Critical Strain Values Research Articles

Strain relaxation in InGaAsP/InP grown by metal-organic vapor-phase epitaxy

We examined experimentally how the surface morphology, photoluminescence (PL) and X-ray diffraction depend on the amount of compressive strain in the InGaAsP layers grown by metal-organic vapor-phase epitaxy (MOVPE). It was found that there are two critical values of strain in the relaxation process. One is the threshold strain value ( ε c1) for the appearance of the cross-hatched pattern on the crystal surface and subsequent decrease in PL intensity. The other is that for the in-coherent growth ( ε c2), which leads to the broadening of the full-width half-maximum (FWHM) in the X-ray diffraction analysis. We also found that ε c1 is in good accordance with the force–balance theory, while ε c2 follows the energy–balance theory. We also examined their compositional wavelength ( λ g) dependence ( λ g of InGaAsP: 0.92 μm (InAsP), 1.15, 1.3 and 1.67 μm (InGaAs)). The ε c1 of InAsP is approximately half those of the other materials. This is probably due to the relatively large Poisson's ratio for InAsP. On the other hand, ε c2 of InGaAsP with λ g of 1.15 and 1.3 μm is slightly smaller than that of InAsP or InGaAs. This can be explained by local strain fluctuation in a nanoscale region, i.e. the fluctuation is stronger for quaternary InGaAsP compared to that for ternary InAsP or InGaAs. These findings are very useful for the crystal growth of high-quality highly strained InGaAsP.

Ultimate load analysis of thin-walled box beams considering shear lag effect

In this paper, the ultimate load of thin-walled box beams undergoing limited plastic strain is investigated with consideration of shear lag effect on the basis of the stress–strain relationship of elastic, linearly hardening materials. In the procedure, calculation formulae for strength increase coefficient, flange effective width ratio, critical values of plastic strain and shear lag coefficient are obtained for thin-walled box beams with elastic, linearly hardening materials. In addition, the relationships among the abovementioned parameters and conditions of boundary, load and aspect ratio L/2 b (span length/beam width) of the box beams are established in this paper. For illustration, the numerical results of box beams under certain boundary and load conditions are presented and some conclusions are drawn which may offer references for the application of this procedure in structural design.

Martensitic Transformations in Neutron Irradiated and Helium Implanted Stainless Steels

Abstract Results of experiments aimed at revealing the phase-structure stability as well as mechanisms of the mechanical property changes formation in austenitic chrome-nickel and manganese steels irradiated with high-energy nuclear particles and subjected to elevated temperatures are presented and discussed. Influence of the phase-structure transformations on radiation hardening and embrittlement of steels used in nuclear power industry is analyzed. Change in the experimentally determined “true” values of critical strains and peculiarities of the α'-phase initiation in deformed steels Cr18Ni9Ti, 12Cr18Ni10Ti as a function of temperature and deformation rate, type and fluence of the bombarding particles are discussed. Influence of irradiation on the martensitic structure morphology, critical γ→α' transformation parameters, and thermal effects accompanying the nondiffusion phase transformation is analyzed. The revealed effects are discussed in terms of the internal strength field changes due to thermal and radiation effects.

Empty and foam-filled circular aluminium tubes subjected to axial and oblique quasistatic loading

Tests on tubular columns made of the aluminium alloy 6060-T4 under axial and oblique, quasi-static loading have been performed. The columns were fixed at one extremity, while a concentrated force was applied at the other through a rigid collar. Empty and foam-filled columns were tested for load angles equal to 0, 5, 15 and 30 degrees with respect to the longitudinal direction of the column. The column's outer diameter was 80 mm and the thickness was 1.5 mm, while the distance from the point of load application to the fixed support was 245 mm. The aluminium foam density was about 0.3 g/cm3. The response parameters were the peak force, the absorbed energy and the mean crush force, in addition to visual observations of the deformation mode and fracture. Furthermore, LS-DYNA simulations of the experiments were performed. The columns were modelled with shell elements, while brick elements were used to model the aluminium foam core. The aluminium alloy was modelled using an isotropic elastoplastic model with isotropic strain hardening. Fracture in the aluminium column was not considered in the simulations. The aluminium foam was modelled using the Deshpande-Fleck model. In selected simulations, fracture was assumed to occur at a critical value of the plastic volumetric strain. The agreement between the experimental and predicted results was in general good.

水中における稲田花こう岩と白浜砂岩の変形・破壊挙動に対する温度の影響

Uniaxial compression test, Brazilian test and fracture toughness test were carried out for Inada granite and Shirahama sandstone in pure water controlling the water temperature between 0 °C and 80 °C and the loading rate between 1.67 × 10-7 m / s and 5.00 × 10-4 m / s. The uniaxial compressive strength, Poisson's ratio, Indirect tensile strength and stress intensity factor decreased with the temperature for the both two rocks. This tendency was clearer for Inada granite. Critical compressive strain value (axial strain value at peak load point) of Shirahama sandstone also decreased with temperature. However, the effect of temperature on the critical extensile strain (radial strain at peak load point) was not clear for the both two rocks. Young's modulus seemed to take the peak value at 20 °C or 40 °C. These results were explained based on thermal stress due to anisotropy and difference of thermal expansion coefficient between the mineral grains, stress corrosion and change in viscosity of water.

Critical displacement for normal fault nucleation from en-échelon vein arrays in limestones: a case study from the southern Apennines (Italy)

The process of fault initiation by the coalescence of en-échelon arrays of tensile cracks has been discussed by several workers and is now well established. However, not many studies have tried to quantitatively describe this process in terms of displacement and shear strain that control the early stages of fault nucleation. In this study, a large number of conjugate en-échelon vein arrays showing extensional offsets have been analysed. These structures are exposed in well bedded micritic limestones deformed at very low-grade conditions in the Apennine mountain belt of southern Italy. Three different types of structures can be distinguished: (i) ‘brittle–ductile’ shear zones, characterised by arrays of en-échelon, calcite-filled tension gashes; (ii) shear zones showing incipient development of discontinuous shear-parallel fractures cutting through the vein array; and (iii) faulted shear zones, in which a continuous, discrete normal fault breaks through—and clearly developed from—an original en-échelon vein array. Critical values of displacement and shear strain have been determined for the onset of normal fault nucleation from ‘brittle–ductile’ shear zones, therefore suggesting that these parameters exert a major control on fault initiation. A diagram of shear zone population vs. displacement also shows that this parameter obeys a power law of the type generally followed by normal faults in the frictional regime. Our results suggest that, during the early stages of fault nucleation, displacement and shear strain control the switch from dominant ductile (viscous) deformation mechanisms—accompanied by brittle fracturing responsible for vein formation—to the frictional regime.

Symmetries and elasticity of nematic gels.

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these materials.

A Study of Buckling of Near Surface Local Delamination in a Cylindrical Laminated Shell

In this paper, an energy method is applied to study the buckling problem of near surface triangular, elliptical and lemniscated delamination in a cylindrical laminated shell. The relationships between critical strain value and the geometrical and physical parameters of base laminated shell and sub-laminated shell are investigated.

Dependence of linear viscoelastic critical strain and stress values on extent of gelation for a thermally activated gelling system

A large body of literature is focused on the accurate determination of a gel point for systems undergoing a sol-gel phase transition. Investigation into the limiting strain and stress for linear viscoelastic behaviour at various stages of a phase transition such as gelation is a subject that is rarely commented on. The small amplitude oscillatory rheological behaviour of a biopolymer cross-linker system through a thermally activated sol-gel transition is presented. Mechanical spectra were interpreted through application of the gelation criteria of Chambon and Winter (Winter and Chambon 1986; Chambon and Winter 1987), where the (so-called gel strength) parameter S, and relaxation exponent, n are obtained. A detailed study of the limit of linear viscoelasticity yields important trends in critical stress (σ°c) and critical strain (γ°c) limits highlighting the possible experimental difficulties associated with mechanical measurements obtained in close proximity to the gel point.

Analysis of the results of mechanical testing of metals by constructing the diagrams of structural states

For polycrystalline metals and alloys with bcc (Mo, Fe, and Fe–Si) and fcc (Ni and Cu) crystal lattices, it is shown that the application of the method of reconstruction of parabolic stress–strain diagrams on S –encoordinates, where S and e are the actual stress and strain, respectively, and n is the strain-hardening index, makes it possible to represent the results of mechanical testing in the form of a diagram of structural states plotted in the form of the dependences of actual stresses and strains on temperature. This diagram practically completely describes the changes in the strength and plastic characteristics of the materials and their structural states in the process of plastic deformation. We study specific features of the construction of these diagrams depending on the composition of the alloy, its structural state, the energy of stacking faults, etc. On the basis of the analysis of the character of correlations between the critical values of strains and stresses and the mechanisms of plastic deformation within broad ranges of temperature and structural states, we discuss the possibilities of scientific and practical application of the diagrams of actual stresses and strains vs temperature.

The rheological properties and hot tearing behaviour of an Al-Cu alloy

An experimental device was constructed for the present research. The strain of Al-4.5Cu alloy during loading and unloading was measured in the solidification temperature range. Based on these experiments and analyses, a five-component elastic-visco-plastic rheological model of the alloy is proposed, the creep equation is obtained, and the rheological property parameter is defined. Based on this investigation, the shrinkage stress of a casting can be measured, which enables the determination of critical values of strain for the formation of hot tearing.

Strain effects and phase transitions in photonic resonator crystals.

Optical structures with periodic variations of the dielectric constant in one or more directions (photonic crystals) have been employed extensively for studying optical diffraction phenomena. Practical interest in such structures arises from the possibilities they offer for tailoring photon modes, and thereby the characteristics of light propagation and light-matter interactions. Photonic resonator crystals comprising two-dimensional arrays of coupled optical microcavities have been fabricated using vertical-cavity surface-emitting laser wafers. In such structures, the light propagates mostly normal to the periodic plane. Therefore, the corresponding lateral Bragg-periodicities are larger, a feature that is advantageous for device manufacture as it allows for larger lattice constants in the lateral direction. Here we investigate strain effects in a photonic resonator crystal by shifting neighbouring lattice rows of microcavities in opposite directions, thereby introducing an alternating square or quasi-hexagonal pattern of shear strain. We find that, for strain values below a critical threshold, the lasing photon mode is virtually locked to the corresponding mode supported by the unstrained photonic crystal. At the critical strain value, we observe a phase-transition-like switching between the square and quasi-hexagonal lattice modes. The tolerance of subcritical strains suggests that the resonator crystal may be useful for applications requiring high spatial coherence across the lattice, while the mode switching could potentially be exploited in free-space optical communications.

00/01214 Are IGCC power plants competitive?

We have investigated the effect of ferrofluid incorporated (5–20% v/v) flake-shaped iron particles in silicion oil based magnetorheological fluid (MR fluid). The fluids physical properties like crystalline phase, shape size distribution and magnetization of both the fluids were studied individually. Thereafter, magnetic stimuli-response of ferrofluid doped MR fluid on rheological properties was determined in static and dynamic modes. The observed enhancement in yield stress due to addition of magnetic nanoparticles is correlated using universal yield stress scaling equation with magnetic field strength. Subsequently, cylindrical measurement technique is used to investigate fluid stability over time. Further, the relative viscosity (η/η∞) −vs- Mason number (Mn) shows scaling (Mn ≤ 10−2), at higher magnetic field confirming negligible thermal and colloidal forces. The oscillatory strain sweep tests reveals a cross-over from viscoelastic-to-viscous behavior of suspension at critical strain value y = 0.1. The increase in dynamic efficiency at is due to the reduction in sliding friction.

Mode switching in shear-strained and modulated photonic lattices by vertical-cavity surface-emitting laser arrays by means of injection locking

Mode switching in shear-strained (i.e., laterally shifted) lattices of vertical cavity surface emitting laser arrays by means of injection locking is theoretically demonstrated. Switching between four- and six-lobed far-fields modes is examined near the critical value of lattice strain. Switching between localized modes of modulated lattices is also considered, and, as an example, mode switching of randomly disordered lattice is demonstrated. Both the shear-strained and the random disordered lattices are shown to be ideal candidates for all-optical switching devices.

Environmental stress cracking of poly(vinyl chloride) in alkaline solutions

The environmental stress cracking (ESC) effects on PVC of various high pH sodium hydroxide environments have been studied. The behaviour of PVC specimens in air and pH 12, 13, 13.5 and 14.39 sodium hydroxide solutions has been examined under three-point bend, tensile and creep conditions. Two parameters were used in three-point bend testing to determine the effect of an applied strain and high pH environment on the stability of PVC, namely time to craze initiation and width of crazing. It was found that, in general, crazing occurred sooner and to a greater degree with increasing strain and pH, although there was some evidence that craze growth was most rapid at pH 13.5. The results also indicated a critical strain value of ∼1.5–1.6%, below which crazing was not observed in any of these alkaline environments. Creep and tensile testing revealed that the time for which a PVC specimen was immersed in the environment was very important in determining the severity of the environmental effect. Creep tests at elevated temperatures showed that the time for the effects to be manifest decreased with increasing temperature. Creep rates were highest in pH 13.5 sodium hydroxide solution indicating that this was the most hostile of the environments considered.

On instability of the Doi–Edwards model in simple flows

A stability characteristic of the Doi–Edwards viscoelastic constitutive equation is studied. Hadamard-type stability determined by the elastic part of the constitutive equation is considered in the case of simple flows. Criteria for general 3-D stability are derived in a complete biquadratic form, and rather simple algebraic condition under 1-D and 2-D disturbances is then formulated. Application of constraints to this rheological equation of state proves inevitable occurrence of the Hadamard-type instability in simple shear and uniaxial (or equi-biaxial) extensional flows, and the threshold of instability is calculated in terms of strain for all the flow types. The obtained values of critical strains are relatively low, hence it is thought that they can be easily achieved even in experiments as well as in industrial processing. We conclude that this instability is not at all related to real physical phenomena and it is merely inappropriateness owned by the constitutive equation.

A constitutive relation and failure criterion for Ti6Al4V alloy at impact rates of strain

Shear stress-strain curves have been obtained for thin-walled tubular specimens of Ti6Al4V alloy at strain rates from ∼7×10 −4/s to ∼1000/s. A specially developed infrared radiometer has been used to measure the rise in specimen surface temperature during the high strain rate tests where the deformation process is essentially adiabatic. The data obtained were used to obtain material constants for a Zerilli–Armstrong type constitutive relation giving the best fit with the observed mechanical response. This relation was incorporated in the ABAQUS/ explicit FE code and shown to predict the experimentally measured flow stress in the impact tests with reasonable accuracy. A failure criterion, based on a critical value of effective plastic strain, is also incorporated, the critical condition being chosen to give agreement between the predicted and the measured overall failure strains. The validity of the constitutive relation and associated failure criterion is then assessed in terms of their ability to predict the observed mechanical response in tensile impact tests on specimens of both cylindrical and rectangular cross-section where the early onset of localised plastic flow and significant temperature rises in this region provide a more rigorous test of the proposed model. High-speed photography was used to monitor the changing specimen cross-section and the infrared radiometer was used to determine the specimen surface temperature in the region of localised deformation. Reasonable agreement was obtained between the experimental results and the numerical predictions using the ABAQUS/ explicit FE code.

Examination of a Rock Failure Criterion Based on Circumferential Tensile Strain

—Uniaxial compression, triaxial compression and Brazialian tests were conducted on several kinds of rock, with particular attention directed to the principal tensile strain. In this paper we aim to clarify the effects of the experimental environment—such as confining pressure, loading rate, water content and anisotropy—on the critical tensile strain, i.e., the measured principal tensile strain at peak load.¶It was determined that the chain-type extensometer is a most suitable method for measuring the critical tensile strain in uniaxial compression tests. It is also shown that the paper-based strain gage, whose effective length is less than or equal to a tenth of the specimen’s diameter and glued on with a rubber-type adhesive, can be effectively used in the Brazilian tests.¶The effect of confining pressure P C on the critical tensile strain ɛ TC in the brittle failure region was between −0.02 × 10−10 Pa−1 and 0.77 × 10−10 Pa−1. This pressure sensitivity is small compared to the critical tensile strain values of around −0.5 × 10−2. The strain rate sensitivities ∂ɛ TC /∂{log(d|ɛ|/dt)} were observed in the same way as the strength constants in other failure criteria. They were found to be from −0.10 × 10−3 to −0.52 × 10−3 per order of magnitude in strain rate in the triaxial tests. The average magnitude of the critical tensile strain ɛ TC increased due to the presence of water by 4% to 20% for some rocks, and decreased by 22% for sandstone. It can at least be said that the critical tensile strain is less sensitive to water content than the uniaxial compressive strength under the experimental conditions reported here. An obvious anisotropy was observed in the P-wave velocity and in the uniaxial compressive strength of Pombetsu sandstone. It was not observed, however, in the critical tensile strain, although the data do show some variation.¶A "tensile strain criterion" was proposed, based on the above experimental results. This criterion signifies that stress begins to drop when the principal tensile strain reaches the critical tensile strain. The criterion is limited to use within the brittle failure region. The critical tensile strain contains an inelastic strain component as well as an elastic one. It is affected by the strain rate, however, it is relatively insensitive to the confining pressure, the presence of water and anisotropy.

Chain stretching effect on domain growth during spinodal decomposition of binary polymer mixtures under simple shear flow

The chain stretching effect on domain growth during spinodal decomposition of binary polymer mixtures under simple shear flow is investigated by computer simulation. The simulation is based on a modified time-dependent Ginzburg–Landau equation, in which the chain stretching effect is introduced in the free energy functional. It is found that, for higher value of Rouse terminal relaxation time, the critical strain value for the burst of the domains is higher, thereby the domains are highly elongated. This may be responsible for the stringlike patterns observed experimentally under strong shear. When the chain stretching effect is introduced, the shear rate dependencies of the shear stress and first normal stress difference become stronger. The shear stress and first normal stress difference reach their maxima for the system of 1:1 mixture. The simulated results agree with the experimental observations qualitatively.

J c vs. strain characteristic of Bi-2223/Ag composite tapes in applied magnetic field

In operative conditions of the most important transport applications of Bi-2223/Ag superconducting tapes, like cables for power transmission lines and superconducting windings, the tapes will be subjected to mechanical stresses and magnetic fields causing the degradation of their transport properties. In this work we investigated the simultaneous effects of mechanical tensile stress and magnetic fields, up to 140 mT, applied parallel and perpendicular to the tape surface on the critical current density Jc at 77 K of Bi-2223/Ag composite tapes. The Jc vs. strain measurements showed an abrupt Jc decay above a critical strain value, ɛcr.