Composite Laminate Theory Research Articles

Developing a stochastic linear elastic material model and composite laminate theory including failures, using the fiber bundle–based approach

This paper presents a novel theoretical statistical material model, which is a kind of extension of the usual 3D Hooke’s law and can take into account the damage process up to the final failure as well. This material model can provide the stress response also together with the damages to multiaxial short time alternating strain loads. It was developed by utilizing our earlier validated results of applying E-bundles for modelling stress-strain curve of different types of fibrous materials and fibre-reinforced composite sheets subjected to simple (uniaxial) mechanical loads. Based on the fiber bundle cells (FBC) theory, we introduced the so-called memory reliability functions to take into account the different changing strain loads including both the monotone, the pulsating and the alternating modes. We proved that the duplex compressive–tensile memory reliability function is the product of the compressive and the tensile memory reliability functions. Utilizing the generalized Hooke’s law and the memory reliability functions, we developed a stochastic linear elastic material law that also represents the damage and failure processes with normal and shear strain loads. This made it possible to calculate the expected value as the variance of the stress response process and determine its confidence interval at any strain load.

Modelling of material behavior for additively manufactured 17-4 PH stainless steel produced by fused filament fabrication

This paper proposes a model to predict the tensile characteristics of metal fused filament fabricated (MFFF) components. The proposed model consists of mathematical, experimental, and finite element (FE) models. The mathematical model was constructed based on the composite laminate theory and was combined with experiments for basic layup of 0° and 90° raster angle to describe the behavior of MFFF parts. The FE model was built to simulate the behavior of MFFF parts in a virtual environment and its validity was verified using independent experiments for a more common layup of +45°/−45°.

Study on Tensile Performance of Double-Bolted Joints between Carbon Fiber Reinforced Polymer Plate and Aluminum Plate

Carbon fiber reinforced polymer (CFRP) with high specific strength, specific modulus, and other outstanding properties, which could be used in aerospace, shipbuilding, and railway. The joint of carbon fiber composite material plate and metal material plate plays an important role in the overall performance of the structure. In this paper, a carbon fiber reinforced polymer (CFRP) progressive damage model is developed based on composite laminate theory and 3D Hashian theory. The model of the double bolt single lap joint shear connection is established for the CFRP plate and the finite element method is used to carry out the stress analysis and failure prediction of the lap structure. The effect on structural performance under tensile conditions was studied through the change of double bolt spacing. The results show that the decrease in bolt row spacing can lead to the interference effect between holes. In addition, the progressive damage of the composite plate is located near the center line of the bolt hole.

An Experimental and Numerical Study of the Influence of Temperature on Mode II Fracture of a T800/Epoxy Unidirectional Laminate.

Studies on mode II fracture have promoted the establishment of the delamination theory for unidirectional composite laminates at room temperature. However, under thermal conditions, the fracture behavior of composite laminates will exhibit certain differences. The delamination theory should be extended to consider the temperature effect. To achieve this goal, in this study, the mode II static delamination growth behavior of an aerospace-grade T800/epoxy composite is investigated at 23 °C, 80 °C and 130 °C. The mode II fracture resistance curve (R-curve) is experimentally determined. A fractographic study on the fracture surface is performed using a scanning electron microscope (SEM), in order to reveal the failure mechanism. In addition, a numerical framework based on the cohesive zone model with a bilinear constitutive law is established for simulating the mode II delamination growth behavior at the thermal condition. The effects of the interfacial parameters on the simulations are investigated and a suitable value set for the interfacial parameters is determined. Good agreements between the experimental and numerical load-displacement responses illustrate the applicability of the numerical model. The research results provide helpful guidance for the design of composite laminates and an effective numerical method for the simulation of mode II delamination growth behavior.

A New Failure Theory and Importance Measurement Analysis for Multidirectional Fiber-Reinforced Composite Laminates with Holes.

In this paper, a failure theory for the multidirectional fiber-reinforced composite laminate with a circular hole is developed. In this theory, the finite fracture mechanics method is combined with the improved Puck’s failure theory including the in situ strength effect. It can predict the notched strength by only basic material properties of unidirectional laminas, geometries and stacking sequence of the laminate. In advance mechanical properties of the laminate are unnecessary. The notched laminates with different material types and stacking sequences are taken as examples to verify this failure theory, and predicted results are in good agreement with experiments. Based on the developed failure theory, importance measurement of uncertain material properties to the notched strength is analysed. Results show that notched strength increases with increasing longitudinal tensile strength and in-plane shear modulus for the laminate with an arbitrary hole diameter. However, it decreases with increasing transverse modulus.

A Decommissioned Wind Blade as a Second-Life Construction Material for a Transmission Pole

This paper demonstrates the concept of adaptive repurposing of a portion of a decommissioned Clipper C96 wind turbine blade as a pole in a power transmission line application. The current research program is aimed at creating a path towards sustainable repurposing of wind turbine blades after they are removed from service. The present work includes modelling and analysis of expected load cases as prescribed in ASCE 74 and NESC using simplified boundary conditions for tangent pole applications. Load cases involving extreme wind, concurrent ice and wind, extreme ice, differential ice, broken conductor, and broken shield have been analyzed and governing load cases for bending, shear, and torsion have been examined. Relative stiffnesses of different parts forming the wind blade’s cross section (i.e., shell, web, and spar cap) are determined. The corresponding stresses associated with each part under the governing loads are compared to allowable strength values which are determined from composite laminate theory and modelling of the known laminate structure of the E-Glass FRP material. Stresses and deflections obtained are compared with governing reliability-based design criteria and code requirements. The results of the structural analysis indicate that the wind blade can resist the expected loads with reasonable safety factors and that the expected deflections are within permissible limits. Recommendations are provided for detailing and modification of the wind blade for a power pole application in which crossarm and davit connections are highlighted, and foundation details are emphasized.

Buckling, vibration, and energy solutions for underwater composite cylinders

This study presents closed-form solutions for the critical buckling pressures and characteristic frequencies of underwater composite cylinders. The analytical solutions were derived using the full stiffness definitions from composite laminate theory, making them suitable for symmetric, asymmetric, hybrid, and/or double-shell (sandwich) cylindrical composite structures. These closed-form solutions were developed for critical buckling pressures in a hydrostatic environment as well as for critical buckling energy in a dynamic environment with combined hydrostatic and transient loads. Also, the characteristic frequencies were derived for a submerged and pressurized environment to account for added fluid mass and hydrostatic pressures. Computational and experimental data were used to validate the derived analytical work. The resulting solutions for critical buckling pressures agreed with numerical and experimental results for single-shell cylindrical structures. Moreover, for double-shell cylindrical structures with foam cores (sandwich structures), the collapse pressure is shown to be proportional to the core’s transverse shear modulus. The solutions were suitable for predicting the collapse pressure for sandwich structures with relatively low-density cores. Lastly, solutions for estimating the energy emitted during an implosion event and the energy required for buckling in sub-critical pressure environments were also derived and validated with the experimental data.

Optimising ply orientation in structural laminated bamboo

Currently, only two forms of laminated bamboo are commercially available as structural materials: unidirectional beams and boards, and cross-laminated boards. As a natural quasi-unidirectional composite, the lamination of bamboo into plies with specific orientations would allow the design and manufacture of a family of multi-axial composite laminates with unique properties. In this study, we test the tensile mechanical properties of single- and two-ply laminated bamboo at various off-axis loading angles and laminate configurations. The data is then compared to micro-mechanical models for predicting modulus and strength of composite laminates. On the basis of our analyses, we believe there is significant scope to extend the current range of laminated bamboo products to include angle-ply laminates. Moreover, we demonstrate that composite laminate theory is applicable to this natural composite and may be used for design of products and structures.

Reliability analysis of a composite laminate using estimation theory

Composite laminates are made up of composite single-plies sequence. The plies generally have the same fiber and resin and their difference in fiber orientation results in a difference in various laminates’ strength. Tsai-Hill failure criterion as a limiting state function to analyze structural reliability of a composite laminate and estimation theory in order to estimate statistical parameters of effective stress were utilized to construct probability box. Finally, we used the Monte Carlo simulation and FERUM software to calculate the upper and lower bounds of probability of failure.

Distributed internal strain measurement of the fluid-solid state coefficients of thermal expansion below the glass transition temperature during a composite manufacturing process

The total distributed strain produced during a vacuum-assisted resin infusion moulding composite manufacture process is measured in real time by using optical fibre sensors embedded in three different layers of a thin 5-harness satin weave flat plate cured with low-viscosity epoxy resin/cycloaliphatic polyamine epoxy resin polymer matrix. We present and discuss the chemical reaction of the epoxy resin polymer matrix adhesive to show that under manufacturing conditions, well below the glass transition point, substrates gradually come into contact with and become covered with epoxy resin polymer matrix strongly bonded to their surfaces. The fluid dynamics of the reaction system under such conditions reduces to a Cauchy equilibrium found in stressed solids, which leads to a strength of materials argument to show that the embedded, distributed optical fibres can accurately measure the motion of the surrounding epoxy resin polymer matrix before the gel point. The same argument is applied to the embedded 5-harness satin carbon fibre weave and leads immediately to an extension of the composite laminate theory for the thermodynamic liquid phase before the glass transition temperature. The predictions of the modified composite laminate theory framework are found to be consistent with experiment.

A Unique and Rational Applications Methodology for Fiber Composite Laminates

An applications methodology is synthesized from the research-based development of failure theory for orthotropic fiber composite laminates. In effect, this work continues and completes the work of Christensen (2017, “Lamination Theory for the Strength of Fiber Composite Materials,” ASME J. Appl. Mech., 84(7), p. 071007). This failure theory applies for the condition of fiber-dominated behavior, appropriate to carbon fiber—polymeric matrix composites and such similar systems. A lamination theory for stiffness and a separate lamination theory for strength are the outcomes derived here. Final forms are given for 0, 90, ± 45 type orthotropic laminates, with the four lamina orientation volume fractions to be specified in any particular application of interest. Many examples are given of using the new methodology in specific design cases.

Thermal buckling and postbuckling analysis of size-dependent composite laminated microbeams based on a new modified couple stress theory

Based on a new modified couple stress theory for composite laminates, considering geometric nonlinear theory and Timoshenko beam hypothesis, the governing equations for size-dependent composite laminated microbeams in thermal environment are derived using Hamilton’s principle. Analytical and numerical solutions are employed in solving the present problem, respectively. An auxiliary function is introduced to reduce the governing equations to a single fourth-order integral-differential equation, and the exact solutions for the thermal buckling and postbuckling of microbeams with combination of in-plane immovable simply supported boundary conditions are obtained. By introducing the differential quadrature method, the governing equations are transferred into a system of nonlinear algebraic eigenvalue equations. In numerical examples, comparison between the present results and those obtained in the literature verifies the validity and efficiency of the present analytical and numerical methods. The effects of thermal expansion coefficients and material length scale parameter are discussed. Numerical results indicate that the above-mentioned effects play very important roles for the thermal buckling and postbuckling of the composite laminated microbeams.

Computational model for supporting SHM systems design: Damage identification via numerical analyses

This work presents a computational model to simulate thin structures monitored by piezoelectric sensors in order to support the design of SHM systems, which use vibration based methods. Thus, a new shell finite element model was proposed and implemented via a User ELement subroutine (UEL) into the commercial package ABAQUS™. This model was based on a modified First Order Shear Theory (FOST) for piezoelectric composite laminates. After that, damaged cantilever beams with two piezoelectric sensors in different positions were investigated by using experimental analyses and the proposed computational model. A maximum difference in the magnitude of the FRFs between numerical and experimental analyses of 7.45% was found near the resonance regions. For damage identification, different levels of damage severity were evaluated by seven damage metrics, including one proposed by the present authors. Numerical and experimental damage metrics values were compared, showing a good correlation in terms of tendency. Finally, based on comparisons of numerical and experimental results, it is shown a discussion about the potentials and limitations of the proposed computational model to be used for supporting SHM systems design.

A new fatigue failure theory for multidirectional fiber-reinforced composite laminates with arbitrary stacking sequence

Fatigue failure is one of the most important failure types of fiber-reinforced composites. In this paper, a new fatigue failure theory for multidirectional fiber-reinforced composite laminates with an arbitrary stacking sequence is developed, by combining nonlinear residual strength and residual stiffness models with the recently improved Puck’s failure theory which includes the in situ strength effect. This fatigue theory can predict the fatigue life, residual strength and residual failure envelope of fiber-reinforced composite laminates under multidirectional loadings. For these predictions it is necessary to recalculate the fatigue lives of laminae after each cycle since the stresses in the laminae change due to stiffness degradation. It is also necessary to account for the nonlinear accumulation of damage at the new stress level in the laminae resulting from stiffness degradation. This is achieved by using the concept of equivalent cycle. The theoretical predictions are in good agreement with available experimental results.

On the use of bend–twist coupling in full-scale composite marine propellers for improving hydrodynamic performance

Marine propellers are designed to work for a particular operating condition. However, a propeller often requires to operate at different off-design conditions, when its hydrodynamic efficiency drops. In this paper, a comprehensive numerical study is presented on the use of bend–twist coupling of composite propeller blades for improving their hydrodynamic efficiency at off-design conditions. The analysis is carried out on a full-scale propeller of diameter 4.2m, considering the complete viscous turbulent flow, as the loading and deformation of model propellers that have been typically studied in literature for this purpose cannot be extrapolated to a full-scale prototype propeller. The open water performance is estimated using the finite volume method employing the pressure based RANS equation for the steady, incompressible, turbulent flow. The deformation analysis is done using the finite element method based on the first order shear deformation theory for composite laminates. The fluid–structure interaction is incorporated in an iterative manner. The effect of laminate configurations on the maximum twist achieved in the blade is studied for four different composite materials. The numerical study reveals that, within the limits of material safety, the twist generated in the deformed propeller using commonly used composite materials is inadequate to create any noticeable change in the hydrodynamic efficiency. When the material failure is ignored, however, it is possible to generate sufficient deformation and twist that can cause appreciable improvement in the hydrodynamic performance.

A novel predictive model for mechanical behavior of single-lap GFRP composite bolted joint under static and dynamic loading

Mechanical connection of composite is critical due to its complicated meso-structure and failure mode, which has become a bottleneck on reliability of composite material and structure. Although many researches on composite bolted joints have been carried out, the theory and experiment on mechanical behavior of such a joint structure under dynamic loading were rarely reported. Here, we propose a novel predictive model for quasi-static and dynamic stiffness of composite bolted joint by introducing the strain rate dependent elastic modulus into the mass spring model. Combined with the composite laminate theory and Tsai-Hill theory, the present model was capable of predicting the strain rate dependent stiffness and strength of the composite bolted joint. Quasi-static and impact loading experiments were carried out by Zwick universal hydraulic testing machine and split Hopkinson tension bar, respectively. The stiffness and strength predicted by our model showed good accordance with the experiment data with errors below 12% under quasi-static loading and below 30% under impact loading. The results indicated that under impact loading, stiffness and strength of the composite bolted joint were significantly higher than their quasi-static counterparts, while the failure mode of the joint structure trended towards localization which was mainly bearing failure. Among various lay-up ratios studied, the optimal lay-up ratio for quasi-static and dynamic stiffness was 0:±45:90 = 3:1:1.

A nth-order shear deformation theory for composite laminates in cylindrical bending

Abstract The present study investigates whether an nthorder shear deformation theory is applicable for the composite laminates in cylindrical bending. The theory satisfies the traction free conditions at top and bottom surfaces of the plate and does not require problem dependent shear correction factor which is normally associated with the first order shear deformation theory. The well-known classical plate theory at (n = 1) and higher order shear deformation theory of Reddy at (n = 3) are the perticular cases of the present theory. The governing equations of equilibrium and boundary conditions are obtained using the principle of virtual work. A simply supported laminated composite plate infinitely long in y-direction is considered for the detail numerical study. A closed form solution for simply supported boundary conditions is obtained using Navier’s technique. The displacements and stresses are obtained for different aspect ratios and modular ratios.

Two-dimensional strain-based interactive failure theory for multidirectional composite laminates

A 2-D strain-based interactive failure theory is developed to predict the final failure of composite laminates subjected to multi-axial in-plane loading. The stiffness degradation of a laminate during loading is examined based on the individual failure modes of the maximum strain failure theory, and a piecewise linear incremental approach is employed to describe the nonlinear mechanical behavior of the laminate. In addition, an out-of-plane failure mode normal to the laminate is also investigated to more accurately predict the failure of multidirectional laminates. The theoretical results of the failure model presented are compared with the experimental data provided by the World-Wide Failure Exercise, and the accuracy of the model’s predictive capabilities is investigated.

An improved Puck’s failure theory for fibre-reinforced composite laminates including the in situ strength effect

Fibre-reinforced composites are being used more and more widely in many fields. However, the theoretical prediction of the failure of these composites is still a challenging task. In this paper, the physically-based failure theory developed by Puck and co-workers is combined with the fracture mechanics based in situ strength theory developed by Wang and Karihaloo. The latter considers the influence of both the thickness of the lamina itself and the ply angles of its neighbouring laminae. This combined failure theory also incorporates a new final failure mode. It is able to predict accurately the initial failure stress, thus overcoming one of the weaknesses of Puck’s theory which significantly underestimates this stress. Also, it explains why the number of non-fatal failure modes predicted by Puck’s theory is different from those observed in experiments under certain loads. Finally, it is able to overcome the problem of discontinuities in the failure envelope under some load combinations predicted by Puck’s original theory.

Bending problem of a finite composite laminated plate weakened by multiple elliptical holes

Based on the classical composite laminate theory, the bending problem of a finite composite plate weakened by multiple elliptical holes is studied by means of the complex variable method. The present work is intended to express the complex potentials in the form of Faber series aided by the use of the least squares boundary collocation techniques on the finite boundaries. As a result, concise and high accuracy solutions are presented for the stress distribution around the holes. Finally, numerical examples are presented to discuss the effects of some parameters on the stress concentration around the holes.