Torsional Deformation Modes Research Articles

Functional fatigue of superelasticity and elastocaloric effect for NiTi springs

In this work, the evolutions of superelasticity (SE) and elastocaloric effect (eCE) for NiTi shape memory alloy (SMA) helical springs under cyclic deformation are investigated experimentally and theoretically. Experimental results show that the functional fatigue of SE and eCE occur simultaneously, and these phenomena aggravate significantly with the increase/decrease of the loading level/spring index. Then, a thermo-mechanically coupled constitutive model is established. Two major inelastic deformation mechanisms, martensitic transformation (MT) and transformation-induced plasticity (TRIP), are incorporated. In addition to the martensitic and austenitic phases, the martensitic influence zone is also considered in the proposed constitutive model to characterize the high local stress in the region near the austenitic-martensitic interface. To accurately describe the deformation behavior of NiTi SMA springs, an analytical model considering both the torsion and bending deformation modes is employed. Furthermore, the lumped heat transfer analysis method is adopted to derive the evolution equation for the overall temperature of the springs. Finally, to verify the rationality of the newly developed model, predicted results for the functional fatigue of SE and eCE are compared with the experimental data.

Thermo-mechanically coupled deformation of pseudoelastic NiTi SMA helical spring

Based on the cyclic tension-unloading tests with various displacements (40, 60 and 80 mm) and at different loading rates (0.3 mm/s, 1 mm/s and 5 mm/s), the thermo-mechanically coupled deformation and temperature evolution of pseudoelastic NiTi shape memory alloy (SMA) helical spring are investigated. Experimental results reveal that the phase transition between austenite (A) and martensite (M) phases undergoes a two-step process involving an intermediate phase, that is, rhombohedral (R) phase; the force-displacement responses of the spring depend on the loading rate strongly, which originates from Clausius-Clapeyron relation between the critical stresses of phase transitions (including R and M transformations), and the competition between the internal heat generation and heat exchange. Then, a three-dimensional phenomenological constitutive model is developed by addressing three possible phase transition processes (that is, A→R→M, A→mixed A + R→M and A→M) and thermo-mechanical coupling effect. Generalized thermodynamic forces for the phase transitions and the evolution equation of temperature are derived based on the second and first laws of thermodynamics, respectively. To accurately describe the loading amplitude-dependent dissipation and hardening behavior of MT, new dissipation and hardening laws are proposed. Furthermore, a new analytical model of helical spring is developed by simultaneously considering the torsion and bending deformation modes, curvature effect and the coupling effect between the deformation and temperature evolution. Finally, the developed model is validated by comparing the simulated results with the experimental data, and the influences of geometrical parameters and ambient temperature on the thermo-mechanical responses of the spring are also predicted and discussed.

Modelling the experimental seismic out-of-plane two-way bending response of unreinforced periodic masonry panels using a non-linear discrete homogenized strategy

A non-linear discrete homogenized strategy is used to reproduce out-of-plane two-way bending shake table tests on full-scale unreinforced masonry walls. The numerical strategy represents unreinforced masonry walls as an assemblage of rigid quadrilateral plates connected through non-linear interfaces represented. The material response laws for these non-linear interfaces are derived from a homogenization procedure performed at the meso-scale by a finite-element plate model. This discrete model can simulate masonry orthotropy, full softening behaviour and failure. Bending and torsional deformation modes are represented. The performance of the numerical models in describing the response of the experimentally tested full-scale specimens is presented. The numerical strategy is then used to study the behaviour of unreinforced masonry walls in configurations hitherto untested. Such numerical results are then compared to state-of-the-art analytical approaches. Potential avenues of improvement for the implemented analytical methods are also highlighted.

Vibration analysis of thin-walled pipes with circular axis using the Generalized Beam Theory

This paper presents the dynamic analysis extension of the Generalized Beam Theory (GBT) formulation developed in [1] for curved thin-walled pipes. The new proposed dynamic curved GBT element formulation goes beyond the current GBT’s analysis of straight pipes, not only concerning the coupling and behavior of pipe bends or toroidal shells, but also concerning the effects of the transverse shear modes. In the preceding paper, the stresses and the deformations of a pipe bend under static conditions have been determined through the potential energy formulation for different loading and support conditions. In this paper, the formulation of the kinetic energy is presented to determine the inertia of the GBT element. The consistent element mass matrix derived from the GBT dynamic formulation involves the coupling of certain types of GBT deformation modes resembling that of the element stiffness matrix. Here, to illustrate the application and capabilities of the developed GBT formulation, numerical examples concerning undamped free vibration analysis of truncated and closed toroidal shells with different support conditions are considered involving a combination and coupling of bending, warping, torsional, axisymmetric and local deformation modes. For the purpose of validation, these examples are compared with refined shell finite element models.

Influence of free torsion deformation modes on the microstructure and mechanical properties of commercially pure copper

The paper investigates the effect of the free torsion rate of cylindrical specimes of commercially pure copper (grade M1) on their deformed state, microstructure, and mechanical properties. The study of the microstructure was carried out by means of transmission electron microscopy and X-ray diffraction analysis in the central region and at the periphery of the deformed rod. The mechanical properties were evaluated by measuring the microhardness. It was found that an increase of the torsion rate, other things being equal, promotes more intensive strengthening and refinement of the microstructure.

Continuum representation of nonlinear three-dimensional periodic truss networks by on-the-fly homogenization

Thanks to scale-bridging fabrication techniques, truss-based metamaterials have gained both popularity and complexity, ultimately resulting in structural networks whose description based on classical discrete numerical calculations becomes intractable. We here present a framework for the efficient and accurate simulation of large periodic three-dimensional (3D) truss networks undergoing nonlinear deformation (accounting for linear elastic beams undergoing finite rotations). Although the focus is on elastic beams, the method is sufficiently general to extend to inelastic material behavior. Our approach is based on a continuum representation of the truss (and its numerical implementation via finite elements) whose constitutive behavior is obtained from on-the-fly periodic homogenization at the microstructural unit cell level. We pursue a semi-analytical strategy (previously reported only in two dimensions) which admits the analytical calculation of consistent tangents for convergent implicit solution schemes; the extension to 3D – through the addition of torsional deformation modes and the handling of 3D rotations – results in a powerful tool for the prediction of the complex mechanical response of large structural networks. We validate the small-strain response by comparison to analytical solutions, followed by finite-strain benchmarks that compare simulation results to those of fully-resolved discrete calculations. The homogenization of beam unit cells results in a regularized macroscale model with an intrinsic length scale, which manifests especially when modeling bifurcations or localization. We finally apply our approach to macroscopic boundary value problems involving complex-shaped truss metamaterials (with truss unit cells near the body's boundary mapped onto a conformal surface), which reveal only an insignificant effect of boundary layers on the overall mechanical response, again supporting the applicability of our homogenization approach.

Experimental Characterization of the Torsional Damping in CFRP Disks by Impact Hammer Modal Testing.

Composite materials are widely used for their peculiar combination of excellent structural, mechanical, and damping properties. This work presents an experimental study on the dissipation properties of disk-shaped composite specimens exploiting vibration tests. Two different polymer matrix composites with the same number of identical laminae, but characterized by different stacking sequences, namely unidirectional and quasi-isotropic configurations, have been evaluated. An ad-hoc steel structure was designed and developed to reproduce an in-plane torsional excitation on the specimen. The main idea of the proposed approach relies on deriving the damping properties of the disks by focusing on the modal damping of the overall vibrating structure and, in particular, using just the first in-plane torsional deformation mode. Experimental torsional damping evaluations were conducted by performing vibrational hammer excitation on the presented setup. Two methods were proposed and compared, both relying on a single-degree-of-freedom (SDOF) approximation of the measured frequency response function (FRF).

Innovative elastoplastic J2‐flow model incorporating cyclic and non‐cyclic failure effects of metals as inherent constitutive features

AbstractA new finite strain elastoplastic J2‐flow model is proposed toward directly simulating cyclic and non‐cyclic failure effects of metals. The main novelties of this model are as follows: The usual notion of yielding is rendered irrelevant in a more realistic sense of representing elastoplastic behaviors of metals up to failure; The thermodynamic consistency requirement from the second law may be identically fulfilled; Failure effects under cyclic and non‐cyclic conditions may be automatically incorporated as inherent constitutive features, with involving neither additional variables nor ad hoc failure criteria; Hardening‐to‐softening effects of metals up to failure may be effectively characterized in a unified manner. Simulation results are provided and compared with experimental data for monotonic and cyclic failure effects for both uniaxial and torsional deformation modes. In particular, both the Swift effects and the failure effects of twisted metal tubes are simultaneously simulated for four cases of finite torsion, including free‐end and fixed‐end torsion under monotonic and cyclic loadings, and accurate agreement with finite strain data for both torsional modes is accomplished for the first time.

Strain dependence of critical current and self-field AC loss in Bi-2223/Ag multi-filamentary HTS tapes: a general predictive model

It is well known that mechanical deformations have a strong impact on the critical current () of Bi-2223/Ag multi-filamentary high-temperature superconducting (HTS) tapes, and a remarkable degradation is induced, which results in a significant AC loss. In this paper, a general predictive model based on the strain dependence of the Weibull distribution function of statistical damage of superconducting filaments and the Norris formula is developed to explore the influence of the uniaxial, bending and torsional deformation on degradation and self-field AC loss of Bi-2223/Ag HTS composite tapes. A unified strain dependence of the formula is suggested, which is extended in view of the degradation mechanism of Bi-2223/Ag HTS tapes under a uniaxial deformation with an introduction of longitudinal strain to unify the strain in uniaxial, bending and torsional deformation modes. Then, a modified Norris formula is deduced in light of the unified strain dependence of the model to predict AC loss of Bi-2223/Ag HTS tapes. With a set of appropriate model parameters determined by the tested data of under uniaxial deformation, the presented model can well predict both degradation and AC loss behaviors under not only a uniaxial deformation mode, but the bending and torsional ones. The proposed model indicates that the significant increase of AC loss for a deformed tape is presented due to the notable degradation of

Influence of Deformation Stress Triaxiality on Microstructure and Microhardness of Pure Copper Processed by Simultaneous Torsion and Tension

Simultaneous torsion and tension deformation (STTD) modes were applied on commercial pure copper to investigate the influence of stress triaxiality on microstructure evolution and hardness distribution at room temperature. STTD was divided into pure torsion (PT, a special STTD) and general STTD according to tension loading. Microstructure evolution was observed by optical microscopy, electron backscattering diffraction and transmission electron microscopy. The microhardness distribution was measured on the cross section, and the fracture morphology was observed by scanning electron microscopy. Microstructure observations show that ultrafine grains are separated by high-angle grain boundaries. Microhardness measurements exhibit hardness increased more significantly and uniformly in the specimen processed by general STTD mode than PT mode. Additionally, the fracture morphology indicates the fracture mechanism is different between STTD and PT.

Dynamic visco-hyperelastic behavior of elastomeric hollow cylinder by developing a constitutive equation

In this study, developments of an efficient visco-hyperelastic constitutive equation for describing the time dependent material behavior accurately in dynamic and impact loading and finding related materials constants are considered. Based on proposed constitutive model, behaviour of a hollow cylinder elastomer bushing under different dynamic and impact loading conditions is studied. By implementing the developed visco-hyperelastic constitutive equation to LS-DYNA explicit dynamic finite element software a three dimensional model of the bushing is developed and dynamic behaviour of that in axial and torsional dynamic deformation modes are studied. Dynamic response and induced stress under different impact loadings which is rarely studied in previous researches have been also investigated. Effects of hyperelastic and visco-hyperelastic parameters on deformation and induced stresses as well as strain rate are considered.

Multi‐scale modeling of beam‐like structures: A new boundary condition concept for the RVE

AbstractIn this work a coupled two‐scale beam model using Timoshenko beam elements [1] with finite displacements on the macro scale and fully non‐linear 3D brick elements on the micro scale is proposed. The calculation is carried out with the so‐called FE2 concept. To achieve the coupling between the beam and the brick elements, the algorithm from [2] is adapted.Within the degenerated concept of the Timoshenko beam, the introduction of a pure shear deformation leads to significant problems concerning the equilibrium condition on the micro scale. Applying this deformation mode on the RVE with periodic boundary conditions results in a rigid body rotation. Using linear displacement boundary conditions instead, the wrapping deformation is suppressed on the boundary, leading to a length dependency in the torsional deformation mode. In addition, the shear forces introduce a bending moment, which depends on the length of the RVE and adds spurious normal stresses and a length dependency of the shear stiffness.To overcome these problems, periodic boundary conditions are applied and the displacement assumptions are modified such that the shear deformation is achieved with force pairs on both ends of the RVE. The resulting model leads to length independent results in tension, bending and torsion and a domain which is able to produce a pure shear stress state. Consequently, only this domain of the model should be homogenized which can be accomplished by modifying the variations in the algorithm [2]. The concept is validated by simple linear and non‐linear test problems. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The effect of a non-circular drawing sequence on delamination characteristics of pearlitic steel wire

In this study, a non-circular drawing (NCD) sequence was applied to investigate the effect of deformation behavior, microstructure and texture evolution on delamination characteristics of pearlitic steel wire under torsional deformation mode. The multi-pass NCD sequence was numerically and experimentally applied up to the 12th pass in comparison with conventional wire drawing (WD). For investigation of the deformation characteristics of the drawn wires, three-dimensional finite element and flownet analyses were carried out. These simulation results indicated that the NCD could impose relatively homogeneous plastic deformation on the wire compared to the WD. From the scanning electron microscopy and X-ray diffraction results, globular cementite and cylindrical texture component, which might increase likeliness of delamination fracture, were rarely observed in the NCD drawn wire. In the torsion test, the delamination fracture was observed in the WD drawn wire for the 10th pass while it did not occur for the 12th pass NCD. In addition, the ultimate tensile strength (UTS) of 2300MPa grade wire was manufactured by the NCD and the UTS value was 257MPa higher than the one of the WD. Therefore, it was demonstrated that the multi-pass NCD could impose relatively homogeneous plastic deformation on the wire, resulting in high-torsional ductility with better strength compared to the WD.

REVIEW WORK ON ANALYSIS OF F1 CAR FRAME USING ANSYS

SAE Supra India organizes the undergraduate racing competition for 2013 in which teams are challenged to design considering the various circumstances and to fabricate the making a design in the campus itself. This paper’s sole focus is the design and analysis for a chassis which has to sustain the racing environment. As chassis plays a vital role in a race car and also it is the back bone of a good race car. Good designs allow a light, stiff and extremely safe chassis to be produced at. The work shown in this research paper was taken participation by Black Hawk SAE Supra team. This paper introduces several concepts of frame’s load distributions such a lateral, longitudinal vertical and horizontal torsion and consequent deformation modes. .Various studies were conducted upon the understanding the relation of the machine elements with the user according to Ergonomics consideration. Ergonomics considers factors such as Drivers visibility, seat inclination, thermal isolation etc. The chassis design was carried out on CAD software such as Pro-Engineers. Design model was prepared using anthropometric parameters of tallest driver as 95th percentile male was selected to SAE rules book. Static and dynamic load distributions were calculated analytically followed by extensive study of various boundary conditions to be applied during diverse FEA (Finite Element Analysis) test which was carried out in Ansys. Stress distributions, lateral displacements during static, dynamic and frequency modes were analyzed and found considerably high factor of safety as 3.85.

Experimental Study on Lateral Stiffness and Dynamic Properties of Steel Drive-in Storage Racks

The static and free vibration tests were carried out to investigate the initial lateral stiffness and dynamic properties of steel drive-in storage racks. The bracing configuration and friction between pallets and rail beams were taken into consideration. The static test results indicate that the tested storage racks show sideways and torsional deformation modes under the single-point horizontal force. Both top plan bracings and back spine bracings can change the load transfer through the rack framework, strengthen the initial lateral stiffness of racks, but only back spine bracings can affect the natural frequency and damping ratio of racks. The friction force between pallets and rail beams makes pallets act as links to connect adjacent rack columns, so the pallets are beneficial factors to increase the lateral stiffness of storage racks. Compared with unload racks, the natural frequencies of loaded racks are smaller.

Effect of Deformation Temperature on the Microstructure of Hard Magnetic Fecr22co15 Alloy Subjected to Tension Combined with Torsion Deformation Modes

The paper presents the results of microstructure evolution studies of hard magnetic FeCr22Co15 alloy deformed until destruction by tension and torsion in the temperature range 725-850ºC. The temperatures and deformation rates resulted from the condition of superplasticity occurrence in the Fe-Cr-Co alloys. Observations of the longitudinal sections of the deformed samples in the scanning electron microscope showed the formation of a weak gradient microstructure with the highest grain refinement in the surface layer of the material. Increasing the deformation temperature from 725 to 850_C increased the homogeneity of the deformation along the tensile axis of the sample. It also brought about the increase of grain size and slight increase of the thickness of fine grains in the surface layer. The precipitation of the intermetallic σ-phase was also observed with its maximum amount in the zones of the highest deformation.

Partitioning of elastic energy in open-cell foams under finite deformations

The challenges associated with the computational modeling and simulation of solid foams are threefold—namely, the proper representation of an intricate geometry, the capability to accurately describe large deformations, and the extremely arduous numerical detection and enforcement of self-contact during crushing. The focus of this study is to assess and accurately quantify the effects of geometric nonlinearities (i.e. finite deformations, work produced under buckling-type motions) on the predicted mechanical response of open-cell foams of aluminum and polyurethane prior to the onset of plasticity and contact. Beam elements endowed with three-dimensional finite deformation kinematics are used to represent the foam ligaments. Ligament cross-sections are discretized through a fiber-based formulation that provides accurate information regarding the onset of plasticity, given the uniaxial yield stress–strain data for the bulk material. It is shown that the (hyper-) elastic energy partition within ligaments is significantly influenced by kinematic nonlinearities, which frequently cause strong coupling between the axial, bending, shear and torsional deformation modes. This deformation mode-coupling is uniquely obtained as a result of evaluating equilibrium in the deformed configuration, and is undetectable when small deformations are assumed. The relationship between the foam topology and energy partitioning at various stages of moderate deformation is also investigated. Coupled deformation modes are shown to play an important role, especially in perturbed Kelvin structures where over 70% of the energy is stored in coupled axial-shear and axial-bending modes. The results from this study indicate that it may not always be possible to accurately simulate the onset of plasticity (and the response beyond this regime) if finite deformation kinematics are neglected.

Dynamic impact analysis of long span cable-stayed bridges under moving loads

The aim of this paper is to investigate the dynamic response of long span cable-stayed bridges subjected to moving loads. The analysis is based on a continuum model of the bridge, in which the stay spacing is assumed to be small in comparison with the whole bridge length. As a consequence, the interaction forces between the girder, towers and cable system are described by means of continuous distributed functions. A direct integration method to solve the governing equilibrium equations has been utilized and numerical results, in the dimensionless context, have been proposed to quantify the dynamic impact factors for displacement and stress variables. Moreover, in order to evaluate, numerically, the influence of coupling effects between bridge deformations and moving loads, the analysis focuses attention on the usually neglected non-standard terms related to both centripetal and Coriolis forces. Finally, results are presented with respect to eccentric loads, which introduce both flexural and torsional deformation modes. Sensitivity analyses have been proposed in terms of dynamic impact factors, emphasizing the effects produced by the external mass of the moving system and the influence of both “A” and “H” shaped tower typologies on the dynamic behaviour of the bridge.

Generalised beam theory to analyse the buckling behaviour of circular cylindrical shells and tubes

A formulation of generalised beam theory (GBT) developed to analyse the elastic buckling behaviour of circular hollow section (CHS) members (cylinders and tubes) is presented in this paper. The main concepts involved in the available GBT are adapted to account for the specific aspects related to cross-section geometry. Taking into consideration the kinematic relations used in the theory of thin shells, the variation of the strain energy is evaluated and the terms are physically interpreted, i.e., they are associated with the geometric properties of the CHS. Besides the set of shell-type deformation modes, the formulation also includes axisymmetric and torsion deformation modes. In order to illustrate the application and capabilities of the formulated GBT, the local and global buckling behaviour of CHS members subjected to (i) compression (columns), (ii) bending (beams), (iii) compression and bending (beam-columns) and (iv) torsion (shafts), is analysed. Moreover, the GBT results are compared with estimates obtained by means of shell finite element analyses and are thoroughly discussed.

Cubic beam elements in practical analysis and design of steel frames

This paper discusses various issues in the use of cubic beam elements for computer structural analysis/design of steel frames. It is pointed out that the concern expressed in recent literature regarding the number of cubic elements required to model a steel member is not justified, and that the inaccuracy of one cubic element in Euler buckling analysis of a simply supported column is largely irrelevant to the second-order elastic analysis/design or advanced analysis of steel frames. The sources of inaccuracy of the cubic element are elucidated. It is also explained that the plastic-zone analysis method is not so inefficient as was previously believed. The spatial cubic element is shown to be capable of accurately accounting for the coupling between axial, flexural and torsional deformation modes. It is concluded that for the purposes of second-order elastic analysis/design and advanced analysis of 2D and 3D steel frames, the well-documented cubic element is a versatile and efficient choice.