Inelastic Mechanisms Research Articles

A micromechanical constitutive model for unusual temperature-dependent deformation of Mg–NiTi composites

Based on the mean-field approach, a micromechanical constitutive model is established to describe the unusual temperature-dependent deformation of Mg–NiTi composites. Firstly, the constitutive equations of two phases are proposed: for NiTi shape memory alloy (SMA), a simplified Hartl–Lagoudas model (Hartl and Lagoudas, 2009) which considering the martensite transformation and plastic deformation is adopted; while, for magnesium (Mg), an elastic-plastic model including a new nonlinear plastic hardening law is employed. The dependence of elastic moduli and yield surfaces of two phases at ambient temperature is addressed. Then, a non-isothermal incremental Mori–Tanaka homogenization method is employed and further extended to describe the interaction between two phases and calculate the macroscopic overall stress-strain response of Mg–NiTi composites. Finally, comparisons between the simulated results and the corresponding experimental ones show that the temperature-dependent deformation of the composites with different volume fractions of NiTi SMA phase can be well captured by the proposed model. Predicted results demonstrate that the unusual temperature-dependent deformation of Mg–NiTi composites originates from the change in the inelastic deformation mechanism of NiTi SMA with the variation of temperature.

Phenomenological modeling on cyclic deformation of superelastic NiTi shape memory alloy

In the present work, a phenomenological constitutive model for the cyclic behavior of superelastic NiTi shape memory alloy is established. Various inelastic mechanisms, i.e. martensitic transformation, martensitic reorientation, transformation-induced plasticity and reorientation-induced plasticity, are included in the model. Within the framework of thermodynamics, the evolution equations of internal variables are derived from Clausius-Duhem inequality. Via finite-element implementation, the mechanical response and the configuration of the specimen subjected to cyclic uniaxial and multiaxial loadings can be obtained. As for uniaxial loading, the degradation of superelasticity, i.e. the increase of residual strain, the drop of transformation stress and the decrease of stress hysteresis, can be reproduced with high fidelity. As for multiaxial loading, the necessity of incorporating martensitic reorientation into the model is substantiated. Satisfactory agreement between simulation and experiment confirms the validity of the proposed approach.

Thermo-mechanical-water migration coupled plastic constitutive model of rock subjected to freeze-thaw

A general thermo-mechanical-water migration coupled constitutive model was proposed to model mechanical degradation of rocks subjected to freeze-thaw cycles. This model is proposed in generalized incremental form under the framework of thermodynamics based on internal state variables theory. Migration of unfrozen water during freezing was considered to match the actual situation in practice. The model can adapt to a variety of inelastic deformation dissipation mechanisms. Therefore, it applies to many kinds of rocks. In the paper, a specific example was presented to demonstrate the application of the general model. In the example, two typical dissipation mechanisms, damage and isotropic hardening are chosen. After degradation of the general model, a practical model is obtained. In the practical model, effect of freeze-thaw on initial damage, damage threshold and isotropic hardening ability were modeled. For verification, an application based on real experimental data was presented. Application results show that this model can well simulate the mechanical response of rock after freeze-thaw cycles.

Discretion of the Monetary Policy: An Exemplification with Bolivia

Abstract In this paper, we evaluate and quantify the role of the discretion of the monetary policy in an open small and open economy (the case of Bolivia). The results suggest that conventional instruments of the Central Bank respond in different ways: interest rates present a sensitive/elastic response to output gap (actual economic cycle) [1.8]; an inelastic mechanism to inflation [0.5]. On the other hand, open market operations in the Central Bank responds elastically to inflation [1.2] and insensible to the output gap. These results are robust to alternative specification utilizing the Generalized Method of moments (GMM), for the quarterly period from 2000(T1)-2015(T4).

Compressive Behavior of Sustainable Steel-FRP Composite Bars with Different Slenderness Ratios

This paper presents experimental studies on the compressive behavior of a sustainable steel-fiber reinforced composite bar (SFCB) under uniaxial compressive loading. The SFCB, combined with steel and fiber reinforced polymer (FRP), is expected to significantly enhance structural safety and sustainability. A new test method with LVDT and extensometer sensors was developed and verified through experiments to test the tensile and compressive behavior of the SFCB. Fifty-four specimens including SFCB and inner steel bar (ISB) with different slenderness ratios were tested. The test results indicated that the initial compressive elastic modulus of the SFCB was essentially the same as its initial tensile elastic modulus. The compressive yield load of the SFCB was essentially irrelevant to the slenderness ratio, and the ultimate compressive stress of the SFCBs varied inversely with the slenderness ratios. The squash load of the SFCB tended to be conservative for predicting the compressive yield load of the SFCB, while the equivalent critical global buckling load of the SFCB was much higher than its corresponding compressive yield load and ultimate load due to the inelastic buckling mechanism of the SFCB within the range of the equivalent slenderness ratios studied in this paper.

The heterogeneous multiscale method applied to inelastic polymer mechanics.

Mechanisms emerging across multiple scales are ubiquitous in physics and methods designed to investigate them are becoming essential. The heterogeneous multiscale method (HMM) is one of these, concurrently simulating the different scales while keeping them separate. Owing to the significant computational expense, developments of HMM remain mostly theoretical and applications to physical problems are scarce. However, HMM is highly scalable and is well suited for high performance computing. With the wide availability of multi-petaflop infrastructures, HMM applications are becoming practical. Rare applications to mechanics of materials at low loading amplitudes exist, but are generally confined to the elastic regime. Beyond that, where history-dependent, irreversible or nonlinear mechanisms occur, not only computational cost but also data management issues arise. The micro-scale description loses generality, developing a specific microstructure based on the deformation history, which implies inter alia that as many microscopic models as discrete locations in the macroscopic description must be simulated and stored. Here, we present a detailed description of the application of HMM to inelastic mechanics of materials, with emphasis on the efficiency and accuracy of the scale-bridging methodology. The method is well suited to the estimation of macroscopic properties of polymers (and derived nanocomposites) starting from knowledge of their atomistic chemical structure. Through application of the resulting workflow to polymer fracture mechanics, we demonstrate deviation in the predicted fracture toughness relative to a single-scale molecular dynamics approach, thus illustrating the need for such concurrent multiscale methods in the predictive estimation of macroscopic properties.This article is part of the theme issue ‘Multiscale modelling, simulation and computing: from the desktop to the exascale’.

Hexagonal germanium formation at room temperature using controlled penetration depth nano-indentation

Thin Ge films directly grown on Si substrate using two-step low temperature growth technique are subjected to low load nano-indentation at room temperature. The nano-indentation is carried out using a Berkovich diamond tip (R ~ 20 nm). The residual impressions are studied using ex-situ Raman Micro-Spectroscopy, Atomic Force Microscopy combined system, and Transmission Electron Microscopy. The analysis of residual indentation impressions and displacement-load curves show evidence of deformation by phase transformation at room temperature under a critical pressure ranging from 4.9GPa–8.1GPa. Furthermore, the formation of additional Ge phases such as r8-Ge, hd-Ge, and amorphous Ge as a function of indentation depth have been realized. The inelastic deformation mechanism is found to depend critically on the indentation penetration depth. The non-uniform spatial distribution of the shear stress depends on the indentation depth and plays a crucial role in determining which phase is formed. Similarly, nano-indentation fracture response depends on indentation penetration depth. This opens the potential of tuning the contact response of Ge and other semiconductors thin films by varying indentation depth and indenter geometry. Furthermore, this observed effect can be reliably used to induce phase transformation in Ge-on-Si with technological interest as a narrow band gap material for mid-wavelength infrared detection.

MODULAR PLATFORM TO MODEL PARALLEL INELASTIC MECHANISMS IN RUBBER-LIKE MATERIALS

ABSTRACT Cross-linked rubber-like materials exhibit an elastic behavior with several inelastic features such as the Mullins effect, Payne effect, permanent set, deformation-induced anisotropy, and hysteresis. Although these features are being modeled individually, few attempts have been made toward systematic integration of these models into one model to consider damage accumulation in rubber-like materials. A new platform is presented to couple constitutive models of different inelastic mechanisms into one generalized model that can simultaneously consider them all. The kinematic structure of the proposed approach is based on two concepts: (1) the concept of microsphere and (2) the concept of network decomposition. The polymer matrix is decomposed into a number of parallel networks, in which each network describes one inelastic feature and is represented by one microsphere. Accordingly, the energy of the polymer matrix, $\Psi$, is the summation of the energies of the parallel networks. A network is considered as a three-dimensional (3D) assembly of unidirectional subnetwork elements distributed in all spatial directions represented by one microsphere. Such structural breakdown allows us to simplify different inelastic mechanisms as 3D assemblies of one-dimensional (1D) elements that host simplified 1D inelastic mechanisms. This concept replaces the complex 3D formulations of finite inelasticity based on the multiplicative decomposition of the F by a simple solution that can be further scaled up and integrates other models. The microsphere enables us to derive the stretch and the deformation history for each direction. Modular design of the platform allows models to be replaced anytime. Any ill-performing or expensive model can be later substituted by an improved version or temporarily deactivated. To validate the concept, a platform is proposed that can host models of permanent set, hysteresis, and Mullins effect. The accuracy of the platform is evaluated in comparison with experimental data and with respect to different models.

Modeling of finite deformation of pseudoelastic NiTi shape memory alloy considering various inelasticity mechanisms

A crystal plasticity finite element (CPFE) model is developed for pseudoelastic NiTi shape memory alloy (SMA). The model includes various inelastic mechanisms of deformation such as martensite transformation, dislocation glide in austenite phase and twinning in the martensite phase. This model is based on the finite deformation theory and predicts phase transformation, stress field and residual strain due to slip and twinning. Following the work of Anand and Gurtin (2003), the Helmholtz free energy is derived and further the thermodynamic driving forces for slip, twin and phase transformation are obtained by using Clausius-Duhem inequality. The developed constitutive model has been implemented within a user material subroutine interface VUMAT in ABAQUS™/Explicit. The activation of different inelasticity mechanisms at different temperatures and strains are first verified by performing various simulations of uniaxial tensile deformation. Then the model is calibrated and validated against the experimental stress-strain response of NiTi single crystal as reported in the literature. The single crystal constitutive model is extended for modeling the response of a polycrystal with both initial random and textured crystallographic orientations using Taylor scale transition technique. A series of simulations are performed on polycrystalline representative volume element (RVE) at various temperatures and strains. The effect of temperature and imposed strain on phase transformation and residual strain is investigated systematically. The residual strain increases due to slip in austenite phase and twinning in the martensite phases that are activated as temperature and imposed strain increase respectively. Further the uniaxial loading conditions are extended to multiaxial loading and the results are compared against the experimental data.

Improved embedded-atom model potentials of Pb at high pressure: application to investigations of plasticity and phase transition under extreme conditions

Local stress relaxation mechanisms of crystals are a long-standing interest in the field of materials physics. Constantly encountered inelastic deformation mechanisms in metals under dynamic loadings, such as dislocation, deformation twinning and phase transition, have been extensively discussed separately or as some of their combinations. Recently, virtual melting is found to be a dominant local stress relaxation mechanism under extreme strain rates. However, these deformation mechanisms have never been investigated in the same metal at an atomic level due to the lack of high pressure interatomic potentials. In this work, an embedded-atom model potential of Pb is developed and tested for high pressure applications. The developed potential of Pb could not only reproduce many energetic, elastic and defective properties at ambient conditions well, but also correctly describe face-centered cubic (fcc)-hexagonal close packed (hcp) and hcp-body-centered cubic phase transition of Pb under high pressures. Shock Hugoniot, as well as equation of states for fcc and hcp phase, also agrees well with the literature ones up to more than 100 GPa. With the developed potential, non-equilibrium molecular dynamic simulations are conducted to investigate dynamic behaviors of Pb single crystal under ramp-shock compressions. Depending on applied strain rates, dislocation-mediated plasticity, phase transition and virtual melting, constantly reported by experiments or theoretical investigations, are observed in our results. Additionally, a new phase transition mechanism of Pb subjected to the ramp compressions is uncovered.

A proposed model for nonlinear analysis of RC beam-column joints under seismic loading

Beam-column joints are generally subjected to significant inelastic deformations and considerably contribute to storey drifts under seismic loading. It is vital to consider joint shear deformation and longitudinal bar slip in the finite element simulation, and neglecting these effects will lead to misleading results. A new macro beam-column joint element model was proposed to consider the influence of joint inelastic deformations for interior joint with stirrups. The proposed macro beam-column joint was developed based on the force transfer mechanisms and inelastic response mechanisms, using axial springs representing bar-slip mechanism of longitudinal reinforcement, concrete and reinforcement in the joint core and interface-shear. In the joint core, eight concrete components and eight reinforcement components worked together to contribute to the effect of joint shear deformation. Constitutive relationship was developed to define the response of proposed joint model based on the dimensions, geometric, and material properties. An applicable model was used for simulating strength reduction of confined concrete strut due to joint damage and cyclic load history. Modifications were made to provide a more reasonable simulation of the anchorage zone response. The numerical analysis results were compared with experimental data of six beam-column subassemblages to validate the proposed macro beam-column joint element model. The comparison between the simulated and the test results shows that the proposed joint model is able to simulate the hysteretic response, joint shear strength and joint shear deformation of the beam-column subassemblages. Additionally, the comparison of the simulated results between proposed joint model and available joint model indicates that the proposed joint model is more accurate and efficient.

Application of multi-angle scattering maps to stepped surfaces

This study examines channeling, multiple scattering, and neutralization/re-ionization of ions scattered along the stepped Al(332) plane. Our experimental approach involves probing the surface with 1–2 keV He+ and Ne+ beams, and then systematically mapping the scattered ion fluxes over a large solid angle. This provides comprehensive ion channeling information over all directions, rather than along a few low-index azimuths, as is common practice in ion scattering spectroscopy. We first probe the surface with 2 keV He+ at near-normal incidence, and then map the backscattered particle flux (both ions and neutrals) via time of flight (TOF) spectrometry. The features contained in these maps can be correlated with axial and inter-planar channeling effects, and are reproduced well via binary collision simulations. Sensitivity to the stepped surface topography is heightened considerably for oblique ion incidence in the forward-scattering direction. In this geometry, we used 2 keV Ne+ to probe the surface and mapped the corresponding scattered fluxes of both single and multiply-charged ions. In both cases, the scattering intensity depends strongly on the precise trajectory taken along the surface, and is particularly sensitive to how extensively the incident ions interact with the step edges. We interpret the information contained in these maps by considering several mechanisms for charge transfer and double ion production. The formation of Ne++ appears to be correlated with a previously observed inelastic mechanism that occurs when the collision apsis, Rmin, is less than 0.65 Å. This contributes to an energy loss of 48 ± 8 eV for Ne+ undergoing single scattering; the Rmin threshold for this inelastic step coincides with the emergence of a distinct Ne++ peak. Using the information gained from the maps, we propose methods for extending this approach to chemisorbed layers.

Micromechanical modeling on thermomechanical coupling of cyclically deformed superelastic NiTi shape memory alloy

The response of NiTi shape memory alloy (SMA) changes drastically with the loading rate. This paper presents a three-dimensional thermomechanically coupled constitutive model to describe the rate dependent cyclic performance of superelastic NiTi SMA. Two inelastic mechanisms, i.e. martensitic transformation and transformation-induced plasticity, are taken into account. The fully coupled heat equilibrium equation is deduced from the first law of thermodynamics. The thermodynamic driving forces of the internal variables are derived from the second law of thermodynamics (Clausius-Duhem inequality). The constitutive model is extended from single crystal scale to polycrystalline version via finite element approach. The validity of the model is verified through simulating thermomechanical response of cyclically tensioned superelastic NiTi SMA at various deformation rates. Moreover, the robustness of the model is checked by simulating the thermomechanical behavior of superelastic NiTi cantilever tube subjected to cyclic bending. The simulation results match with the experimental observation reasonably.

Deformation patterning in finite-strain crystal plasticity by spectral homogenization with application to magnesium

Complex microstructural patterns arise as energy minimizers in systems having non-convex energy landscapes such as those associated with phase transformations, deformation twinning, or finite-strain crystal plasticity. The prediction of such patterns at the microscale along with the resulting, effective material response at the macroscale is key to understanding a wide range of mechanical phenomena and has classically been dealt with by simplifying energy relaxation theory or by expensive finite element calculations. Here, we discuss a stabilized Fourier spectral technique for the homogenized response at the level of a representative volume element (RVE). We show that the FFT-based method admits sufficiently high resolution suitable to predict the emergence of energy-minimizing microstructures and the resulting effective response by computing the approximated quasiconvex energy hull. We test the method in the classical single-slip problem in single- and bicrystals. Especially the latter goes beyond the scope of traditional finite element and analytical relaxation treatments and hints at mechanisms of pattern formation in polycrystals. We also demonstrate that the chosen spectral finite-difference approximation, important for removing ringing artifacts in the presence of high contrasts, adds a natural regularization to the non-convex minimization. Finally, the technique is applied to polycrystalline pure magnesium, where we account for the competition between dislocation-mediated plasticity and deformation twinning. These inelastic deformation mechanisms result in complex texture evolution paths at the polycrystalline mesoscale and are simulated within RVEs of varying grain size and texture by a constitutive crystal plasticity model with an effective, volume fraction-based description of twinning.

FE temperature- and residual stress prediction in milling inserts and correlation with experimentally observed damage mechanisms

In milling applications thermal and mechanical loadings are affecting the damage behavior of milling inserts. There are several open questions regarding the influence of loading and tool temperature on inelastic deformations and damage mechanisms. The aim of the current work is to simulate industrial milling processes with the finite element method and generate knowledge about the acting damage mechanisms. The validation of the results is made by two recently reported experimental milling setups. The focus of the simulations is set on investigations of the evolution of tensile residual stresses orientated parallel to the cutting edge of a milling insert. These tensile residual stresses foster the formation and growth of so-called comb cracks growing in planes perpendicular to the cutting edge which are detrimental to the performance of the tool. The insert is made of WC-Co hard metal with 8 wt.% Co-binder and an average WC grain size of 1 μm. It is coated with a 7 μm thick TiAlN layer acting as a thermal shield. The workpiece material is 42CrMo4, described by a Johnson-Cook constitutive material model. The milling process is modeled with a 2D Arbitrary Lagrangian-Eulerian (ALE) approach. Results of the 2D simulations are used to generate the temperature and contact load imposed on a 3D solid-model of the milling insert that is in turn used to predict the evolution of stress and temperature over 50 milling cycles. The simulations reproduce a shift of residual stresses toward tension in the milling insert at the same location as observed in experiments from which one failed due to comb cracks and one due to wear.

Controlled spin switching in a metallocene molecular junction

The active control of a molecular spin represents one of the main challenges in molecular spintronics. Up to now spin manipulation has been achieved through the modification of the molecular structure either by chemical doping or by external stimuli. However, the spin of a molecule adsorbed on a surface depends primarily on the interaction between its localized orbitals and the electronic states of the substrate. Here we change the effective spin of a single molecule by modifying the molecule/metal interface in a controlled way using a low-temperature scanning tunneling microscope. A nickelocene molecule reversibly switches from a spin 1 to 1/2 when varying the electrode–electrode distance from tunnel to contact regime. This switching is experimentally evidenced by inelastic and elastic spin-flip mechanisms observed in reproducible conductance measurements and understood using first principle calculations. Our work demonstrates the active control over the spin state of single molecule devices through interface manipulation.

Diminution of impact ionization rate of charge carriers in semiconductors due to acoustic phonon scattering

The effects of acoustic phonon scattering on the impact ionization rate of charge carriers in a semiconductor have been studied in this paper. The inelastic interactions of charge carriers with both deformation and piezoelectric acoustic phonons have been considered. An analytical expression of impact ionization rate has been developed by considering all possible types of inelastic collision mechanisms such as acoustic phonon scattering, optical phonon scattering, and inter-carrier scattering prior to the ionizing collision. The said expression has been used to calculate the impact ionization rate of electrons and holes in 4H-SiC as functions of electric field and doping concentration at room temperature. Numerical results show that the ionization rate of charge carriers deteriorates significantly due to the interactions of those with acoustic phonons. This deterioration is found to be more pronounced in hot carriers. The numerical results calculated from the present model have been compared with the ionization rate data calculated numerically using an earlier developed analytical expression of ionization rates, which does not take into account the acoustic phonon-scattering events. The calculated results have also been compared with earlier reported experimental data. It is observed that the numerical results obtained from the present model are in better agreement with the experimental results.

Pre-stretch dependency of the cyclic dissipation in carbon-filled SBR

This work explores for the first time the inelastic fatigue process in filled rubbers using the internal state variable theory. The theory is used to qualitatively and quantitatively analyze the complex history-dependent cyclic response of filled rubbers, but also to reveal the underlying physical mechanisms. Experimental observations are reported on a styrene-butadiene rubber (SBR) containing different amounts of carbon-black and cyclically loaded under a wide range of pre-stretch levels. The effects of pre-stretch and filler content on the carbon-filled SBR history-dependent cyclic response, characterized by stress-softening and hysteresis along with dissipative heating, are examined. The intrinsic dissipation, regarded as a consequence of two types of rearrangements in the rubber-filler material system, i.e. viscoelastic and damage mechanisms, is quantified and used to propose a plausible explanation of the underlying inelastic fatigue mechanisms consistent with our experimental observations.

Validity Examination of the Dissipative Quantum Model of Olfaction

Despite some inconclusive experimental evidences for the vibrational model of olfaction, the validity of the model has not been examined yet and therefore it suffers from the lack of conclusive experimental support. Here, we generalize the model and propose a numerical analysis of the dissipative odorant-mediated inelastic electron tunneling mechanism of olfaction, to be used as a potential examination in experiments. Our analysis gives several predictions on the model such as efficiency of elastic and inelastic tunneling of electrons through odorants, sensitivity thresholds in terms of temperature and pressure, isotopic effect on sensitivity, and the chiral recognition for discrimination between the similar and different scents. Our predictions should yield new knowledge to design new experimental protocols for testing the validity of the model.

Multiple inelastic mechanisms analysis (MIMA): A simplified method for the estimation of the seismic response of RC frame buildings

In the last decade, a number of methodologies for the seismic performance assessment of existing buildings have been proposed. They are based on comprehensive probabilistic procedures where uncertainties related to ground motions, construction and material quality are explicitly accounted for. Structural analysis is performed to evaluate the seismic demand to the structure through a number of Engineering Demand Parameters (EDPs) (i.e.: inter-story drift ratios, floor accelerations, etc.). In this respect, the use of Nonlinear Response History Analyses (NRHAs) appears to be computationally expensive, time demanding and potentially tricky for most practicing engineers. On the other hand, simplified approaches, based on linear static analysis, are affected by strong limitations of use and loss of accuracy towards seismic performance assessment. In this paper, an alternative approach, referred to as Multiple Inelastic Mechanisms Analysis (MIMA), based on the principles of the Displacement-based Assessment (DBA) method, is proposed in the attempt of reducing the complexity related to NRHAs, while maintaining a sufficient accurateness in the estimation of expected losses. MIMA is a practice-oriented approach that provides the seismic response of a structure at different intensity levels. The most important novelties of MIMA with respect to the current state-of-the-art are the possibility of accounting for the contribution of different inelastic mechanisms, the record-to-record variability, and the effects of infills and stairs. In the current version, the proposed approach is specialized for pre-70 RC frame buildings. However, it could be extended to other building types with minor efforts. In this paper, MIMA is applied on a six-stories building, representative of typical RC frame buildings realized in Italy (and other European countries) in the 60’s and 70’s. A good accordance between approximate predictions and accurate results (from NRHAs) is observed.