 32: 689-738 [CrossRef]
  9. Gutkin R, Pinho ST, Robinson P, PT Curtis. Micro-mechanical modelling of shear-driven fibre compressive failure and of fibre kinking for failure envelope generation in CFRP laminates. Compos Sci Technol. 2010; 70: 1214-1222 [CrossRef]
  10. Naya F, Herráez M, Lopes CS, González C, Van der Veen S, Pons F. Computational micromechanics of fiber kinking in unidirectional FRP under different environmental conditions. Compos Sci Technol. 2017; 144: 26-35 [CrossRef]
  11. Barulich ND, Godoy LA, Barbero EJ. On micro-buckling of unidirectional fiber-reinforced composites by means of computational micromechanics. Lat Am J Solids Struct. 2016; 13: 3085-3106 [CrossRef]
  12. Sun Q, Guo H, Zhou G, Meng Z, Chen Z, Kang H, et al. Experimental and computational analysis of failure mechanisms in unidirectional carbon fiber reinforced polymer laminates under longitudinal compression loading. Compos Struct. 2018; 203: 335-348 [CrossRef]
  13. Samborsky D, Mandell J, Agastra P. 3-D static elastic constants and strength properties of a glass/epoxy unidirectional laminate. Bozeman MT: Montana State University; 2012.
  14. Romanowicz M. Determination of material parameters for microbuckling analysis of fiber reinforced polymer matrix composites. Int J Appl Mech Eng. 2015; 20: 373-383. [CrossRef]
  15. Rosen W, Dow N. Evaluations of filament-reinforced composites for aerospace structural applications. Washington D.C.: NASA: 1965; NASw-817
  16. Jelf PM, Fleck NA. Compression failure mechanisms in unidirectional composites. J Compos Mater. 1992; 26: 2706-2726. [CrossRef]
  17. Johnson N, Bortolotti P, Dykes KL, Barter GE, Moriarty PJ, Carron WS, et al. Investigation of innovative rotor concepts for the big adaptive rotor project. Golden CO: National Renewable Energy Laboratory; 2019; NREL/TP-5000-73605. [CrossRef]
Download PDF
0 0