Loading direction-dependent shear behavior at different temperatures of single-layer chiral graphene sheets

The loading direction-dependent shear behavior of single-layer chiral graphene sheets at different temperatures is studied by molecular dynamics(MD) simulations.Our results show that the shear properties(such as shear stress–strain curves, buckling strains, and failure strains) of chiral graphene sheets strongly depend on the loading direction due to the structural asymmetry. The maximum values of both the critical buckling shear strain and the failure strain under positive shear deformation can be around 1.4 times higher than those under negative shear deformation. For a given chiral graphene sheet, both its failure strain and failure stress decrease with increasing temperature. In particular, the amplitude to wavelength ratio of wrinkles for different chiral graphene sheets under shear deformation using present MD simulations agrees well with that from the existing theory. These findings provide physical insights into the origins of the loading direction-dependent shear behavior of chiral graphene sheets and their potential applications in nanodevices.     

Tension–compression asymmetry of phosphor bronze for electronic parts and its effect on bending behavior

In-plane tension and compression experiments on copper alloy sheets (phosphor bronze) and 6000 series aluminum alloy sheets (AA6016-T4) were conducted using a specially designed testing apparatus. The apparatus is equipped with comb-type dies so that stress–strain curves of a sheet specimen subjected to tension followed by compression, and vice versa, can be measured without buckling of the specimen, as well as those for monotonic tension and compression. A difference was observed in the flow stresses between tension and compression for the as-received copper alloy, but not for the aluminum alloy. Moreover, stress reversal tests, such as tension followed by compression and compression followed by tension, were carried out in order to measure the Bauschinger effect. In the second part of the experiment, bending moment–curvature diagrams were measured for the as-received and pre-stretched specimens. The bending moment–curvature diagrams were compared with those calculated using the stress–strain curves obtained from the tension–compression tests, and were in good agreement with those calculated with the tension–compression asymmetry and the Bauschinger effect correctly reproduced.     

Sandwich column buckling – A hyperelastic formulation

The macro-buckling equations for a sandwich column are developed. A layer-wise Timoshenko beam displacement approximation is assumed. The constitutive relationships and equilibrium equations for the core and face sheets are derived using a consistent hyperelastic neo-Hookean formulation. The derivations in this paper are consistent with that of Haringx’s and Reissner’s proposal for beam actions. The buckling formulation includes the axial deformation prior to buckling and the transverse shear deformation of the core and face sheets. The buckling equations derived agree with the equation of [Allen, H.G., 1969. Analysis and Design of Structural Sandwich Panels, Pergamon, Oxford] for thick faces but are also applicable to any ratio of face sheet to core thickness and material properties. The formulation is compared to experimental results for sandwich columns and shows good comparison except for very short columns. The formulation is also compared to the buckling experimental results for short rubber rods and also compared well. The formulation does not predict a shear buckling mode.     

A combined necking and shear localization analysis for aluminum sheets under biaxial stretching conditions

A combined necking and shear localization analysis is adopted to model the failures of two aluminum sheets, AA5754 and AA6111, under biaxial stretching conditions. The approach is based on the assumption that the reduction of thickness or the necking mode is modeled by a plane stress formulation and the final failure mode of shear localization is modeled by a generalized plane strain formulation. The sheet material is modeled by an elastic-viscoplastic constitutive relation that accounts for the potential surface curvature, material plastic anisotropy, material rate sensitivity, and the softening due to the nucleation, growth, and coalescence of microvoids. Specifically, the necking/shear failure of the aluminum sheets is modeled under uniaxial tension, plane strain tension and equal biaxial tension. The results based on the mechanics model presented in this paper are in agreement with those based on the forming limit diagrams (FLDs) and tensile tests. When the necking mode is suppressed, the failure strains are also determined under plane strain conditions. These failure strains can be used as guidances for estimation of the surface failure strains on the stretching sides of the aluminum sheets under plane strain bending conditions. The estimated surface failure strains are higher than the failure strains of the forming limit diagrams under plane strain stretching conditions. The results are consistent with experimental observations where the surface failure strains of the aluminum sheets increase significantly on the stretching sides of the sheets under bending conditions. The results also indicate that when a considerable amount of necking is observed for a sheet metal under stretching conditions, the surface failure strains on the stretching sides of the sheet metal under bending conditions can be significantly higher.     

An experimental and numerical investigation of different shear test configurations for sheet metal characterization

Simple shear tests are widely used for material characterization especially for sheet metals to achieve large deformations without plastic instability. This work describes three different shear tests for sheet metals in order to enhance the knowledge of the material behavior under shear conditions. The test setups are different in terms of the specimen geometry and the fixtures. A shear test setup as proposed by Miyauchi, according to the ASTM standard sample, as well as an in-plane torsion test are compared in this study. A detailed analysis of the experimental strain distribution measured by digital image correlation is discussed for each test. Finite element simulations are carried out to evaluate the effect of specimen geometries on the stress distributions in the shear zones. The experimental macroscopic flow stress vs. strain behavior shows no significant influence of the specimen geometry when similar strain measurements and evaluation schemes are used. Minor differences in terms of the stress distribution in the shear zone can be detected in the numerical results. This work attempts to give a unique overview and a detailed study of the most commonly used shear tests for sheet metal characterization. It also provides information on the applicability of each test for the observation of the material behavior under shear stress with a view to material modeling for finite element simulations.     

微尺度金属薄膜屈曲稳定性的实验研究

微尺度金属薄膜的脱粘和屈曲严重影响着膜基结构的性能和使用寿命。本文对微尺度的金属铜薄膜在残余应力和外部压力共同作用下的脱粘屈曲和后屈曲模式进行了研究,用自行设计的单轴对称加载装置进行压力加载,用一台光学显微镜观察薄膜表面的屈曲形貌。在外力作用下薄膜会出现垂直于加载方向的直线型屈曲,但在外力卸载过程中该屈曲并不稳定,会演化成电话线型屈曲,完全卸载后形成泡状屈曲。再次加载后,恢复到直线型屈曲。研究表明:直线型屈曲的不稳定现象主要与薄膜的残余应力、基底的泊松比以及薄膜沿纵向与横向的应力比有关。     

Buckling analysis of plain knitted fabric sheets under simple shear in an arbitrary direction

Knitting structures make plain knitted fabric different from woven fabric. With the aid of a micro-constitutive model the buckling of a knitted fabric sheet subjected to simple shear in an arbitrary direction is investigated. The large deformation of the fabric sheet in its critical configuration is considered. The theory of stability for finite deformations is applied to the analysis. All the stress boundary conditions of the knitted fabric sheet are satisfied. An equation for determining the buckling direction angle is derived. It is shown that there are two possible buckling modes: a flexural mode and a barreling mode. The buckling conditions for the two modes are also obtained, respectively. A numerical calculation reveals that only the flexural mode can occur, which agrees with experimental observations.     

Plasticity of formable all-metal sandwich sheets: Virtual experiments and constitutive modeling

The mechanical behavior of a metallic sandwich sheet material composed of two flat face sheets and two bi-directionally corrugated core layers is analyzed in detail. The manufacturing of the sandwich material is simulated to obtain a detailed unit cell model which accounts for the non-uniform thickness distribution and residual stresses associated with the stamping of the core layers. Virtual experiments are performed by subjecting the unit cell model to various combinations of bi-axial in-plane loading including the special cases of uniaxial tension, uniaxial compression, equi-biaxial tension and shear. The results demonstrate that the core structure’s contribution to the in-plane load carrying capacity of the sandwich sheet material is similar to that of the face sheets. The numerical results are also used to identify the effective yield surface and hardening response of both the core layer and the face sheets. An anisotropic yield function with linear pressure dependency is proposed to approximate the equal-plastic work surfaces for the core structure and face sheets. Furthermore, a new two-surface model with non-linear interpolation based on plastic work density is presented to describe the observed combined isotropic-distortional hardening of the core structure.     

Column buckling with shear deformations—A hyperelastic formulation

Column constitutive relationships and buckling equations are derived using a consistent hyperelastic neo-Hookean formulation. It is shown that the Mandel stress tensor provides the most concise representation for stress components. The analogous definitions for uniaxial beam plane stress and plane strain for large deformations are established by examining the virtual work equations. Anticlastic transverse curvature of the beam cross-section is incorporated when plane stress or thick beam dimensions are assumed. Column buckling equations which allow for shear and axial deformations are derived using the positive definiteness of the second order work. The buckling equations agree with the equation derived by Haringx and are extended to incorporate anticlastic transverse curvature which is important for low slenderness, high buckling modes and with increasing width to thickness ratio. The work in this paper does not support the existence of a shear buckling mode for straight prismatic columns made of an isotropic material.     

Optomechanical soft metamaterials

We present a new type of optomechanical soft metamaterials, which is different from conventional mechan-ical metamaterials, in that they are simple isotropic and homogenous materials without resorting to any complex nano/microstructures. This metamaterial is unique in the sense that its responses to uniaxial forcing can be tailored by programmed laser inputs to manifest different nonlinear con-stitutive behaviors, such as monotonic, S-shape, plateau, and non-monotonic snapping performance. To demonstrate the novel metamaterial, a thin sheet of soft material impinged by two counterpropagating lasers along its thickness direction and stretched by an in-plane tensile mechanical force is con-sidered. A theoretical model is formulated to characterize the resulting optomechanical behavior of the thin sheet by com-bining the nonlinear elasticity theory of soft materials and the optical radiation stress theory. The optical radiation stresses predicted by the proposed model are validated by simula-tions based on the method of finite elements. Programmed optomechanical behaviors are subsequently explored using the validated model under different initial sheet thicknesses and different optical inputs, and the first-and second-order tangential stiffness of the metamaterial are used to plot the phase diagram of its nonlinear constitutive behaviors. The proposed optomechanical soft metamaterial shows great potential in biological medicine, microfluidic manipulation, and other fields.     

Continuous, large strain, tension/compression testing of sheet material

Modeling sheet metal forming operations requires understanding of the plastic behavior of sheet alloys along non-proportional strain paths. Measurement of hardening under reversed uniaxial loading is of particular interest because of its simplicity of interpretation and its application to material elements drawn over a die radius. However, the compressive strain range attainable with conventional tests of this type is severely limited by buckling. A new method has been developed and optimized employing a simple device, a special specimen geometry, and corrections for friction and off-axis loading. Continuous strain reversal tests have been carried out to compressive strains greater than 0.20 following the guidelines provided for optimizing the test. The breadth of application of the technique has been demonstrated by preliminary tests to reveal the nature of the Bauschinger effect, room-temperature creep, and anelasticity after strain reversals in commercial sheet alloys.     

An extended Marciniak-Kuczynski model for anisotropic sheet subjected to monotonic strain paths with through-thickness shear

Some metal sheet forming processes may induce an amount of plastic shear over the sheet thickness. This paper investigates how formability of anisotropic sheet metal is affected by such through-thickness shear (TTS). The Marciniak-Kuczynski (MK) model framework, a commonly used analytical tool to predict the limit of sheet formability due to the onset of localized necking, is extended in this paper in order to explicitly account for TTS in anisotropic metal sheets. It is a continuation of previous work by the present authors (Eyckens et al., 2009), in which TTS is incorporated for isotropic sheet. This is achieved by the introduction of additional force equilibrium and geometric compatibility equations that govern the connection between matrix and groove in the MK model. Furthermore, in order to integrate plastic anisotropy, a material reference frame available in recent literature is incorporated, as well as a particular model for anisotropic yielding that relies on virtual testing of anisotropic properties (Facet plastic potential), since out-of-plane anisotropy related to TTS cannot be measured experimentally.It is found that formability may be increased by TTS, depending on the direction onto which it is imposed by the forming process. TTS is thus a relevant aspect of the formability in, for instance, sheet forming processes in which sliding contact with friction between sheets and forming tools occur.     

Anisotropic Hardening of Sheet Metals at Elevated Temperature: Tension-Compressions Test Development and Validation

New test equipment has been developed to measure the in-plane cyclic behavior of sheet metals at elevated temperatures. The tester has clamping dies with adjustable side force to prevent the sheet specimens from buckling during compressive loading. In addition to the room temperature experiment, cartridge type heaters are inserted in the clamping dies so that the specimen can be heated up to 400 °C during the cyclic tests. For the strain measurement, a non-contact type laser extensometer is used. In order to validate the newly developed test device, the tension-compression (and compression-tension) tests under pre-strains and various temperatures have been performed. As model materials, the aluminum alloy sheet which exhibits a large Bauschinger effect and the magnesium alloy sheet which exhibits different amounts of asymmetry under cyclic loading are used. The developed device can be well-suited to measure the cyclic material behavior, especially the anisotropic and asymmetric hardening of light-weight materials.     

Stretch-induced stress patterns and wrinkles in hyperelastic thin sheets

Wrinkles are commonly observed in stretched thin sheets and membranes. This paper presents a numerical study on stretch-induced wrinkling of hyperelastic thin sheets based on nonlinear finite element analyses. The model problem is set up for uniaxial stretching of a rectangular sheet with two clamped ends and two free edges. A two-dimensional stress analysis is performed first under the plane-stress condition to determine stretch-induced stress distribution patterns in the elastic sheets, assuming no wrinkles. As a prerequisite for wrinkling, development of compressive stresses in the transverse direction is found to depend on both the length-to-width aspect ratio of the sheet and the applied tensile strain in the longitudinal direction. A phase diagram is constructed with four different distribution patterns of the stretch-induced compressive stresses, spanning a wide range of aspect ratio and tensile strain. Next, an eigenvalue analysis is performed to find the potential buckling modes of the elastic sheet under the prescribed boundary conditions. Finally, a nonlinear post-buckling analysis is performed to show evolution of stretch-induced wrinkles. In addition to the aspect ratio and tensile strain, it is found that the critical condition for wrinkling and the post-buckling behavior both depend sensitively on the sheet thickness. In general, wrinkles form only when both the magnitude and the distribution area of the compressive stresses are sufficiently large. The wrinkle wavelength decreases with increasing strain, in good agreement with the prediction by a scaling analysis. However, as the tensile strain increases, the wrinkle amplitude first increases and then decreases, eventually flattened beyond a moderately large critical strain, in contrast to the scaling analysis.     

Experimental and numerical investigation of combined isotropic-kinematic hardening behavior of sheet metals

To prevent a sheet specimen from buckling subjected to a tension-compression cyclic loading, a new fixture has been developed to use with a regular tensile-compression machine. The novelty of this device lies in 4-block wedge design with pre-loaded springs. This design allows blocks to freely move in the vertical direction while providing the normal support to the entire length of the specimen during the tension-compression cycle. The entire test is easy to setup, which is another advantage of this design. In order to measure the strain accurately, the transmission type laser extensometer was utilized together with the implementation of double-side fins in the specimen. Experimental results of tension-compression tests are presented followed by a review of existing testing methods. In order to describe the accurate cyclic tension-compression behavior, the combined isotropic-kinematic hardening law based on the modified Chaboche model and the practical two-surface model based on Dafalias-Popov and Krieg models have been modified in this work, considering the permanent softening behavior during reverse loading and the non-symmetric behavior during reloading. Through tension-compression tests, the material characterization has been performed for three base materials, BH180, DP600 steels and AA6111-T4 sheets.     

Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach

This paper presents an analytical investigation on the buckling analysis of symmetric sandwich plates with functionally graded material (FGM) face sheets resting on an elastic foundation based on the first-order shear deformation plate theory (FSDT) and subjected to mechanical, thermal and thermo-mechanical loads. The material properties of FGM face sheets are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. An analytical approach is used to reduce the governing equations of stability and then solved using an analytical solution which is named as power series Frobenius method for symmetric sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of the plate aspect ratio, side-to-thickness ratio, loading type, sandwich plate type, volume fraction index, elastic foundation coefficients and boundary conditions on the buckling response of FGM sandwich plates. This has not been done before and serves to fill the gap of knowledge in this area.     

CFRP加筋板剪切稳定性试验和数值分析模型研究

为研究数值模型对碳纤维增强复合材料(CFRP)加筋板面内剪切稳定性试验计算结果的影响,采用画框式夹具对CFRP加筋板进行了屈曲试验,获得了初始屈曲载荷和载荷-应变曲线;同时基于ABAQUS有限元软件建立了四种数值模型,分别进行线性屈曲和非线性屈曲分析,通过将计算结果与试验结果的比较,确定了有效的数值模型．在此基础上,通过对屈曲前、后有效区边界上的内力分布的比较分析,明确了夹具的传力效果、试件真实的受力状态,以及偏差产生原因．     

Fundamentals of a liquid (soap) film tunnel

 The continuously running liquid film tunnel (LFT) is a novel device suitable for the study of two-dimensional flows. In this innovation, the films start from a reservoir, run over a horizontal or non-horizontal wire frame and get pulled/washed by a water sheet or by gravity of liquid film. How-ever, despite the simple design and widespread application of LFT, its working mechanisms are not well understood. In the present work, an experimental effort for explaining these mechanisms is reported. The results show that both film velocities and film flow rates increase with water sheet velocity up to a saturation level. This behavior is described via a force balance between the shear force produced by the water sheet and the opposing pulling force of reservoir and boundary layer frictions. The results also show that the average film thickness depends on the surfactant concentration. This is as predicted by a model based on Langmuir’s adsorption theory, in which the liquid film contains two external monolayers of surfactant and a slab of surfactant solution in between. When a film is drawn from the reservoir to the water sheet, the surfactant molecules start migrating from the former to the latter. To restore the thermodynamic equilibrium, the dragged film pulls more surfactant due to Marangoni elasticity, and thus a flow is established. The film flow soon reaches an equilibrium rate as required by the force balance mentioned above. Received: 15 August 1996/Accepted: 12 November 1996     

Non-linear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate

We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric fold, while periodic solutions are unstable. Upon further compression, the solution breaks symmetry and stabilizes into a recumbent fold. Using linear analysis and numerics, we theoretically predict the buckling force and energy as a function of the compressive displacement. We compare our theory to experiments employing cylindrical neoprene sheets and find remarkably good agreement.     

Critical state shear behavior of the soil-structure interface determined by discrete element modeling

The interface between soil and structure can be referred to as a soil-structure system, and its behavior plays an important role in many geotechnical engineering practices. In this study, results are presented from a series of monotonic direct shear tests performed on a sand-structure interface under constant normal stiffness using the discrete element method (DEM). Strain localization and dilatancy behavior of the interface is carefully examined at both macroscopic and microscopic scales. The effects of soil initial relative density and normal stress on the interface shear behavior are also investigated. The results show that a shear band progressively develops along the structural surface as shear displacement increases. At large shear displacement a unique relationship between stress ratio and void ratio is reached in the shear band for a certain normal stress, indicating that a critical state exists in the shear band. It is also found that the thickness and void ratio of the shear band at the critical state decreases with increasing normal stress. Comparison of the DEM simulation results with experimental results provides insight into the shear behavior of a sand-structure interface and offers a means for quantitative modeling of such interfaces based on the critical state soil mechanics.