Ply Thickness Research Articles

Experimental study of the size effect on transverse cracking in cross-ply laminates and comparison with the main theoretical models

Transverse cracking of off-axis plies is typically the first step of some failure mechanisms in long fiber reinforced laminated composites. It is well known that the off-axis ply thickness affects strongly the strain level which this ply is able to withstand without cracking. Experimental evidences show that this critical strain level increases strongly with decreasing ply thickness for the thinnest plies, confirming a clear size effect. This fact could be used to inhibit transverse cracking with the use of the recently developed ultra-thin plies. However the classical failure criteria for composites are not able to predict this size effect. From the first tests in the 1970s, several models with very different hypotheses were proposed to predict this size effect. Surprisingly there is still not a clear consensus in the scientific community about which is the adequate model, though their fundamentals are radically different. In this work an extensive test campaign is carried out on self-similar [0/90]s cross-ply laminates of AS4/8552 carbon/epoxy. The size effect is evaluated spanning a broader spectrum of thicknesses than in the tests presented in the literature until now, in order to explore the range of thicknesses where the differences between predictions of the main theoretical models are larger. In spite of the inherent dispersion in the experimental results, the comparison shows that the purely stress-based criteria underestimates the apparent strength of the off-axis ply. The other models predict very similar results, particularly for the thinnest laminates, with slight underestimations or overestimations, depending on the model.

Design and analysis of filament-wound composite pressure vessels based on non-geodesic winding

In this paper a novel design approach was proposed for determining the optimal winding parameters of composite pressure vessels based on non-geodesic trajectories. With the aid of the differential theory and winding principles, the non-geodesic trajectories were derived for various tangent points. The obtained non-geodesics for composite pressure vessels were simulated using MATLAB to verify the validity of the trajectory design. The influence of the number of the tangent points and the roving bandwidth on the non-geodesic winding patterns was evaluated. The optimal number of the tangent points and the roving bandwidth were then determined while ensuring fiber stability and full coverage on the mandrel. The finite element model of the pressure vessel was established, taken variable ply thicknesses and angles along the dome meridian into account. In addition, the stress distributions of the aluminum liner and the composite overwrap were obtained and the burst pressure of the pressure vessel was predicted. The specimen of a composite pressure vessel was fabricated using the filament winder and the experimental results were consistent with the theoretically predicted ones. It is concluded that the present method is of great significance for design and manufacture of composite pressure vessels.

Simulation of the Mechanical Response of Thin-Ply Composites: From Computational Micro-Mechanics to Structural Analysis

This paper provides an overview of the current approaches to predict damage and failure of composite laminates at the micro-(constituent), meso-(ply), and macro-(structural) levels, and their application to understand the underlying physical phenomena that govern the mechanical response of thin-ply composites. In this context, computational micro-mechanics is used in the analysis of ply thickness effects, with focus on the prediction of in-situ strengths. At the mesoscale, to account for ply thickness effects, theoretical results are presented related with the implementation of failure criteria that account for the in-situ strengths. Finally, at the structural level, analytical and computational fracture approaches are proposed to predict the strength of composite structures made of thin plies. While computational mechanics models at the lower (micro- and meso-) length-scales already show a sufficient level of maturity, the strength prediction of thin-ply composite structures subjected to complex loading scenarios is still a challenge. The former (micro- and meso-models) provide already interesting bases for in-silico material design and virtual testing procedures, with most of current and future research focused on reducing the computational cost of such strategies. In the latter (structural level), analytical Finite Fracture Mechanics models—when closed-form solutions can be used, or the phase field approach to brittle fracture seem to be the most promising techniques to predict structural failure of thin-ply composite structures.

Towards aerospace grade thin-ply composites: Effect of ply thickness, fibre, matrix and interlayer toughening on strength and damage tolerance

Thin-ply composites represent a promising approach to further improve the performance of carbon fibre composite structures thanks to their ability to delay the onset of matrix cracking and delamination up to the point of fibre dominated failure. However, this increased strength comes with a more brittle failure response which raises concerns on damage tolerance. Thus a careful material optimization is needed to address this trade-off. In this work, eight different formulations of thin-ply composites ranging from low modulus to high modulus carbon fibres are evaluated to understand the effects of the fibre and matrix constituents on the onset of damage and strength in unnotched tensile (UNT) tests of quasi isotropic laminates for ply thicknesses between 300 and 30 microns. The obtained experimental data are combined in master curve diagrams for simplified material selection process. It is observed that certain thin-ply composites with a ply thickness t < 134 μm can reach UNT strength corresponding to or approaching the ultimate strain of the fibres as well as UNT stress at onset of damage as high as 92% of the latter. Based on this knowledge, a novel aerospace grade toughened thin-ply composite system is developed which can reach a quasi-isotropic UNT strength above 1 GPa (>95% of the fibre strain). The newly developed composite is further optimized to improve damage tolerance by toughening the resin and selected interfaces. The effect of those modifications on damage tolerance are evaluated through compression strength after impact (CAI) tests and open hole tensile tests (OHT). It is found that an optimized interlayer toughened thin-ply composite based on 68 microns plies of intermediate modulus fibre can reach both outstanding strength properties with comparable or better CAI and OHT strength compared to current aerospace grade composites.

Identification of failure modes of composite thin-ply laminates containing circular hole under tension by acoustic emission signals

Composite thin-ply laminates have been reported to exhibit superior performance in various loading conditions than standard-ply laminates due to positive size effects. However, the ultimate tensile strength of the thin-ply (<0.125 mm) laminates containing circular hole was lower than that of the thick (>0.125 mm) or standard-ply (0.125 mm) laminates with same size of the hole. Besides, fracture morphologies showed a transition from a combined mode of matrix crack, delamination and pull-out at 45° and −45° ply in the thick and standard-ply laminates to a quasi-brittle fracture in the thin-ply laminates. In order to explain the experimental phenomena, acoustic emission was used in this paper to identify and distinguish the failure modes of laminate specimens containing circular hole with different ply thickness, and finite element simulation was adopted to investigate the cause of lower tensile strength in the thin-ply specimen. Carbon fiber reinforced polymer matrix composite laminate specimens were prepared using prepregs with different ply thicknesses (0.02 mm, 0.055 mm and 0.125 mm). In tensile test, higher initial stress of damage, lower ultimate strength and quasi-brittle fracture morphology could be observed in the thin-ply laminate specimens with an open hole. The results of acoustic emission analysis demonstrated that the matrix damage and delamination were suppressed in the thin-ply laminates, and superior damage suppression and crack-propagating resistance in the thin-ply laminates lead to quasi-brittle fracture morphology. Besides the more homogeneous micro-structure and isotropic behavior of the thin-ply laminates leaded to higher initial damage stress compared to the laminates with thick plies. However, according to finite element analysis, the thin-ply laminates exhibited much stronger stress concentration after initial damage until ultimate failure of the specimens, leading to lower ultimate strength under tensile loading.

Analysis on the impact response of fiber-reinforced composite laminates: an emphasis on the FEM simulation

Abstract The effects of units, material parameters, and constitutive relationships on the dynamic mechanical response of composite laminates subjected to high- and low-velocity impacts were investigated. Additionally, the role of impact or shape, including hemispherical, flat, and conical, on the damage area of the adhesive layer and displacement of the center of the laminated plates was investigated. The results show that the energy absorption of composite laminates increases with impact velocity, and specific energy absorption changes with the density of the contact surface, which is affected by ply thickness. Moreover, the target energy absorption decreases with increasing layer angle. Under a low-velocity impact, the maximum contact force, damage area of the adhesive layer, and displacement of the center of the laminated plate increase as the impact energy increases, thus showing that impact energy is not directly related to contact duration and energy absorption of composite laminates. The results of different geometric shapes show that the damage area of the adhesive layer and the displacement of the center of the laminated plates are largest for a conical impactor and smallest for a flat impactor.

Concurrent optimization of stacking sequence and stiffener layout of a composite stiffened panel

ABSTRACTThis article is to optimally design laminated composite stiffened panels by optimizing both stacking sequences of the panel skin and stiffeners as well as the layout of stiffeners. Starting from initial designs of stiffener layout and stacking sequences for each stiffener and the panel skin, the problem is formulated with discrete and continuous variables, where discrete 0/1 variables represent the absence/presence of each layer in initial stacking sequences, and continuous variables represent layer thicknesses. A first-level approximate problem is established to make the problem explicit. Genetic algorithm is used to determine the existence of each layer in the laminates. When the number of retained layers in stiffener becomes zero, that stiffener can be seen as unnecessary and removed. For individual fitness calculation, a second-level approximate problem is constructed to optimize continuous ply thicknesses of retained layers. Correspondingly, laminated stacking sequences and stiffener layout are concurrently optimized.

The limits of Timoshenko beam theory applied to impact problems of layered beams

The aim of this article is to demonstrate and discuss the possibilities of the application of classical Timoshenko beam theory to problems of three-layered elastic beams with symmetric composition. In particular, the equivalent single-layer first-order shear deformation theory (FSDT) with the variation of Timoshenko shear coefficient is applied. Three common types of beams are chosen for this study: (i) a beam composed of two stiff thick plies bonded by a thin soft layer, (ii) a soft-core sandwich beam and (iii) a beam of sandwich-like composition having a core stiffer than the face sheets. The possibilities of the application of FSDT to these basic types of beams and their modifications are studied on their transient responses to a pulse of impact character. Comparing the FSDT results with the results of the exact two-dimensional theory under the assumption of plane stress problem, the limits and the precision of FSDT are discussed. It is shown that FSDT can give very precise results in the case (iii), quite good results in the case (i) and questionable results for soft-core sandwiches.

The Relationship of Prosthetic Sock Ply Thickness to Percentage of Transtibial Limb Volume Outside of the Socket

ABSTRACT Introduction Prosthetic socks are typically used to accommodate volume fluctuations throughout the day. Clinically, prosthetists often use sock ply thickness to assess the fit of a prosthetic socket and the amount of volume reduction necessary for the next socket iteration. This is done by using various sock plies to determine the proper socket fit. The amount of volume reduction needed for a specific sock ply fit is unclear. Objective This preliminary study aimed to measure the relationship between sock ply and percentage of volume change. Methods The Rodin4D scanner was used to scan three transtibial sample foam models. Each model had an appropriately sized liner, which was scanned as a baseline measurement. Each sock ply combination (one, two, three, five, one + one, one + two, two + three, two + one, and three + two) was scanned six times per model. Scan order was randomly assigned for each model. Results Significant differences in volume change were found between one-ply (5.188%) and three-ply (10.42%) and five-ply (8.83%) socks, but not two-ply socks (7.15%). A significant volume increase was shown for the use of multiple socks (three + two ply, 18.33%, or two + three ply, 18.33%) compared with a single five-ply sock (8.83%). However, no significant differences were found in a similar comparison of a single three-ply sock (10.42%) versus the one + two–ply (11.68%) or two + one–ply (11.57%) socks. Conclusion Our results showed that the use of multiple socks for the same ply, specifically the order of socks donned for the two + three ply and three + two ply, resulted in greater volume than a single sock of the same ply (i.e., five ply). The volumetric change for five-ply is significantly different from one-ply, but not from two-ply and three-ply socks. A limitation of this study was that the scans were completed on foam models with the point of measurement at the distal patella causing potential for the posterior wall to be outside of the socket. This may change on a human subject. The percentage of volume changes based on sock ply thickness that were determined from this study may be used as a starting point for prosthetists during modifications, but further research is needed to determine how this volume changes within the socket.

Stability Analysis of Composite Perforated Annular Sector Plates Under Thermomechanical Loading by Finite Element Method

This paper presents the stability analysis of a perforated plate with sector geometry made of composite materials. The sector of concern is a compound of graphite-epoxy and glass-epoxy with identical ply thickness but different fiber angles for each layer. The mechanical load conditions considered include uniform axial, circumferential, and biaxial pressure, while the thermal loading is specified to be uniform temperature increase over the whole sector. The existence of one or two circular holes has increased the complexity of analysis. To obtain solutions of high accuracy, the three-dimensional elasticity theory relations have been employed. Using the finite element method along with the stability condition of Trefftz, the buckling equation of the structure is derived. Green nonlinear strain-displacement relations are used to form the geometrical stiffness matrix. Unlike the finite element method used by other researches, a novel curved 3D B-Splined element is used to more accurately trace the displacement and stress variations of the structure. This element can be used in solution domains with geometric discontinuities, such as perforated plates and also meshed in the thickness direction. Moreover, instead of using the common von Karman assumptions, the most general form of the strain tensors in the curvilinear coordinates is adopted. The buckling load is obtained by extremizing the second variations of the total potential energy. The finite element formulation is coded in the MATLAB software. The effects of various parameters such as sector dimensions, dimensions of the hole, mechanical load directions, and fiber angles of each layer on the thermomechanical buckling is investigated.

Charpy test investigation of the influence of fabric weave and fibre nature on impact properties of PEEK-reinforced composites

The aim of the work is to use Charpy impact test for quick evaluations of different Polyether-ether-ketone (PEEK)-reinforced composites to be used for impact protection. In the first part, the influence of weave pattern was first analysed by comparing the impact behaviour of three PEEK composites reinforced with plies of unidirectional (UD) tapes, 5H satin fabrics and 2 × 2 twill fabrics made of high-strength carbon fibres. In the second part, the influence of fibre nature was investigated for the same weave pattern. The impact behaviour of five 2 × 2 twill fabrics made from inorganic fibre (carbon, glass and basalt) and organic fibre (aramid and poly(p-phenylene-2,6-benzobisoxazole) (PBO)) has been compared. Two main types of failure modes were identified: a brittle behaviour mode with high failure strength and a highly deformable behaviour mode in which energy absorption is more important. The balance between brittle behaviour and highly deformable behaviour results from competition between the yarn crimp, weave pattern and fibre properties of the composite. Slight yarn crimp and small ply thickness increase the stiffness of the composite and induce brittle behaviour characterized by fibre failure in tension and a steep peak on the loading curves. This behaviour is observed in UD and 5H satin carbon-reinforced composites or 2 × 2 twill glass and basalt fabric-reinforced composites. In contrast, aramid and PBO 2 × 2 twill fabric composites exhibit high shear strength. The highly deformable behaviour of the specimens during the Charpy impact led, in the case of organic fibres, to a non-breakage of the fibres and consequently to a high level of energy absorption. This behaviour is necessarily interesting in armour applications.

Damage Progression in Thick Curved Composite Laminates under Static and Fatigue Loading

In this study, damage behavior of curved carbon fiber reinforced polymer (CFRP) composite laminates that are important sub-structures (ribs, shear webs and spar flanges etc.) for wind turbine blades are investigated under static and fatigue loading conditions. Cross-ply curved specimen consisting of groups of three 0° and 90° layers is used for clear observation of the matrix cracking in thicker plies. Damage mechanisms and locations under static and fatigue loadings are examined. In the experiments, failure is found to initiate in the first group of 90° layers under static loading while it is found to occur in the second group of 90° layers under fatigue loading. The overall goal of the project is to contribute to development of design techniques or local reinforcement methods to increase fatigue life and durability of these curved sub-structures used in wind turbine blades.

Cured shape prediction of fiber metal laminates considering interfacial interaction

During the manufacturing process of fiber metal laminates (FMLs), incompatible residual strain leads to the problem of slippage interaction at the interface between the metal layer and the fiber layer. An analytical model and finite element (FE) model considering slippage effect are established to obtain the cured shape and deformation of cross-ply [Al/0/90/Al] FMLs. Both analytical and FE results are in good agreement with experimental results. The predicted models proposed in this paper can accurately and effectively calculate the equilibrium configurations of FMLs at room-temperature. In order to reveal the curing deformation characteristics of FMLs, the influence laws of geometry dimensions and metal ply thickness on the cured stable shapes are obtained by using the prediction models for the square and rectangular laminates.

Effects of bend-twist coupling on flutter limits of composite wind turbine blades

The effects of bend-twist coupling on the flutter limits of large composite wind turbine blades are investigated in this work. A mixed, geometrically exact, and nonlinear finite element for anisotropic beams is developed based on Hellinger-Reissner variational principle. The nonlinear beam model is combined with Blade Element Momentum method and an unsteady dynamic stall model to perform flutter analysis of composite blades. A 5-MW composite wind turbine blade with shallow-angled skins is studied, where unbalanced laminates (i.e. ply angle and ply thickness unbalances) are implemented to introduce the bend-twist coupling in the blade through material anisotropy. The results show that with bend-twist coupling due to geometrical nonlinearities, the predicted flutter limits are around 23% lower than the same predicted in linear flutter analysis. The unbalanced skin laminates show no significant influence on the flutter limits of the blade in nonlinear flutter analysis.

A novel reliability-based two-level optimization method for composite laminated structures

Due to the existence of large number of design variables for large-scale composite laminated structures, such as ply thicknesses and stacking sequence, etc., it has become one of most important concerns to build an efficient optimization design method for composites. In this paper, the purpose is to propose a novel reliability-based two-level optimization design method including thickness and stacking sequence optimizations, where uncertain parameters of composites are taken into account for reliability evaluation. Firstly, by characterizing existing uncertain parameters of composites as random or interval variables, one can carry out uncertainty analysis for structural responses. Then the evaluation models of probabilistic and non-probabilistic reliabilities are separately introduced when treating uncertainties as random and interval variables. Furthermore, by combining the reliabilities with the two-level optimization model, a novel reliability-based two-level optimization model is advanced and the detailed optimization procedures are listed for convenience of understanding. Lastly, two numerical examples including a simple-supported composite plate and a composite wingtip of aerospace plane are given out to demonstrate the validity and availability of the proposed method. The results show that the proposed method can be successfully and efficiently applied in the optimization design of composite structures.

Ply thickness dependence of the intralaminar fracture in thin-ply carbon-epoxy laminates

The effect of ply thickness t in intralaminar fracture of unidirectional thin-ply carbon-epoxy laminates is characterized by testing double cantilever beam (DCB) and compact tension (CT) specimens with different t. While the average intralaminar energy release rate (ERR) at initiation is found equal to the corresponding interlaminar values, the steady-state intralaminar ERRs, only reached in the DCB configuration, are approximately three times higher than the corresponding interlaminar values. Due to changes in the extent of bridging, intralaminar steady-state ERRs are ∼30% higher in thick-ply (t = 0.150 mm) than in thin-ply laminates (t = 0.030 mm). Thin-ply composite laminates exhibit a faster ERR growth with crack length, and for DCB, reach steady-state at a much shorter crack extension than thick-ply composites. Traction profiles, due to bridging, are identified using R-curves and implemented in cohesive element simulations to predict intralaminar fracture of DCB and CT specimens. The experimental and simulated load–displacement responses are in good agreement.

Multi-objective optimization of a composite stiffened panel for hybrid design of stiffener layout and laminate stacking sequence

This paper presents a two-level approximation method for multi-objective optimization of a composite stiffened panel. The purpose is to seek the minimum structural mass and maximum fundamental frequency subject to given displacement constraints and manufacturing limitations. The design variables are the stiffener layout, and laminate stacking sequences for stiffeners and the panel skin. By introducing the concept of ground structure in both stiffener layout and laminate stacking sequence, the design problem is formulated with mixed discrete and continuous variables. Two types of discrete variables represent the existence of each stiffener and the existence of each ply in the laminate, respectively, with continuous ones for ply thicknesses. Considering the objectives are of different dimensions, a weighted min-max objective function is defined and minimized. The problem is firstly made explicit with branched multipoint approximate functions. Genetic algorithm (GA) is then adopted to optimize two types of discrete variables, determining which stiffeners/layers are deleted or retained. For fitness calculation in GA, a second-level approximation is built to optimize continuous ply thicknesses of the necessary layers that are retained. By giving different initial designs of stiffener layout and laminate stacking sequences, reasonable optimization results, which are tradeoffs between the considered two objectives, are obtained as design options. From the number of required structural analysis, it shows that the proposed method has a good efficiency in seeking rational solutions, which are tradeoffs between conflicting objectives and also feasible designs satisfying all considered constraints.

Coupled stress and energy criterion for multiple matrix cracking in cross-ply composite laminates

Transverse cracking, i.e. matrix cracking in the off-axis plies of the laminate, is widely recognized as the first damage mode to appear in continuous fibre-reinforced composite laminates subjected to in-plane loading. Since transverse cracking has a great influence on the subsequent damage steps such as delaminations or oblique cracks, it is important to be able to predict its onset and growth accurately. In this paper, it is proposed to use a combination of the Coupled Criterion of Finite Fracture Mechanics (FFM) and the Equivalent Constraint Model (ECM) to predict the evolution of crack density with increasing applied load. Two formulations – a discrete formulation and a continuous formulation – are developed for the energy criterion within the Coupled Criterion. Some dependences between the two formulations are proved, which justifies the good agreement found by the models based on continuous formulations presented by other authors despite the inherent discrete nature of the phenomenon. Dependence of the failure load predicted by the Coupled Criterion on the layer thickness ratio and brittleness number (a structural parameter that characterizes a combination of the stiffness, strength, fracture toughness and the thickness of the cracked ply of the laminate) is examined and discussed for carbon/epoxy and glass/epoxy laminates. Finally, a comparison against experimental results shows a good agreement.

Prediction of outer-ply matrix crack density at saturation in laminates under static and fatigue loading

The onset of dominant damage mode transition from matrix cracking to induced delamination in laminates containing outer-ply matrix cracks is experimentally and analytically investigated. Stress states of a [θm(o)/θn(i)]s laminate containing staggered outer-ply matrix cracks with or without induced delaminations are derived implementing a developed unit-cell based analysis in the framework of variational principles. A damage mode competition criterion is implemented to predict crack density at saturation which is argued to be a characteristic damage state (CDS) independent from loading conditions. Several carbon/epoxy specimens of type [θm/0n]s are prepared with different off-axis ply orientation, θ, and thickness. Optical microscopy is used to identify matrix crack density during both static and fatigue loading with different loading conditions. The analytically predicted crack densities at saturation are shown to be in acceptable agreement with experimental observations and saturated crack density is confirmed to be a characteristic damage state (CDS) identical during both static and fatigue loading.

Characterizing buckling behavior of matrix-cracked hybrid plates containing CNTR-FG layers

In this paper, the effect of matrix cracks on the buckling of a hybrid laminated plate is investigated. The plate is composed of carbon nanotube reinforced functionally graded (CNTR-FG) layers and conventional fiber reinforced composite (FRC) layers. Different distributions of single walled carbon nanotubes (SWCNTs) through the thickness of layers are considered. The cracks are modeled as aligned slit cracks across the ply thickness and transverse to the laminate plane, and the distribution of cracks is assumed statistically homogeneous corresponding to an average crack density. The first-order shear deformation theory (FSDT) is employed to incorporate the effects of rotary inertia and transverse shear deformation, and the meshless kp-Ritz method is used to obtain the buckling solutions. Detailed parametric studies are conducted to investigate the effects of matrix crack density, CNTs distributions, CNT volume fraction, plate aspect ratio and plate length-to-thickness ratio, boundary conditions and number of layers on buckling behaviors of hybrid laminated plates containing CNTR-FG layers.