Classical Lamination Theory Research Articles

Experiments and Modeling of Three-Dimensionally Printed Sandwich Composite Based on ULTEM 9085

This article presents the concept, research, and modeling of a sandwich composite made from ULTEM 9085 and polycarbonate (PC). ULTEM 9085 is relatively expensive compared to polycarbonate, and the composite structure made of these two materials allows for maintaining the physical properties of ULTEM while reducing the overall costs. The composite consisted of outer layers made of ULTEM 9085 and a core made of polycarbonate. Each layer was 3D-printed using the fused filament fabrication (FFF) technology, which enables nearly unlimited design flexibility. The geometry of the test specimens corresponds to the ISO 527-4 standard. Tensile and three-point bending tests were conducted. The structure was modeled in a simplified manner using averaged stiffness values, and with the classical laminate theory (CLT). The models were calibrated through tensile and bending tests on ULTEM and polycarbonate prints. The simulation results were compared with experimental data, demonstrating good accuracy. The 3D-printed ULTEM-PC-ULTEM composite exhibits favorable mechanical properties, making it a promising material for cost-effective engineering applications.

Analytical calculation approach for rocket nose cone structure with orthotropic material

The Authors of this research developed an analytical calculation method to estimate the strength of nose cone structures made of orthotropic materials, which were crucial components in aircraft and spacecraft. Strength analysis of nose cones had been comprehensively addressed for isotropic materials; however, the lack of efficient approaches for orthotropic materials presented a challenge. In this research, a new analytical method was proposed, combining membrane stress theory for isotropic materials with classical laminate theory for orthotropic materials. This approach enabled the determination of stresses on the nose cone shell structure in both meridional and circumferential directions in an efficient and straightforward manner. The analysis results indicated that the developed analytical method exhibited stress distribution trends similar to those obtained using the Finite Element Method. Stresses in the +45° and –45° direction, as well as in-plane shear stress and Tsai-Wu failure indices, showed trend similarity between the two methods. Despite specific numerical differences in the calculation results, these consistent trends suggested that the analytical method could serve as a tool for the preliminary design of a nose cone structure with a similar configuration analyzed in this study.

Multi-objective optimization design of automobile seat backrest considering coupling effect

To investigate the impact of the coupling effects of carbon fiber reinforced polymer in the seat back layer on the performance of car seats, this paper presents a comprehensive optimization design method for composite materials. In detail, the finite element models firstly established and validated through five typical working conditions of automotive seats based on experimental data. Then, the optimized variables are divided and determined through backrest stress nephograms for each working conditions of the automotive seats, in which the various perspective are taken into account, such as the total mass of seat backrest, safety performance, and comfort index. Subsequently, an optimization strategy for unequal thickness layers lay-up design is constructed, which combines strength factors, optimal Latin hypercube sampling, best-worst method, gray relational analysis, and Visekriterijumsko KOmpromisno Rangiranje method for the optimal design of the automotive CFRP seat backrest. Additionally, the impact of layer coupling effects on different performance indices of the seat is examined through simulating and analyzing the seat backrest with various layer coupling types, while incorporating the classical laminate theory. The study reveals that by minimizing the laminate coupling effect, the comfort of the seat can be enhanced. Finally, a comprehensive comparative analysis of the optimal trade-off solution is carried out in terms of optimization strategies. The results show that ensuring the safety performance, the total mass of the seat backrest decreased by 21.3%, as a result of the optimization strategy proposed in this paper, and the comfort performance is also improved to some extent. Therefore, the multi-objective optimization strategy proposed in this paper performs well in terms of effectiveness and provides a reliable reference for related composite material multi-objective optimization.

Machine learning-based analytical approach for mechanical analysis of composite hydrogen storage tanks under internal pressure

This study is a practical exploration of the application of machine learning for the mechanical analysis of filament-wound thin-composite hydrogen storage tanks under internal pressure. Our innovative approach seamlessly integrates classical laminate theory, comprehensive parametric analysis, and machine learning to advance the state-of-the-art in composite tank design. This versatile framework holds promise for addressing challenges in other structurally complex systems. A comprehensive parametric study was then conducted to explore the influence of key design parameters, such as internal pressure, tank radius, order of layer, and layer orientation. Pearson's correlation analysis was used to determine the parameters that had the most significant impact on the mechanical behavior of the tank. In addition, five machine learning models, namely, Extreme Gradient Boosting, Adaptive Boosting, Artificial Neural Network, Support Vector Machine, and Random Forest, were examined to determine their predictive capability for the mechanical performance of these composite tanks. Key findings demonstrate XGBoost's superior predictive capabilities, achieving a remarkable 99% accuracy in predicting stress in the x-direction compared to Random Forest's 96%. XGBoost also outperformed Random Forest in terms of Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) with values of 26 and 0.02, respectively, versus 207 and 0.16. These results underscore XGBoost's potential to revolutionize hydrogen storage tank design. The development of a user-friendly GUI application further enhances the practicality of this research, allowing engineers and composite designers to efficiently simulate the mechanical behavior of these tanks in real time by adjusting the cursors for variables such as the pressure, radius, layer order, and layer orientation. This tool, with its intuitive interface and elimination of manual calculations, promises significant enhancements in the design process, providing a platform for the rapid assessment and optimization of tank architectures, thereby improving the efficiency and reliability of the design process.

Warpage analysis of multilayer thin film/substrate systems using the Eigenstrain method

Warpage resulting from the deposition of films on substrates remains a persistent challenge that significantly impacts the application of numerous advanced devices. To precisely evaluate warpage in multilayer thin film/substrate systems, we employ the eigenstrain method in the warpage analysis. An analytical model is developed to predict warpage and residual stress in multilayer film/substrate system based on classical laminate theory. We introduce a novel concept termed “Eigenstress”, which serves as the fundamental cause of warpage and characterizes the influence of the manufacturing process on warpage. Theoretical analysis and simulation demonstrate that warpage is entirely determined by eigenstress and other process-independent parameters. This model also explains that there is little interaction between thin films deposited on the same substrate. An experimental method is studied for measuring eigenstress using a standard plate. The measured eigenstress differs significantly from the corresponding thermal stress. We also propose a critical condition and its governing equation for warpage in multilayer film/substrate systems. Experimental results confirm that adding a compensation layer on a warped substrate can considerably reduce warpage. The warpage model based on “Eigenstress” provides a theoretical foundation for accurately predicting and controlling warpage in multilayer thin film/substrate systems.

A study on interactive fiber rubber composite structures subjected to bend-twist coupling

Abstract This paper investigates the deformation behavior of shape memory alloy (SMA)-integrated fiber-reinforced composites, with an emphasis on how different fiber orientations influence bend-twist coupling. The study combines experimental analysis, finite element simulations using Ansys, and analytical modeling via Classical Laminate Theory (CLT) to assess the mechanical response of these composites. The experiments revealed that composites with higher fiber angles (60°) exhibited dominant twisting behavior, while those with lower angles (30° and 45°) showed more pronounced bending deformation. The simulations corroborated these trends, offering detailed insights into the displacement behavior. The CLT model further predicted a decrease in deflection with increasing fiber angles, which was consistent with experimental results, although some deviations in Z-deformation were attributed to material and manufacturing factors. This research highlights the critical role of fiber orientation in achieving desired deformations in SMA-integrated composites, offering valuable insights for the design of adaptive structures. The findings demonstrate the potential for optimizing fiber configurations to tailor bend-twist coupling in advanced composite applications.

Predictive analysis of tensile strength ratios in laminated bamboo composites: Unraveling the stochastic impact of ply angle variations through machine learning model

Laminated bamboo composites (LBC), made by sandwiching bamboo strips, offer promising alternatives to traditional construction materials, especially for housing. However, subjection to the continuous static loading makes these materials initiate cracks inside their various ply. This study uses classical laminate theory (CLT) to determine the strength ratio (SR) of the LBC at different ply orientations by applying Tsai-Wu and Tsai-Hill failure criteria using MATLAB. The study aims to calculate the SRs for LBCs using CLT, employing an ANN model and stochastic finite element (FE) modeling to investigate SRs of five-layered LBCs with varying ply orientations. Applying CLT, the highest SR was determined to be 1.5375 × 107 N/m for the [0°/0°/0°/0°/0°] laminate, as per both failure theories. The study reveals substantial SR variations depending on ply orientation, consistently showing higher SR predictions with the Tsai-Wu theory compared to the Tsai-Hill theory. Next, the study emphasizes the deterministic methodologies to account for the stochastic effects of ply angle on the obtained SR of LBCs. Monte Carlo simulation (MCS) was utilized to model 10,000 randomly generated ply angle inputs and their associated SRs. By incorporating MCS to introduce ±1% variations in ply angles and utilizing normally distributed data, this research effectively captures uncertainties associated with ply orientation. Finally, to forecast the random SR of LBC with various ply orientations, an artificial neural network (ANN) surrogate model is employed. The stochastic analysis confirms the need to quantify the associated uncertainties. The findings of this study are crucial for advancing the application of LBC in sustainable construction, providing valuable insights into their mechanical behavior under different ply orientations, considering the stochastic effect in properties.

Study on stable configurations and snap through of the rectangular VS bi-stable laminates with curvilinear fiber alignment

With advances in fiber placement technology, variable stiffness bistable laminates (VSBL) composited by curvilinear fiber format become a subject of intense interest for morphing structures due to their lower weight, adjustable stiffness and a richer range of stable configurations compared to straight fiber bistable laminate. Merely conducting research on square laminates is not enough allowing for practical application scenarios. This article investigates the influence of geometrical parameters of VSBL on the stable state configuration and static snap through actuated by MFC systematically. A quadratic variable curvature polynomial is used to fit the transverse displacement according to classical laminate theory. By means of von-Karman geometrical relationship and the Rayleigh-Ritz method, stable configurations of the VS bistable laminate are solved. By comparing with finite element results, the reliability and precision of the current results are verified. It shows that changing fiber orientation leads to significant effects on the steady state configuration and critical bifurcation points. Theoretical analysis of VS bistable laminates containing the smart piezoelectric material MFC is followed by analytical modeling. The voltage threshold required for actuating snap through of two stable states is acquired by smart material layer MFC. The specific reasons for the differences in the configurations of VS bistable laminates are illustrated by analyzing distribution of the stiffness of VSBL in the plane.

Buckling optimization of Double-Double (DD) laminates with gradual thickness tapering

Double-double (DD) laminates are promising replacements for conventional Quad laminates in aerospace applications because of their inherent design simplicity and, more importantly, the ease of tapering. However, the thickness thinning due to tapering will significantly increase the risk of buckling failure. In this paper, we proposed an implicit global & local model for thickness tapering optimization of DD laminates to maximize buckling resistance under the given weight constraint or weight reduction under buckling constraints. Firstly, a global model is established for buckling load calculation, with material properties calculated from homogenization of local laminates using the classical laminate theory. Then, nodal repeats of a four-plies DD sub-laminate are chosen as design variables to interpolate the tapered thickness profile. Sensitivities of structural responses are calculated semi-analytically to achieve efficient gradient-based optimization. Tapering spacing constraints between adjacent thicknesses are introduced to mitigate the potential delamination due to the stress concentrations caused by sharp thickness variation at the cost of a reduced optimization effect. Finally, typical numerical examples show that DD laminates with optimal gradual thickness tapering can remarkably increase the structural buckling resistance or the weight reduction.

Experimental study on the effects of temperature on mechanical properties of 3D printed continuous carbon fiber reinforced polymer (C[sbnd]CFRP) composites

Design for safety of 3D printed continuous carbon fiber reinforced polymer (CCFRP) composites remains challenging for accommodating harsh service environments with a wide range of temperatures. To investigate thermal effects on mechanical properties and failure mechanism of CCFRP materials, this study carried out a series of experimental tests on the laminates with layups of [0]n, [90]n and [0/90]n for tension, as well as [±45]n for in-plane shearing. The application of classical laminate theory and rule of mixtures to the 3D printed CCFRP composites under varying temperatures is then evaluated. The results indicate that the transverse elastic modulus/strength and in-plane shear modulus/strength increase at a low temperature, but all the mechanical properties decrease at a high temperature. Notably, an unexpected decrease in strength of [0/90]n laminates is observed when the temperature drops from −10 °C to −40 °C. Significant strain concentrations are visualized during tensile experiments at high temperature through the digital image correlation (DIC) technique. With increasing temperature, the [0]n laminates undergo a transition from an explosive to a jagged failure mode, while the [90]n laminates shift from brittle to ductile failure. The alteration is attributed to decrease in the mechanical properties of both the matrix and the matrix fiber interface, as revealed by scanning electron microscopy (SEM) analysis. It is found that although the classical laminate theory exhibits an acceptable prediction accuracy for the 3D printed CCFRP composites under varying temperature conditions, the rule of mixtures is not applicable. For this reason, the new formulations for the rule of mixtures are then proposed to enable accurate predictions for 3D printed CCFRP composites under different temperatures. This study is anticipated to provide insightful understanding on mechanical properties and failure mechanisms for 3D printed CCFRP composites at different temperatures.

Study on the delamination damage prediction of wind turbine blade spar cap based on morphology feature recognition

In order to study the degradation of local mechanical properties caused by delamination defects of wind turbine blades, a progressive damage prediction method of blade spar cap based on quantitative identification of delamination morphology features by infrared thermal image was proposed in this paper. Firstly, based on the thermal conduction theory of laminate plates, infrared thermal imaging technology was used to realize quantitatively identify delamination morphology features. Then, based on the cohesive zone model (CZM) and the classical laminate theory (CLT), a numerical analysis model of unidirectional laminate with delamination defects was established, and the accuracy of the numerical model was verified by comparison with the experimental results of axial tensile and compressive displacement loads. Finally, a 2 MW-45.3 blade spar cap with maximum chord cross-section was used as a prediction model, and the effect of different delamination sizes and depths on the failure mode, failure strength and damage evolution of the blade spar cap was successfully predicted by using the equivalent fatigue load. The research shows that the delamination depth has a more profound influence on the damage of spar cap compared with the delamination size. With the increase of delamination depth, the delamination failure modes undergo the evolution process of non-buckling, local buckling, delamination expansion and strength failure. Shallow delamination causes local buckling and strength failure of blade spar cap. When the delamination depth reaches half of the spar cap thickness, the delamination extends to intralaminar and interlaminar, the local failure changes to global failure.

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

This paper presents a numerical investigation of the influence of the stacking sequence and fibre variation of the plies on the flexural properties of carbon fibre-reinforced polymer laminates. The numerical approach utilised a three-point flexural test to evaluate different quasi-isotropic stacking sequences. It also analysed attempts to reinforce failure-prone plies only using a stronger prepreg material to reduce the cost of the laminate. The results were validated by conducting a cantilever bending test and compared with calculations based on classical lamination theory. The beam deflection, normal stress per ply, and the Puck failure criterion inverse reverse factor per ply were used for evaluation and result comparison. The results showed that the quasi-isotropic stacking sequence [0/90/+45/−45]s is the most suitable for beam applications. Replacement of the outer plies of the composite laminate by a stronger ply material made the hybrid laminate performance almost identical to a pure composite laminate consisting of stronger material only.

Elastic Property Evaluation of Fiberglass and Epoxy Resin Composite Material Using Digital Image Correlation.

This study focused on evaluating the sensitivity and limitations of the simplified equipment used in the Digital Image Correlation (DIC) technique, comparing them with the analog extensometer, based on the mechanical property data of a composite made of fiberglass and epoxy resin. The objectives included establishing a methodology based on the literature, fabricating samples through manual lamination, conducting mechanical tests according to the ASTM D3039 and D3518 standards, comparing DIC with the analog extensometer of the testing machine, and contrasting the experimental results with classical laminate theory. Three composite plates with specific stacking sequences ([0]3, [90]4, and [±45]3) were fabricated, and samples were extracted for testing to determine tensile strength, modulus of elasticity, and other properties. DIC was used to capture deformation fields during testing. Comparisons between data obtained from the analog extensometer and DIC revealed differences of 11.1% for the longitudinal modulus of elasticity E1 and 5.6% for E2. Under low deformation conditions, DIC showed lower efficiency due to equipment limitations. Finally, a theoretical analysis based on classical laminate theory, conducted using a Python script, estimated the longitudinal modulus of elasticity Ex and the shear strength of the [±45]3 laminate, highlighting a relative difference of 31.2% between the theoretical value of 7136 MPa and the experimental value of 5208 MPa for Ex.

A shell theory approach for the analysis of metal-FRP hybrid toroidal pressure vessels

This study focuses on the analysis of metal-FRP hybrid toroidal pressure vessels (TPV) using shell theory. The analytical approaches for the design of metal-FRP TPVs considering bending effects are currently not available. Invariably the designs are done based on the most simplified approach like linear membrane theory. In this work, a potential energy functional for the metal-FRP TPV considering the membrane and bending deformations is developed using Love's shell theory. The classical laminate theory is employed to determine the stresses/strains throughout the thickness of the FRP laminate. The Rayleigh-Ritz method is adopted to solve the proposed potential energy functional. A finite element analysis (FEA) is conducted using ABAQUS to validate the proposed analytical solution. In addition, a parametric analysis is carried out to understand the influence of various parameters viz. thickness of base metal, thickness of FRP, and ratio between radii of toroid and cross-section on bending deformations in the hybrid TPV. The results from the proposed solution are in good agreement with that from FEA. Therefore, the proposed solution can be used in the analysis and design of the metal-FRP TPV irrespective of any variations in the geometric parameters. It is found that the inclusion of bending deformations can improve the accuracy of solution and the bending deformations in the base metal decreases or become negligibly small with the increase in R/r ratio and thickness of FRP. The orientation of fibers can change the direction of failure in the base metal. The important design parameters that influence the yield pressure are thickness of base metal and FRP, orientation of fibers and R/r ratio.

Prediction method of thermal expansion coefficient for 2D composite fabric

In this article, an analytical method for predicting the thermal expansion coefficient of 2D composite fabrics is established. First of all, different from the traditional prediction of thermal expansion coefficient by classical laminate theory, this paper extends the self-consistent method of micromechanics to 2D composite fabrics to improve the accuracy of thickness direction prediction. Analytical Prediction method of Thermal expansion coefficient of 2D Composite fabric (APTC)was established. In the x section of Representative Volume Element(RVE) model, the stress balance equation and deformation coordination equation are applied to derive the internal thermal expansion coefficient. In the z section, the coefficient of thermal expansion is derived from the Poisson effect. Secondly, the formula of thermal expansion coefficient is derived for plain fabric, twill fabric and satin fabric respectively, which is consistent with the APTC method, indicating that the method is representative. Finally, RVE finite element model is established according to the braided structure parameters of 5284/T800 composite fabric. Comparing analytical solution, numerical solution and experimental solution, the α 1 and α 2 of the numerical and experimental solutions is close enough to be considered equal, which is consistent with the transverse isotropy of the composite fabric in xOy plane predicted by theoretical analysis.When predicting α 1 and α 2 , the maximum error between numerical solution and analytical solution is 1.79%, the maximum error between numerical solution and experimental solution is 22.29%, and the error remains at about 4% during predicting α 3 . In general, the APTC method for predicting the thermal expansion coefficient of composite fabrics is accurate and effective, and the simplified formula is more convenient to popularize and apply.

Tailoring the extension-bending-twisting coupling in composite laminates using carbon nanotube hybridization

The existence of extension-bend-twist coupling of deformations in composites is a complex problem. Ability to tailor the coupling response as per the requirement is desirable to harness the high strength-to-weight ratio of composites in many structural applications. Here we report a feasible design strategy to tune the extent of deformation coupling in composite laminates. To this end, carbon nanotube (CNT) grafted lamina is incorporated in the lay-up of conventional composites. Classical laminate theory (CLT) and finite element analysis show that the coupling extent of extension-twist, extension-bending and extension- bending-twist can be suitably designed by varying the number, location and distribution of CNT grafted lamina in a laminate configuration. Theoretical and computational results reveal maximum extension-twist coupling when a single CNT grafted lamina is placed closer to the mid-plane in a 16 ply antisymmetric laminate. Symmetrical placement of CNT grafted lamina avoids the extension-bend coupling. Finite element analysis shows that the lateral bending of composite cantilever beam under combined axial and bending loads can be designed by suitably choosing the configuration of the modified laminate. These findings will significantly contribute in designing structural composites for advanced applications.

Determining the optimal dome shape using a novel variable slippage coefficient non‐geodesic

AbstractThe research of high‐performance composite pressure vessels in practical application has become the focus of attention, and fiber paths play an important role in the structural performance of composite pressure vessels. Therefore, a method is proposed for determining the optimal geometric parameters of the pressure vessel head shape under a novel variable slippage coefficient non‐geodesic(NVSCNG). First, NVSCNG is used as the dome fiber path design mode, and the classical lamination theory is used to construct a dome stress field model. In addition, on the basis of the Tsai‐Wu failure criterion, the minimum laminate thickness is determined to satisfy the strength constraints. Second, the performance factor (pressure*volume/weight) is used to calculate the structural performance of the dome with variable geometric parameters under the novel variable slippage coefficient fiber path. Moreover, the stability constraints are considered to determine the optimal geometric parameter values of the dome. Finally, the structural properties, stress response and thickness were analyzed under two types of fiber paths based on the optimal dome profile. Results show that compared to the conventional variable slippage coefficient, the performance factor can be maximally improved by nearly 60.94% using the novel variable slippage coefficient, and the thickness of the composite layer at the equator of the dome can be maximally reduced by nearly 34.88%. In addition, the research shows that NVSCNG can improve the structural performance of the dome and realize the lightweight of dome components, which are greatly important in guiding the design of fiber paths for pressure vessels.Highlights No unconstrained linear problem between NVSCNG and initial winding angle. Optimal dome profile geometry parameters are m = 0.8, rc = 0.5. The dome structural failure is controlled by the longitudinal stresses. Winding angle distribution has a strong influence on dome stress distribution. Higher dimensionless performance factor and lighter mass for NVSCNG.

A stochastic modelling framework for predicting flexural properties of ultra-thin randomly oriented strands

A stochastic modelling framework is developed to predict the flexural properties of high-strength sheet moulding compounds made of randomly oriented ultra-thin carbon fibre-reinforced thermoplastic prepreg tapes. The model enables reliable designs using ultra-thin randomly oriented strands with less testing, leading to potential applications in automotive primary structures. The stochastic model is based on a Monte Carlo simulation. The flexural modulus is predicted using classical laminate theory, while the flexural strength is predicted by following a Weibull distribution. Fibre discontinuities are considered through stress concentrations introduced by tape overlaps. The results are validated against new 3-point bending and previously reported 4-point bending experimental results. A scaling effect on strength and scatter is predicted, and its implications for structural applications are also discussed.

Prediction and analysis of flexural stiffness for 3D-printed continuous fiber–reinforced composites with different matrix fill ratios and layer orders

Bending load is often encountered in engineering applications, but it is less studied for 3D-printed continuous fibre–reinforced composites (CFRC). We present the flexural properties of 3D-printed composites as a function of layer order and matrix fill ratio. We applied Classic Laminate Theory to estimate the flexural modulus and showed that the Kerner-Hashin model is suitable for taking voids into account when calculating the elastic properties of the matrix layer. Using optical microscopic analysis, we identified the main defect sources of 3D-printed CFRC structures, such as voids, fibre waviness, fragmentation and poor bonding between laminas. By performing failure analysis based on the Fibre Bundle Cell method, we found that the use of top/bottom-type reinforcement instead of alternating layering will increase the reliability of the 3D-printed composites under bending load. Furthermore, the failure process will be more gradual and cover higher load levels, which increases safety.

Characterisation and damage modelling of oxide/oxide composites considering temperature dependence

Continuous fibre reinforced ceramic matrix composites (CMCs) are increasingly being employed in safety critical applications. As a result, their use in these applications requires the adoption of appropriate design methodologies that are able to consider their complex non-linear mechanical behaviour. In this paper, a simple but robust formulation for continuum damage model, thermodynamically consistent and written under plane stress condition, is proposed for a laminated 2D woven composite material. This model is implemented via the Classical Laminate Theory (CLT) extended to non-linear behaviour to predict the behaviour of different stacking sequences. In-plane tensile tests were performed on an oxide/oxide composite up to 1000 °C to fully identify the model. The procedure is described and used on tests at room temperature before being extended higher temperature tests. Finally, the law and its coupling with the CLT are validated by means of tests on quasi-isotropic and cross-ply laminates at different temperatures.