In-plane Tension Research Articles

AlN缓冲层对Si基GaN外延薄膜性质的影响

GaN epitaxial films with different thickness of AlN buffer layers were grown on Si( 111) by metal-organic chemical vapor deposition( MOCVD).The effects of AlN buffer thickness on inplane stress,surface morphology and crystal quality of GaN materials were investigated.It is observed that the AlN buffer with thickness of 15 nm can effectively suppress the diffusion of Si from the substrate.Moreover,the AlN buffer can also introduce a relatively large compressive stress to GaN layers and eliminate the crack.The crack-free and mirror-like GaN layer was obtained by depositing on the AlN buffer layer with thickness of 15 nm.The full width at half maximum of the film is as low as 536 arcsec for( 0002) and 594 arcsec for( 1012) reflection,the in-plane tension stress is 0.3 GPa,and the RMS roughness tested by atomic force microscopy is 0.2 nm.

Flexural behavior of composite curved beams on an elastic foundation

The effects of the inner outer radius ratio on the through-thickness tensile stress and the in-plane tension stress are discussed with a focus on the curved beam based on an elastic foundation. The curved beam composed of two different materials was analyzed,and the location of the neutral axis for the in-plane tension stress was determined. Combining the boundary conditions of the zero internal and external surface stress,interlaminar normal stress,and continuous displacement in the thickness direction,the analytical solutions of the through-thickness tensile stress of the composite curved beam and in-plane normal stress were obtained under pure bending. Furthermore,the effects of volume fraction,material parameters and the placed position of the two kinds of materials on the stress of the composite curved beam were investigated. As a convenient and effective calculation strategy,the method could be extended to the application of curved beams with multiple layers of different materials for solving the strength of rectangular composite curved beams,especially the interlaminar strength in practical engineering.

Constitutive Modeling of Pia–Arachnoid Complex

The pia-arachnoid complex (PAC) covering the brain plays an important role in the mechanical response of the brain during impact or inertial loading. Recent studies have revealed the complicated material behavior of the PAC. In this study, the nonlinear viscoelastic, transversely isotropic material properties of the PAC were modeled as Mooney-Rivlin ground substance with collagen fibers strengthening within the meningeal plane through an exponential model. The material constants needed were determined using experimental data from in-plane tension, normal traction, and shear tests conducted on bovine specimens. Results from this study provide essential information to properly model the PAC membrane, an important component in the skull/brain interface, in a computational brain model. Such an improved representation of the skull/brain interface will enhance the accuracy of finite element models used in brain injury mechanism studies under various loading conditions.

Non-uniqueness and stability of two-family fiber-reinforced incompressible hyper-elastic sheet under equibiaxial loading

The problems on the non-uniqueness and stability of a two-family fiber-reinforced anisotropic incompressible hyper-elastic square sheet under equibiaxial tensile dead loading are examined within the framework of finite elasticity. For a two-family fiber-reinforced square sheet, which is in-plane symmetric and subjected to the in-plane symmetric tension in dead loading on the edges, three symmetrically deformed configurations and six asymmetrically deformed configurations are possible for any values of the loading. Moreover, another four bifurcated asymmetrically deformed configurations are possible for the loading beyond a certain critical value. The stability of all the solutions is discussed in comparison with the energy of the sheet. It is shown that only one of the symmetric solutions is stable when the loading is less than the critical value. However, this symmetric solution will become unstable when the loading is larger than the critical value, while one of the four bifurcated asymmetric solutions will be stable.

Quasi static analysis of creasing and folding for three paperboards

The creasing and folding behavior of three paperboards have been studied both experimentally and numerically. Creasing and folding studies were performed on strips in both the machine direction and the cross machine direction. A finite element model that mimicked the experimental creasing and folding setup was developed, and the creasing and folding behavior could be well predicted for all three paperboards.An experimental characterization scheme consisting of three experiments was proposed, and was shown to be sufficient to predict the creasing and folding behavior. For the whole paperboard the shear strength profiles in the through thickness direction was determined with the notched shear test. Each ply was laid free by grinding, and density measurements and in-plane tension tests were performed on the bottom, middle and top plies of each paperboard. Instead of assuming uniform properties in each ply, the shear strength profiles were used to map the measured properties in the through thickness direction.Numerical simulations were performed when the ply and interface properties of the paperboards were altered to follow different shear strength profiles. This was done in order to mimic different production strategies. It was shown that the interface strengths mainly influenced the folding behavior. Whereas altered the ply properties affected the creasing force needed.

Homogenization in periodically heterogeneous elastic bodies with multiple micro-contact

The aim of this contribution is to compute the effective in-plane tension and shear behaviour of textile-like elastic materials, that is, plates or shells with a periodic micro-structure composed of long woven or knitted fibres. The knitting or weaving results in multiple periodic contact between fibres. Mathematically the problem can be formulated as an in-plane elasticity problem defined in a heterogeneous domain with ε-periodic micro-structure, including multiple micro-contact between the structural components, which is described by the Signorini and Tresca-friction contact conditions. The asymptotic analysis and homogenized limit for such problems was recently obtained by Damlamian et al. via periodic unfolding strategy. These results are briefly recalled in the paper. The obtained two-scale algorithm is implemented for some specific textile materials, which are macroscopic shells with a 3-D microstructure including contact. For each macroscopic deformation state, a contact problem in the periodicity cell or representative volume element is solved and the corresponding non-linear macroscopic stress–strain relation is obtained. The results are illustrated by the simulation of woven and knitted textiles.

Modelling the vibration of tyre sidewalls

The dynamical behaviour of the sidewall has an important influence on tyre vibration characteristics. Nonetheless, it remains crudely represented in many existing models. The current work considers a geometrically accurate, two-dimensional, sidewall description, with a view to identifying potential shortcomings in the approximate formulations and identifying the physical characteristics that must be accounted for. First, the mean stress state under pressurisation and centrifugal loading is investigated. Finite-Element calculations show that, while the loaded sidewall shape remains close to a toroid, its in-plane tensions differ appreciably from the associated analytical solution. This is largely due to the inability of the anisotropic sidewall material to sustain significant azimuthal stress. An approximate analysis, based on the meridional tension alone, is therefore developed, and shown to yield accurate predictions. In conjunction with a set of formulae for the ‘engineering constants’ of the sidewall material, the approximate solutions provide a straightforward and efficient means of determining the base state for the vibration analysis. The latter is implemented via a ‘waveguide’ discretisation of a variational formulation. Its results show that, while the full geometrical description is necessary for a complete and reliable characterisation of the sidewall's vibrational properties, a one-dimensional approximation will often be satisfactory in practice. Meridional thickness variations only become important at higher frequencies (above 500Hz for the example considered here), and rotational inertia effects appear to be minor at practical vehicle speeds.

Molecular mechanics simulations of the deformation mechanism of graphene monolayer under free standing indentation

Using molecular mechanics simulations, we investigate the deformation mechanism of graphene monolayer under free standing indentation. During indentation, the van der Waals (VDW) interaction between the indenter tip and graphene monolayer will cause: (i) a phase lag between the indentation force P and the indentation displacement δ (i.e., δ>0 when P=0); (ii) a different strain energy function than that in in-plane tension; (iii) a larger nonlinear deformation than its counterpart in in-plane tension. Thus, the elastic properties of graphene monolayer (including the second-order elastic stiffness E and the third-order nonlinear elastic constant cmi) determined by free standing indentation are different than those determined by in-plane stretching, especially for cmi. The VDW effect rapidly decreases with the increase of the indentation load. Under a small load (i.e., in-plane strain ε⩽2.5%, typically used in the real tests), the classic indentation analysis cannot give the correct results, especially for cmi. Under a large load (e.g., ε increases to 5%), the error caused by the classic indentation analysis can be effectively reduced. Therefore, the deformation mechanism must be understood in order to accurately determine the elastic properties of graphene from free standing indentation.

Crystal Plasticity Finite-Element Simulation of Deformation Behavior during Unloading under Compression in Magnesium Alloy Sheet

Magnesium (Mg) alloys are the lightest metals that can be used for structural components, and the press forming of Mg alloy sheets has recently attracted attention in automobile and electrical industries. To increase the number of applications of the press forming, it is crucial to understand mechanical properties of Mg alloy sheets. Because Mg alloys are hexagonal close-packed (hcp) materials, mechanical properties of Mg alloy sheets are significantly different from those of conventional structural sheet metals that have cubic structures. Crystal plasticity models can analyze numerically the interaction between mesoscopic crystalline and macroscopic deformation in metals; thus the models are powerful tools to further understand the mechanical properties of Mg alloy sheets. In the present study, the nonlinear response that arose during unloading under in-plane compression of a rolled magnesium alloy sheet was investigated using a crystal-plasticity finite-element method, focusing on the effects of twinning and detwinning. The mechanism that the nonlinear response was more pronounced under in-plane compression than that under in-plane tension was also discussed. In the simulation, a twinning and detwinning model that has originally been proposed by Van Houtte (1978) and recently extended to the detwinning process by the authors [Hama and Takuda, 2012] was employed. From numerical experiments, it was confirmed that, as already pointed out in literature, the activity of detwinning played an important role on the nonlinear response during unloading. On the other hand, it was also found that the basal slip systems could be very active during unloading because of the dispersion of crystal orientations owing to the activity of twinning during loading, which increased the nonlinear response. It was concluded that the nonlinear response during unloading was more pronounced under in-plane compression than that under in-plane tension owing to these two factors that did not present under in-plane tension.

Crack growth behavior of 7075-T6 under biaxial tension–tension fatigue

Crack growth behavior of aluminum alloy 7075-T6 was investigated under in-plane biaxial tension–tension fatigue with stress ratio of 0.5. Two biaxiality ratios, λ (=1 and 1.5) were used. Cruciform specimens with a center hole, having a notch at 45° to the specimen’s arms, were tested in a biaxial fatigue test machine. Crack initiated and propagated coplanar with the notch for λ=1 in L–T orientation, while it was non-coplanar for λ=1.5 between L–T and T–L orientations. Uniaxial fatigue crack growth tests in L–T and T–L orientations were also conducted. Crack growth rate in region II was practically the same for biaxial fatigue with λ=1 in L–T orientation and for the uniaxial fatigue in L–T or T–L orientations, while it was faster for biaxial fatigue with λ=1.5 at a given crack driving force. However, fatigue damage mechanisms were quite different in each case. In region I, crack driving force at a given crack growth rate was smallest for biaxial fatigue with λ=1.5 and for uniaxial fatigue in T–L orientation, followed by biaxial fatigue with λ=1 and uniaxial fatigue in L–T orientation in ascending order at a given crack growth rate.

An Analytical Theory for Radial Crack Propagation: Application to Spherical Indentation

A simple analytical theory is proposed for estimating the number of radial cracks which will propagate in brittle materials subjected to axisymmetric transverse surface loads. First, an expression is obtained for the stress intensity factor of a traction-free star-shaped crack in an infinite elastic membrane subjected to axisymmetric transverse loads. Combining this relation with the critical stress intensity factor criterion for fracture, an implicit expression is obtained which defines the number of cracks as a function of the applied loading, initial flaw size, and fracture toughness. Based on the form of this expression, we argue that if the initial flaw size is sufficiently small compared to the length scale associated with the loading, then the number of cracks can be determined approximately in closed-form from the analysis of a traction-free star-shaped crack in a thin body subjected to uniform equibiaxial in-plane tension. In an attempt to validate the theory, comparisons are made with spherical micro-indentation experiments of silicon carbide (Wereszczak and Johanns, 2008, “Spherical Indentation of SiC,” Advances in Ceramic Armor II, Wiley, NY, Chap. 4) and good agreement is obtained for the number of radial cracks as a function of indentation load.

Fatigue behavior of laminated composites with a circular hole under in-plane multiaxial loading

A modified fiber failure fatigue model is presented for characterizing the behavior of laminated composites with a central circular hole under in-plane multiaxial fatigue loading. The analytical model presented is based on minimum strength model and fiber failure criterion under static loading available in the literature. The analysis starts with the determination of location of a characteristic curve around the hole and the stress state along the characteristic curve under in-plane multiaxial fatigue loading. Number of cycles to failure and location of failure are determined under given fatigue loading condition. Based on ply-by-ply analysis, ultimate fatigue failure and the corresponding number of cycles are determined. Analytical predictions are compared with the experimental results for uniaxial and multiaxial fatigue loading cases. A good match is observed. Further, studies are carried out for different in-plane biaxial tension–tension and biaxial compression–compression loading cases.

Optimization and Analysis of Processes with Moving Materials Subjected to Fatigue Fracture and Instability

We study systems of traveling continuum modeling the web as a thin elastic plate of brittle material, traveling between a system of supports at a constant velocity, and subjected to bending, in-plane tension and small initial cracks. We study crack growth under cyclic in-plane tension and transverse buckling of the web analytically. We seek optimal in-plane tension that maximizes a performance vector function consisting of the number of cycles before fracture, the critical velocity and process effectiveness. The present way of applying optimization in the studies of fracture and stability is new and affords an analytical tool for process analysis.

Van der Waals effect on the nanoindentation response of free standing monolayer graphene

Using molecular mechanics simulations we investigate the elastic properties of monolayer graphene determined from free standing indentation and the effects of graphene size and indenter tip size are considered. In free standing indentation, the overall system potential energy includes two parts: the strain energy of graphene monolayer and the van der Waals (VDW) interaction energy between indenter tip and graphene. The VDW interaction will strongly affect the elastic properties of graphene monolayer determined from free standing indentation. Without considering the VDW interaction, the classical free standing indentation analysis is not able to accurately estimate the second-order elastic stiffness (E) and the third-order nonlinear elastic constant (cm) (E will be underestimated and cm will be overestimated). It is found that both E and cm determined from free standing indentation are quite close to their counterparts determined from in-plane tension after properly considering the VDW interaction. The results can provide a useful guideline to understand the elastic properties of graphene monolayer determined from free standing indentation tests.

Modelling the Shear-Tension Coupling of Woven Engineering Fabrics

An approach to incorporate the coupling between the shear compliance and in-plane tension of woven engineering fabrics, in finite-element-based numerical simulations, is described. The method involves the use of multiple input curves that are selectively fed into a hypoelastic constitutive model that has been developed previously for engineering fabrics. The selection process is controlled by the current value of the in-plane strain along the two fibre directions using a simple algorithm. Model parameters are determined from actual experimental data, measured using the Biaxial Bias Extension test. An iterative process involving finite element simulations of the experimental test is used to normalise the test data for use in the code. Finally, the effectiveness of the method is evaluated and shown to provide qualitatively good predictions.

Wrinkling of Sandwich Materials with Nonorthogonal Plain Woven Composite Facesheets

Fabric is often attached on lightweight core to form a sandwich plate. When complex sandwich structure is manufactured, the fabric facesheets are in a state of in-plane tension or shear deformation, and the angle between the warp and weft yarns is altered. An analytical model to calculate the wrinkling load of sandwich plates with nonorthogonal plain woven composite facesheets is established, and the effects of various parameters are demonstrated. Analysis results indicate that the core modulus and thickness, fiber modulus, and yarn orientation of facesheets can influence the facesheets’ wrinkling behavior of sandwich plate on different levels.

Thermal–mechanical modelling of laminates with fire protection coating

This paper presents a modelling approach to analyse the protection provided by passive and intumescent surface coatings on glass fibre reinforced laminate substrates exposed to fire. The modelling involves a multi-stage analytical approach: (i) thermal analysis of heat transfer from the fire through the surface insulation coating, which includes decomposition and expansion in the case of an intumescent material; (ii) thermal–chemical analysis of heat transfer through the fibreglass laminate substrate (beneath the fire protective coating), including decomposition of the polymer matrix; and (iii) thermal–mechanical analysis of softening and failure of the laminate under in-plane tension or compression loading. The modelling approach is validated using experimental temperature and strength data from fire structural tests performed on woven glass–vinyl ester laminates insulated with passive (ceramic fibre mat) or organic intumescent surface coatings.

Stress Concentration Calculation of Silo Wall Opening Subjected to In-Plane Tension or Pressure

In this paper, by using complex variable function and conformal mapping technique, the author studies the stress concentration intensities of silo wall opening through predigesting the stress calculation of silo wall opening as a problem of plane calculation and obtains the stress concentration factor of opening. When simplified silo wall is subjected to in-plane tension or pressure, maximal stress concentration point around opening is at the corner of opening. this paper may provide some referenced value to the designers.

Membrane tension homeostasis of epithelial cells through surface area regulation in response to osmotic stress

Osmotic stress poses one of the most fundamental challenges to living cells. Particularly, the largely inextensible plasma membrane of eukaryotic cells easily ruptures under in-plane tension calling for sophisticated strategies to readily respond to osmotic stress. We describe how epithelial cells react and adapt mechanically to the exposure to hypotonic and hypertonic solutions in the context of a confluent monolayer. Site-specific indentation experiments in conjunction with tether pulling on individual cells have been carried out with an atomic force microscope to reveal spatio-temporal changes in membrane tension and surface area. We found that cells compensate for an increase in lateral tension due to hypoosmotic stress by sacrificing excess of membrane area stored in protrusions and invaginations such as microvilli and caveolae. At mild hypotonic conditions lateral tension increases partly compensated by surface are regulation, i.e. the cell sacrifices some of its membrane reservoirs. A loss of membrane–actin contacts occurs upon exposure to stronger hypotonic solutions giving rise to a drop in lateral tension. Tension release recovers on longer time scales by an increasing endocytosis, which efficiently removes excess membrane from the apical side to restore the initial pre-stress. Hypertonic solutions lead to shrinkage of cells and collapse of the apical membrane onto the cortex. Exposure to distilled water leads to stiffening of cells due to removal of excess surface area and tension increase due to elevated osmotic pressure across the plasma membrane.

Theoretical study on travelling web dynamics and instability under non-homogeneous tension

Problems of dynamics and stability of a moving web, travelling between two rollers at a constant velocity, are studied using analytical approaches. Transverse vibrations of the web are described by a partial differential equation that includes the centrifugal force, in-plane tension, elastic reaction and nonstationary inertial terms. The model of a thin elastic plate subjected to bending and non-homogeneous tension is used to describe the bending moment and the distribution of membrane forces. The stability of the plate is investigated with the help of studies of small out-of-plane vibrations. The influence of linearly distributed in-plane tension on the characteristics of the web vibrations is studied. The static forms of instability are investigated using numerical methods. It can be concluded that inhomogeneities in the applied tension may significantly decrease the critical web velocities and even small inhomogeneities in the tension may have a large effect on the divergence forms.