Superelastic shape memory alloy cables: Part I – Isothermal tension experiments

Cables (or wire ropes) made from NiTi shape memory alloy (SMA) wires are relatively new and unexplored structural elements that combine many of the advantages of conventional cables with the adaptive properties of SMAs (shape memory and superelasticity) and have a broad range of potential applications. In this two part series, an extensive set of uniaxial tension experiments was performed on two Nitinol cable constructions, a 7 × 7 right regular lay and a 1 × 27 alternating lay, to characterize their superelastic behavior in room temperature air. Details of the evolution of strain and temperature fields were captured by simultaneous stereo digital image correlation and infrared imaging, respectively. Here in Part I, the nearly isothermal, superelastic responses of the two cable designs are presented and compared. Overall, the 7 × 7 construction has a mechanical response similar to that of straight wires with propagating transformation fronts and distinct stress plateaus during stress-induced transformations. The 1 × 27 construction, however, exhibits a more compliant and stable mechanical response, trading a decreased force for additional elongation, and does not exhibit transformation fronts due to the deeper helix angles of the layers. In Part II that follows, selected subcomponents are dissected from the two cable’s hierarchical constructions to experimentally break down the cable’s responses.     

Analytical study of the nonlinear behavior of a shape memory oscillator: Part II—resonance secondary

In this work, the response of a single-degree-of-freedom shape memory oscillator subjected to the excitation harmonic has been investigated. Equation of motion is formulated assuming a polynomial constitutive model to describe the restitution force of the oscillator. Here the method of multiple scales is used to obtain an approximate solution to the equations of the motion describing the modulation equations of amplitude and phase, and to investigate theoretically its stability. This work is presented in two parts. In Part I of this study we showed the modeling of the problem where the free vibration of the oscillator at low temperature is analyzed, where martensitic phase is stable. Part I also presents the investigation dynamics of the primary resonance of the pseudoelastic oscillator. Part II of the work is focused on the study in the secondary resonance of a pseudoelastic oscillator using the model developed in Part I. The analysis of the system in Part I as well as in Part II is accomplished numerically by means of phase portraits, Lyapunov exponents, power spectrum and Poincare maps. Frequency-response curves are constructed for shape memory oscillators for various excitation levels and detuning parameter. A rich class of solutions and bifurcations, including jump phenomena and saddle-node bifurcations, is found.     

Internal loops in superelastic shape memory alloy wires under torsion – Experiments and simulations/predictions

Understanding torsional responses of shape memory alloy (SMA) specimens under partial or fully transformed cases with internal loops is of particular importance as the entire response might not be always utilized and only a portion of the entire response (internal loop) might be of significance to designers. In this work, we present experimental results of large complex loading and unloading torsional cycles which were conducted on superelastic SMA wires, under isothermal conditions with the purpose of elucidating the torsional internal loop response during loading and unloading. Such data hereto has not been available in open literature. Utilizing this data, we model the torsional response of superelastic SMA wires subjected to various loading and unloading situations that can result in different extents of transformation.A thermodynamically consistent Preisach model (Rao and Srinivasa, 2013) captures such complex internal loops with a high degree of precision by modeling driving force for phase transformation vs. volume fraction of martensite relationships. This approach is different from capturing purely phenomenological stress–strain or stress–temperature Preisach models. The thermodynamic approach utilized here has broader predictive capability. The model predictions indicate good agreement with the internal loop structures even though only the outer loop information was used for model calibration. The addition of a single inner loop information for model calibration greatly improves the predictions.     

Dynamic crushing of aluminum foams: Part II – Analysis

Part II of this study uses micromechanically accurate foam models to simulate and study the dynamic crushing of open-cell foams. The model starts as random soap froth generated using the Surface Evolver software to mimic the microstructure of the foams tested. The linear edges of the cellular microstructure are “dressed” with appropriate distributions of solid to match those of ligaments in the actual foams and their relative density. The ligaments are modeled as shear-deformable beams with variable cross sections discretized with beam elements in LS-DYNA, while the Al-alloy is modeled as a finitely deforming elastic–plastic material. The numerical contact algorithm of the code is used to model ligament contact and limit localized cell crushing. The quasi-static and all dynamic crushing experiments in Part I are simulated numerically. The models are shown to reproduce all aspects of the crushing behavior including the formation and evolution of nearly planar shocks, the force acting at the two ends, the shock front velocity, the strain in the crushed material behind the shock, and the energy absorbed.     

Finite deformation pseudo-elasticity of shape memory alloys – Constitutive modelling and finite element implementation

In this paper we suggest a new phenomenological material model for shape memory alloys. In contrast to many earlier concepts of this kind the present approach includes arbitrarily large deformations. The work is motivated by the requirement, also expressed by regulatory agencies, to carry out finite element simulations of NiTi stents. Depending on the quality of the numerical results it is possible to circumvent, at least partially, expensive experimental investigations. Stent structures are usually designed to significantly reduce their diameter during the insertion into a catheter. Thereby large rotations combined with moderate and large strains occur. In this process an agreement of numerical and experimental results is often hard to achieve. One of the reasons for this discrepancy is the use of unrealistic material models which mostly rely on the assumption of small strains. In the present paper we derive a new constitutive model which is no longer limited in this way. Further its efficient implementation into a finite element formulation is shown. One of the key issues in this regard is to fulfil “inelastic” incompressibility in each time increment. Here we suggest a new kind of exponential map where the exponential function is suitably computed by means of the spectral decomposition. A series expansion is completely avoided. Finite element simulations of stent structures show that the new concept is well appropriate to demanding finite element analyses as they occur in practically relevant problems.     

Study on interface failure of shape memory alloy （SMA） reinforced smart structure with damages

Shape memory alloy (SMA) reinforced smart structure can be used to make structural shape and strength self-adapted and structural damage self-restrained. Although SMA smart structures without damages were extensively studied, researches on SMA smart structures with damages have rarely been reported thus far. In this paper, thermo-mechanical behaviors of SMA fiber reinforced smart structures with damages are analyzed through a shear lag model and the variational principle. Mathematical expressions of the meso-displacement field and the stress-strain field of a typical element with damages are obtained, and a failure criterion for interface failure between SMA fibers and matrix is established, which is applied to an example. Results presented herein may provide a theoretical foundation for further studies on integrity of SMA smart structures.The project supported by the National Natural Science Foundation of China (10072026, 50135030) and Aeronautical Science Foundation of China (01G52041)The English text was polished by Keren Wang.     

Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part II – Micromechanical analyses

This paper presents the application of a new constitutive damage model for an epoxy matrix on micromechanical analyses of polymer composite materials. Different representative volume elements (RVEs) are developed with a random distribution of fibres. Upon application of periodic boundary conditions (PBCs) on the RVEs, different loading scenarios are applied and the mechanical response of the composite studied. Focus is given to the influence of the interface between fibre and matrix, as well as to the influence of the epoxy matrix, on the strength properties of the composite, damage initiation and propagation under different loading conditions.     

Macro-performance evaluation of friction stir welded automotive tailor-welded blank sheets: Part II – Formability

Formability of automotive friction stir welded TWB (tailor-welded blank) sheets was experimentally and numerically investigated in this work for four automotive sheets, aluminum alloy 6111-T4, 5083-H18, 5083-O and DP590 steel sheets, each having one or two different thicknesses. In particular, formability in three applications including the simple tension test with various weld line directions, hemisphere dome stretching and cylindrical cup drawing tests was evaluated. For numerical simulations, mechanical properties previously characterized in a joint paper (Chung et al., 2010) were utilized. To represent the mechanical properties, the non-quadratic orthogonal anisotropic yield function, Yld2000-2d, was utilized along with the (full) isotropic hardening law, while the anisotropy of the weld zone was ignored for simplicity.     

Mathematical models of shape memory alloy behavior for online and fast prediction of the hysteretic behavior

In this contribution, a new closed form of a mathematical model of Nickel–Titanium (NiTi) shape memory alloy (SMA) and its thermo-mechanical wire hysteresis behavior is developed. The approach is based on experimental data. The behavior of the heated and naturally cooled wire is modeled by mathematical expression. The cycle of heating and cooling is performed under a constant load. The prediction of the hysteretic behavior is realized through models adaptation, as predetermination, or real time determination of the models values, is developed and presented in detail. Simulations for position control using PID controller is shown for comparison purposes. The developed approach is incorporated in a feed forward control scheme. A comparison between the actual position and the predicted models position shows promising results.     

A new model for porous nonlinear viscous solids incorporating void shape effects – II: Numerical validation

The aim of this work is to critically assess the new model for porous, nonlinear viscous solids incorporating void shape effects proposed in Part I, by comparing its predictions with the results of some numerical micromechanical simulations. Two kinds of simulations are performed. First, the gauge surface of spheroidal representative volume elements, as considered in Part I, is determined for various values of the porosity, the aspect ratio of the void and the Norton exponent. This is done through minimization of the macroscopic viscous potential over a family of trial velocity fields especially adapted to the spheroidal geometry, which was proposed by Lee and Mear. Such simulations allow not only for satisfactory validation of the approximate analytical gauge surface proposed, but also for adjustment of the heuristic coefficients involved in the evolution equation for the void shape parameter. Second, the evolution in time of cylindrical cells subjected to various mechanical loads is determined by the finite element method. The quasi-periodicity of this new geometry is intended to approximately represent interactions between neighbouring voids. These simulations also reveal very good agreement between model predictions and numerical calculations, provided that the effect of the new geometry considered is accounted for by using a non-unity value for the analog of Tvergaard's famous “$q_1$” parameter for porous plastic solids.     

The G2 constant displacement discontinuity method – Part II: Solution of half-plane crack problems

In the previous Part I, the G2 constant displacement discontinuity element was presented that is dedicated for the fast (only one collocation point per element), stable and accurate numerical solution of modes I, II and III cracks of arbitrary shape in an infinite plane isotropic elastic body. Herein, another G2 constant displacement discontinuity element is constructed for the case of cracks in the half-plane. It is successfully validated against existing semi-analytical and numerical solutions of crack problems in the half-plane.     

Overspeed burst of elastoviscoplastic rotating disks: Part II – Burst of a superalloy turbine disk

Burst of a turbo-engine disk in case of overspeed is investigated both from experimental and computational point of view. Two twin disks made of the same nickel based superalloy are tested. For the first one (B-disk), rotation rate in increased till burst. The second one (S-disk) is kept safe by stopping rotation just before burst, and unloading it to measure residual deformations. The material model parameters are deduced either from simple tension tests, or using an inverse method on the S-disk test. Two corresponding finite element simulations of the B-disk are then performed, using either an arc-length control method to overcome the limit point, or dynamic simulations. In both cases, the numerical burst rotation rate, associated with the loss of stability of the structure, is found to be in good agreement with the experimental result.     

Effect of shock–wave loading on the properties of cryogenic TiNi — a shape–memory alloy

Results of an experimental study of the shock–wave deformation of TiNi and its effect on the crystallographic structure and temperature of austenite–martensite transformations are given. It is found that, for pressures of up to 2 GPa, shock–wave loading changes the defect structure and parameters of the lattice; however, this does not lead to a noticeable change in the temperature of the austenite–martensite transformation and the manifestation of the shapeNdash;memory effect.     

A second strain gradient elasticity theory with second velocity gradient inertia – Part II: Dynamic behavior

This paper is the sequel of a companion Part I paper devoted to the constitutive equations and to the quasi-static behavior of a second strain gradient material model with second velocity gradient inertia. In the present Part II paper, a multi-cell homogenization procedure (developed in the Part I paper) is applied to a nonhomogeneous body modelled as a simple material cell system, in conjunction with the principle of virtual work (PVW) for inertial actions (i.e. momenta and inertia forces), which at the macro-scale level takes on the typical format as for a second velocity gradient inertia material model. The latter (macro-scale) PVW is used to determine the equilibrium equations relating the (ordinary, double and triple) generalized momenta to the inertia forces. As a consequence of the surface effects, the latter inertia forces include (ordinary) inertia body forces within the bulk material, as well as (ordinary and double) inertia surface tractions on the boundary layer and (ordinary) inertia line tractions on the edge line rod; they all depend on the acceleration in a nonstandard way, but the classical laws are recovered in the case of no higher order inertia. The classical linear and angular momentum theorems are extended to the present context of second velocity gradient inertia, showing that the extended theorems—used in conjunction with the Cauchy traction theorem—lead to the local force and moment (stress symmetry) motion equations, just like for a classical continuum. A gradient elasticity theory is proposed, whereby the dynamic evolution problem for assigned initial and boundary conditions is shown to admit a Hamilton-type variational principle; the uniqueness of the solution is also discussed. A few simple applications to wave propagation and dispersion problems are presented. The paper indicates the correct way to describe the inertia forces in the presence of higher order inertia; it extends and improves previous findings by the author [Polizzotto, C., 2012. A gradient elasticity theory for second-grade materials and higher order inertia. Int. J. Solids Struct. 49, 2121–2137]. Overall conclusions are drawn at the end of the paper.     

Heat convection from a cylinder performing steady rotation or rotary oscillation – Part II: Rotary oscillation

This paper deals with the problem of combined (forced and natural) convection from a horizontal cylinder performing oscillating rotary motion in a quiescent fluid of infinite extent. While forced convection is caused by cylinder oscillation, the natural convection is caused by the buoyancy driven flow. The heat transfer process is governed by Rayleigh number, Ra, Reynolds number, Re, and the dimensionless frequency of oscillation, S. The study covers Ra up to 10³, Re up to 400 and S up to 0.8. The results showed that, for the same Ra, the time-averaged rate of heat transfer lies in between two limiting values. The first, is the steady state heat rate due to natural convection from a fixed cylinder and the second is the steady state heat rate from a cylinder rotating steadily at a speed equal to the maximum speed of rotational oscillation. The smaller the value of Re the nearer the time-averaged Nusselt number to that of fixed cylinder at the same Ra and the higher Re the lower the average Nusselt number. The effect of frequency is only limited to changing the amplitude of the fluctuating Nusselt number. Received on 15 December 1997     

In-plane biaxial crushing of honeycombs—: Part II: Analysis

The in-plane biaxial crushing experiments on polycarbonate honeycomb presented in Part I are simulated using large scale finite element models. The models account for nonlinearities in geometry and due to contact while the polycarbonate is modeled as an elastic-powerlaw viscoplastic solid. Full-scale simulations of the uniaxial crushing of this honeycomb were shown in the past to reproduce experiments with accuracy. In biaxial crushing, it was not practical to model specimens the same size as those in the experiments due to computational limitations; instead, a smaller model with 10×11 cells was adopted. Results from simulations of seven of the crushing experiments in Part I with various biaxiality ratios are presented. Through parametric studies it is demonstrated that the size of the specimen and friction between the specimen and the loading surfaces affect the initial elastic parts of the stress–displacement responses and the onset of instability. By contrast, for average crushing strains higher than approximately 10%, their effect was relatively small and the calculated responses were in good agreement with the experimental ones. As a consequence, the energy absorption capacity was predicted to good accuracy for all biaxiality ratios. In addition, many of the modes of cell collapse seen in the experiment are reproduced in the simulations.     

The Hohenheim Tyre Model: A validated approach for the simulation of high volume tyres – Part II: Validation

This publication series describes the development of the Hohenheim Tyre Model – an approach that considers the properties of high volume, agricultural tyres. The research project was conducted in accordance with the V-Model, which proposes a standardised development methodology for mechatronic systems. The previous publication described amongst others the model structure and parameterisation. This paper elucidates the validation, which is an essential part of the V-Model. Validation received special attention and is divided into three parts. First, three-dimensional tyre behaviour on level surfaces was investigated. Within the second step, single tyre behaviour is validated during obstacle passages. Similar obstacles were then used in the final step that shows up the correlation between measured and simulated whole vehicle behaviour. Throughout the validation a very high level of accuracy is achieved.     

Analytical study of the nonlinear behavior of a shape memory oscillator: Part I—primary resonance and free response at low temperatures

In this work, the response of a single-degree-of-freedom shape memory oscillator subjected to the excitation harmonic has been investigated. Equation of motion is formulated assuming a polynomial constitutive model to describe the restitution force of the oscillator. Here the method of multiple scales is used to obtain an approximate solution to the equations of the motion describing the modulation equations of amplitude and phase, and to investigate theoretically its stability. This work is presented in two parts. In Part I of this study we showed the modeling of the problem where the free vibration of the oscillator at low temperature is analyzed, where martensitic phase is stable. Part I also presents the investigation dynamics of the primary resonance of the pseudoelastic oscillator. Part II of the work is focused on the study in the secondary resonance of a pseudoelastic oscillator using the model developed in Part I. The analysis of the system in Part I as well as in Part II is accomplished numerically by means of phase portraits, Lyapunov exponents, power spectrum and Poincare maps. Frequency-response curves are constructed for shape memory oscillators for various excitation levels and detuning parameter. A rich class of solutions and bifurcations, including jump phenomena and saddle-node bifurcations, is found.     

Dynamic crushing of aluminum foams: Part I – Experiments

The two-part series of papers presents the results of a study of the crushing behavior of open-cell Al foams under impact. In Part I, direct and stationary impact tests are performed on cylindrical foam specimens at impacts speeds in the range of 20–160 m/s using a gas gun. The stress at one end is recorded using a pressure bar, while the deformation of the entire foam specimen is monitored with high-speed photography. Specimens impacted at velocities of 60 m/s and above developed nearly planar shocks that propagated at well-defined velocities crushing the specimen. The shock speed vs. impact speed, and the strain behind the shock vs. impact speed representations of the Hugoniot were both extracted directly from the high-speed images. The former follows a linear relationship and the latter asymptotically approaches a strain of about 90% at higher velocities. The Hugoniot enables calculation of all problem variables without resorting to an assumed constitutive model. The compaction energy dissipation across the shock is shown to increase with impact velocity and to be significantly greater than the corresponding quasi-static value. Specimens impacted at velocities lower than 40 m/s exhibited response and deformation patterns that are very similar to those observed under quasi-static crushing. Apparently, in this impact speed regime inertia increases the energy absorption capacity very modestly.