Bending Deformation Mode Research Articles

Effect of microstructure on two-way shape memory effect in Cu-A1-Mn alloys

The shape memory effect (SME) and the two-way shape memory effect (TWME) of Cu-Al-Mn alloys induced by single bending deformation at room temperature were investigated in relation to the microstructural features of grain size and texture. It was found that the control of the texture and/or grain size significantly improves not only the SME, but also the TWME. Especially, the specimen with near {112} texture obtained by cold-rolling and further recrystallization showed a high degree of TWME (e TWME = 3.6%) in the surface strain which is of the highest level of the TWME in the Cu-base shape memory alloys. It can be concluded that a high level of TWME in the bending deformation mode can be obtained from specimens with an excellent SME.

Impact-induced deformation fields in 2D and 3D woven composites

The deformation fields and kinematics of woven composite material systems, due to impact loads, were analyzed and characterized for various structural and load parameters. Target plates comprising of woven composites with 3D and 2D preforms were considered. Kinetic energies in the range of 18–39,000 J, due to projectile velocities in the range of 2–1000 m/s, were investigated. The impact problem model accounts for geometrical details of the flat target plates and the hemispherical projectile. Contact solutions at dissimilar surfaces were modeled with gap elements, and the solution of the nonlinear dynamic problem was obtained by the finite element method. In the present study, we investigated wave propagation effects, and how their spatial and temporal distribution is related to the evolution of multi-dimensional elastic fields and potential damage modes. Unit cells representative of the 2D and 3D woven composites were used to obtain estimates of the overall elastic moduli. It was found that the compression wave induced by impact reflected several times between the free surfaces of the target plate before fiber failure initiated, and that this was one of the major mechanisms leading to penetration. At low velocity impact, the deformations were similar to quasi-static bending deformation modes, and failure is predicted to be due to fiber breakage at the backside of the target plate. At higher impact velocities, wave propagation effects are more significant and lead to penetration at the impact face. For all material systems, localized shear damage in 3D woven systems and extensive shear delamination in 2D woven systems preceded complete penetration.

Preparation of poly( tert-butyl acrylate- g-styrene) as precursors of amphiphilic graft copolymers: 2. Relaxation processes and mechanical behavior

Viscoelastic relaxations of four poly( tert-butyl acrylate- g-styrene) copolymers are studied over a wide range of temperatures. The temperature location and apparent activation energy of the distinct relaxations observed under tension mode are discussed. As grafted polystyrene content increases in the copolymer, microdomains of both components occur and, consequently, two relaxations associated with cooperative motions of either the acrylate backbone or the graft are observed. A bending deformation mode is also analyzed in the region of the glass transition of the two components to study the phase separation. Moreover, the glass transition temperature of the acrylic backbone is estimated by microhardness measurements. The relationship between microhardness and storage modulus is established either below or above the glass transition of the tert-butyl acrylate backbone.

Monotonic and cyclic loading models for panel zones in steel moment frames

This paper presents the development of analytical models to predict the elastic and inelastic response of the panel zone portion of columns in steel moment resisting frames. In many practical cases, the panel zone can dominate the inelastic response of a moment frame, and accurate panel zone models are needed to realistically predict overall frame performance. Similar to previous models, the newly proposed models are based on the concept of representing the panel zone as a nonlinear rotational spring. These new models build on previously developed models, and introduce a number of features and refinements that show better correlation with available experimental data. The model for monotonic loading is based on quadri-linear panel zone moment–deformation relations. In this model, both bending and shear deformation modes are considered. The model proposed for cyclic loading is based on Dafalias' bounding surface theory combined with Cofie's rules for movement of the bound line. Additional modifications are suggested to the cyclic loading model to account for the influence of a composite floor slab on panel zone response. Extensive comparisons with experimental data are presented.

Finite element analysis and design in stainless steel sheet forming and its experimental comparison

Bending and drawing processes are analyzed in stainless steel sheet forming using solid element and finite-strain formulation by the Finite Element Code MARC. In bending deformation, the springback increases through augmentations of the clearance between punch and workpiece. Divergences between theoretical and experimental results occur due to the simplification of the contact condition at the die–workpiece interface. For the square cup deep drawing process which includes bending and drawing deformation modes, the lubrication conditions are critical factors for producing sound products. All the results derived from the FEM analysis show reasonable agreement with the experimental data.

Semi-analytical finite elements in the higher-order theory of beams

The paper presents semi-analytical finite elements leading to the development of a higher-order theory for beams. An analysis of existing beam theories reveals their semi-analytical character. The semi-analytical finite element (SFE) method proposed assumes the cross-section of a solid beam to be an assemblage of certain semi-analytical elements. The SFE method is based on independent approximations of three-dimensional fields of displacements and stresses. The method reflects the multi-level nature of beams where conventional finite elements are transferred to the level of beam equations for heuristic considerations. A mathematical formulation of the linear theory of a solid beam involves the equations of compatibility, equilibrium and constitutive relationships, i.e. the elastic law as well as static and kinematic boundary conditions. Compatibility conditions are derived directly by using finite element approximations, while equilibrium equations, constitutive equations and boundary conditions may be derived by applying stationarity of a modified Hellinger-Reissner functional. This derivation may be also defined by straightforward application of a generalised virtual work formulation. The equations of a beam are formulated in terms of generalised variables — integral resultants of stresses and strains as well as of nodal displacements. The definition of generalised variables is assigned to the nodes of the finite element mesh. Bending, warping and other higher-order deformation modes are described automatically. Finally, the set of governing equations includes mixed algebraic-differential operators. Their explicit expressions depend on one of the element types — isoparametric, subparametric or superparametric. The versatility of SFE is demonstrated in practical applications involving well-known solutions. The classical Euler-Bernoulli and Timoshenko theories are derived using a single one-dimensional element. The beams with a thin-walled cross-section are described as an assemblage of semi-analytical elements. On the basis of a higher-order theory, the conventional semi-analytically based finite elements (SABFE) are derived. Their basic relations are also presented. Some numerical examples of the applications to thin-walled beams illustrate the basic features. Possible extensions of SFE to dynamics, geometric non-linearity and shells are briefly discussed.

Loss Factors Of Damping Treated Structural Cables

The Ross-Ungar-Kerwin theory of damping treatment in plates/beams is extended to estimate the loss factors of damping treated structural cable, which is made by introducing some viscoelastic material between the strands and the outer cover. The loss factors for axial and bending deformations are analytically investigated. It is concluded that the maximum magnitude of the axial loss factor, as well as the bending loss factor, for the case of a soft outer cover could be of the order of 10 -2, because even in the bending deformation mode, the bending-induced axial deformation acts as the main source of damping when a comparatively soft outer cover is chosen. For the case of an extremely stiff outer cover, however, the maximum magnitude of the bending loss factor obtained could be of the order of 0·2.

Symmetry and Intervalent Charge Transfer in Copper‐Oxide Superconducting Precursors

AbstractA vibrationally coupled intervalent charge transfer theory is proposed for the copper oxide‐superconductors. The proposed B1g‐vibrational distortion exactly interchanges the chemical environment of the neighboring copper atoms. A quadruple cell is constructed to accommodate the non‐stoichiometry and a double copper‐oxide‐conducting chain with distorted symmetry is postulated. The distorted structure, prone to switching of the copper sites by vibration, is postulated to be the superconducting precursor. The left over‐oxygen, due to oxygen deficiency, is allowed to serve as a bridge between the chains and 10 oscillate with the vibration. Symmetry of the system, before and after distortion, is used to explain the spin‐angular momentum change, needed to arrive at Cooper‐paired electron/holes. The O− and O= atoms are postulated to be the bridge for superexchange and charge flow between the Cu+1/Cu+3 and Cu+1/Cu+2 pairs. The same theory is used to interpret the mechanisms for the following three types of copper oxide‐superconductors: YBa2Cu3OT‐x; La2‐xSrxCuO4 and the newly discovered electron superconductor Nd2‐xCexCuO4‐y. The bridge oxygen oscillation may be chosen not to come from the breathing mode but from the bending deformation mode that involves the relative motion of the Cu atoms (to the oxygen) giving rise to smaller oxygen isotope effect.

Raman Spectral Characteristics of Bis(terdentate)cobalt(III) Complexes with N and O Donor Atoms

Abstract The Raman spectra were measured for the bis and mixed type cobalt(III) complexes with ethylenediamine-N-acetate (edma) in an aqueous solution in the skeletal vibration region. The Raman bands could be classified into five vibration modes; a totally symmetric stretching vibration mode in the 510–650 cm−1 region, a stretching vibration mode excluding the totally symmetric one in the 410–540 cm−1 region, a skeletal breathing vibration mode in the 370–490 cm−1 region, a skeletal bending deformation mode in the 270–420 cm−1 region, and a chelate ring deformation mode in the 220–270 cm−1 region. Differences in the skeletal vibrations were observed between the fac and mer isomers for the chelate ring arrangement. Further, differences for the chelate ring arrangement between the Raman spectra of sym-fac and unsym-fac isomers were observed in the skeletal bending deformation mode. The cobalt(III) complexes with the terdentate ligands containing N-methyl group exhibited Raman bands shifted to a lower frequency than those of the corresponding cobalt(III) complexes containing no N-methyl group in the totally symmetric stretching vibration mode region.

Raman Spectral Characteristics of Cobalt(III) Complexes with Quadridentate Ligands

Abstract The Raman spectra of cobalt(III) complexes with quadridentate ligands such as triethylenetetramine (trien), ethylenediamine-N,N′-diacetate (edda), tris(2-aminoethyl)amine (tren), and N-(2-aminoethyl)iminodiacetate (aeida), were measured for the skeletal vibration region of 200–700 cm−1 in order to obtain general information on the relation between the spectra and the structures of these complexes. The Raman bands can be classified into four vibration modes; a totally symmetric stretching vibration mode in the 420–670 cm−1 region, a stretching vibration mode excluding the totally symmetric one in the 390–450 cm−1 region, a metal-ligand skeletal bending deformation mode in the 300–420 cm−1 region, and the chelate ring deformation mode in the 240–290 cm−1 region. The skeletal vibrations of cis-α and cis-β isomers of the cobalt(III) complexes with linear quadridentate ligands correspond to those of the tris(bidentate)cobalt(III) and the mer isomers of bis(terdentate)cobalt(III) complexes, respectively. In addition, the skeletal vibrations of the cobalt(III) complexes with tripodlike quadridentate ligands also correspond to those of the mer isomers of bis(terdentate)cobalt(III) complexes. The Raman spectra of the present complexes depend primarily on the configuration of the quadridentate ligands and the effect due to the bidentate ligands is of secondary importance.

Raman Spectra of Tris(bidentate)cobalt(III) Complexes Containing 1,3-Propanediamine and β-Alaninate

Abstract The Raman spectra of the tris(bidentate)cobalt(III) complexes containing the six-membered tn and/or β-ala chelate ring, where tn and β-ala denote 1,3-propanediamine and β-alaninate respectively, were measured in order to investigate the relation between the Raman spectra and the structures of the complexes. The Raman bands can be classified into four vibration modes: A totally symmetric stretching vibration mode in the 440–640 cm−1 region, a stretching vibration mode excluding the totally symmetric one in the 380–480 cm−1 region, a metal-ligand skeletal bending deformation mode in the 260–400 cm−1 region, and a chelate ring deformation mode in the 220–290 cm−1 region. The present complexes characteristically exhibited more Raman bands than the complexes with the five-membered chelate rings in the totally symmetric stretching vibration mode. For the [Co(β-ala)2(tn)]+ complex, the three geometrical isomers, trans(O), C2-cis(O), and C1-cis(O), which were prepared for the first time, each exhibited characteristic Raman spectral features.

Raman Spectral Characteristics of [Co(ida)n(dien)2−n]-Type and Related Complexes

Abstract The Raman spectra of [Co(ida)n(dien)2−n](3−2n)+(n=0, 1, and 2), where ida and dien denote iminodiacetate and diethylenetriamine respectively, and related complexes in the skeletal vibration region were measured in order to deduce the relation between their spectra and their geometrical structures. The Raman bands could be classified into five vibration modes: Totally symmetric stretching vibration modes (polarized bands in the 510–625 cm−1 region); Co–O and Co–N stretching vibration modes (depolarized bands in the 430–525 cm−1 region); metal-ligand skeletal breathing vibration modes (polarized bands in the 360–480 cm−1 region); skeletal bending deformation modes (depolarized bands in the 290–405 cm−1 region), and chelate ring deformation modes (polarized bands in the 220–260 cm−1 region). The polarized bands around 400 cm−1 were regarded as characteristic of the mono and bis(terdentate)cobalt(III) complexes. The mer isomers of each complex gave Raman spectra clearly different from those of the fac isomers in the stretching vibration region.

Raman Spectra in the Skeletal Vibration Region of [Co(gly)x(ox)y(en)z](3−x−2y)+ Complexes (x+y+z=3)

Abstract The Raman spectra were measured for the complete series of cobalt(III) complexes, [Co(gly)x(ox)y-(en)z](3−x−2y)+, where gly, ox, and en denote glycinate, oxalate, and ethylenediamine, respectively, and x+y+z is equal to 3, in aqueous solution in the skeletal vibration region to deduce their structure-spectra relation. The spectra could be classified into four categories: polarized bands in the 610–520 cm−1 region due to a totally symmetric stretching vibration mode, depolarized bands in the 520–400 cm−1 region due to Co–O and Co–N stretching vibration modes, depolarized bands in the 400–300 cm−1 region due to the metal-ligand skeletal bending deformation mode, and polarized bands in the 300–200 cm−1 region due to the chelate ring deformation mode. The depolarized bands due to the stretching vibration mode could be used for the differentiation of C2-cis and C1-cis isomers of [Co(N)4(O)2] and [Co(N)2(O)4] type complexes.

Deuterium shifts in the high resolution photoelectron spectra of acetaldehyde

By comparing the high-resolution photoelectron spectra of acetaldehyde and three of its deuterated derivatives (CH3CDO, CD3CHO, and CD3CDO) in the first system (?), the assignment of six vibrational modes in the ground state of the acetaldehyde ion was possible. The vibronic structure of this system is very sensitive to deuteration of the CH3 or CHO group, showing that the active vibrations include complex motions of all the hydrogen atoms in acetaldehyde. The most prominent vibrations are the CH bending and CH3 deformation modes which reveal that the oxygen lone pair electrons play an important role in determining the bond angles in the acetaldehyde ion.