Deformation Laminate Research Articles

Analysis and Verification on Buckling Mechanism of Spatial Tow Steering in Automated Fiber Placement

Automated fiber placement (AFP) enables the efficient and precise fabrication of complex-shaped aerospace composite structures with lightweight and high-performance properties. However, due to the excessive compression on the inner edge of the tow placed along the curved trajectory, the resulting defects represented by buckling and wrinkles in spatial tow steering can induce poor manufacturing accuracy and quality degradation of products. In this paper, a theoretical model of tow buckling based on the first-order shear deformation laminate theory, linear elastic adhesion interface and Hertz compaction contact theory is proposed to analyze the formation mechanism of the wrinkles and predict the formation of defects by solving the critical radius of the trajectory, and finite element analysis involving the cohesive zone modeling (CZM) is innovated to simulate the local buckling state of the steered tow in AFP. Additionally, numerical parametric studies and experimental results indicate that mechanical properties and geometric parameters of the prepreg, the curvature of the placement trajectory and critical process parameters have a significant impact on buckling formation, and optimization of process parameters can achieve effective suppression of placement defects. This research proposes a theoretical modeling method for tow buckling, and conducts in-depth research on defect formation and suppression methods based on finite element simulation and placement experiments.

Approximate postbuckling analysis of shear deformable laminates

AbstractIn the lightweight design of aircraft, spacecraft and marine vessels, often advanced materials are utilised. Advanced materials such as laminated composites made of fibre‐reinforced plastics show transverse shear deformations if they are considered “thick” or possess little transverse shear stiffness. In most cases, the effect of the shear deformations is neglected, and few computational models exist that consider the closed‐form approximate analysis of the postbuckling behaviour. Thus, a new computational model based on high‐order shear deformation theories is introduced. The solution is derived based on the principle of the minimum of the total elastic potential and is evaluated in comparison to finite element analyses. The highly efficient approximate computational model is developed to offer a valuable tool for the preliminary design of lightweight structures utilising shear deformable advanced materials.

Numerical Investigation of the Dynamic Responses of Fibre-Reinforced Polymer Composite Bridge Beam Subjected to Moving Vehicle.

In modern industry, heavy traditional materials are being substituted with light and strong fibre-reinforced polymer composite materials. Bridges and railroads made of composite laminates are considerably affected by traffic loads. Therefore, it is very important to analyse this effect which would find practical applications in engineering designs. This paper explains the theoretical formulation that governs the dynamic response of a composite beam subjected to a moving load. The governing equations for the dynamic effect on the laminated composite bridge beam are explained here. The main theories in the micro–macro modelling of composite laminates are also described in the paper. Within the macro modelling, the Classical Laminate and Shear Deformation Laminate Theory of beams are presented. The symmetric cross-ply laminated bridge, made of boron/epoxy is under consideration. The computational two-dimensional model of the vehicle is adopted. The governing equations for the dynamic effect on the laminated composite bridge beam are explained. The calculation of the time response of the bridge for the characteristic speeds of the vehicle is performed in the environment of the MATLAB software. The maximum dynamic magnification factor for the dynamic analysis of a composite beam is found.

Liquefaction structures induced by the M5.7 earthquake on May 28, 2018 in Songyuan, Jilin Province, NE China and research implication

An earthquake of magnitude M5.7 occurred in Yamutu village, Songyuan City, Jilin Province, NE China (45°16′12″N/124°42′35″E) on May 28, 2018, with a focal depth of 13 km. The epicenter is located at the intersection of the Fuyu/Songyuan-Zhaodong Fault, Second Songhua River Fault and Fuyu North Fault which lies northwest of Tancheng-Lujiang Fault (Tan-Lu Fault). The earthquake-induced widespread liquefaction structures and ground surface fissures within 3 km from the epicenter, caused serious disasters to the local surroundings. The visible liquefied structures include sand volcanoes, liquefied sand mounds, sand dikes and sand sills. Sand volcanoes can be divided into sand volcano with a crater, sand volcano without a crater and water volcano (no sand). Other soft-sediment deformation structures (SSDS) induced by the earthquake include deformation lamination, load and flame structures, deformation folds, dish structures, convolute bedding and water-escape structures. The formation process of the sand volcanoes comprises three stages: (1) building up excess pore-fluid pressure in the liquefied layer, (2) cracking of the low-permeable overlying layer, and (3) mixture of sand-water venting out of the ground surface. During the upward movement, the liquefied sand is injected into the low-permeable layer to form sand veins, sand sills and various types of deformation structures. Vertical distribution of seismic liquefaction structure can be divided into four zones: the thoroughly liquefied zone, the lower liquefied zone with SSDS, the upper liquefied zone with SSDS, and the ground surface liquefied zone. The liquefaction occurred at a burial depth of 2–5 m, and the thickness of liquefied sand is 2 m. NE-SW (35°–215°) trending compressive stress is possibly the seismogenic trigger of the Songyuan M5.7 earthquake that caused the fault (Fuyu/Songyuan-Zhaodong Fault) to reactivate. The study of the Songyuan seismic liquefaction structures gives insight into the prediction of modern earthquakes and disaster-prone areas. Meanwhile it provides abundant basic material for studying earthquake-induced SSDS in both ancient and modern sediments. The research is obviously of great significance to reveal that the northern Tan-Lu Fault has entered a stage of active seismic activity since the twenty-first century.

Dynamic analysis for anti-symmetric cross-ply and angle-ply laminates for simply supported thick hybrid rectangular plates

In this paper, static and vibration analysis for anti-symmetric cross-ply and angle- ply carbon/glass hybrid laminates rectangular composite plate are presented. In this analysis, the equations of motion for simply supported thick laminated hybrid rectangular plates are derived and obtained through the use of Hamilton\'s principle. The closed-form solutions of anti-symmetric cross-ply and angle- ply laminates are obtained using Navier solution. The effects of side-to-thickness ratio, aspect ratio, and lamination schemes on the fundamental frequencies loads are investigated. The study concludes that shear deformation laminate theories accurately predict the behavior of composite laminates, whereas the classical laminate theory over predicts natural frequencies. The excellent accuracy of the present analytical solution is confirmed by making some comparisons of the present results with those available in the literature. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behaviors of anti-symmetric cross-ply and angle- ply hybrid laminated composite plates.

Investigation of the internal substructure of microbands in a deformed copper single crystal: experiments and dislocation dynamics simulation

We investigate the internal structure of microbands in a shear-deformed copper single crystal. The microstructure is characterized using high-resolution electron backscatter diffraction. The occurrence of microbands is due to the alternation of local orientation, which is characteristic of a deformation laminate. These microbands contain a substructure consisting of further local 1°-orientation alternations. A two-dimensional discrete dislocation dynamics model is used to describe the orientation substructure within the microbands. The boundary conditions for the simulation were estimated from the distribution of the geometrically necessary dislocation density obtained from the orientation map. The dislocation arrangement in the dynamic simulation explains the formation of the experimentally observed substructure.

Concept and Electro-elastic Modeling of Shear Actuated Fiber Composite using Micro-mechanics Approach

A Shear Actuated Fiber Composite (SAFC) concept is developed that may find application in structural actuation and health monitoring tasks. The fabrication aspects of SAFC are briefly discussed. A uniform field model is employed to study electro-elastic behavior of the SAFC. The composite actuator is modeled as a general laminate having seven layers, and the effective properties are evaluated further using shear deformation lamination theory. The geometric parameters such as fiber volume fraction, fiber thickness, and fiber orientation are considered, and their influence on the characteristics of SAFC is analyzed. It is observed that a higher fiber thickness may provide better shear actuation capability for the SAFC actuator; but conformability requirements bring a constraint on fiber thickness that needs to be optimized. A fiber volume content of 85—95% appears to provide a design envelope for the SAFC actuator. SAFC has shown a promising feature of simultaneously coupling both transverse shear strains, if the poled PZT fibers are oriented directionally. Therefore, SAFC can be used as a torsional actuator for developing electro-elastically tailored smart laminated or sandwich structures. It is also expected that the SAFC actuator may provide a better solution for active aeroelastic control applications, where torsion mode is critical.

Analysis of the dynamic flexural behaviour of composite beams at low temperature

In this study, the dynamic flexural behaviour at low temperatures of beams of three carbon/epoxy laminates is evaluated, analysing the influence of temperature on the mechanical strength, stiffness and absorbed energy until failure. Three-point bending tests were performed under dynamic conditions at three different temperatures (20 °C, −60 °C and −150 °C), and the results were compared with those found under static conditions at the same temperatures. Both the mechanical strength and the absorbed energy decreased when the temperature diminished in all the laminates. No significant influence of temperature was noted on the effective flexural modulus. Two analytical models, using the classical laminated theory and the first-order shear deformation laminate theory, and a numerical model were used to analyse the experimental results of the tests. The models allowed to ensure the use of the equations, which do not consider inertia forces, to calculate the test parameters, and they provided the specimen support span to neglect shear effects. They served also to determine the origin of the noise present in the load measured in the dynamic tests.

Application of the flexibility influence function method in the dynamic analysis of composite beams

The flexibility influence function technique is validated as a method for calculating the displacements and the rotations of a laminated beam subjected to a dynamic load, using the first-order shear deformation laminate theory and comparing the results with those obtained by modal analysis and two finite element models (one-dimensional and three-dimensional). The movements (displacements and rotations) were calculated from a single-span beam subjected to a time-variable load with four boundary conditions: clamped-clamped, hinged-hinged, clamped-free, clamped-hinged. A carbon/epoxy cross-ply laminated beam was selected to avoid bending-torsion coupling. The maximum movements calculated by the flexibility influence function method differs very little from those calculated with the other two models accounted for by the first-order shear deformation laminate theory: modal analysis and the one-dimensional numerical model. The differences in the rotations between the three-dimensional numerical model and the flexibility influence function method are slightly bigger, and could be due to the warping of the cross-section of the beam, which is not included in the first-order shear deformation laminate theory.

Modelling of mixed mode debonding in externally FRP reinforced beams

In this paper a refined model able to analyze edge debonding problems in beams strengthened with externally bonded composite laminated plates, is presented. The structural system is viewed as composed by three physical different components: the base beam (made of steel or concrete), the adhesive layer and the bonded plate. Each component may be comprised by one or several mathematical layers which adopts the first-order shear deformation laminate theory. Bonding and continuity conditions between different layers are simulated by using the interface modelling technique. Strong and collapsed interface models are introduced in order to capture stress singularities and to reduce the complexity of the analysis, respectively. Governing equations for displacement fields complemented with boundary and continuity conditions, are obtained by a variational approach. According to a fracture mechanics approach, the analysis is carried out by evaluating the total and individual mode components of energy release rate (ERR). Applications for typical strengthened systems, carried out by numerical integration procedures, are proposed in which the energy release rates are evaluated by means of interface displacement jumps, leading to a very efficient numerical procedure. The approximations introduced in the model with respect to the adopted number of mathematical layers are analyzed and comparisons with existent models are given. For the simpler two-layer model of the structure, comparisons are given with the closed-form solutions obtained in [Greco F, Nevone Blasi P, Lonetti P. An analytical investigation of debonding problems in beams strengthened using composite plates. Eng Fract Mech 2006, in press]. The convergence to the results from continuum analysis is investigated when a refined assembly of layers is adopted, by means of comparisons with predictions from very careful FE solutions. Finally, the effect of different debonding modes on the overall behaviour of the structural system is analyzed. These results show the capability and the accuracy of the proposed approach to predict debonding failure behaviour in both steel and concrete strengthened beams. As a matter of fact, the proposed approach involves reduced computational cost with respect to FE solutions based on 2D continuum elements and the use of a multi-layer structural model leads to avoid some complexities related to the classical elasticity theory for bimaterial interface cracks.

Fabrication of iron aluminum alloy/steel laminate by clad rolling

Laminates of an iron-aluminum alloy (20Al) and three types of steel—chromium molybdenum (CrMo), high carbon (FeCMn), and precipitation hardening steel with niobium carbide (FeCNb)—were fabricated at 600 °C and 1000 °C by clad rolling based on the compression stress ratio of 20Al to steel. The laminates fabricated at 600 °C exhibit a deformation microstructure with partial recrystallization, while those at 1000 °C reveal a refined microstructure. The 20Al layer of all the laminates exhibit a {001}〈110〉 texture, and the intensity of the texture increases with a decrease in the fabrication temperature and an increase in the reduction. The bending deformability of a laminate increases with a decrease in the compression stress ratio and by a reduction in the intensity of the {001}〈110〉 texture. The clad plate is further rolled at room temperature to a thickness of approximately 150 µm, which enables winding without damage. It is concluded that a high-strength steel at high temperatures and a high Al content in the Fe-Al alloy is beneficial for the fabrication of deformable laminates.

Combination resonance characteristics of laminated composite plates subjected to non‐uniform harmonic edge loading

PurposeTo predict the occurrence of the combination resonances in parametrically excited, simply supported laminated composite plates in contrast to the simple resonances by using first‐order shear deformation lamination theory considering the effects of shear deformation and rotary inertia.Design/methodology/approachFinite element technique is applied to obtain the equilibrium equation of a plate. Modal transformation is applied to transform the equilibrium equation into a suitable form for the application of the method of multiple scales (MMS). The MMS is applied to obtain the boundaries of the simple and combination resonances.FindingsThe combination resonance zones contribute a considerable amount to the local instability region and the widths of combination resonance zones are comparable to those of the simple resonance zones for the loading of the small bandwidth at one end or for the concentrated edge loading.Practical implicationsAircrafts, spacecrafts and many other structures such as ships, bridges, vehicles and offshore structures use the plate type elements, which are susceptible to dynamic instability.Originality/valueIt will assist the researchers of stability behavior of elastic systems.

007 大変形・高出力型アクティブラミネートの創製(知的材料・構造システム)

007 大変形・高出力型アクティブラミネートの創製(知的材料・構造システム)

An effective composite laminated curved beam element

AbstractIn this study, we present a new highly accurate composite laminated hybrid‐mixed curved beam element. The present element, which is based on the Hellinger–Reissner variational principle and the first‐order shear deformation lamination theory, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees of freedom in order to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out to obtain the (6 × 6) element stiffness matrix. Several numerical examples confirm the superior behaviour of the present hybrid‐mixed laminated curved beam element. Copyright © 2005 John Wiley & Sons, Ltd.

A new hybrid-mixed composite laminated curved beam element

In this study, we piesent a new efficient hybrid-mixed composite laminated curved beam element The present element, which is based on the Helhnger-Reissnet vatiational principle and the first-order shear deformation lamination theory, employs consistent stress parameters coriespondmg to cubic displacement polynomials with additional nodeless degrees in order to lesolve the numerical difficulties due to the spurious constraints The stress parameters are eliminated and the nodeless degrees are condensed out to obtain the (6X6) element stiffness matrix The present study also incorporates the straightforwaid prediction of interlaminar stresses from equilibrium equations Seveial numencal examples confirm the superioi behavior of the present composite laminated curved beam element

Refined First-Order Shear Deformation Theory Models for Composite Laminates

In the present work, new mixed variational formulations for a first-order shear deformation laminate theory are proposed. The out-of-plane stresses are considered as primary variables of the problem. In particular, the shear stress profile is represented either by independent piecewise quadratic functions in the thickness or by satisfying the three-dimensional equilibrium equations written in terms of midplane strains and curvatures. The developed formulations are characterized by several advantages: They do not require the use of shear correction factors as well as the out-of-plane shear stresses can be derived without post-processing procedures. Some numerical applications are presented in order to verify the effectiveness of the proposed formulations. In particular, analytical solutions obtained using the developed models are compared with the exact three-dimensional solution, with other classical laminate analytical solutions and with finite element results. Finally, we note that the proposed formulations may represent a rational base for the development of effective finite elements for composite laminates.

OPTIMIZATION CONTROL OF COMPOSITE LAMINATES FOR MAXIMUM THERMAL BUCKLING AND MINIMUM VIBRATIONAL RESPONSE

The problem of maximizing the thermal buckling and minimizing the vibrational response of composite laminates is solved using optimal design and active control procedures. The problem is formulated based on a first-order shear deformation laminate theory with various cases of boundary conditions. The design objective is to maximize thermal buckling using ply thickness and the fiber orientation angle as design variables. The active control objective is to minimize the laminate vibrational response with the minimum possible expenditure of control energy. The vibrational response is expressed in terms of the total elastic energy of the laminate and a penalty functional of closed-loop control force. Liapunov-Bellman theory is used to obtain solutions for controlled deflections and optimal control force. Comparative examples are given for angle-ply antisymmetric laminates subjected to a uniform temperature distribution. A general representation for the design variables is presented such that the ply thickness is a function of the number of layers. Some of the obtained numerical results are compared with their counterparts in the literature.

Differential quadrature element method for static analysis of shear deformable cross-ply laminates

In this paper, the two-dimensional differential quadrature element method (DQEM) is developed for the static analysis of symmetric cross-ply laminates using the first-order shear deformation plate theory. In this study, the laminated plate, which may contain different discontinuities in loading, geometry, material, and boundary conditions, is first divided into several simple plate elements and then the differential quadrature method (DQM) is applied to each simple element. Compatibility conditions are derived to connect the plate elements so that the overall matrix equation system for the whole plate is obtained and solved. The reliability of the DQEM for solving the titled problems is examined carefully through convergence and accuracy studies and finally some numerical test examples are given to demonstrate the applicability and flexibility of this method for practical use. The methodology presented here has overcome some critical drawbacks of the global DQM but is different from the Quadrature Element Method (QEM) since only one grid point is employed to represent the interface point. Copyright © 1999 John Wiley & Sons, Ltd.

Stiffness degradation induced by multilayer intralaminar cracking in composite laminates

A theoretical model for the prediction of the elastic properties of a general symmetric laminate containing multilayer matrix cracks is proposed. A five-layer equivalent constraint model (ECM) laminate [SL/ϕp/θq/φr/SR]s and seven others degenerated from such a model laminate by eliminating some of the sublaminates, [ϕp],[φr], SL and SR, are designed for the analyses of the degraded stiffnesses of the cracked laminae in the laminate; the crack configuration in the θ-lamina is explicitly represented (designated by underline `_') while the primary and secondary constraining effects are taken into account by the stiffness-equivalent homogeneous layers, [ϕp] and [φr], as well as SL and SR. A sublaminate-wise first-order shear deformation laminate theory is developed to analyze the stress and displacement fields in the ECM laminates under the combined tension–shear loading. The in-situ damage effective functions (IDEFs), Λ22 and Λ66, for characterizing the in-plane stiffness reductions of a cracked lamina constrained, are then expressed as explicit functions of the transverse ply crack spacing in such a lamina, as well as of the stiffness properties and the geometric parameters of the constraining layers by using the obtained stress field. The theory's predictions are in a good agreement with the experimental E-modulus data for [0/90/±45]s glass fiber reinforced epoxy composite laminates under fatigue.

Application of the laminate plate theory to the analysis of symmetric laminates containing a cracked mid-layer

The elastic properties of symmetric laminates containing a cracked mid-layer are predicted by using the equivalent constraint model (ECM) proposed recently by the authors. In accordance with the ECM methodology the symmetric laminates subjected to an in-plane tension/shear load are subdivided into such sublaminates as the cracked central-layer, two nearest laminae and two homogeneous layers smeared from the remaining plies (if applicable). The first-order shear deformation laminate plate theory is applied to each sublaminate, and the traction and displacement continuity conditions between sublaminates are then enforced. The boundary conditions of the uncracked constraining sublaminates are satisfied exactly, however, the stress-free conditions at the crack faces are specified in an average sense. The stress and displacement fields are used to derive the mathematical expressions for the effective stiffness properties of the cracked layer. The comparisons between the ECM approach and McCartney's model are carried out for the [−45/45/0/90] s carbon fiber and [30/90] s glass fiber epoxy laminates having 90°-ply cracks, suggesting that both models predict the close values for the reduced elastic properties. It is emphasized that the ECM approach is much simpler than McCartney's model which needs a numerical technique to solve the governing equations, providing a closed-form solution for modeling the stiffness reduction.