FEM simulation of viscous properties for granular materials considering the loading rate effect

The deformation and strength characteristics of sandy soils as a kind of granular materials are very complex. The experimental results show that when the strain rate suddenly changes in monotonic loading (ML) case, the stress–strain curve of sandy soils changes sharply and then gradually converges into the original inferred one that would be obtained by continuous ML at constant strain rate after having exhibited clear yielding. Similar behaviors are also observed when ML is restarted at a constant strain rate following a creep loading or stress relaxation stage. An elasto-viscoplastic constitutive model for granular materials is developed, which consists of three components. One of the most important features of the model is that it can take into account the effects of loading rate due to viscous properties on the stress–strain behavior. The stress ratio-axial strain–time relations from four drained plain strain compression (PSC) tests on the saturated Toyoura sand are successfully simulated by the finite element method (FEM) code incorporating the proposed constitutive model. It is shown that the FEM code can simulate the viscous behaviors of sand accurately under arbitrary loading history.     

Determination of material parameters of a viscoplastic model by genetic algorithm

Macroscopic (continuum) and microscopic models, used for simulation of material behaviors under different loading conditions, contain a large number of material parameters and determination of these parameters is an important and difficult issue in the modeling. The aim of this work essentially deals with parameter determination procedure of any viscoplasticity model. In this study, genetic algorithm (GA) parameter optimization procedure has been proposed to determine material parameters of viscoplastic models. Parameter determination capability of the GA optimization method was tested by using VBO model which one of the viscoplasticity theory with no yield surface and loading–unloading conditions. Fourteen material parameters of VBO model are determined using uniaxial loading–unloading stress strain curves of high density polyethylene (HDPE). Using these material parameters, creep and relaxation behaviors of HDPE are simulated. A good match with experimental results is obtained. Apart from many existing studies in the literature, GA optimization procedure is applied to determine material parameters instead of trial and error procedure. This method can also be used to determine materials parameters of other viscoplasticity theories for all kinds of materials.     

Deformation response and constitutive modeling of vinyl ester polymer including strain rate and temperature effects

The deformation behavior of vinyl ester polymer under monotonic tensile loading is characterized and modeled. The Standard Linear Solid model, which is a physical model, was used and modified to represent the stress–strain behavior of this polymer over a wide range of strain rates and temperatures. This model was also used to predict the stress-relaxation and short-term creep behavior of this material. The comparisons between the predictions and experimental data from tensile and relaxation tests demonstrate that this model can represent the deformation behavior of the material reasonably well.     

Effect of a temperature change from 20 to 50°C on the basic creep of HPC and HPFRC

This research was performed in order to study the basic creep of High Performance Concretes (HPC) under uniaxial compression at 20 and 50°C. The aim of this work is to contribute to a better understanding of the basic creep phenomena of HPC at moderate temperature and to provide experimental data which will be used in Thermo-Hydro-Mechanical models such as those necessary for the National project CEOS.FR (Sellier, Thermo hydro mechanical numerical modelling, invited paper at the CEOS International workshop on Control of cracking in R.C. structures: a major step towards serviceability, 2009). The article also presents the fitting of a model considering the effect of temperature via an Arrhenius law affecting its viscous modules (Sellier and Buffo-Lacarriere, Eur J Environ Civ Eng 10:1161–1182, 2009). The concretes are those envisioned for future storage structures of Intermediate Level Long-Life Nuclear Wastes. The research programme has been established with four HPC, two non fibrous and two fibrous; the kinetics and amplitude of basic creep under uniaxial compression are measured during several months at 50°C and compared to those obtained at 20°C for the same materials (Camps, PhD thesis, 2008). Experimental results show that the average creep at 50°C is about twice the creep at 20°C. Besides, results show that this amplification depends on the binder type; the sensitivity to the temperature rise is greater for blended cement based concretes than for OPC based ones. The creep increase due the temperature rise is higher for the HPC under study than for ordinary concretes inventoried in a literature survey. The creep amplitude of HPC seems correlated to their amount of secondary C–S–H. At last, the fitting of the model parameters on the experimental results shows that the values of activation energy are quite close to those obtained by other authors on ordinary concretes (Bazant et al., J Eng Mech ASCE 130(6): 691–699, 2004).     

Effect of Uniaxial Pressure on the Isotope Effect on the Spectrum of Hamiltonians with Electron–Phonon Coupling

We have studied the effect of a change in the equilibrium nearest neighbour distances on the dynamics of charge and ions on a three-site cluster, identified with an O–Cu–O cluster present in high temperature superconductors. We consider a model Hamiltonian that contains an electronic part represented by a single band Hubbard model with onsite electronic correlations and a phononic part consisting of non-interacting Raman and infrared active phonons. The electron–phonon coupling is introduced through the change in interatomic distances generated by Coulomb repulsion between charges at neighbouring sites. For intermediate and strong values of the electron–phonon coupling, this model generates correlated electron–ion motion, i.e., polaron formation. In order to simulate the effect of change in the equilibrium nearest neighbour distances, we assume that the main effect such a change is a variation of the intersite electron hopping probability, t. We, therefore, studied the excitation spectrum of this model and the local lattice distortion in the Cu–O bond length as a function of t. We also studied the effect of a change in t in the polaron tunnelling energy when we use different oxygen isotopic masses, i.e., O¹⁶ and O¹⁸. We find that as function of t, the isotopic shift does not show a monotonic behaviour, as it does as a function of the electron–phonon coupling constant. It exhibits a minimum for values of t for which the electron–phonon coupling generates local lattice distortions with magnitudes similar to those observed experimentally in high-temperature superconductors. This observation could be related with the observed maximum on T _c as a function of the microstrain of the Cu–O bonds (Sanna et al. in Int. J. Mod. Phys. B 14(29–31), 2000; Bianconi et al. in J. Phys.: Condens. Matter 12:10655, 2000; Agrestini et al. in J. Phys. A: Math. Gen. 36:9133, 2003).     

Creep failure of polypropylene: experiments and constitutive modeling

Observations are reported on isotactic polypropylene in uniaxial tensile tests with various strain rates, relaxation tests with various strains, and creep tests with various stresses at ambient temperature. Constitutive equations are derived for the viscoelastic–viscoplastic responses and damage of a semicrystalline polymer at three-dimensional deformations. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. The model is applied to predict creep-failure diagrams in the entire interval of stresses. A phenomenological approach is proposed to determine a knee stress, at which transition occurs from ductile to brittle rupture. Accuracy of this method is evaluated by numerical simulation.     

On Comparison of Experiment and Theory for Ultrasonic Attenuation in Polycrystalline Niobium

In this communication comparison of experimental attenuation results in polycrystalline niobium (Zeng et al., J. Nondestruct. Eval. 29:93–103, 2010) with scattering-induced attenuation models is reexamined. Reasonable agreement is found between those results and the standard Stanke and Kino model (in J. Acoust. Soc. Am. 75:665–681, 1984) contradicting the conclusions of Zeng et al.     

Analysis of Garofalo equation parameters for an ultrahigh carbon steel

Isothermal stress–strain curves data from torsion tests conducted at high temperature (950–1200 °C) and strain rates (2–26 s⁻¹) were analyzed in an ultrahigh carbon steel (UHCS) containing 1.3%C. The sine hyperbolic Garofalo equation was selected as an adequate constitutive equation for the entire range of the forming variables considered. The Garofalo parameters were assumed strain dependent allowing the prediction of stress–strain curves under transient and steady-state conditions. The average relative errors obtained were below 3% in stress. In addition, the creep deformation mechanisms in the UHCS were analyzed from the Garofalo equation parameters. For this aim, the stress exponent of the Garofalo equation was, for the first time, related to that of the power law equation. The results show that the controlled deformation mechanism at steady state is lattice diffusion-controlled slip creep.     

An iterative procedure for determining effective stress–strain curves of sheet metals

An iterative correction procedure using 3D finite element analysis (FEA) was carried out to determine more accurately the effective true stress–true strain curves of aluminum, copper, steel, and titanium sheet metals with various gage section geometries up to very large strains just prior to the final tearing fracture. Based on the local surface strain mapping measurements within the diffuse and localized necking region of a rectangular cross-section tension coupon in uniaxial tension using digital image correlation (DIC), both average axial true strain and the average axial stress without correction of the triaxiality of the stress state within the neck have been obtained experimentally. The measured stress–strain curve was then used as an initial guess of the effective true stress–strain curve in the finite element analysis. The input effective true stress–strain curve was corrected iteratively after each analysis session until the difference between the experimentally measured and FE-computed average axial true stress–true strain curves inside a neck becomes acceptably small. As each test coupon was analyzed by a full-scale finite element model and no specific analytical model of strain-hardening was assumed, the method used in this study is shown to be rather general and can be applied to sheet metals with various strain hardening behaviors and tension coupon geometries.     

Crack tip fields in a viscoplastic solid: monotonic and cyclic loading

The asymptotic stress and strain field near the tip of a plane strain Mode I stationary crack in a viscoplastic material are investigated in this work, using a unified viscoplastic model based on Chaboche (Int J Plast 5(3):247–302, 1989). Asymptotic analysis shows that the near tip stress field is governed by the Hutchinson–Rice–Rosengren (HRR) field (Hutchinson in J Mech Phys Solids 16(1):13–31, 1968; Rice and Rosengren in J Mech Phys Solids 16(1):1–12, 1968) with a time dependent amplitude that depends on the loading history. Finite element analysis is carried out for a single edge crack specimen subjected to a constant applied load and a simple class of cyclic loading history. The focus is on small scale creep where the region of inelasticity is small in comparison with typical specimen dimensions. For the case of constant load, the amplitude of the HRR field is found to vanish at long times and the elastic K field dominates. For the case of cyclic loading, we study the effect of stress ratio on inelastic strain and find that the strain accumulated per cycle decreases with stress ratio.     

Modeling of uniaxial and biaxial ratcheting behavior of 1026 Carbon steel using the simplified Viscoplasticity Theory Based on Overstress (VBO)

Summary.  Hassan and Kyriakides [1], Hassan et al. [2], and Corona et al. [3] performed uniaxial and biaxial ratcheting experiments on heat-treated 1026 Carbon steel. The loading histories performed with uniaxial and tubular specimens were selected to simulate those encountered in nuclear reactor vessels. The stress-strain diagram of 1026 Carbon steel was used to determine the material constants in a simplified version of VBO. Small rate dependence was allowed. The model represents some nonlinear rate dependence, kinematic hardening and cyclically neutral behavior. The set of material constants determined only from uniaxial tests was used throughout the paper. Numerical experiments included are: (i) uniaxial stress-controlled cycling with various mean stresses, (ii) strain-controlled axial tests with tubular specimens under constant and variable internal pressure, and (iii) examination and variation of certain material constants of the VBO model that can influence ratcheting. Very good agreement with the experiments is found for the uniaxial case. However the ratchet strain accumulation during biaxial cycling is over-predicted by VBO and other constitutive models. Received November 5, 2001; revised June 12, 2002 Published online: January 16, 2003     

Asymptotic behavior of robust estimators in partially linear models with missing responses: the effect of estimating the missing probability on the simplified marginal estimators

In this paper, we consider a semiparametric partially linear regression model where missing data occur in the response. We derive the asymptotic behavior of the robust estimators for the regression parameter and of the weighted simplified location estimator introduced in Bianco et al. (Comput. Stat. Data Anal. 54:546–564, 2010a). For the latter, consistency results and the asymptotic distribution are derived when the missing probability is known and also when it is estimated.     

A modified Johnson–Cook model for 30Cr2Ni4MoV rotor steel over a wide range of temperature and strain rate

The compressive behaviors of 30Cr2Ni4MoV rotor steel were investigated at the temperatures from 1223 to 1523 K and strain rates from 0.001 to 0.1 s⁻¹. A modified Johnson–Cook (JC) model was proposed to describe the compressive behaviors of the studied alloy steel. In the modified JC model, the coupling effects of strain, strain rate, and deformation temperature were considered. Comparisons between the predicted stress–strain values by the modified JC model and measured ones indicate a good agreement, which confirms that the modified JC model is valid for the predicting the flow stress of 30Cr2Ni4MoV rotor steel over a wide range of temperature and strain rate.     

Tensile behaviour of nonwoven structures: comparison with experimental results

Nonwoven structures have been recently explored for numerous novel applications ranging from composites to scaffolds. The tensile property of nonwovens is a pre-requisite and indeed, one of the main parameters to determine their performance for such applications. In the first part, a modified micromechanical model describing the tensile behaviour of thermally bonded nonwovens was proposed by incorporating the effect of fibre re-orientation during the deformation (Rawal et al., J Mater Sci 45:2274, 2010). In this study, an attempt has been made to compare the theoretical and experimental stress–strain curves of thermally bonded and spunbonded nonwoven structures. These theoretical findings have been obtained from the most popular analytical tensile models of nonwovens available in the literature in addition to our modified tensile model. Poisson’s ratio has also been determined experimentally in order to predict the stress–strain behaviour of nonwoven, and its relationship with longitudinal strain has clearly distinguished between the randomly and preferentially orientated types of structures. In thermally bonded nonwovens, the tensile strength in various test directions is computed through pull-out stress and a comparison is made with the experimental results.     

Strain- and strain-rate-dependent mechanical properties and behaviors of Cu<Subscript>3</Subscript>Sn compound using molecular dynamics simulation

This work aims at investigating the mechanical properties and behaviors of orthorhombic Cu₃Sn crystals at room temperature through molecular dynamics (MD) simulation. The focuses are placed on the tensile stress–strain behaviors and properties of the Cu₃Sn single crystal and also their dependence on applied strain and strain rate. An attempt to characterize the deformation evolution of the Cu₃Sn nanostructure during the stress–strain test is also made. In addition, the elastic properties of bulk polycrystalline Cu₃Sn are estimated, as a function of strain rate and applied strain, by using the monocrystal results. The effectiveness of the MD model is demonstrated through comparison with the nanoindentation results and also published theoretical and experimental data. The calculated orthotropic elastic and shear moduli and Poisson’s ratio of Cu₃Sn single crystal reveal not only high anisotropy, but also the great effects of applied strain and strain rate only as the strain rate exceeds a threshold value of about 0.072% ps⁻¹. Specifically, raising the strain rate increases the orthotropic elastic properties and also the ultimate tensile and shear strengths of the nanocrystal, whereas increasing the applied strain reduces them.     

Thermal creep and fracture behaviors of the lead-free Sn–Ag–Cu–Bi solder interconnections under different stress levels

In our previous study, the creep behavior of the lead-free Sn–Ag–Cu–Bi solder joints has been proven to follow the Arrhenius power-law relationship, and the thermal fatigue behavior of the solder joints exhibits the typical creep deformation characteristics with a superposition of the pulsating features. In this study, the thermal creep and fracture behaviors of the lead-free Sn–Ag–Cu–Bi solder interconnections were characterized under different stress levels, with a systematical comparison to that of a traditional Sn60Pb40 near-eutectic solder. The results show that the creep strain rate of both solder connections follows Weertman-Dorn equation, and the calculated creep stress exponent for two solders is reasonably close to other published data. The SEM inspection and analysis of fractographies of creep fractured solder joints manifest that the creep failure of the lead-free Sn–Ag–Cu–Bi solder joint shows obviously intergranular fracture mechanism, while the Sn60Pb40 joint ruptures dominantly by a transgranular sliding mechanism.     

Nanoparticle structural organisation and scaffolding in organic media

To create advanced nano-structured materials and fluid media with unique tailored properties, it is often necessary to form nanocomposites or nano-dispersions, which may include homogenous and heterogeneous mixtures of nanoparticles dispersed in a matrix or medium of another compound such as a polymer. Recent and ongoing research on polymer/inorganic nanocomposites has shown dramatic improvement of the performance properties, such as stiffness, strength, electrical, optical and thermal properties over those of unfilled polymers, without compromising their possibility (Becker et al. in Polymer 43:4365–4373, 2002; Alexandre and Dubois in Mater Sci Eng R Rep 28(1–2):1–63, 2000; Arias et al. in Polymer 44:1537–1546, 2003). The aim of this study was to examine the structuring of nanoparticles within liquid based epoxy resins and their ability to form clusters and scaffolds in which the nanoparticles form a network with potentially interesting end properties. In particular, we considered nano-cluster formation and growth as function of the dispersion and concentration.     

Rashba Conduction Band Spin-Splitting for Asymmetric Quantum Well Potentials

Asymmetric quantum well potentials are expected to produce a conduction band spin-splitting which contributes to Dyakonov–Perel (Sov. Phys. Solid State 13:3023, 1971) spin relaxation. Much experimental work has focused on the effect of an electric field on spin dynamics (Karimov et al., in Phys. Rev. Lett. 91:246601, 2003) and little on asymmetry from alloy engineering. By combining time-resolved Kerr rotation measurements with transient spin grating measurements in GaAs/AlGaAs quantum wells we have compared the conduction band spin-splitting resulting from asymmetric alloy engineering with that from applied electric field. The latter is easily measurable, whilst the former is no greater than that in symmetric wells. These results are consistent with an envelope function approximation model that considers the potential profile in both the conduction and the valence bands (Winkler, in Springer Tracts in Modern Physics, vol. 191, 2003).     

木质素磺酸钙/高密度聚乙烯复合材料的力学性能

采用木质素磺酸钙（CL）填充高密度聚乙烯（HDPE）制备CL/HDPE复合材料,利用SEM、DSC、XRD对CL/HDPE复合材料进行表征,并对其强度、蠕变行为及应力松弛等力学性能进行测试。结果表明,CL/HDPE复合材料具有良好的结合界面和热稳定性;CL的加入可以提高CL/HDPE复合材料的弯曲强度,但对其冲击强度会产生不利影响;CL含量的增加有利于提高CL/HDPE复合材料的抗蠕变性能和抗应力松弛能力,而温度的升高会对CL/HDPE复合材料的蠕变行为和应力松弛产生不利影响。