Sheet Tension Research Articles

Mechanical Response and Microstructural Evolution of AZ31B Alloy Sheet in Uni-Axial Tension at Middle-Low Strain Rates and Temperatures

Mechanical Response and Microstructural Evolution of AZ31B Alloy Sheet in Uni-Axial Tension at Middle-Low Strain Rates and Temperatures

Effect of Magnetic Field on Deformation Behavior of a Steel Sheet in Uniaxial Tension

Abstract This paper discusses the effect of magnetic fields on the tensile properties of high-strength carbon-manganese steel sheets in uniaxial tension. An electromagnetic tool was designed and fabricated such that it produced a constant magnetic field of 0.35 T in the gauge length of a tensile specimen during testing. Experimental measurements of magnetic flux density distribution confirm the model, which is further validated with theoretical analysis. The tensile properties are examined with and without the effect of a magnetic field. A significant improvement is observed in tensile strength and normal anisotropy of the material because of the effect of the magnetic field. Samples were taken from the middle of specimens that were tested with 20 % plastic strain for microstructural investigations using the electron backscattered diffraction technique, and in all cases experiments were performed with and without the magnetic field. Geometrically necessary dislocations maps exhibiting the measure of dislocation density during plastic deformation show lesser accumulation of dislocations at the grain boundaries with the effect of the magnetic field, which indicates hindrance to the movement of dislocations as a result of the severe interaction of dislocations with the magnetic domains. The results also show an increase in grain size and the development of a weak texture for the tested specimens with the applied magnetic field as compared with the specimens tested without the magnetic field. The microstructural findings correlate with changes in the tensile properties.

Effect of U-Wrap Anchors on Flexural Behavior of Reinforced Concrete Beams Flexurally Strengthened with Externally Bonded CFRP Sheets

Externally bonded carbon fiber–reinforced polymer (CFRP) composites have been instrumental in the flexural strengthening of concrete structures. However, intermediate crack debonding from the concrete substrate is a governing failure mode in most externally bonded CFRP applications, limiting the composite strength utilization and deformability of a strengthened member. The addition of transverse U-wrap anchorage for longitudinally oriented CFRP sheet tension reinforcement can improve performance in terms of both deformability and ultimate strength. Due to the scarcity of experimental data, design guidance for U-wrap anchorage to mitigate intermediate crack debonding is lacking. The results of flexural tests on large-scale reinforced concrete beams strengthened in flexure with externally bonded CFRP anchored with U-wraps are reported in this paper. Test results indicate that U-wraps can increase the strain utilization of longitudinal CFRP between 40% and 57%, while also mitigating the intermediate crack debonding failure mode. Varying the ratio of the area of U-wrap anchorage to area of flexural CFRP had little effect on the beams’ flexural capacity.

Modelling moving contact lines on inextensible elastic sheets in two dimensions

Elastocapillarity has attracted increasing interest in recent years due to its important roles in many industrial applications. In this work, we derive a thermodynamically consistent continuum model for the dynamics of two immiscible fluids on a thin and inextensible elastic sheet in two dimensions. With the sheet being modelled by a deformable curve with the Wilmore energy and local inextensibility constraint, we derive a two-phase hydrodynamics model with the interfacial and boundary conditions consistent with the second law of thermodynamics. In particular, the boundary conditions on the sheet and at the moving contact line take the form of force balances involving the fluid stress, surface tensions, the sheet bending force and sheet tension, as well as friction forces arising from the slip of fluids on the sheet. The resulting model obeys an energy dissipation law. To demonstrate its capability of modelling complex elastocapillary interactions, we consider two applications: (1) the relaxation dynamics of a droplet on an elastic sheet and (2) the transport of a droplet driven by bendotaxis in a channel bounded by elastic sheets. Numerical solutions for the coupled fluid–sheet dynamics are obtained using the finite element method. The detailed information provided by the full hydrodynamics model allows us to better understand the dynamical processes as compared to other simplified models that were used in previous work.

Origins of improved elongation to fracture in cyclic bending under tension of AA6022-T4 sheets as revealed using crystal plasticity modeling

Plastic instabilities can be suppressed by imposing cyclic bending during tension to increase elongation-to-fracture (ETF) of metallic sheets. This work is a combined experimental and modeling study into the origins of the improved ETF in cyclic bending during tension facilitated by a continuous-bending-under-tension (CBT) test. Load-displacement is measured during the CBT test under an optimized combination of band depth and pull speed process parameters for aluminum alloy (AA) 6022-T4. Monotonic and load reversal response of the alloy is also characterized under strain histories that resemble the history in CBT. Electron-backscattered diffraction and neutron diffraction are employed to characterize the initial microstructure and texture evolution of the alloy after CBT and simple tension (ST). Monotonic, load reversal, and texture data are used to adjust and verify the parameters of an elasto-plastic self-consistent crystal plasticity-based finite element model for simulating CBT. Additionally, a flow stress curve based on a bulge test is used to calibrate the model to capture the large strain hardening behavior of the alloy. The model is then used to simulate the CBT test while predicting the load-displacement and texture evolution data. The model successfully reproduced the succession of spikes and plateaus during CBT validating the prediction of the extrapolated hardening. After the validation, the development of stress and strain is probed through the sheet thickness to determine the underlying profiles as well as along the sheet to elucidate the location and onset of failure axially. The model reveals the development of more strain and dislocation density at the surface then at the center of the sheet and correctly predicts the strain localizations. Comparisons of texture evolution and mechanical fields developed in ST and CBT reveal very similar mechanical states in the sheet. These results in combination with experimental results suggest that the origins of improved ETF during CBT pertain primarily to the incremental deformation structural effects and secondary to the microstructural evolution effects.

Acoustic emission monitoring for necking in sheet metal forming

There is extensive evidence in the literature that plastic deformation of metals is associated with an increase in Acoustic Emission (AE) activity. Thus, AE measurement techniques have the potential to monitor a forming process in real time and provide a signal for feedback control, to exploit optimum formability. In this work, custom-made AE sensors employing piezoelectric crystals are implemented to measure the emitted acoustic signal during uniaxial tension and cup drawing tests of an AA6013-T4 aluminum sheet (1.5 mm thick). The uniaxial tension tests are conducted with two AE sensors clamped to each end of the specimen gage section, along with full-field surface strain measurement using Digital Image Correlation (DIC) techniques. The AE signals along with the interrogation of the DIC images reveal that the maximum AE amplitude corresponds to the onset of diffuse necking, i.e., when the strain field starts to become spatially inhomogeneous. Interestingly, this onset occurs before the maximum force is attained. Comparing these observations to a model of dislocation activity supports the notion that dislocation is the main driver of AE activity. With these findings, AE measurements are performed in a cup drawing process where a custom-made Marciniak-type punch incorporates three AE sensors. These sensors are used to triangulate and determine the location of necking and eminent fracture based on the time difference of arriving signals to each sensor. The results from the cup drawing tests show that AE signals can identify the onset of necking and accurately predict the location of necking and fracture.

Cyclic bending under tension of alloy AZ31 sheets: Influence on elongation-to-fracture and strength

This paper describes the main results from an experimental investigation into the consequence of cyclic bending under tension on elongation-to-fracture (ETF) and strength of AZ31 sheets. The deformation is imparted on test specimens of the alloy using a recently built continuous-bending-under-tension (CBT) apparatus conceived to increase ETF relative to simple tension (ST). The apparatus pulls the specimen in tension with a certain velocity while the specimen reciprocates through a set of three rollers, which impart a given amount of bending. The parameter space consisting of bending depth, crosshead velocity, and sheet thickness is explored to achieve the greatest ETF for the alloy. However, only moderate improvements in ETF are obtained. The small improvements are attributed to the relatively uniform elongation of the alloy during both CBT and ST with a small amount of the remaining ductility to deplete throughout the sheet by CBT after exhausting the uniform elongation. Measurements of the grain structure and texture evolution using electron-backscattered diffraction and neutron diffraction reveal slip dominated deformation with some twinning followed by de-twinning. The behavior of the alloy upon CBT processing to a certain number of CBT cycles followed by heat treatments (HT) is also investigated to achieve tradeoffs in strength and ductility. Results and insights from these investigations are presented and discussed. Significantly, it is shown that the strength of the alloy can be increased for over 30% while preserving at least 5% of its ductility.

Analysis of Interfacial Mechanical Properties of Steel Beams Strengthened with CFRP Sheets under Temperature and Creep.

Under the combined action of temperature and creep of CFRP (Carbon Fiber Reinforced Polymer) sheet, the interface between CFRP sheet and steel beams which are strengthened with CFRP sheet will produce relative slip. This slip will affect the interface interaction, reduce the bearing capacity and stiffness of members as well as increase the deformation. In this paper, the elastic method is used to introduce the creep effect of CFRP sheet and the temperature effect of steel beam. The calculation formulas of interface slip between CFRP sheet and steel beam, CFRP sheet tension and steel beam deformation under the combined action of temperature and CFRP creep are established. The accuracy of the analytical formula is verified by finite element analysis using the software ABAQUS. The results show that the CFRP sheet tension is smallest at the beam end while largest at the middle of the span. When the stiffness reaches about 3 ka, CFRP sheet tension basically does not change. When the temperature increases by 5 °C, the tensile force of CFRP sheet increases by about 3.7 kN, 1.8 kN and 2.3 kN, respectively. The increase of stiffness under creep has little effect on the change of CFRP sheet tension. The deformation is largest in the middle of the span while smallest at the beam end. Stiffness, temperature (5–25 °C), CFRP thickness and stiffness under creep have little effect on deformation. When the load increases by 5 kN under creep, the deformation increases by about 2.2 × 10−7 mm, 1.8 × 10−6 mm and 9.4 × 10−7 mm, respectively.

Linear instability of a liquid sheet in a transverse standing acoustic field

This work examines the instability of a plane liquid sheet under the action of a transverse acoustic field. The mechanical definition of the acoustic field is introduced first, and the Floquet theory is applied to derive the dispersion equation and dispersion curve. The dominant instability mechanism of each unstable region on the dispersion curve is distinguished by calculating the oscillation frequencies of the disturbance waves. Next, the parameters within the dispersion equation are set as variables to analyze the development of the instability mechanisms of the unstable regions on the dispersion curve and the oscillation modes on the two surfaces of the liquid sheet. The results prove that the distribution of unstable regions can be affected by the amplitude and frequency of the acoustic field, the viscosity and surface tension of the liquid sheet, and the density ratio of the two gas–liquid phases. Variation in the thickness of the liquid sheet causes development and competition within the oscillation modes, which were found to be related to the development of the instability mechanism. Such evolutionary competition between the sinuous and the varicose oscillation modes was also reflected in the experimental study, where it was observed that the disturbance wave has the characteristics of Faraday waves.

Nonlinear Boussinesq and Rosseland approximations on 3D flow in an interruption of Ternary nanoparticles with various shapes of densities and conductivity properties

<abstract> <p>In current days, hybrid models have become more essential in a wide range of systems, including medical treatment, aerosol particle handling, laboratory instrument design, industry and naval academia, and more. The influence of linear, nonlinear, and quadratic Rosseland approximations on 3D flow behavior was explored in the presence of Fourier fluxes and Boussinesq quadratic thermal oscillations. Ternary hybrid nanoparticles of different shapes and densities were also included. Using the necessary transformation, the resulting partial differential system is transformed into a governing ordinary differential system, and the solution is then furnished with two mixed compositions (Case-Ⅰ and Case-Ⅱ). Combination one looked at aluminum oxide (Platelet), graphene (Cylindrical), and carbon nanotubes (Spherical), whereas mixture two looked at copper (Cylindrical), copper oxide (Spherical), and silver oxide (Platelet). Many changes in two mixture compositions, as well as linear, quadratic, and nonlinear thermal radiation situations of the flow, are discovered. Case-1 ternary combinations have a wider temperature distribution than Case-2 ternary mixtures. Carbon nanotubes (Spherical), graphene (Cylindrical), and aluminum oxide (Platelet) exhibit stronger conductivity than copper oxide (Spherical), copper (Cylindrical), and silver oxide (Platelet) in Case 1. (Platelet). In copper oxide (Spherical), copper (Cylindrical), and silver (Platelet) compositions, the friction factor coefficient is much higher. The combination of liquids is of great importance in various systems such as medical treatment, manufacturing, experimental instrument design, aerosol particle handling and naval academies, etc. Roseland's quadratic and linear approximation of three-dimensional flow characteristics with the existence of Boussinesq quadratic buoyancy and thermal variation. In addition, we combine tertiary solid nanoparticles with different shapes and densities. In many practical applications such as the plastics manufacturing and polymer industry, the temperature difference is remarkably large, causing the density of the working fluid to vary non-linearly with temperature. Therefore, the nonlinear Boussinesq (NBA) approximation cannot be ignored, since it greatly affects the flow and heat transport characteristics of the working fluid. Here, the flow of non-Newtonian elastomers is controlled by the tension of an elastic sheet subjected to NBA and the quadratic form of the Rosseland thermal radiation is studied.</p> </abstract>

Performance of Dual Viscoelastic Wave Barrier System with Unequal Draft

This work investigated the interaction of surface waves with a dual-barrier system comprising two vertical viscoelastic thin sheets with variable spacing in finite water depth without preassumption of its dynamic behavior. The two sheets were assumed to be made of the same material and under different tensions, and both penetrated into the water depth partially with unequal drafts. The viscoelastic behavior of the sheet material, which accounts for its elastic deformation and internal energy dissipation, is represented by the Voigt model. Using the eigenfunction expansion and least square determination, analytical solutions were obtained for the dual-barrier system, including the asymptotic case of a single sheet when the second sheet draft approaches zero. Subsequently, the effects of hydroelastic regimes and viscoelasticity were examined. With the single-sheet system, the wave transmission decreases as the tensioned sheet shifts from platelike to membranelike, and its material has higher internal energy dissipation (i.e., viscosity). When the size of the bottom opening increases to a gap ratio larger than ∼0.6, however, the wave transmission becomes dominated by the diffraction through the gap, and the influence of sheet material characteristics is no longer significant. With the double-sheet system, the results show that the performance of the wave barrier improves significantly by the presence of the second sheet, even with a small draft. Complex resonating patterns can be observed with increase in sheet spacing for the dual-barrier system, which reduces the wave transmission. The presence of viscosity of the double-sheet system dampens the resonance, but also reduces the wave transmission by itself through the viscous dissipation of the incident wave energy.

Tension, compression, and shear behavior of advanced sheet molding compound (A-SMC): Multi-scale damage analysis and strain rate effect

Advanced sheet molding compounds (A-SMC) are a new generation of alternative materials to steels for applying in automotive structures. It contains a thermoset matrix involving mineral charge (CaCO 3 ) reinforced with a high fraction of discontinuous bundles of glass fibers (around 50% in mass) compared to the other types of SMC composites. The crashworthiness evaluation and multi-scale mechanical characterizations of this automotive material is essential. In this study, at first, the microstructure of A-SMC composite was investigated by Scanning Electron Microscopy (SEM), ultrasonic analysis, and X-ray micro-tomography. Two configurations’ plates of Randomly Oriented (RO) and Highly Oriented (HO) were analyzed under quasi-static tension, compression, and shear loadings. To study the effect of fiber orientation, for HO plate, two fiber directions were chosen: HO-0° (parallel to the Mold Flow Direction (MFD)) and HO-90° (perpendicular to the MFD). Strain rate effect (from 0.25 s −1 to 10 s −1 ) on shear properties and visco-damage behavior of A-SMC composite has been studied. For this purpose, a new setup for shear testing was designed after optimization via ABAQUS FE code to achieve constant strain rate. HO-0° samples represented higher strength in tension and compression loadings, unlike shear loading compared to RO and HO-90° samples. A multi-scale damage study confirmed that predominant damage mechanism is decohesion at fiber/matrix interface under tension, compression, and shear loadings.

Stabilisation of compliant floating platforms with sheet barriers under wave action

Excessive surface displacement of a compliant floating platform made of interconnected modular floats due to wave action can cause damage to the utility system (solar power, etc.) or endanger the safety of the service personnel on top. This study examines the use of a vertical tensioned sheet barrier installed in front of the floating platform for its stablisation under incident waves. Two configurations are investigated, namely finite and semi-infinite, representing a medium and large size platform respectively. Analytical analysis is performed without the pre-assumption of the dynamic behavior of the sheet barrier, and solutions are obtained using the eigenfunction expansion together with the least square method. For both configurations, the wave transmission to the floating platform reduces when the dynamic of the sheet barrier shifts from plate-like to membrane-like with increasing tension and also deeper draft and larger viscosity, which in turn reduces the platform displacement and the hydrodynamic pressure force on the platform. Overall, the results in the present study show that the installation of the barrier in front of the platform in the membrane-like hydroelastic regime with a penetration ratio more than ∼0.4 can significantly improve the stability of the compliant floating platform in the coastal environment.

Advanced Design of Steel to Timber Bolted Joints

AbstractThe paper is focused on the topic of steel to timber joints with inserted steel sheet. These joints have significantly higher load‐bearing capacity compared to the classic timber joints with timber parts only. In order to study the mechanical behaviour of these joints with inserted steel sheet in tension, experiments were prepared at Czech Technical University in Prague, and the numerical model was created using the ABAQUS code. The test specimens were designed for the most accurate approximation of realistically designed structures based on the recommendation given in the standard. The eight different specimens varied in the diameter of the fastener, the size of the steel washers, the number of rows of fasteners, their spacing and the strength class of the timber. For this experimental study, a set of timber of the C24 strength class and glue‐laminated timber of GL24h strength class was prepared. Results of experimental work cover failure modes of timber and diagrams of displacement in control points. In the model, timber was described as an orthotropic elastic material with defined nine independent elastic constants. Contact bonds were defined between the bolts and the timber member as well as between the bolts and the steel based on experiments. Part of the work is dedicated to the verification and validation of the numerical model. The verification of the numerical model was based on the results of the analytical model given in the current design standard. The validation approved the good agreement of the numerical model with results of tension tests, with maximal deviation up to 19 %.

Uniaxial tension of Kevlar-filled EPDM rubber sheet: effect of fiber orientation and distribution

Uniaxial tension of Kevlar-filled EPDM rubber sheet: effect of fiber orientation and distribution

Poking and bulging of suspended thin sheets: Slippage, instabilities, and metrology

Measurement of in-plane elasticity of thin sheets often leverages out-of-plane poking or bulging, also known as indentation or bulge tests. For linear elastic sheets, a load-cubic deflection relation has been frequently assumed so that the stiffness of the sheet could be readily extracted. However, we find that recent results of indentation and bulge tests on 2D materials do not support the assumption, which can be attributed to the slippage of 2D materials against their supporting substrates. Besides, the interfacial slippage could cause instabilities in the sheet such as radial wrinkles in suspended region, with finite lengths. To gain a quantitative understanding, we assume constant interfacial shear traction and study the wrinkling extent and the effective stiffness of thin sheets upon poking and bulging. We identify a single dimensionless parameter governing these mechanical responses—the sliding number—defined by comparing the sheet tension (that drives the slippage) with the interfacial traction (that resists the slippage). We discuss several useful asymptotic behaviors emerging at small and large sliding numbers. These understandings inspire when the effect of the interfacial slippage (as well as other substrate-associated subtleties) can be neglected in these tests. For instance, traditional bulge and indentation tests suffer from complexities caused by the slippage, pretension, Poisson's ratio, substrate roughness, and various interfacial traction-separation laws. Based on such understandings, we propose a simple poking/bulging methodology immune to all of these complexities, enabling an alternative way to measure the sheet stiffness.

A pressure-coupled Drucker function for plasticity and fracture modelling of AA5182

In this paper, a pressure-coupled Drucker function is proposed to model the plastic deformation and fracture from shear to plane strain tension of AA5182 sheet. Experiments are conducted for AA5182 in shear, uniaxial tension and plane strain tension, and the force-stroke curves are measured during the tests. The plastic deformation is modeled by the Drucker function. The Drucker function is modified to consider the pressure effect for fracture limit stress prediction of the alloy. The pressure-coupled Drucker function for plasticity and fracture is calibrated by an inverse engineering approach. The calibrated plasticity models are then applied to numerical prediction of plastic deformation of the alloy under various loading conditions. It is observed that the pressure coupled Drucker function accurately describes the plastic deformation under large plastic deformation as well as the onset of ductile fracture under these loading conditions.

Size effects affected uniaxial tensile properties and formability in rubber pad microforming process of pure nickel thin sheets

The size effects on plastic deformation behaviors of metal thin sheets have a profound impact on the development of microforming process. In this study, the deformation and forming behaviors of pure nickel thin sheets with t/d < 2 (thickness t /average grain size d) were demonstrated by micro tensile tests and rubber pad forming tests. The flow stress decreased evidently and the relationship between true stress and d−0.5 deviated from the Hall-Patch relationship when t/d <1.2 and the surface layer model is no longer applicable. Based on Hollomon equation, a new constitutive equation considering the effect of t/d was established to predict both the ductility and strength in micro tension of thin sheets. The experimental and calculated data matched well. The fracture mechanism and deformation behavior changed significantly when t/d < 1.2 based on the fracture characteristics and morphologies. The experimental results of rubber pad forming tests of microchannel indicated that the thickness thinning and surface roughening behaviors became more severe when t/d < 1.2 owing to strongly localized and inhomogeneous deformation behaviors. Local severe deformation easily occurs at the position where there is only one grain across the thickness direction. And the micro-part is likely to fracture at this location, which should be avoided as much as possible in the manufacturing process.

Effects of surface tension of graphene sheet on impact and rebound behavior of colliding nanoparticle

Abstract In the present work, the classical theory of plate, the von Karman nonlinear theory and the nonlocal theory of elasticity are adopted to analyze the impact between a nanoparticle and an orthotropic rectangular nanoplate with surface tensions. Employing an analytical contact law to explain the von der Waals forces, the equations of motion are solved for the indenter-plate system. As an application, this approach is taken for a nanoparticle colliding with a simply supported single-layered graphene sheet and the rebound behavior of the particle is discussed. Then, the influences of surface tension and the nonlocal parameter on the dynamics response of the particle are investigated. When enough surface tension is applied, the membrane theory gives an acceptable estimate for the restitution behavior of the indenter otherwise, the estimates are associated with a maximum error of 15%. The effects of disregarding the flexural stiffness of the graphene sheet and ignoring the attraction part of the von der Waals forces are also examined. Studying the dimensional effects on the system behavior revealed that optimum dimensions of the plate maximize its capacity for energy absorption when it is employed as an energy absorber against colliding particles. Finally, a contact law for large nanoparticles is proposed and then is applied to an example including an SLGS colliding with a multi-atom indenter.

Vibration measurements of paper prints and the data analysis

Abstract This paper discusses about the scatter of the intensity of vibration signals of paper prints and analyses their mechanical parameters applying the theory of covariance functions. It is an important practical problem, before starting printing process of colour prints, expecting the correct position of fixed raster points, to adjust the paper sheet tension between printing machine sections. The results of measuring the intensity of vibration signals at the fixed points were presented on a time scale in the form of arrays (matrices). The estimates of cross-covariance functions between digital arrays result in measuring the intensity of vibrations, and the estimates of auto-covariance functions of single arrays were calculated upon changing the quantization interval on the time scale. Application of normed auto-covariance and cross-covariance functions enables reduction of preprinting experimental measurements, which saves time (what is actual for industry). Tension force depends on the mechanical properties of the paper sheet and print. These characteristics depend on paper type, layers of printing colors and positioning of the coverage. In the calculation, the software Matlab 7 in batch statement environment was applied.