Effect Of Shear Strain Research Articles

Influence of HPT and Accumulative High-Pressure Torsion on the Structure and Hv of a Zirconium Alloy

The authors previously used the accumulative high-pressure torsion (ACC HPT) method for the first time on steel 316, β-Ti alloy, and bulk metallic glass vit105. On low-alloyed alloys, in particular, the zirconium alloy Zr-1%Nb, the new method was not used. This alloy has a tendency to α → ω phase transformations at using simple HPT. When using ACC HPT, the α → ω transformation can be influenced to a greater extent. This article studies the sliding effect and accumulation of shear strain in Zr-1%Nb alloy at various stages of high-pressure torsion (HPT). The degree of shear deformation at different stages of HPT was estimated. The influence of various high-pressure torsion conditions on the micro-hardness and phase composition by X-ray diffraction (XRD) of Zr-1%Nb was analyzed. It is shown that at high-pressure torsion revolutions of n = 2, anvils and the specimen significantly slip, which is a result of material strengthening. It was found that despite sliding, regular high-pressure torsion resulted in the high strengthening of Zr-1%Nb alloy (micro-hardness more than doubled), and after high-pressure torsion n = 10, up to 97% of the high-pressure ω-phase was formed in it (as in papers of other researchers). Accumulative high-pressure torsion deformation leads to the strongest transformation of the Zr-1%Nb structure and Hv and, therefore, to a higher real strain of the material due to composition by upsetting and torsion in strain cycles.

圧縮せん断法により作製したCu-Zn合金薄板の機械特性に与えるせん断ひずみの影響

圧縮せん断法により作製したCu-Zn合金薄板の機械特性に与えるせん断ひずみの影響

Dissipative port-Hamiltonian Formulation of Maxwell Viscoelastic Fluids

Abstract In this paper we consider general port-Hamiltonian formulations of multidimensional Maxwell’s viscoelastic fluids. Two different cases are considered to describe the energy fluxes in isentropic compressible and incompressible fluids. In the compressible case, the viscoelastic effects of shear and dilatational strains on the stress tensor are described individually through the corresponding constitutive equations. In the incompressible case, an approach based on the bulk modulus definition is proposed in order to obtain an appropriate characterization, from the port-Hamiltonian point of view, of the pressure and nonlinear terms in the momentum equation, associated with both dynamic pressure and vorticity of the flow.

Free vibration of FGM conical–spherical shells

Natural frequencies of a conical–spherical functionally graded material (FGM) shell are obtained in this study. It is assumed that the conical and spherical shell components have identical thickness. The system of joined shell is made from FGMs, where properties of the shell are graded through the thickness direction. The first order shear deformation theory of shells is used to investigate the effects of shear strains and rotary inertia. The Donnel type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations are discretized using the semi-analytical generalized differential quadrature (GDQ) method. Considering various types of boundary conditions for the shell ends and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells with the data of conventional finite element software, parametric studies are carried out for the system of combined moderately thick conical–spherical joined shells made of FGMs and various types of end supports.

Gap opening in graphene nanoribbons by application of simple shear strain and in-plane electric field

The effects of shear strain and applied in plane electric field on the electronic properties of monolayer graphene nanoribbons (GNRs) are theoretically investigated. Band structures and the probability densities are calculated within the tight-binding model and the mechanical stresses submitted to the GNRs are taken into account by using the theory of linear elasticity with joint modifications in the elongation of the nearest-neighbor vectors and the modification of the hopping parameters. The energy gaps for specific widths of (semiconducting) armchair nanoribbons are verified also in the presence of either strain or field, whereas zigzag nanoribbons are metallic for any value of strain and exhibit a small gap for any value of field. However, our results demonstrate that when both strain and electric field are combined, a significant energy gap is always observed in the band structure, for any width or edge type of the ribbon. Moreover, the obtained total wave function is asymmetric along the ribbon width due to the applied electric field that pushes the electrons to one side of the ribbon and, under shear strain, a peak at the center of the ribbon in the spatial distribution is also observed owing to the preferable localization around the almost undeformed carbon bonds at ribbon center.

Evaluation of optimum length scale parameters in longitudinal wave propagation on nonlocal strain gradient carbon nanotubes by lattice dynamics

Longitudinal wave propagation in carbon nanotubes has been investigated by using Rayleigh-Bishop rod model and nonlocal strain gradient elasticity theory in the present study. Size dependent governing equation of motion has been obtained with variational formulation. Validation of the proposed model has been achieved with developed lattice dynamics model which considers neighborhood interaction. Least squares approach has been used in addition to the traditional calibration methodology. Number of atomic interactions, shear strain and rotary inertia effects have important effects on the calibration of scale parameters. Present results could help to continuum modeling of carbon nanotubes with accurate scale parameters.

Vibration attenuation and dynamic control of piezolaminated plates with coupled electromechanical actuation

Vibration attenuation and dynamic control of the piezolaminated plate actuated with coupled electromechanical loading are aimed and achieved in the present work. Efficient finite element methodology with higher-order shear deformation theory is assisted to blend the effects of shear strains in the computational model. An isoperimetric eight-noded rectangular element is implemented through linear electric potential distribution along the thickness to set up the relations. Coupled electromechanical loading is considered in the formulation to consider the piezoelectric sensing and actuation mechanism. Piezolaminated plates with both cross-ply and angle-ply orientation of bonded substrate lamina are considered in the analysis. Vibration responses of multilayered composite plates with surface-mounted piezolaminates are evaluated for open-circuit and closed-circuit boundary conditions of the electric field. Results obtained from the analysis are well revealed for frequencies of various modes of simply supported piezolaminated plates. Dynamic vibrational response and effect of the control gain (Gv) in terms of velocity feedback on the dynamic characteristics of a piezoelectric laminated plate are examined. Another aim of proposing this FE model is to demonstrate the effect of placement of fibers in a different orientation for the PVDF layer to achieve active damping, and attenuation of vibrations of the laminated composite plate is also achieved and demonstrated.

The role of shear strain during Accumulative Roll-Bonding of multilayered composite sheets: Pattern formation, microstructure and texture evolution

The present study was designed to determine the effect of shear strain on the macro- and microstructure and texture evolution in the AA1050/AA7050 Al multilayered composite sheets. The sheets were processed by Accumulative Roll-Bonding (ARB) and Asymmetric ARB (AARB) at 450 °C and 500 °C. The shear strain in the AARB process has a remarkable influence in achieving a macrostructural wavy-pattern, more than the flow behavior of the materials. For ARB, a flat-pattern with slight waviness was produced mainly due to flow incompatibility, as estimated by finite element simulation and observed by macrostructural analysis. In addition, friction at the surfaces and at the interfaces, and the strain distribution, together with the coarsening or dissolution of precipitates in the AA7050 layers have also influenced the shear banding and microstructure evolution in the sheets. A reduction in the texture intensity by AARB was observed. The grain refinement in the AA1050 layers was controlled by continuous dynamic recrystallization and static recovery during the thermo-mechanical cycles for both processing routes. The AA7050 layers presented a more complex grain refinement behavior that was influenced by dissolution of the η- and η′-phases, which was observed for both temperatures in the ARB. In contrast, the shear strain accelerated this dissolution kinetics and grain growth in the AA7050 layers of sheets processed by AARB.

STATIC ANALYSIS OF FGM CYLINDRICAL SHELLS UNDER LOCAL LOAD USING QUASI-3D HIGHER-ORDER SHEAR DEFORMATION THEORY

The paper presents static analysis results of functionally graded material (FGM) cylindrical shells under concentrated load by an analytical approach. The basic equations are formulated based on a higher-order shear strain theory, taking into account the effects of transverse shear strain and stress. The one-dimensional material distribution in the thickness direction follows Voigt’s power law. In this article influences of several geometric parameters and material distribution coefficients on the stress state of FGM cylindrical shells are considered. Based on the analysis results at the clamped boundary zone, the local load concentration is found, and the transverse normal stress is demonstrated to be considerable at this zone.

The Effect of Additional Shear Strains Induced by Die Rotation on the Radial Pressing of Metal Powder Billets

The axial pressing of a tubular metal powder billet accompanied by simultaneous rotation of the billet synchronously with the inner rod relative to the outer die wall has been considered. Such a compaction pattern for nonporous compact materials is known as ‘high-pressure tube twisting’ and used to improve the structure and design features of the tubular product by strain accumulation. Unlike a compact material, the behavior of a powder billet is determined both by hardening its solid phase and compaction with a gradual decrease in pores volume. These factors specify the peculiar behavior of porous materials under the formulated above conditions, which requires the plasticity theory for porous bodies to be applied. Additional assumptions concerning kinematic restrictions enabled finding explicit expressions for hardening and compaction pressure in analytical form. The derived analytical solution is multi-parametric and describes the influence exerted on the compaction pressure by hardening constants of the material, initial and final density of the compacts, and degree of mutual die walls rotation. The performed analysis allowed concluding that the short-term application of shear strains induced by the mutual rotation of the die elements reduces, in any case, the value of the current operating pressure during compaction. On the other hand, in the long-term compaction process, the hardening of the solid phase in a porous body caused by additional shear strains can lead to an increase in radial pressure at the same final density. The change from the pressure decrease stage to pressure increase stage significantly depends on how hard the powder material is. Therefore, the die is advised to be rotated for powders produced of a nearly ideal plastic material. In most cases, the rotation of a die throughout the entire pressing process is advisable only for sufficiently porous billets subjected to very insignificant compaction. In the case of billets compacted to small porosities, the die walls should be rotated only at the end of the compaction process.

Prediction on grinding force during grinding powder metallurgy nickel-based superalloy FGH96 with electroplated CBN abrasive wheel

In this article, a grinding force model, which is on the basis of cutting process of single abrasive grains combined with the method of theoretical derivation and empirical formula by analyzing the formation mechanism of grinding force, was established. Three key factors have been taken into accounts in this model, such as the contact friction force between abrasive grains and materials, the plastic deformation of material in the process of abrasive plowing, and the shear strain effect of material during the process of cutting chips formation. The model was finally validated by the orthogonal grinding experiment of powder metallurgy nickel-based superalloy FGH96 by using the electroplated CBN abrasive wheel. Grinding force values of prediction and experiment were in good consistency. The errors of tangential grinding force and normal grinding force were 9.8% and 13.6%, respectively. The contributions of sliding force, plowing force and chip formation force were also analyzed. In addition, the tangential forces of sliding, plowing and chip formation are 14%, 19% and 11% of the normal forces on average, respectively. The pro-posed grinding force model is not only in favor of optimizing the grinding parameters and improving grinding efficiency, but also contributes to study some other grinding subjects (e.g. abrasive wheel wear, grinding heat, residual stress).

Effects of local shear strain on the zigzag graphene nanoribbon with a topological line defect

Abstract First-principles density functional theory calculations are performed to study the effects of local shear strain on the structural, mechanical and electronic properties of zigzag graphene nanoribbon with a topological line defect (LD-ZGNR). By changing the nanoribbon width N (N is the number of zigzag chains in the left or right ribbons of the topological line defect) and deformation positions, the optimal position is obtained. The mechanical properties of the LD-ZGNR such as stress-strain curves exhibit nonlinear behavior with strain, and the shear modulus is strongly dependent on the nanoribbon width N and deformation positions. Furthermore, the strong interactions among atoms of the LD-ZGNR under local shear strain induce dramatic changes to the electronic properties of the system. This work reveals mechanism of LD-ZGNR under local shear strain, and provides new idea and more accurate data for the design and application of graphene flexible elastic electronic devices.

Characterization of Shear Strain on PDMS: Numerical and Experimental Approaches

Polydimethylsiloxane (PDMS) is one of the most popular elastomers and has been used in different fields, especially in biomechanics research. Among the many interesting features of this material, its hyperelastic behavior stands out, which allows the use of PDMS in various applications, like the ones that mimic soft tissues. However, the hyperelastic behavior is not linear and needs detailed analysis, especially the characterization of shear strain. In this work, two approaches, numerical and experimental, were proposed to characterize the effect of shear strain on PDMS. The experimental method was implemented as a simple shear testing associated with 3D digital image correlation and was made using two specimens with two thicknesses of PDMS (2 and 4 mm). A finite element software was used to implement the numerical simulations, in which four different simulations using the Mooney–Rivlin, Yeoh, Gent, and polynomial hyperelastic constitutive models were performed. These approaches showed that the maximum value of shear strain occurred in the central region of the PDMS, and higher values emerged for the 2 mm PDMS thickness. Qualitatively, in the central area of the specimen, the numerical and experimental results have similar behaviors and the values of shear strain are close. For higher values of displacement and thicknesses, the numerical simulation results move further away from experimental values.

The vibration of two-dimensional imperfect functionally graded (2D-FG) porous rotating nanobeams based on general nonlocal theory

A comprehensive vibrational analysis of bi-directional functionally graded (2D-FG) rotating nanobeams with porosities is studied for the first time. The beam is modeled based on general nonlocal theory (GNT) where the beam governing equations are derived depending on two different nonlocal parameters. Unlike Eringen’s conventional form of nonlocal theory, the general nonlocal theory can reveal both hardening and softening behaviors of the material. Here, the attenuation functions are altered in both transverse and longitudinal directions of 2D-FG nanobeam. This feature, which has a significant effect on the vibrational characteristics, has not been considered in previous studies. Moreover, to estimate the effects of the higher-order transverse shear strains on the vibration of the nanobeam, Reddy’s beam theory (RBT), which includes higher-order shear deformation, is employed. The material properties of the 2D-FG rotating nanobeam vary both in the length and thickness directions according to a power law. The generalized differential quadrature method (GDQM) is used to predict the vibration response. Also, the effects of material variation along the length and thickness directions, the rotating velocity of the nanobeam, the porosity volume fraction and the length to thickness ratio of the rotating nanobeam are illustrated and discussed in detail. The investigations performed in this study expose new phenomena for the vibration of nanobeams.

Vibrational behavior of beams made of functionally graded materials by using a mixed formulation

This paper investigates the vibrational behavior of beams made of functionally graded materials using a mixed formulation. Unlike the other high order shear deformation theories (HSDTs), the proposed formulation is elaborated within a double field of displacements and stresses which offers the possibility of the development of low order linear elements with enhanced accuracy. As well as, the effect of the transverse shear strains and the zero condition of the transverse shear stresses on the top and bottom surfaces are verified. The material characteristics of the beams are described via a power law distribution in order to take into account the continuous variation of the volume fraction of its constituents along the thickness direction. Numerical simulations are conducted to show the influence of power law index, slenderness ratios, and boundary conditions on natural frequencies of functionally graded beams. Results demonstrate the efficiency and the applicability of the model based on a refined mixed formulation and its ability to predict the vibrational behavior of functionally graded beams with good accuracy.

Effect of straining on spiral wave dynamics in excitable media

The present article envisages to explore the dynamics of stable rotating spiral waves in excitable media under the effect of shear strain through the Oregonator model. We employ an existing unconditionally stable, implicit high order compact finite difference scheme to discretize the highly nonlinear system governing the spiral wave patterns. In the process, we also study the effect of reaction parameters on the dynamics of spiral waves in the absence of straining, which results in the transition from the stable (periodic) rotation to compound (non-periodic) rotation of spiral waves. Our study reveals the existence of three regimes with a new time range, which is different from the earlier ones reported in literature; they characterize the extremely complex behaviour of the patterns under the effect of straining. The aforesaid conclusion is arrived at by carrying out a comprehensive analysis of the power spectrum of the tip motion. Besides establishing the stability of simulated rotating waves, the accuracy of the computed solutions has been ascertained through a convergence analysis and mesh independence study.

Microstructural Evolution and Microhardness Variations in Pure Titanium Processed by High‐Pressure Torsion

A grade 2 pure titanium with an initial grain size of ≈50 μm is processed by high‐pressure torsion (HPT) at room temperature under an imposed pressure of 6.0 GPa. The microhardness variations are examined and the results show that the disks are reasonably homogeneous after 10 turns of torsional straining. The microstructural evolution is systematically characterized by optical microscopy, X‐ray diffraction, and transmission electron microscopy to provide information on the effect of shear strain on grain size and microstructure. The results demonstrate that the initial coarse structure is gradually refined from the edge to the center of the disk under the shear stress during HPT processing and an ultrafine‐grained pure Ti is achieved with an average grain size of ≈96 nm after 10 turns. A model is developed by considering the formation of subgrain boundaries, twins, and high‐angle grain boundaries for the grain refinement of pure Ti processed by HPT.

Highlighting the impact of shear strain on the SiO2 glass structure: From experiments to atomistic simulations

SiO2 glass structure has been permanently modified by uniaxial compression. Within such a loading, the structure is supposed to be affected both by densification and shear flow. We propose to compare recovered silica samples with similar densities, initially deformed plastically under a hydrostatic compression or under a uniaxial compression. From micro-Raman spectroscopy experiments, the shear strain effects have been highlighted on the structural modifications of the glass and have been confirmed from molecular dynamic simulations. In particular, medium range order depends on the mechanical history in plastically deformed glasses. Indeed, both experiments and simulations demonstrate that small rings are favored when permanent shear strain acts with densification, thus allowing a structural signature identification of the densification process.

Effect of shear strain on increase of strength and plastic properties of products made of refractory powder materials

The analysis of modern development of plastic deformation methods of powdered materials, porous bodies and powders is carried out. The technology for obtaining of heavy-loaded parts from hard-to-form powder materials is considered. It is shown that repeated shear deformation increases the uniformity, equalizes the structure increases the strength characteristics of the deformable workpiece material and has little effect on the level of plastic properties.

Study on effects of strong shear strain on recrystallized grain size of pure iron and microstructure control method

The effects of severe plastic deformation by orthogonal cutting on static recrystallization is discussed, and a simpler microstructure control method by using metal cutting and heat treatment is proposed. Pure iron was used as a test material. Large shear strain of 6.60 and 5.04 was induced by orthogonal cutting. Chips were straightened by skin-pass rolling to produce thin metal specimens. After rolling, the specimens were subjected to heat treatment under argon gas atmosphere at 500 °C and 600 °C for 1 min. Microstructure was analyzed by the SEM-EBSD method and mechanical properties were measured by a tensile test. Ultrafine grained sheets with average grain diameter of 0.2 µm were produced by cutting. It was observed that different recrystallized grain structure in different heat treatment temperature. The mechanical properties of the specimen could be controlled by heat treatment conditions. The proposed method is useful to produce an ultrafine grained sheet and to control mechanical properties.