Linear Strain Distribution Research Articles

Hybrid hemp/glass fiber reinforced high-temperature shape memory photopolymer with mechanical and flame-retardant analysis

Cultivated natural fibers have a huge possibility for green and sustainable reinforcement for polymers, but their limited load-bearing ability and flammability prevent them from wide applications in composites. According to the beam theory, normal stress is the maximum at the outermost layers but zero at the mid-plane under bending (with (non)linear strain distribution). Shear stress is the maximum at the mid-plane but manageable for most polymers. Accordingly, a laminated composite made of hybrid fiber-reinforced shape memory photopolymer was developed, incorporating strong synthetic glass fibers over a weak core of natural hemp fibers. Even with a significant proportion of natural hemp fibers, the mechanical properties of the hybrid composites were close to those reinforced solely with glass fibers. The composites exhibited good shape memory properties, with at least 52% shape fixity ratio and 71% shape recovery ratio, and 24 MPa recovery stress. After 40 s burning, a hybrid composite still maintained 83.53% of its load carrying capacity. Therefore, in addition to largely maintaining the load carrying capacity through the hybrid reinforcement design, the use of shape memory photopolymer endowed a couple of new functionalities to the composites: the plastically deformed laminated composite beam can largely return to its original shape due to the shape memory effect of the polymer matrix, and the flame retardancy of the polymer matrix makes the flammable hemp fiber survive the fire hazard. The findings of this study present exciting prospects for utilizing low-strength and flammable natural fibers in multifunctional load-bearing composites that possess both flame retardancy and shape memory properties.

Coir/glass hybrid fiber reinforced thermoset polymer composite laminates with room-temperature self-healing and shape memory functions

Natural fibers have a lot of potentials as renewable reinforcements for polymers. However, their lower load-carrying capacity compared with synthetic fibers made it a challenge to use them as polymer reinforcements. When a laminated composite beam is bent, the normal stress is the highest on the top and bottom layers and zero in the midplane due to the (non)linear distribution of normal strain. Even though the shear stress is the highest in the midplane, most polymers can tolerate the high shear stress. Therefore, hybrid composite laminates with strong synthetic glass fibers stacked over the core of weak natural coir fiber reinforcement have been designed. Even using a significant portion of coir fibers in the composites, the samples with hybrid fiber reinforcement showed almost similar mechanical properties compared with the samples with glass fiber reinforcement alone. Delamination and matrix crack induced by low velocity impact inside the composite panels were repeatedly healed at room temperature due to the self-healing capability of the diglycidyl 1,2-cyclohexanedicarboxylate (DCN) and polyethylenimine (PEI) polymer matrix. The healing efficiency was up to 99% for the first healing cycle and 72% for the fourth healing cycle. The composites also had good shape memory properties, with a shape fixity ratio up to 51% and a shape recovery ratio up to 93%, which were well maintained even after the several damage/healing cycles of the composites. This study opens new opportunities for applications of natural fibers in multifunctional load-bearing composites.

Thermoset polymer composites with gradient natural and synthetic fiber reinforcement: Self-healing, shape-memory, and fiber recyclability

Natural fibers have high potential as renewable reinforcement for polymers; however, their lower load-carrying capacity compared to synthetic fibers significantly limits the wide application in fiber-reinforced polymer composites. In laminated composite beams under bending load, the normal stress is the highest on the top and bottom layers but is zero at the mid-plane, with almost a linear normal strain distribution. Although the shear stress is the highest at the mid-plane, it may not be a major concern as most polymers can survive the high shear stress. Using this concept, we have designed a hybrid fiber reinforcement in a gradient manner: from the surface to the mid-plane were carbon fiber, glass fiber, and natural jute fiber, respectively. A newly synthesized self-healable shape memory polymer was used for laminating the fibers. Performance characterizations demonstrated that even using a significant amount of natural fibers in the composites, the samples with gradient fiber reinforcement showed competitive mechanical properties to fully carbon or glass fiber reinforced composites and much higher mechanical properties than the composite prepared with entirely natural fibers or glass fibers. For example, the gradient composites show up to 550 % flexural strength of the composites made of fully natural fibers, and around 14 % and 34 % higher flexural strength than that of the composites made of pure glass and pure carbon fibers, respectively. In addition, the composites retain excellent self-healing, shape-recovery, and fiber-recycling properties.

Prestress Force Monitoring and Quantification of Precast Segmental Beams through Neutral Axis Location Identification

This paper proposes using neutral axis locations to monitor and quantify the prestress force in post-tensioned precast segmental beams. Strain measurements are used to obtain the neutral axis locations of specific cross-sections of the precast prestressed segmental beams, based on the plane–remains–plane and linear strain distribution assumption. A theoretical calculation method based on the static equilibrium of a specific cross-section is developed to calculate the prestress force in segmental beams based on the neutral axis location. To verify the accuracy of the proposed method, a post-tensioned prestressed segmental beam is built and tested in the laboratory. A corresponding high-fidelity finite element model is also developed based on the beam design and material properties. Experimental studies and numerical simulations are conducted to verify the feasibility and accuracy of the proposed method in quantifying the prestress force in precast segmental beams. Both experimental and numerical results demonstrate that the proposed method can reliably estimate the prestress force, which can be used to monitor the prestress force loss in post-tensioned structures.

Opto-mechanical modeling and experimental implementation of an FBG-based piezoelectric bimorph actuator for high voltage sensing applications

This paper proposes a highly simplified optical voltage sensor by using a piezoelectric bimorph and a Fiber Bragg Grating (FBG) that can be used for high voltage applications with a relatively good accuracy and stability. In this work the theoretical framework for the whole opto-mechanical operation of the optical sensor is detailed and compared to experimental results. In the analysis, a correction term to the electric field is derived to account for the linear strain distribution across the piezoelectric layer improving the designing equations and giving more criteria for future developments. Finally, some experimental results from a laboratory scale optical-based high voltage sensing setup are discussed, and shown to be in excellent agreement with theoretical expected behavior for different voltage magnitudes.

A comprehensive review in incremental forming on approaches of deformation analysis and surface morphologies

Abstract Incremental forming is an effective way of manufacturing the part with customized geometry to the end user. The flexible deformation of sheet is the effect of tool squeeze and traverse over strategic paths with significant increment in step depth. The formability is mainly dependent on localized plastic-deformation of blank, ensures that validation of deformation stability, linear wall strain distribution and material characteristics. This review article begins with deformation analysis and discusses the influential factors and ends-up with surface integrity. Reviewing various research articles based on deformation mechanism expresses the various outlines such as texture evolution, transition of plane-strain mode in both SPIF and DSIF samples. These discussions provide the enlarged view of the current research gap and establish a strong perspective to industrial applications.

Fibre direction strain measurement in a composite ply under pure bending using Digital Volume Correlation and Micro-focus Computed Tomography

This paper presents an experimental demonstration and validation of high-resolution three-dimensional experimental strain measurement using Digital Volume Correlation (DVC) on Carbon Fibre-Reinforced Polymers, via through-thickness strain analysis under a state of pure bending. To permit the application of DVC to displacements and/or strain measurements parallel to the fibre direction in well-aligned unidirectional materials at high volume fractions, a methodology was developed for the insertion of sparse populations of 400 nm BaTiO3 particles within the matrix to act as displacement trackers (i.e. fiducial markers). For this novel material system, measurement sensitivity and noise are considered, along with the spatial filtering intrinsic to established DVC data processing. In conjunction with Micro-focus Computed Tomography, the technique was applied to a simple standard specimen subjected to a four-point flexural test, which resulted in a linear strain distribution through the beam thickness. The high-resolution, fibre-level strain distributions (imaged at a voxel resolution of ∼0.64 µm) were compared against the classical beam theory (Euler–Bernoulli) in incrementally decreasing averaging schemes and different sub-set sizes. Different sampling and averaging strategies are reported, showing that DVC outputs can be obtained that are in very good agreement with the analytical solution. A practical lower limit for the spatial resolution of strain is discerned for the present materials and methods. This study demonstrates the effectiveness of DVC in measuring local strains parallel to the fibre direction, with corresponding potential for calibration and validation of micromechanical models predicting various fibre-dominated damage mechanisms.

Surface plasmon resonance manipulation through application of mechanically generated planar and linear strain

This paper reports a method of manipulating surface plasmon resonance (SPR) by mechanically straining a substrate to induce reconfigurations of photonic nanostructures patterned above the substrate with handling simplicity, operation practicality, application variety, and design flexibility. Results indicate that the proposed method linearly expands nanostructures in the xy-plane, switching SPR and consequently changing the perceived color. Comprehensive structural design, numerical evaluation, device fabrication, experimental verification, and optical analysis were conducted in this study. In addition to the demonstrations, a tendency toward color purity improvement along with the enhancement of the completeness of linear strain distribution was observed.

Flexural behavior of a composite steel and precast concrete open web dissymmetric framing system

The use of composite construction has been incorporated into the design of steel components for decades, creating efficient and stiffer structures through the combined benefits of structural steel and reinforced concrete. Traditional floor systems develop composite action between vertically aligned elements using shear studs or other mechanical transfer elements. In this paper, the behavior of a composite structural system that combines steel beams, precast hollow core slabs, steel reinforcement, and cementitious grout in a unique geometry to create a shallow, monolithic, and composite floor assembly for use in residential and commercial construction is evaluated. Composite action is developed through a linear strain distribution between horizontally aligned concrete slab and steel beam elements. Experimental results from large-scale assembly testing of the composite system, known as the Girder-Slab System, are presented. The sensitivity of the system to material properties and structural geometry is investigated including effective width, section properties, and flexural strength. Comparisons of flexural section properties and strength are made between experimental performance and predictions using mechanics- and code-based principles.

A semi-analytical solution for bending response of SMA composite beams considering SMA asymmetric behavior

This paper develops a novel and robust semi-analytical model to investigate the bending response of an SMA composite beam during a loading-unloading cycle based on an improvement of Brinsons model for an Euler–Bernoulli beam. The improvement of Brinsons model is taken into account to consider the asymmetric behavior of SMAs in tension and compression. In the proposed semi-analytical solution first a linear distribution of strain along the cross section is assumed and then employing Newton–Raphson method, an iterative numerical procedure is implemented to satisfy the classical equilibrium equations. The proposed method in this paper is applicable to any Euler–Bernoulli beam with any material and layup as well as any cross sectional geometry (with a plane of symmetry). To validate the results of the proposed model a homogeneous SMA beam is studied and the results are compared to the results of a 2D finite element (FE) solution. The results of the bending response of the beam are reported for both the symmetric and asymmetric behavior and also for both FE and semi-analytical solution. The results for both approaches are generally in good agreement with each other, and a maximum error of 3.6% is observed between FE and semi-analytical solution. Further, a Bi-layer composite beam consisting of two different SMAs is studied. Accordingly, Load-deflection, moment-curvature and also variation of the location of the neutral axis with respect to the center line of the cross-section is investigated. In one of the case studies there is 15% error in the prediction of the symmetric model with respect to the asymmetric model which is a more actual prediction, proves the importance of employing the asymmetric model. Moreover, for the same case the maximum deviation of the neutral axis with respect to the centroid is 17% for the asymmetric model and 24% for the symmetric model. Furthermore, hysteresis inner loops for the Bi-layer composite beam is investigated. The proposed formulation is appropriate for design or optimization of smart structures consisting of multilayer SMA components under bending where a large number of simulations are necessary.

Developing a semi-analytical model for thermomechanical response of SMA laminated beams, considering SMA asymmetric behavior

In this study, thermomechanical behavior of a beam reinforced with Shape Memory Alloy (SMA) elements is investigated (an elastic core with upper and bottom SMA layers). The improved Brinson constitutive model is used in order to account for the asymmetric behavior of SMA in tension and compression. Assuming a plane stress model for the beam reinforced with SMA layers, a semi-analytical formulation is proposed. This formulation has two parts: the first part consists of a linear distribution of strain along the cross section and the second part is an iterative numerical procedure to satisfy classical equilibrium equations. For the numerical procedure, bisection method is used. Moreover, the semi-analytical results are compared with a 2D Finite Element (FE) solution. The proposed model is applicable for Euler–Bernoulli beams with any material and geometric features. For example, for a composite beam including both superelastic and shape memory SMA layers the proposed model can be employed. Regarding the results, there is more than 95% agreement between the present numerical solutions and those of 2D FE method. Also, for the numeric examples discussed in this paper, it is shown that considering the asymmetry between the tension and compression behavior of SMA, leads to at least 25% change in the force–displacement plot with respect to the cases when considering symmetric behavior and also, there is 8% (of the width of the structure) shift in the location of the neutral axis from the centerline. In addition, hysteresis inner loops are investigated, using the asymmetric proposed model and compared against 2D FE solution, where results show a good agreement between two solutions.

A linear smoothed quadratic finite element for the analysis of laminated composite Reissner–Mindlin plates

It is well known that the high-order elements have significantly improved the accuracy of solutions in the traditional finite element analysis, but the performance of high-order elements is restricted by the shear-locking and distorted meshes for the plate problems. In this paper, a linear smoothed eight-node Reissner-Mindlin plate element (Q8 plate element) based on the first order shear deformation theory is developed for the static and free vibration analysis of laminated composite plates, the computation of the interior derivatives of shape function and isoparametric mapping can be removed. The strain matrices are modified with a linear smoothing technique by using the divergence theorem between the nodal shape functions and their derivatives in Taylor’s expansion. Moreover, the first order Taylor’s expansion is also employed for the construction of stiffness matrix to satisfy the linear strain distribution. Several numerical examples indicate that the novel Q8 plate element has good performance to alleviate the shear-locking phenomenon and improve the quality of the solutions with distorted meshes.

Development of a Simplified Procedure for the Determination of the Ultimate Load and Associated Spindle Torque of Propeller Blades

Blade deflection observed in experiments regarding the ultimate strength of controllable pitch propeller blades does not agree with the one that is assumed in the load case for the blade failure load currently defined in the Polar Class Rules. The reason is that a failure of the blade tip due to large plastic deformation is not taken into account, but can occur in reality if the load is applied relatively close to the trailing edge of skewed propellers. The plastic blade deformation can be computed by numerical simulations using an elastic-plastic material curve. These simulations, however, are time consuming and, hence, unpractical in the daily design process of propeller blades. Therefore, a simplified approach to determine the ultimate load and the associated spindle torque of the blade is presented. It requires elastic finite element (FE) analyses with varying point of load application, geometrical data, and a simplified material curve. The critical blade section is determined from highly stressed locations found in the elastic FE analysis. Afterward, the ultimate bending moment which the section can carry is determined by assuming a linear strain distribution over the thickness and a definite limit strain on the pressure surface. This allows the stress distribution to be transferred directly from the material curve. The ultimate load is determined by integrating the stress distribution over the section thickness and along the chord length, the latter in a simplified way. The approach is supported by various numerical simulations showing the fundamental elastic-plastic behavior of propeller blades and their response due to superimposed bending and torsional loads. In conclusion, the ultimate strength is mainly controlled by bending loads and the approach considers a failure of the blade tip, leading to more realistic spindle torques compared to the approach in the Polar Class Rules.

Development of a Simplified Procedure for the Determination of the Ultimate Load and Associated Spindle Torque of Propeller Blades

Blade deflection observed in experiments regarding the ultimate strength of controllable pitch propeller blades does not agree with the one that is assumed in the load case for the blade failure load currently defined in the Polar Class Rules. The reason is that a failure of the blade tip due to large plastic deformation is not taken into account, but can occur in reality if the load is applied relatively close to the trailing edge of skewed propellers. The plastic blade deformation can be computed by numerical simulations using an elastic-plastic material curve. These simulations, however, are time consuming and, hence, unpractical in the daily design process of propeller blades. Therefore, a simplified approach to determine the ultimate load and the associated spindle torque of the blade is presented. It requires elastic finite element (FE) analyses with varying point of load application, geometrical data, and a simplified material curve. The critical blade section is determined from highly stressed locations found in the elastic FE analysis. Afterward, the ultimate bending moment which the section can carry is determined by assuming a linear strain distribution over the thickness and a definite limit strain on the pressure surface. This allows the stress distribution to be transferred directly from the material curve. The ultimate load is determined by integrating the stress distribution over the section thickness and along the chord length, the latter in a simplified way. The approach is supported by various numerical simulations showing the fundamental elastic-plastic behavior of propeller blades and their response due to superimposed bending and torsional loads. In conclusion, the ultimate strength is mainly controlled by bending loads and the approach considers a failure of the blade tip, leading to more realistic spindle torques compared to the approach in the Polar Class Rules.

Nonlinear analysis of laminated shells with alternating stiff/soft lay-up

This paper proposes a multi-layer formulation for the nonlinear analysis of laminated shells with an alternating stiff/soft lay-up. The zigzag variation of planar displacements is taken into account by adding to the Reissner–Mindlin formulation a specific set of zigzag function which is effective for the considered lay-up. Furthermore, a piecewise linear through-thickness distribution of the material transverse shear strain is assumed, which agrees well with the real distribution. The proposed lamination model with a low-order nonlinear strain–displacement relationship is incorporated within a co-rotational framework for geometric nonlinear analysis, thus upgrading the low-order local element formulation to large displacement analysis with relative ease. In addition, a local shell system is employed for direct definition of the additional zigzag displacement fields and associated parameters, which are thus excluded from the large displacement co-rotational transformations. The application of the proposed laminated shell modelling approach is illustrated in this paper for a 9-noded co-rotational shell element, which utilises the Mixed Interpolation of Tensorial Components (MITC) method in the local system for overcoming locking effects. Several linear and nonlinear numerical examples of multi-layer shell structures with alternating stiff/soft lay-ups are used to illustrate the effectiveness and efficiency of the proposed modelling approach.

Exact Solution for Bending of Shape Memory Alloy Beams

Bending is an attractive mode of operation and application of shape memory alloys (SMA). To date numerical methods, such as the finite element method, have been used to model the coupled thermo-mechanical behavior of these alloys. In this article, an analytical approach is developed to calculate the exact solution of SMA beams deflection due to an external force. The approach is based on the assumption of linear distribution of strain along the height of a beam cross section. The approach is validated by comparing the results with the existing plastic solution and experimental data.

Method for tuning chirp ratio of fiber gratings without central wavelength shift

A method for tuning the chirp ratio of a fiber grating without the central wavelength shift is proposed by using a two-fixed-end compressive beam, which induces a linear strain distribution along the grating. This technique allows dynamic control of the grating’s chirp ratio by changing the displacement of the translation stage. The 3-dB bandwidth tuning range is from 6.52 to 13.5 nm when the grating is tuned in the broadening way, while the bandwidth tuning range is from 6.52 to 0.95 nm in the compressing way. The proposed method has potential applications for the dynamic dispersion compensation and the sensors of pressure and displacement, etc., by detecting the change of bandwidth information.

Application of Optical Fiber Sensing Real-Time Monitoring Technology Using in Ripley Landslide

Nowadays, fiber optic technology has been used in sensing. Using the distributed optical fiber sensing technology in the landslide monitoring, the linear strain distribution information of the whole landslide can be obtained, and adopting the Fiber Bragg Grating sensing technology in the landslide monitoring, the key pot strain and displacement information can be gained. This paper firstly reviews the basic principle of optical fiber sensing, and then describes the optical fiber sensing real-time monitoring system by combining with FBG technology, BOTDR technology, database technology and web server technology, and finally presents a field application experiment using the real-time monitoring system in Ripley landslide in Canada. The experiment indicated that the real-time monitoring system can be realized real-time monitoring of FBG and BOTDR for landslide, and the experience can be extended to other landslide.

Double linear strain distribution assumption of RC beam strengthened with external-bonded or near-surface mounted fiber reinforced plastic

Rehabilitation of existing structures with fiber reinforced plastic (FRP) has been growing in popularity because they offer superior performance in terms of resistance to corrosion and high specific stiffness. The strain coordination results of 34 reinforced concrete beams (four groups) strengthened with different methods were presented including external-bonded or near-surface mounted glass or carbon FRP or helical rib bar in order to study the strain coordination of the strengthening materials and steel rebar of RC beam. Because there is relative slipping between concrete and strengthening materials (SM), the strain of SM and steel rebar of RC beam satisfies the double linear strain distribution assumption, that is, the strain of longitudinal fiber parallel to the neutral axis of plated beam within the scope of effective height (h0) of the cross section is in direct proportion to the distance from the fiber to the neutral axis. The strain of SM and steel rebar satisfies the equation ɛGCH=βɛsteel, where the value of β is equal to 1.1–1.3 according to the test results.

Évaluation de la longueur du tendon du semi-tendineux en fonction de paramètres cliniques. Analyse et application clinique

The main concern of this paper is to establish an analytical solution giving the shear stress profile in a double-lap adhesive joint subjected to harmonic loading. The proposed model is based on the improved “shear-lag” model assuming a linear shear strain distribution in the adherends. The modified shear-lag model is equivalent to the simple shear-lag model when the shear stiffness of the adhesive is insignificant when compared to the shear stiffness of the adherends. We compared the modified and simple shear-lag models to a finite element model when both shear stiffnesses are comparable. It comes out that our modified shear-lag model is closer to the finite element model. Subsequently, we analysed results of our model in terms of newly proposed dimensionless parameters. This study was limited to frequencies lower than a critical defined one and to elastic behaviour of both adherends and adhesive.