Simple Bending Research Articles

Nanoindentation and whole-bone bending estimates of material properties in bones from the senescence accelerated mouse SAMP6

The senescence accelerated mouse, strain P6 (SAMP6) has been described as a model of senile osteoporosis. Recent results from whole-bone bending tests indicate that, despite having increased moments of inertia, SAMP6 long bones are weak and brittle compared to SAMR1 controls. In the current study we determined material properties of cortical bone from SAMP6 and SAMR1 femora and tibiae by two methods—nanoindentation and whole-bone bending tests combined with simple beam theory. We hypothesized that: (1) SAMP6 mice have reduced cortical bone material properties compared to SAMR1 controls; and (2) modulus estimated from whole-bone bending tests correlates well with modulus determined by nanoindentation. Results from nanoindentation indicated that modulus and hardness are approximately 10% higher in SAMP6 mice compared to SAMR1 controls ( p<0.001), a finding consistent with slightly higher mineralization in SAMP6 bones. Despite their superior elastic and hardness properties, the bending failure properties of SAMP6 bones were markedly inferior—ultimate stress and toughness were reduced by 40% and 60%, respectively ( p<0.001). Comparisons between the two testing methods for determining modulus showed poor agreement. Modulus estimated from whole-bone bending tests was not correlated with modulus determined by nanoindentation ( p=0.054; r 2=0.03) and the absolute values differed by a factor of five between the two methods (bending [wet], 6 GPa; nanoindentation [dry], 31 GPa). Moreover, relative differences between groups were inconsistent between the two methods. We conclude: (1) cortical bone from the SAMP6 mouse has increased modulus and hardness but poor material strength and toughness, which underscores the relevance of the SAMP6 mouse for studies of skeletal fragility, and (2) values of elastic modulus of bone tissue estimated using simple beam theory and bending tests of mouse femora and tibiae are inaccurate and should be interpreted with caution.

An Assessment of In-Service Stress Relaxation of a Work-Hardened Aluminum Magnesium Alloy

Time-dependent relaxation processes continue after forming of sheet metal components. Mechanical properties and even the shape of the part may evolve with time. Beverage can ends, made of an aluminum-magnesium alloy, provide one example of relaxation in a metal product. Ends are manufactured in a series of forming operations, and the can end buckle pressure plays an important role in the design. It has been established that buckle pressure decreases with time in service. In this work, we outline a simple bending test to study relaxation at stress levels well below the usual 0.2 percent offset yield stress. The evolution of stress and development of plastic strain with time are assessed through a simple analysis of springback. The microplastic processes that lead to permanent deformation of the bent beam are well characterized by a model developed by Garmestani and Hart.

Measurement of orientation dependent stress-optic coefficient of GaAs single crystals

The stress-optic coefficient C for (001) and (111) GaAs single crystal wafers at various observation directions was measured precisely using a simple four-point bending technique. Our experimental values of C for (001) GaAs wafers vary from 0.65×10−12 cm2/dyn (at 〈100〉 directions) to 1.43×10−12 cm2/dyn (at 〈110〉 directions). For (111) GaAs wafers, the experimental values of C show much smaller dependence on the observation direction and vary from 1.97×10−12 cm2/dyn (at 〈112〉 directions) to 2.11×10−12 cm2/dyn (at 〈110〉 directions). The combinations of piezo-optic coefficients π11–π12 and π44 were also derived from C for GaAs.

The kink-turn motif in RNA is dimorphic, and metal ion-dependent.

The kink-turn (K-turn) is a new motif in RNA structure that was identified by examination of the crystal structures of the ribosome. We examined the structural and dynamic properties of this element in free solution. The K-turn RNA exists in a dynamic equilibrium between a tightly kinked conformation and a more open structure similar to a simple bulge bend. The highly kinked form is stabilized by the noncooperative binding of metal ions, but a significant population of the less-kinked form is present even in the presence of relatively high concentrations of divalent metal ions. The conformation of the tightly kinked population is in excellent agreement with that of the K-turn structures observed in the ribosome by crystallography. The end-to-end FRET efficiency of this species agrees closely with that of the ribosomal K-turn, and the direction of the bend measured by comparative gel electrophoresis also corresponds very well. These results show that the tightly kinked conformation of the K-turn requires stabilization by other factors, possibly by protein binding, for example. The K-turn is therefore unlikely to be of itself a primary organizing feature in RNA.

STUDY ON THE EFFCTS OF VANE WORKS REDUCING SCOUR DEPTH IN A CURVILINEAR COMPOUND CHANNEL

It is important to evaluate the effect of vane works not only in the simple uniform bend but also in the reach of various forms in river. In this study we investigate the effects of vane works reducing scour depth in the compound channel whose plan form changes longitudinally. In this paper, at first we describe the idea of the design of vane works based on the recent topics of the flow and bed topography characteristics in a compound meandering channel, and show vane works fulfill their functions through flood from vane's effects in simple and compound channel flows. Bed variation in a channel with vane works is reproduced by using 3D-flow model considering drag and lift forces exerting on vanes.

Young's modulus degradation in fatigue of filled polymers for household appliances

Monotonic and fatigue tests in simple bending were carried out on a particulate composite made of polypropylene charged with CaCO3 particles, fixing the maximum displacement. Under monotonic conditions, the material underwent a considerable loss in modulus with increasing the displacement, without exhibiting a typical fracture in two pieces. The same phenomenon was found in fatigue, suggesting that a failure criterion should be based on the modulus degradation, rather than on fracture. To model the modulus variation as a function of the number of cycles and the maximum displacement, an exponential law was assumed. From the experimental results, the parameters appearing in the model could be found having available two sets of data, concerning two distinct values of the maximum displacement. The analysis of the model revealed that a simplified form of the exponential law, needing only two experimental constants, is effective in predicting the modulus degradation. This finding considerably shortens the characterisation stage, yet allowing a satisfactory correlation with the experimental results.

Mechanics of Solids and Shells: Theories and Approximations

Mechanics of Solids and Shells: Theories and Approximations

Si-Wafer Bending Technique for a Three-Dimensional Microoptical Bench

We propose and demonstrate a Si-wafer bending technique for preparing a three-dimensional microoptical bench (MOB). The process for preparing the three-dimensional MOB is based on the usual planar photolithography, anisotropic wet etching and preparation of the photoresist V-groove joint. The bending angle is controlled by the jig on which the wafer is fixed. This jig is prepared separately by the usual machining. The measured accuracy of the bending angle is within ±0.2°. The advantage of this method is that an arbitrary bending angle can be set by changing the jig without the restriction of micromachining. This is a combination of the usual machining technique and the micromachining technique which realizes a three-dimensional microstructure. This simple and flexible bending technique can yield three-dimensional MOBs on which optical elements can be aligned by chip bonding or by preparing an alignment guide.

Enhancement of the buckling strength of glass beams by means of lateral restraints

New material applications and transparency are desired by contemporary architects. Its superb transparency and high strength make glass a very suitable building material -in spite of its brittleness- even for primary load bearing structures. Currently we will focus on load bearing glass beams, subjected to different loading types. Since glass beams have a very slender, rectangular cross section, they are sensitive to lateral torsional buckling. Glass beams fail under a critical buckling load at stresses that lie far below the theoretical simple bending strength, due to the complex combination of torsion and out-of-plane bending, which characterises the instability phenomenon. The critical load can be increased considerably by preventing the upper rim from moving out of the beam's plane. Different boundary conditions are examined for different loading types. The load carrying capacity of glass beams can be increased three times and more using relatively simple, cheap lateral restraints.

Strengthening of unidirectionally reinforced concrete slabs with composite material Theoretical and experimental study

This paper deals with the flexural strengthening of unidirectionally reinforced concrete slabs by means of thin carbon fibre reinforced plastic (CFRP) plates. A simplified laminated plate model has been used to describe the behaviour of a three layered plate in simple (cylindrical) bending in response to three point line loads. The static and kinematic methods of limit analysis were used to approximate the ultimate load capacity for multilayered plates and identify different collapse mechanisms. A unidirectionally reinforced concrete slab strengthened with CFRP was designed as a three layered plate. Experimental results were obtained and compared with theoretical predictions.

Creep deformation of grain boundary in a highly crystalline SiC fibre.

Silicon carbide (SiC) matrix composites reinforced by SiC fibres (SiC/SiC composites) are currently being considered as alternative materials in high Ni alloys for high-temperature applications, such as aerospace components, gas-turbine energy-conversion systems and nuclear fusion reactors, because of their high specific strength and fracture toughness at elevated temperatures compared with monolithic SiC ceramics. It is important to evaluate the creep properties of SiC fibres under tensile loading in order to determine their usefulness as structural components. However, it would be hard to evaluate creep properties by monoaxial tensile properties when we have little knowledge on the microstructure of crept specimens, especially at the grain boundary. Recently, a simple fibre bend stress relaxation (BSR) test was introduced by Morscher and DiCarlo to address this problem. Interpretation of the fracture mechanism at the grain boundary is also essential to allow improvement of the mechanical properties. In this paper, effects of stress applied by BSR test on microstructural evolution in advanced SiC fibres, such as Tyranno-SA including small amounts of Al, are described and discussed along with the results of microstructure analysis on an atomic scale by using advanced microscopy.

Mechanics of thin ultra-light stainless steel sandwich sheet material: Part I. Stiffness

Three variants of a novel steel sandwich sheet material have been studied. The geometrical arrangements of the steel fibres in the core have been characterised. Certain mechanical properties of the fibres have also been investigated. The beam stiffnesses of the sheets, and also their through-thickness Young’s moduli, have been measured. These results have been compared with model predictions. It is shown that the beam stiffnesses are in all cases significantly lower than expected from simple bending theory. This is attributed to the low through-thickness stiffness of the core and also to a low resistance to shear. Modelling of these properties has facilitated the identification of changes to the core structure, which should lead to improved beam stiffness, while retaining a low density. Increased fibre diameter, and possibly an alteration to the fibre sectional shape, are the most promising changes. Of course, implications for other properties, and for ease of manufacture, will also need to be borne in mind.

Analytical solutions for bending and flexure of helically reinforced cylinders

There has been a great deal of interest in the problems of modelling cables and ropes. A recent review by Cardou and Jolicoeur [Appl. Mech. Rev. 50 (1997) 1] considers the modelling of a cable which consists of a central core surrounded by one or several helically wound wire layers. One approach has been to consider the deformations of an individual helical wire and to synthesise the model of a cable by using contact conditions between the various wires. Other authors have adopted a continuum approach regarding each layer as a transversely isotropic material whose principal direction is along a helix surrounding the central axis of the cable. In each layer the helix angle is constant so that, when referred to cylindrical polar co-ordinates, the cylinder has a constant stiffness matrix in each layer. The intention in this paper is to use the continuum approach and describe the analytical solutions that govern the simple bending, flexure, or bending under a uniform load, of an anisotropic elastic cylinder consisting of a single material of this type. The extension of this work to a composite cylinder consisting of several concentric layers, surrounding a central core, which are either bonded together or make a frictionless contact, is briefly described.

Nematic Homopolymers: From Segmented to Wormlike Chains

We present a density functional approach to orientational ordering in homopolymeric systems. The polymers are modeled as chains of identical rodlike segments connected via a simple generic bending potential. The segments are impenetrable to each other, and it is their mutual excluded volume that drives the transition from the orientationally disordered isotropic phase to the orientationally ordered nematic fluid. These excluded volume effects are accounted for within the so‐called Onsager approximation at the chain–chain level and in an independent pairwise overlap approximation at the segment–segment level. The Khokhlov and Semenov formalism for nematic wormlike polymers is shown to be an exact limiting case of our treatment. The ordering transition is studied analytically by using a linear stability analysis of the isotropic phase yielding the properties of the system at the isotropic‐nematic (I–N) bifurcation point. Using a numerical scheme, the equilibrium distribution functions in the nematic phase are calculated, and the location of the thermodynamic I–N transition is determined. For stiff bending potentials, chains with a relatively small number of segments are found to behave like wormlike chains, and we determine the regime of model parameters for which this identification holds.

Thermal peel, warpage and interfacial shear stresses in adhesive joints

Thermal stresses are determined in a single lap joint with identical adherends, which are due solely to temperature changes. The simple bending model used here includes bending and extension of the adherends and extensional and shear strains in the adhesive. The analytical solution shows 'sinusoidal' deformation consistent with warpage (bending) of the adherends due to thermal mismatch. While a modified shear lag model (MSLM) with no adherend bending leads to peak bondline shear stresses which occur only at the ends of the overlap, the bending model shows that such stresses occur not only near the ends, but also at interior points of the overlap region. Results for aluminum adherends and an epoxy adhesive show how the peel, warpage and interfacial shear stresses are distributed over the overlap region.

Paleogene clockwise tectonic rotations in the forearc of central Andes, Antofagasta region, northern Chile

For the Central Valley of northern Chile (Antofagasta region), a paleomagnetic analysis of data from 108 sites, mainly in Mesozoic and Paleogene volcanic rocks, has yielded stable remanent magnetization directions for 86 sites. From these data, we infer clockwise tectonic rotations of up to 65° within the forearc domain of the central Andes. The apparent relationship between tectonic rotations and structural trends suggests that rotations occurred mainly during the Incaic orogenic event of Eocene–early Oligocene age. A few paleomagnetic results obtained in Neogene rocks do not show evidence of clockwise rotations. Hence the development of the Bolivian orocline during late Neogene time cannot be explained by simple bending of the whole margin. These results demonstrate that tectonic rotations within the forearc and pre‐Cordillera are key elements of early Andean deformation, which should be taken into account by kinematic models of mountain building in the central Andes.

Homogenization of corrugated core sandwich panels

The present work is devoted to the computation of the effective properties of corrugated core sandwich panels. Due to their periodic structure, the homogenization theory is used, based on the asymptotic expansion method. At the leading order, an equivalent Kirchhoff–Love homogeneous plate is derived, with an overall behavior obtained from basic cell problems posed on the three-dimensional period of the panel. The finite element computation of these effective properties is presented in this paper. The accuracy of the homogenization method is proved, since the real panel and equivalent plate responses are very close for membrane and pure bending loadings. However, a discrepancy appears for simple bending loading, underlining that transverse shear effects cannot be neglected. Therefore, a specific study is developed in order to derive the transverse shear stiffness, thus enabling to determine an equivalent Reissner–Mindlin homogeneous plate.

Bending of circular-section bonded rubber blocks

Convenient exact closed-form expressions are derived for calculating the bending stiffness of and stresses within loaded cylindrical bonded rubber blocks of circular cross-section. The particular solutions for simple bending, cantilever loading and apparent shear situations are deduced and studied in detail. The shapes of the deformed profiles are discussed and confirmation is provided that the previously adopted assumption of parabolic profiles of the deformed lateral curved surface is only valid for blocks of very small aspect ratio. In simple bending a relationship which is more realistic than those hitherto suggested is derived for the couple required to maintain a specified rotation of the loaded end of the block. In apparent shear an exact expression for the ratio of the true to the apparent shear modulus is derived, and compared with the experimental data. An improved approximate relation is deduced.

The effect of microstructure on the shape recovery of a Fe–Mn–Si–Cr–Ni stainless steel shape memory alloy

In this work the effect of varying the microstructure on the shape memory properties of a Fe-15Mn-7Si-9Cr-5Ni (wt.%) stainless steel shape memory alloy was evaluated using a simple bend test. The best shape recovery was obtained for a single-phase austenite microstructure and for a two-phase microstructure composed of an austenite matrix and Fe 5Ni 3Si 2 type intermetallic grain boundary phase. The maximum shape recovery was achieved at the reversion temperature of 600 °C and when the pre-stain was less than 2%.

The rediscovery of the Combe Capelle skull

A novel apparatus, the laboratory roller screen extruder (termed the LRS), was developed to replicate key aspects of the geometry and shear strain rates generated near the screen of industrial screen extruders. The configuration of the LRS is reported alongside a commissioning study employing a cohesive 45 wt% water/microcrystalline cellulose paste. The key operating parameters which controlled the extrudate mass flowrate, force on the screen and roller torque were (i) the size of the gap between the top of the roller blade and the screen, and (ii) the roller rotational speed. The data suggest that the apparent shear rate, based on the blade-screen clearance, provides a quantitative criterion for scale-up. The amount of screen flex showed good agreement with a simple bending deformation model. Spheronisation of the extrudates gave pellets with a narrow size distribution and acceptable sphericity which would be acceptable for capsule filling. Optimisation of the pellet shape was not performed. The results indicate that the LRS can be used to assess formulations for industrial screen extrusion-spheronisation.