Influence of stacking sequence on flexural properties of hybrid carbon fibre reinforced polymer laminates

November 2024

Engineering researchers in the Faculty of Arts, Computing and Engineering, Dr Shafiul Monir, Maria Kochneva, Professor Richard Day, Dr Nataliia Luhyna and Dr Yuriy Vagapov, recently co-authored a paper on Influence of stacking sequence on flexural properties of hybrid carbon fibre reinforced polymer laminates, with Dirk Banhart. The paper was published in the Engineering Research Express journal, a multidisciplinary journal covering all areas of engineering science.

The study investigated the impact of stacking sequence and fibre variation on the flexural properties of carbon fibre-reinforced polymer (CFRP) laminates using numerical methods and multiple testing methods. The paper provides an overview of the numerical investigation.

Carbon fibre reinforced polymers (CFRPs)

The authors set the scene that the carbon fibre industry is currently undergoing a period of rapid growth in both popularity and economic terms. 

CFRPs are composite materials made up of carbon fibres and a polymer matrix. CFRP have a high strength-to-weight ratio, they are resistant to environmental factors, and they have a low thermal conductivity and expansion. As a result, CFRPs are being increasingly used in aerospace, automotive, and civil engineering. CFRP properties have many advantages including the capability to reduce the weight of aircraft made up of composite materials, which in turn, can reduce fuel consumption by around 25%.
CFRP structural beams also have many applications in terms of minimal weight and high load bearing capabilities. The operational performance of CFRP components is influenced by both their geometrical configuration and the properties of the composite material. Key factors that affect the mechanical properties of these components include:

•    Type of carbon fibre used
•    Matrix material in the composite
•    Fibre fraction of fibre to matrix material
•    Stacking sequence of material 

The specific combination and arrangement of these factors will dictate how well a CFRP component performs in its intended application.

Analysing and improving the flexural characteristics of composite materials and CFRP laminates is a popular area of research and the paper provides an overview of the existing research on the flexural properties of composite laminate beams, which mainly focus on optimising stacking sequences and enhancing material properties using three-point tests to validate the results.

The authors explain that their research provides analyses of the impact of stacking sequence and the fibre variation of the plies on the flexural properties of CFRP composite laminates using cantilever bending and three-point flexural tests. The implicit (applicable for static and quasi-static analysis) Finite Element Methods (FEM) approach was used to conduct the numerical investigation.
As well as optimising the flexural impact via the stacking sequence, the research also aimed to reinforce failure-prone plies by switching the carbon fibre prepreg, taking control factors such as potential delamination, into account. Reinforcement would yield greater economic efficiencies by using the more costly carbon fibre prepreg in the failure-prone plies rather than having to produce the whole laminate in the more expensive product. 

Flexural Test Setups

Two numerical flexural setups were developed to investigate the material properties:

•    The cantilever bending test 
•    The three-point flexural test

Key dimensions and material properties are listed within the paper.

Governing Equations

The study used a number of governing equations to calculate the properties of the orthotropic unidirectional composite ply, all of which are contained within the paper:

Voigt rule of mixture and Hashin relations 

The simple Voigt rule of mixture was applied to determine the density of the composite and the equations used to ultimately obtain the shear modulus G23 are detailed.

Classical Lamination Theory (CLT)

CLT is applied to predict the mechanical behaviour of composite materials under load, with specific assumptions made in order to simplify the problem. Example assumptions used in the study include (not exhaustive):

• The beam is made of orthotropic plies adhered together with the orthotropic plies principal material axes aligned at arbitrary angles relative to the X and Y axes
• The thickness T of the beam is considerably smaller than any characteristic dimension
• The displacements u, v, and w are insignificant in comparison to the thickness T

CLT enabled the beam deflection and ply stresses of a cantilever beam under load to be determined and the subsequent equations applied to enable the estimation of the maximum beam tip deflection are set out.

Puck Failure Criterion

The Puck failure criterion is widely used to assess failure modes in CFRP, considering tensile, compressive, and shear stresses. Specific equations for fibre and matrix failure within the study are provided. 

CFRP Laminate Material Properties

Toray T300 and Toray T1100G fibres were used in the research and the material properties are summarized, including the orthotropic composite material properties of the two CFRP laminates.

Comprehensive testing programmes were used to identify the Puck failure criterion parameters for CFRP and numerical FEM simulations were performed, including:

Cantilever bending test

This acted as a validation case in combination with CLT calculations as a comparison. The generated cantilever bending test mesh resulted in exciting mesh quality indicator values (element quality, skewness, and aspect ratio) that exceeded recommendations.

Three-point flexural test

All main simulations utilised the three-point flexural test, with quality indicators being reduced due to the loading nose and support form, the values were still deemed to be excellent. Modifications were then made based on this test including modifications to the test specimen, additional loads were applied and hybrid laminates were investigated.

Results and Discussion

The results of the numerical FEM investigations are considered satisfactory, with limitations in the number of elements and nodes considered alongside fixed support interference in the cantilever bending test validation case.

Cantilever Bending Test—Validation Case

The validation case showed a strong correlation between CLT and finite element analysis (FEA) results, confirming the reliability of the numerical methods used. Correlations of the beam tip deflection and the ply stresses in the validation case are documented, noting that the ply stresses are symmetrical in magnitude.

Stacking Sequences

The tensile and compressive stresses during the three-point flexural tests are not symmetrical, resulting in differing ply stresses. A breakdown of the deflection, ply stress, and Puck IRF of T300 test specimen with different stacking sequences under a load of 250 N is provided in the paper. Among the tested stacking sequences, QISS-7 demonstrated superior performance with lower deflection and better resistance to ply failure.

T300 and T1100G CFRP Laminate

Comparisons between T300 and T1100G laminates (under varying loads of N) revealed that T1100G exhibited lower deflection under load, indicating better performance. The deflection and normal stress versus length curves are documented.

T300 + T1100G Hybrid CFRP Laminate

The deflection and normal stress versus length of the T300+T1100G hybrid test specimen (with QISS-7 stacking sequence under varying loads) were compared with the ‘pure’ T1100G test specimen. The authors detail that “replacing the outer plies of a T300 composite laminate with T1100G prepreg resulted in behaving very similar to a pure T1100G composite laminate in the application of a beam. This approach is significantly reduced cost of the composite beam”, demonstrating cost-effectiveness without compromising performance.

Conclusions

The study concluded that optimal stacking sequences and strategic material use can significantly enhance the performance of CFRP laminates and reduce costs. The quasi-isotropic stacking sequence [0/90/+45/−45]s was proven to be the most suitable for the application of a beam. The replacement of the outer plies of a composite laminate with a stronger ply material provided similar results (in deflection and ply failure) when compared to ‘pure’ composite laminates. 

Recommendations for future research, including investigating hybrid composite laminates with differing combinations of fibre materials and more complex beam geometries.

You can read the paper in full here.