Region Of Small Deformations Research Articles

Investigation of microstructure evolution and mechanical properties of 2A10 aluminum alloy during ultrasonic vibration plastic forming

Ultrasonic vibration-assisted plastic forming technology is promising since it can reduce the forming force and improve the quality of surface. However, the microstructure and deformation uniformity in the whole sample were rarely taken into account. In this paper, 2A10 Al alloy, which is commonly used in aviation rivets, is selected as the research object for ultrasonic assisted compression test. The test results show that ultrasonic vibration can significantly reduce the flow stress during Al deformation and increase the material hardness. Ultrasonic vibration provides energy for dislocation movement, which makes easier the dislocation to overcome an obstacle. In addition, it also refine the grain, increases the deformation degree of the small deformation region, and reduces the difference of deformation degree between different areas, resulting in improved deformation homogeneity.

Study on microstructure and tensile damage evolution of 2205 duplex steel at different solution temperatures

2205 dual-phase steel was subjected to solution heat treatment experiments at 1000℃～1160℃. Electron backscatter diffraction (EBSD) was used to analyze the evolution of its microstructure; the evolution of its surface damage was analyzed by a tensile testing machine combined with digital image correlation (DIC). The results show that the FCC phase in the microstructure of 2205 dual-phase steel grows into strips after solid solution treatment. With the increase of the solution temperature, local phase boundary dissolution and fracture of the FCC phase occur, the yield strength and tensile strength of the stainless steel plate after heat treatment are the same, showing a downward trend. 2205 dual-phase steel presents the morphological characteristics of ductile fracture. The average strain factor of the critical large deformation region and the small deformation region of the original specimen are both maximum. The average strain factor at 1080℃ specimen is the smallest. With the increase in annealing temperature, the speed of damage deformation becomes slower. At different solution temperatures, in 2205 dual-phase steel, the austenite texture type changes to a certain extent, but eventually, a typical brass texture is formed; that is, the brass texture is the main texture, accompanied by a certain strength, the S texture. The grain orientations in the BCC phase are concentrated between {100}<011> and {112<110>, forming a significant a-fiber texture (<110>//RD).

Dynamic response of wind turbine blade surface material under water droplet high velocity impact

When a wind turbine blade exposure to some degree of rainfall, water droplets in the atmosphere impact the blade at high velocity will causes erosion damages of the leading edge. The damages have significant influence to the aerodynamic performance of the blade, and also the cost of power generation. In this paper, a high velocity impact dynamics model of water droplet impact on wind turbine blade is develops based on SPH-FEM coupling method, where SPH model is used to model the large deformation region of the fluid domain, and FEM method is used to model the small deformation region of the structure domain. Together with properties of gelcoat material on the blade surface, effects of varying impact velocities and angles on the impact response of the gelcoat material are analysed through numerical simulation. The results show that during a high velocity impact event of water droplet, the contact force history appears two peaks. Also contact forces and strains on the blade material decreases with decreasing droplet impact velocity and impact angle, the total contact duration of the droplet during the impact decreases with increasing droplet impact velocity and angle. The present study is expected to provide theoretical guidance for enhancing the erosive capacity of wind turbine blade gelcoat material.

Lightweight auxetic metamaterials: Design and characteristic study

In the past decades, auxetic metamaterials have attracted extensive attention due to their desirable properties. In order to further improve the energy absorption properties of auxetic metamaterials, this work investigates the design of lightweight auxetic metamaterials based on the elliptic perforated plate. The material in the large deformation region is retained and the material in the small deformation region is removed as much as possible. The experimental and numerical results indicate that the mechanical properties of the novel metamaterials are almost unchanged, but the specific energy absorption is substantially enhanced owing to the reduced material overall and the distribution of the optimized materials to the most needed area. In this paper, the influence of the amount and mode of the material removal on the mechanical properties of the auxetic metamaterial is explored through the numerical method. The proposed auxetic metamaterials with lightweight characteristics have potential applications in many fields, e.g., civil engineering, aerospace and vehicle engineering.

Extraction of intrinsic effects of glassy domain cross-linking on the tensile properties of ABA block copolymer elastomers via photo cross-linking approach

Chemical or physical cross-links into the A glassy domains have been reported to enhance mechanical properties for glassy-b-soft-b-glassy ABA triblock copolymer-based elastomers. However, no reports dealt with the pure effects of the domain cross-linking, since the cross-linking processes inevitably altered the morphological characteristics. This study extracts the intrinsic effects of domain cross-linking on the tensile properties based on the ABA triblock copolymer with the A blocks cross-linked via photo cross-linking without heat and cross-linker molecules. Differential scanning calorimetry, viscoelasticity measurements, and small-angle X-ray scattering (SAXS) with a model function analyses were used to confirm preservation of the segmental dynamics of the B block and the morphology of the self-assembled structure after cross-linking, which are all important for a fair discussion. Tensile properties were then investigated by simple elongation and cyclic tests, revealing that the domain cross-linking enhanced the stress in the small deformation region and the recovery property primarily. These changes of the tensile properties were discussed in terms of the deformation resistance of the micro-phase separated structure based on the SAXS data under elongation. The superiority or inferiority of cross-linking the end block domains or middle block strands for mechanical property enhancement was interpreted based on the observed difference between the neat and cross-linked samples. In the last section, effects of domain photo cross-linking for the different morphologies were also examined. Throughout the article, this study can provide new and essential knowledge of the mechanical properties of block copolymer-based materials, and some valuable hints for further modification of the physical properties of these materials.

Analysis of strain hardening of ADI at isothermal hardening temperatures

The effect of isothermal hardening temperature on the mechanical properties of ADI materials is investigated. The heat treatment of the test samples consisted of the heating above the temperature of transformation of the ferrite component in austenite and isothermal hardening at temperatures from 280 to 380 °C. In the indicated temperature ranges, the plastic characteristics and strength parameters of the samples were studied depending on the heat treatment conditions. Particular attention is paid to the strain hardening parameters. It was found that at isothermal hardening temperatures in the range of 330-360 °C with plastic deformation, the TRIP effect appears, the appearance of which is accompanied by a high hardening rate due to the conversion of residual austenite to martensite. Plastic characteristics change with increasing quenching temperature. At 280 °C, the strength and hardness of the metal is maximum, and the plastic properties are minimal. The mechanical properties of the studied bainitic iron, quenched at various temperatures, satisfy ASTM 897-90 requirements except for samples quenched at 400 °С. Hardness, yield strength, and tensile strength decrease with increasing quenching temperature, ductility and impact strength increase. During compression, two sections of hardening are observed: in the region of small deformations, the rate of change of stress is higher, the lower the temperature of quenching, in the region of large deformations, on the contrary, the rate of hardening is much higher in materials quenched at higher temperatures. The effect is explained by a change in the hardening mechanism from dislocation - at small strains to the TRIP effect at large.

Field-Dependent Stiffness of a Soft Structure Fabricated from Magnetic-Responsive Materials: Magnetorheological Elastomer and Fluid

A very flexible structure with a tunable stiffness controlled by an external magnetic stimulus is presented. The proposed structure is fabricated using two magnetic-responsive materials, namely a magnetorheological elastomer (MRE) as a skin layer and a magnetorheological fluid (MRF) as a core to fill the void channels of the skin layer. After briefly describing the field-dependent material characteristics of the MRE and MRF, the fabrication procedures of the structure are provided in detail. The MRE skin layer is produced using a precise mold with rectangular void channels to hold the MRF. Two samples are produced, namely with and without MRF, to evaluate the stiffness change attributed to the MRF. A magnetic field is generated using two permanent magnets attached to a specialized jig in a universal tensile machine. The force-displacement relationship of the two samples are measured as a function of magnetic flux density. Stiffness change is analyzed at two different regions, namely a small and large deformation region. The sample with MRF exhibits much higher stiffness increases in the small deformation region than the sample without MRF. Furthermore, the stiffness of the sample with MRF also increases in the large deformation region, while the stiffness of the sample without MRF remains constant. The inherent and advantageous characteristics of the proposed structure are demonstrated through two conceptual applications, namely a haptic rollable keyboard and a smart braille watch.

Numerical study of the shear-thinning effect on the interaction between a normal shock wave and a cylindrical liquid column

Based on adaptive mesh refinement, the SIM (Sharp-Interface Method) is utilized to numerically study the interaction between a shock wave and a liquid column as well as the evolution of the flow field. The SIM consists of the LSM (Level Set Method) and the GFM (Ghost Fluid Method). The LSM tracks the gas-liquid interface, and the GFM generates the virtual domains near the interface based on the gas-liquid interface condition. The hybridized GFM has been developed by integrating the Riemann GFM and the modified GFM together, which ensures the accuracy of the interface Riemann problem in the small deformation region of the interface while ensuring that the large interface deformation can be processed correctly. By comparing with the experimental results and the numerical results in previous literature, the good agreement shows that the above algorithm can accurately simulate the interactions between shock waves and liquid columns along with achieving the evolutions of the sharp gas-liquid interfaces. Based on the algorithm above, the interactions between the shock waves and the inviscid, the Newtonian, and the shear-thinning liquid columns are simulated, respectively. The numerical results indicate that the viscous effect can cause the bending of the liquid column and large deformation in the high shearing region. However, the shear thinning effect alleviates the bending and the deformation of the liquid column in the high shear region.

Prevention of network destruction of partially hydrolyzed polyacrylamide (HPAM): Effects of salt, temperature, and fumed silica nanoparticles

Polymer flooding is one of the most effective enhanced oil recovery (EOR) methods. High temperature and a high salt content in oil reservoirs significantly decrease the performance of polymer flooding. In this work, the viscoelastic properties of a partially hydrolyzed polyacrylamide (HPAM) solution with and without salt (NaCl) and at two different temperatures (35 °C and 70 °C) were evaluated using rheological approaches. Two fumed silica nanoparticles (NPs) featuring different surface chemistries were used, and their ability to prevent destruction of the polymer network structure against salt addition and temperature increase was investigated. Linear rheological tests (frequency sweep, creep, and creep recovery) and nonlinear rheological tests (large amplitude oscillatory shear) were employed to evaluate the network structure of these systems. The results showed that either adding salt or increasing the temperature destroyed the mechanical integrity of the HPAM 3-dimensional elastic network. However, the introduction of both types of NPs at a sufficient concentration maintained the network structure of HPAM solutions in the small deformation region. In the large deformation region, it was shown that the extent of intra-cycle shear-thickening behavior in the HPAM solution (T = 35 °C and without any salt) decreased by incorporating salt or by increasing the temperature. Moreover, upon incorporating either of the NPs to the HPAM solution, the nonlinear viscoelastic behavior dramatically changed, and the critical strain (linear to nonlinear transition) decreased to a much lower strain amplitude. The outcomes of this study will help petroleum scientists to design more efficient EOR methods.

Combination of DEM/FEM for Progressive Collapse Simulation of Domes Under Earthquake Action

In this paper, a coupled DEM/FEM model is presented to overcome the disadvantages generated by individually using discrete element method (DEM) or finite element method (FEM). The model divides the domain into two independent parts: the DEM sub-domain and the FEM sub-domain. First, the governing equations of the coupled model are established according to the virtual work equation and variational principle, the formula of interface-coupled force is derived based on the penalty function method, and the corresponding program is coded. Second, the key problems involved in the coupled model are investigated, which are the selection of the penalty parameter, the determination of the time-step, and the formulation of the governing equations of the system in the DEM and FEM domains. Finally, the coupled model is applied to progressive collapse simulation of single-layer reticulated domes subjected to severe earthquakes. Both the collapse process and failure mechanism of the numerical results are consistent with the shaking table test phenomena, thereby verifying the validity of the coupled model proposed. The method proposed realizes the balance between computational efficiency and accuracy, that is, the small deformation region is simulated by FEM, while the DEM is applied to discretize the large deformation or failure region. Additionally, it is of high computational efficiency and of reliable precision.

Coercive Force of Low-Carbon Steels During Elastic and Plastic Tensile Deformation

Dependences of the coercive force of samples of St3-grade steel (with chemical composition Fe–0.324C–0.187Si–0.457Mn–0.026Cr–0.029Cu–0.008Co) during elastic and plastic tensile deformation are investigated. It is demonstrated that in the region of small deformations, plastic deformation is non-uniform over the length of the operating part of the sample. For well-annealed steel, the dependences of the coercive force on the elastic sample deformation became reversible, and for plastically deformed steel, a hysteresis is observed that increases with the degree of plastic deformation of the samples. Possible reasons for the hysteresis of the dependence of the coercive force on the elastic cyclic tensile deformations are discussed.

A preliminary study into the correlation of stiffness of the laminar junction of the equine hoof with the length density of its secondary lamellae

The relationship between mechanical behaviour and microscopic structure of the laminar junction of equine hooves under testing conditions requires elucidation. To determine mechanical parameters and 2D length density of profiles of secondary lamellae of the laminar junction in the dermal region and to assess possible correlations. Specimens (25 samples in total) of the laminar junction were taken from front, quarter and heel parts from 3 equine hooves and exposed to a uniaxial tensile test until rupture to obtain Young's moduli of elasticity, ultimate stress and strain. Neighbouring specimens to those used for the biomechanical experiment were processed histologically to assess the length density of laminar junction basement membrane using stereological grids. The estimated median (interquartile range) length density of the laminar junction basement membrane was 0.024 (0.020-0.027)/µm. Young's modulus of elasticity was 0.15 (0.11-0.35) MPa in the small deformation region, and 7.58 (6.14-8.68) MPa in the linear region was. The ultimate stress was 1.67 (1.41-2.67) MPa, and the ultimate strain was 0.50 (0.38-0.70). The Young's modulus of elasticity in the region of small deformations has a moderate correlation with the length density of the laminar junction basement membrane. As with most soft biological tissues, the laminar junction has a nonlinear mechanical behaviour. Within the range of small deformations, which correspond to physiological loading of the laminar junction, a higher length density of the laminar junction basement membrane is correlated with a higher resistance of the laminar junction against high stresses transmitted from the distal phalanx to the hoof wall. The condition of the laminar junction apparatus may be easily quantified as the length density of profiles of secondary dermal lamellae. This quantification provides a simple tool that could be used for comparing the proneness of the various parts of the laminar junction to initial stages of laminitis.

1006 発電機器用繊維強化ゴムの直交異方性超弾性モデルによるFEM解析(OS10-(2)オーガナイズドセッション《発電機器の材料・構造解析と評価》)

In this paper, we propose an orthotropic hyperelastic model for the fiber-reinforced rubber material used as rubber seals in electric generators. The fiber-reinforced rubber is composed of rubber matrix material that is reinforced by two families of fibers. The mechanical property is anisotropic on directions of two fiber families. We improved an anisotropic model by adding terms to the strain energy function to consider its mechanical properties in small deformation region. The energy functions of the fiber families was represented by power series of invariants of stretch and shear deformation in fiber families. In order to identify material parameter of the proposed model, uniaxial tensile test result of the fiber-reinforced rubber were approximated by the nonlinear least squares method. Finally, applicability to the fiber-reinforced rubber of proposed model by FEM simulation was demonstrated to evaluate the applicability of the proposed model to the rubber seal.

Proposal of an Orthotropic Hyperelastic Model and Application to Fiber-Reinforced Rubber Seals in Electric Generator

In this paper, we propose an orthotropic hyperelastic model for the fiber-reinforced rubber material used as rubber seals in electric generators. The fiber-reinforced rubber is composed of rubber matrix material that is reinforced by two families of fibers. The mechanical properties is anisotropic on directions of two fiber families. We improve an anisotropic model by adding terms to the strain energy function to consider its mechanical properties in small deformation region. The energy functions of the fiber families was represented by power series of invariants of stretch and shear deformation in fiber families. Moreover, the proposed strain energy function was polyconvex in totality. In order to identify material parameter of the proposed model, biaxial tensile test result of the rubber matrix and uniaxial tensile test result of the fiber-reinforced rubber were approximated by the nonlinear least squares method. Finally, applicability to the fiber-reinforced rubber of proposed model by FEM simulation of tensile, shear and compression was demonstrated to evaluate the applicability of the proposed model to the rubber seal.

Rheology and nuclear magnetic resonance measurements under shear of sodium dodecyl sulfate/decanol/water nematics

We report on the rheology and deuteron nuclear magnetic resonance (NMR) measurements performed on the nematic lyotropic system sodium dodecyl sulfate, decanol, and water. For total surfactant and cosurfactant concentrations of about 30% by weight, we prepared nematic calamitic NC and nematic discotic ND solutions. We have studied the flow behavior of the NC and ND phases in terms of the transient shear stress using different rheological histories. In flow-reversal experiments, the transient response exhibits nonperiodic oscillations in the region of small deformations (γ=20), which is followed by a long-lasting relaxation toward the stationary state. In the pseudo-Newtonian regime of the viscosity, we have found that the stress, when normalized to its long term value and plotted versus deformation, is shear-rate independent. 2H NMR measurements at rest and under shear were performed on nematic calamitic and discotic solutions prepared in D2O. At rest, the NMR spectra exhibit well-resolved doublet structures, which indicate an alignment of the director along the axis of the magnetic field. At shear rates large enough (γ̇ > 0.3 s−1), alignment is achieved with respect to the flow velocity. One finds alignment angles of 12 ° and 105 ° for the directors of the calamitic and discotic phase, respectively. Combining the results obtained by rheology and by NMR, we provide strong evidence that the NC and ND nematics of the sodium dodecyl sulfate / decanol system are textured nematics of the flow-aligning type.

Thermal and i.r.-dichroic properties of side-chain type liquid-crystalline elastomers

Several liquid-crystalline elastomers (LCEs) have been prepared by crosslinking side-chain type liquid-crystalline polymers (precursors) in which mesogens are dangling from flexible main chains through spacers. Thermal properties and phase behaviour of the precursors and LCEs have been investigated by means of differential scanning calorimetry (d.s.c.) and polarizing microscopy. The glass transition and meso-to-isotropic phase transition temperatures are slightly affected by an introduction of crosslinks to precursors. Orientation of the mesogens in the LCEs under uniaxial elongation has been evaluated in terms of order parameter for orientation ( f) obtained by i.r.-dichroism measurements. All the LCEs under deformation show negative values of f, meaning the orientation direction of mesogens perpendicular to the axis of elongation. The value of f changes greatly in the small deformation region, and reaches equilibrium at ca. 70% elongation, suggesting that a high degree of orientation for the mesogens in LCEs is achieved by a relatively small elongation. Dependence of f on elongation ratio is not influenced by spacer length nor by crosslinking density, implying that the interaction between mesogens is the most dominant factor for the orientational order of mesogens in the LCE system in this study.

Improvement in the Objective Evaluation of Fabric Hand for Thin Dress Fabrics

For the objective evaluation of primary hands of women's thin-dress fabrics, the improved equations converting fabric mechanical properties into hand values are presented. The purpose of this improvement is to improve the accuracy of an evaluation of primary hand “Fukurami” of which objective evaluation has not been so successful in the past for the thin-dress fabrics.The improvement is done by the use of the mechanical data measured by the “high-sensitivity condition” for tensile and compressional properties of fabric. In the high sensitivity conditions, the tensile property is measured in the very small deformation region where the maximum tensile load is 50 gf/cm instead of 500 gf/cm of the standard condition which has been used for men's suitings also for the compressional property, the maximum pressure is 10 gf/cm2 instead of 50 gf/cm2 pressure in the standard condition.It has been also found that the other mechanical parameters in the total 16 parameters of KES-F measuring system can be used to obtain the best result.The new equations KN202-LDY derived on the basis of the new measurement condition provide the higher accuracy in the objective evaluation of the primary hand of “Fukurami” of the thin-dress fabrics.

The strain-energy density function of the urinary bladder.

In previous articles we proposed a finite deformation theory of the urinary bladder. The present paper is the third article in a series of these works. Our aim is to study more carefully the strain-energy density function W of the urinary bladder, because the determination of this function W is one of the central problems in the finite deformation theory of a hyperelastic continuum. We found that, except for an infinitesimally small deformation region where Hook's law is valid, the third term in W of the Valanis-Landel type takes much smaller values than the other two terms, so that this term can be neglected. Hence, the formula giving the true stress t1 for the uniaxial extension test is reduced to the same one as the true stress t for the equal-biaxial extension test. This may be useful in practical applications.

Contribution to the determination of relative increment of internal energy at low deformation of cross-linked rubber

The relative charge of the internal energy, fU/f, during deformation of cross-linked elastomers, poly(ethylene-co-propylene) and poly(ethylene-co-vinyl acetate), was determined at various temperatures. Anomalies in the dependence of fU/f on relative dilatation in the region of small deformations ( 35%) are to a large extent besides other factors due to the sensibility of the formula used to calculate fU/f to temperature changes.

The Energetic Contribution to Rubber Elasticity in the Range of Small Uniaxial Compression and Moderate Elongation

Abstract The relative energetic contribution to the retractive force of a deformed rubber sample, fe/f, has been evaluated from thermoelastic measurements at constant pressure. Extension ratios λ have been studied in the range 0.88⩽λ⩽1.79 at 20° and 40°C. The results are given for a reference temperature, 30°C. Since data in the transition region from uniaxial elongation to compression were to be evaluated, a new set of equations was derived on the basis of the Gaussian force law, because the usual equation for measurements at constant pressure tends towards infinity when approaching the undeformed state λ=1. Considerable difference between the results obtained by different, though apparently equivalent, equations have their origins in the deviation of the experimental data from ideal Gaussian behavior. The influence of this inaccuracy on the terms of the equations is discussed and the most reliable functions for small deformations 0.88⩽λ⩽1.15 and for moderate elongation λ&amp;gt;1.10 have been identified. With these precautions the Gaussian force law is a satisfactory approximation for the determination of reliable values of fe/f. The evaluation of data at small deformations is extremely sensitive to experimental error. Even smoothed polynomials L(f) were not sufficient to eliminate an apparent maximum in the fe/f vs. λ curve. Therefore the linear thermal expansion coefficient, βlin(λ), which is a major term in all the fe/f equations at small deformations, had to be scrutinized critically. Although experimental data in this range showed that βlin(λ) is a slightly S-shaped function, a linear approximation is adequate at moderate elongations. Using one of the new equations together with the linear approximation for βlin(λ) in the region of small deformations, and two equivalent equations at moderate elongation, the energetic contribution to the total stress was found to be fe/f=0.18±0.02 for lightly crosslinked natural rubber. Little variation in fe/f was observed over the full range of measurements: 0.88⩽λ⩽1.70.