Anisotropy of elasticity and fabric of granular soils

Anisotropy of elasticity is a very important feature of granular soils. In this paper, numerical experiments using discrete element method were performed to emulate drained triaxial tests and simple shear tests at different stress levels. From these numerical experiments the macroscopic elasticity parameters were determined. The results show that at isotropic stress states the stiffness of the numerical specimen increases, while the Poisson’s ratio decreases with increasing confining pressure. The small strain shear modulus of the numerical specimen agrees well with the laboratory experimental results on a specimen with similar conditions. At anisotropic stress states, there is a threshold stress ratio (\({ SR}_{\mathrm{th}}\)), which characterizes the degrees of stiffness change and fabric change during the shearing. When the stress ratio (SR) is less than \({ SR}_{\mathrm{th}}\), the microscopic contact number does not change and its distribution remains nearly isotropic, while the distribution of contact forces change and become anisotropic to resist the applied anisotropic stress. Therefore the stiffness anisotropy of the specimen mainly results from the anisotropy of contact forces. When SR is larger than \({ SR}_{\mathrm{th}}\), however, the contact number decreases significantly in the minor principal stress direction resulting in the fabric anisotropy, along with the adjustments of contact forces. The stiffness anisotropy of the specimen results from both the fabric anisotropy and the contact force anisotropy. It also indicates that the stress normalized stiffness may be used as an index of the degree of fabric anisotropy. Moreover, the Poisson’s ratio of the specimen increases continuously with increasing stress ratio and its anisotropy can be approximately related to the stiffness anisotropy.     

Finite element implementation of a thermo-damage-viscoelastic constitutive model for hydroxyl-terminated polybutadiene composite propellant

A thermo-damage-viscoelastic model for hydroxyl-terminated polybutadiene (HTPB) composite propellant with consideration for the effect of temperature was implemented in ABAQUS. The damage evolution law of the model has the same form as the crack growth equation for viscoelastic materials, and only a single damage variable \(S\) is considered. The HTPB propellant was considered as an isotropic material, and the deviatoric and volumetric strain-stress relations are decoupled and described by the bulk and shear relaxation moduli, respectively. The stress update equations were expressed by the principal stresses \(\sigma_{ii}^{R}\) and the rotation tensor \(M\), the Jacobian matrix in the global coordinate system \(J_{ijkl}\) was obtained according to the fourth-order tensor transformation rules. Two models having complex stress states were used to verify the accuracy of the constitutive model. The test results showed good agreement with the strain responses of characteristic points measured by a contactless optical deformation test system, which illustrates that the thermo-damage-viscoelastic model perform well at describing the mechanical properties of an HTPB propellant.     

Unexpected liquefaction under isotropic consolidation of idealized granular materials

The drained isotropic compression behaviour of very loose and fully saturated monodisperse glass beads in triaxial compression is investigated in this paper. Short cylindrical samples were prepared by moist-tamping technique and isotropically compressed in a classical axisymmetric triaxial machine. Very loose glass bead samples exhibit numerous local collapses with sudden volumetric compaction and axial contraction of very large amplitude and experience ultimately global collapse with spontaneous liquefaction under undetermined external isotropic stress. Excess pore pressure instantaneously generated at the beginning of the collapse phenomenon, and rapidly dissipated with the usual drainage system, shows a global complex system with local dynamic instability. The dynamic time evolution of the excess pore pressure \(\varDelta U\) consists in a first and fast transient phase I at constant volume and constant axial strain with large spikes \(\varDelta U^{peak}\), followed by an intermediate second phase II of large increase of volumetric compaction and axial contraction at stabilizing \(\varDelta U_{stable}\) or constant effective stress \(\sigma ^{\prime }\) and finally a third and longest phase III of excess pore water pressure dissipation at nearly constant axial strain toward the initial back-pressure. For local collapses, the second phase is totally missing. Upon ignoring the local collapses, very loose idealized granular materials have a unique and global isotropic compressibility behaviour, independently of the void ratio at the end of the fabrication stage; and liquefaction-free for dense state below a threshold void ratio at fabrication \(e_{30}^{liq}\), representing the transition from global instability with total failure to local instability with partial collapse. This paper provides the first reported spontaneous liquefaction instability under isotropic consolidation. It gives the necessarily conditions for an isotropic liquefaction and emphases some usually hidden or partially developed mechanisms underlying the diffuse instability phenomenon and adds a new intriguing layer to the complex behaviour of idealized granular materials in classical drained triaxial isotropic compression.     

Pressure-driven plug flows between superhydrophobic surfaces of closely spaced circular bubbles

Fully developed convective flow in a tube filled with an anisotropic porous material with viscous dissipation due to an internal heat source is considered. An analytical solution is obtained subject to constant heat flux at the wall of the tube. The effect of the anisotropy parameters (anisotropic permeability ratio \(\lambda \) and inclination angle of principal axes \(\varphi \)) of the porous medium on the hydrodynamic and convective heat transfer inside the tube is shown. The singular behavior of the Nusselt number is discussed. Asymptotic analysis for high and low Darcy numbers is shown to support the validity of the present study. Detailed analysis showing the effect of anisotropy on the convective heat transfer is performed.     

The influence of rolling resistance on the stress-dilatancy and fabric anisotropy of granular materials

The effects of rolling resistance on the stress-dilatancy behavior and fabric anisotropy of granular materials were investigated through a three-dimensional discrete element method (DEM). A rolling resistance model was incorporated into the DEM code PFC3D and triaxial DEM simulations under simulated drained and undrained conditions were carried out. The results show that there existed a threshold value of the rolling friction. When the rolling friction was smaller than this value, the mechanical behavior of granular materials under both drained and undrained conditions were substantially influenced by the rolling friction, but the influence diminished when it was larger than the threshold value. A linear relationship has been observed between the dilatancy coefficient and the natural logarithm of the rolling-friction coefficient when it was smaller than the threshold value. An increase in the rolling friction led to an increase in the fabric anisotropy of all strong contacts under both testing conditions until the threshold value was attained. The investigation on the effect of rolling friction on the microstructure of granular materials revealed that the rolling friction enhanced the stability of force chains, which resulted in the difference in the stress-dilatancy behavior. Finally, the relationship between the stress ratio q/p\(^{\prime }\) and the fabric measure at strong contacts \(\hbox {H}_{\mathrm{d}}^{\mathrm{s}} /\hbox {H}_{\mathrm{m}}^{\mathrm{s}}\) was found independent of the inter-particle friction, rolling friction and testing conditions.     

On the use of tensor paths to estimate the nonproportionality factor of multiaxial stress or strain histories under free-surface conditions

Nonproportional (NP) strain hardening is caused by multiaxial load histories that induce variable principal stress/strain directions, activating cross-slip bands in several directions, due to the associated rotation of the maximum shear planes. This effect increases the strain-hardening behavior observed under proportional loads, those with fixed principal directions, and must be considered in multiaxial fatigue calculations, especially for materials with low stacking fault energy, such as austenitic stainless steels. NP hardening depends on the material and on the shape of the multiaxial load history path in a stress or strain diagram as well. It can be evaluated by a nonproportionality factor \({F_{\rm NP}}\) that varies from zero, for a proportional load history, to one, for a \({90^{\circ}}\) out-of-phase tension–torsion loading with the same normal and effective shear amplitudes. Originally, \({F_{\rm NP}}\) was estimated from the aspect ratio of a convex enclosure that contains the load history path, such as an ellipse or a prismatic enclosure, but such convex enclosure estimates can lead to poor predictions of \({F_{\rm NP}}\). Another approach consists on evaluating the shape of the six-dimensional (6D) path described by the six normal and shear components of the stress tensor, where the stress path contour is interpreted as a homogeneous wire with unit mass. The moment of inertia (MOI) tensor of this hypothetical wire is then calculated and used to estimate \({F_{\rm NP}}\). The use of 6D stress paths to estimate \({F_{\rm NP}}\) is questionable, since 6D formulations implicitly include the effect of the hydrostatic stress, while NP hardening is caused by the deviatoric plastic straining, not by stresses alone or by their hydrostatic component. In this work, the NP factor \({F_{\rm NP}}\) of a multiaxial load history is estimated from the eigenvalues of the MOI tensor of the plastic strain path, which are associated with the accumulated plastic straining in the principal directions defined by the associated eigenvectors. The presented formulation assumes free-surface conditions, but allows a surface pressure, covering the conditions of most critical points, which indeed are located on free surfaces. Experimental results for 14 different tension–torsion multiaxial histories prove the effectiveness of the proposed method.     

Influence of Plastic Deformation Capacity on Failure Behavior of Pipelines

Plastic deformation capacity parameters affect the deformability of steel in the plastic stage and then affect the limit pressure of pipelines. This paper investigates the influence of plastic deformation capacity parameters on the limit bearing capacity of pipelines. These parameters include yield-to-tensile ratio (\(\sigma_{y} /\sigma_{u}\)), percentage uniform elongation (\(\delta\)) and strain hardening exponent (n). Based on the Swift strain hardening model, the relational expression of the plastic deformation capacity parameters is theoretically deduced. Ninety-five groups of material tensile test data have been collected. Based on these test data, the variation tendency of the plastic deformation capacity parameters has been analyzed statistically, and the empirical formula of the key parameters has been fitted numerically. Twenty groups of finite element examples are designed to analysis the influence of yield-to-tensile ratio and uniform elongation on the limit pressure of pipeline. Results show that, with the improvement in strength grade of steel, the plastic deformability of steel decreases; the recommended critical plastic deformation capacity indexes are: (1) pipeline steel below X65, \(\sigma_{y} /\sigma_{u}\) ≤ 0.85 and \(\delta\) ≥ 10%; (2) pipeline steel for X70–X80, \(\sigma_{y} /\sigma_{u}\) ≤ 0.93 and \(\delta\) ≥ 8%.     

Finite deformation cohesive polygonal finite elements for modeling pervasive fracture

In the present study, mode I crack subjected to cyclic loading has been investigated for plastically compressible hardening and hardening–softening–hardening solids using the crack tip blunting model where we assume that the crack tip blunts during the maximum load and re-sharpening of the crack tip takes place under minimum load. Plane strain and small scale yielding conditions have been assumed for analysis. The influence of cyclic stress intensity factor range (\(\Delta \hbox {K})\), load ratio (R), number of cycles (N), plastic compressibility (\({\upalpha })\) and material softening on near tip deformation, stress–strain fields were studied. The present numerical calculations show that the crack tip opening displacement (CTOD), convergence of the cyclic trajectories of CTOD to stable self-similar loops, plastic crack growth, plastic zone shape and size, contours of accumulated plastic strain and hydrostatic stress distribution near the crack tip depend significantly on \(\Delta \hbox {K}\), R, N, \({\upalpha }\) and material softening. For both hardening and hardening–softening–hardening materials, yielding occurs during both loading and unloading phases, and resharpening of the crack tip during the unloading phase of the loading cycle is very significant. The similarities are revealed between computed near tip stress–strain variables and the experimental trends of the fatigue crack growth rate. There was no crack closure during unloading for any of the load cycles considered in the present study.     

Stress Assessment in Precipitation Hardened IN718 Nickel-Base Superalloy Based on Hall Coefficient Measurements

The feasibility of residual stress assessment in precipitation hardened IN718 nickel-base superalloy based on Hall coefficient measurement is investigated through studying the influence of thermal hardening, cold work, and applied stress. Measurements in IN718 specimens of various hardness levels show that the Hall coefficient increases from 8 ± 0.1\(\,\times \,\)10\(^{-11}\) m\(^{3}\)/C in the fully annealed state of 14 HRC to 9.4 ± 0.1\(\,\times \,\)10\(^{-11}\) m\(^{3}\)/C in the fully hardened state of 45 HRC. Measurements in IN718 specimens of various cold work levels show that plastic deformation exerts negligible effect on the Hall coefficient of fully annealed IN718, while in fully hardened IN718 the Hall coefficient decreases more or less linearly with cold work from its peak value of 9.4 ± 0.1\(\,\times \,\)10\(^{-11}\) m\(^{3}\)/C in its intact state to 8.9 ± 0.1\(\,\times \,\)10\(^{-11}\) m\(^{3}\)/C in its most deformed state of 22% plastic strain. Measurements taken under applied stress show that elastic strain significantly increases the Hall coefficient of IN718 regardless of the state of hardening. The relative sensitivity of the Hall coefficient to elastic strain is called the galvanomagnetic gauge factor and defined as the ratio of the relative change of the Hall coefficient divided by the axial strain under applied uniaxial stress. The gauge factor of IN718 is in the range of 2.6–2.9 depending on the hardness level. Besides the fairly high value of the gauge factor, it is important that it is positive, which means that compressive stress in surface-treated components decreases the Hall coefficient in a similar way as plastic deformation does, therefore the unfortunate cancellation that occurs in fully hardened IN718 in the case of electric conductivity measurements does not happen in this case. In addition, the influence of thermal exposure up to 700 \({{}^{\circ }}\)C and the reversible temperature dependence of the Hall coefficient at room temperature are studied in IN718 at different hardness levels.     

Periodic flow of a second-grade fluid induced by non-torsional oscillations of eccentric rotating disks

This paper deals with the periodic flow of a second-grade fluid caused by non-torsional oscillations of two disks rotating about non-coincident axes. While the two parallel disks are initially rotating with the same angular velocity about distinct axes, they start to execute non-torsional oscillations in their own planes and in the opposite directions. An exact solution is obtained for the components of the horizontal force per unit area exerted by the top and bottom disks on the fluid in the periodic state. The results are graphically displayed and the influence of the second-grade fluid parameter, the ratio of the frequency of oscillation to the angular velocity of the disks, the Reynolds number and the dimensionless velocity amplitudes of oscillation is discussed. It is observed that the change in the \( x \)-component of the mentioned force gets larger when the second-grade fluid parameter increases. However, an opposite effect is seen for the change in the \( y \)-component.     

Experimental determination of contraction coefficient and velocity coefficient for radial gates with elliptical lips

Radial gates are widely used to control the flow in irrigation channels and spillways. Radial gates require lower hoisting force and have better discharge characteristics in partial gate openings. The accurate discharge measurement through a radial gate is a challenging problem especially in submerged flow conditions. The coefficient of contraction \( C_{c} \) is an important parameter for accurate discharge measurement in open channels. In this study, an attempt has been made to determine the coefficient of contraction\( C_{c} \) and velocity coefficient \( C_{v} \) for radial gates both for free flow and submerged flow conditions. The flow emanating from a gate is similar to the wall jet emerging from a nozzle. The \( C_{c} \) and \( C_{v} \) values under free and submerged flow conditions are obtained from the measured jet velocity and the discharge. The coefficient of discharge values under submerged flow conditions show large variations with submergence and hence discharge characteristics needs to be improved for better control of flow. Hence, experiments are conducted so as to improve the discharge characteristics by modifying the exit geometry of the radial gate by attaching a quarter of an elliptical lip. Three different geometries of elliptical lips were attempted and the results show reasonable increase in the contraction coefficient.     

Experimental investigation of fracture under controlled stress triaxiality using shear-compression disk specimen

Experimental investigation of the effect of stress triaxiality on fracture strain has been performed using the shear-compression disk (SCD) specimen. A series of experiments was carried out under quasi-static loading conditions at triaxiality levels in the range of \(-\,0.7\) to \(+\,0.05\). The experiments were designed to generate relatively uniform strain and triaxiality in the sheared zone of the specimen, and a constant level of triaxiality along the entire loading path. The results obtained for SAE 1045 steel are compared to previous studies on the same material which revealed considerable differences. Discussion on possible contributing factors to the differences, and the potential of the SCD specimen for fracture investigations are discussed.     

Sodium-dodecyl-sulphate-assisted synthesis of Ni nanoparticles: electrochemical properties

Stabilized nickel nanoparticles (SNNPs) were prepared using \(\hbox {Ni(acac)}_{2}\) (\(\hbox {acac} = \hbox {acetylacetonate}\)) via a simple solvothermal method. The synthesis of the nickel nanoparticles was performed in the presence of sodium dodecyl sulphate (SDS) of different concentrations (mole ratios of SDS:\(\hbox {Ni(acac)}_{2} = 1{:}1\), 2:1 and 4:1), as the stabilizer, in order to appraise their influence on the morphology, size, dispersion, magnetic properties and electrochemical activity of the nickel nanoparticles. The synthesized products have been characterized by powder X-ray diffraction, scanning electron microscopy, transmission electron microscopy, Fourier transform infrared spectra, energy-dispersive X-ray spectroscopy, vibrating sample magnetometry and electrochemical studies. It is noteworthy that the average particles size of the SNNPs has been reduced by increasing the SDS concentration, while at high concentration (mole ratio of SDS:\(\hbox {Ni(acac)}_{2} = 4{:}1\)), the small particles tend to coalesce and create a big one. The stabilized Ni nanoparticles could be used as electrode materials for hydrogen evolution in alkaline medium. The electrochemical measurements demonstrated that the higher conductivity and lower value of faraday resistance of the as-prepared samples were when the mole ratio of SDS:\(\hbox {Ni(acac)}_{2}\) was 2:1.     

Uniaxial deformation of face-centered-cubic(Ni)-ordered B2(NiAl) bicrystals: atomistic mechanisms near a Kurdjumov–Sachs interface

Creating tailored interfaces between soft and hard materials is a promising route to simultaneously enhance ductility and strength of multicomponent materials. Here, we study deformation mechanisms in a model bicrystal, with a Kurdjumov–Sachs (KS) interface, between face-centered-cubic Ni and ordered-B2 NiAl slabs using molecular dynamics simulations. The bicrystals were uniaxially deformed by strain rates of \(10^7\) and \(10^9\,\hbox {s}^{-1}\) by holding temperatures constant at 300, 500, 700, and 900 K for each strain rate. Our simulations reveal atomistic processes that create sessile and glissile dislocations, and their reactions during high-strain rate deformation. At \(10^9\,\hbox {s}^{-1}\) strain rates, dislocation processes enhance ductility and cause large-scale atomic rearrangements in the KS interfacial region. This subsequently causes nucleation, growth, and coalescence of nano-voids into cracks inside the harder B2-ordered phase bordering the interface. Our results suggest that interfaces between “soft”–“hard” materials likely withstand high-strain rates better.     

Modifying continuous-time random walks to model finite-size particle diffusion in granular porous media

The continuous-time random walk (CTRW) model is useful for alleviating the computational burden of simulating diffusion in actual media. In principle, isotropic CTRW only requires knowledge of the step-size, \(P_l\), and waiting-time, \(P_t\), distributions of the random walk in the medium and it then generates presumably equivalent walks in free space, which are much faster. Here we test the usefulness of CTRW to modelling diffusion of finite-size particles in porous medium generated by loose granular packs. This is done by first simulating the diffusion process in a model porous medium of mean coordination number, which corresponds to marginal rigidity (the loosest possible structure), computing the resulting distributions \(P_l\) and \(P_t\) as functions of the particle size, and then using these as input for a free space CTRW. The CTRW walks are then compared to the ones simulated in the actual media. In particular, we study the normal-to-anomalous transition of the diffusion as a function of increasing particle size. We find that, given the same \(P_l\) and \(P_t\) for the simulation and the CTRW, the latter predicts incorrectly the size at which the transition occurs. We show that the discrepancy is related to the dependence of the effective connectivity of the porous media on the diffusing particle size, which is not captured simply by these distributions. We propose a correcting modification to the CTRW model—adding anisotropy—and show that it yields good agreement with the simulated diffusion process. We also present a method to obtain \(P_l\) and \(P_t\) directly from the porous sample, without having to simulate an actual diffusion process. This extends the use of CTRW, with all its advantages, to modelling diffusion processes of finite-size particles in such confined geometries.     

The influence of particle geometry and the intermediate stress ratio on the shear behavior of granular materials

The behavior of granular materials is very complex in nature and depends on particle shape, stress path, fabric, density, particle size distribution, amongst others. This paper presents a study of the effect of particle geometry (aspect ratio) on the mechanical behaviour of granular materials using the discrete element method (DEM). This study discusses 3D DEM simulations of conventional triaxial and true triaxial tests. The numerical experiments employ samples with different particle aspect ratios and a unique particle size distribution (PSD). Test results show that both particle aspect ratio (AR) and intermediate stress ratio \((b=({\upsigma }_{2}'-{\upsigma }_{3}')/({\upsigma }_{1}'-{\upsigma }_{3}'))\) affect the macro- and micro-scale responses. At the macro-scale, the shear strength decreases with an increase in both aspect ratio and intermediate stress ratio b values. At the micro-scale level, the fabric evolution is also affected by both AR and b. The results from DEM analyses qualitatively agree with available experimental data. The critical state behaviour and failure states are also discussed. It is observed that the position of the critical state loci in the compression \((e-p')\) space is only slightly affected by aspect ratio (AR) while the critical stress ratio is dependent on both AR and b. It is also demonstrated that the influence of the aspect ratio and the intermediate stress can be captured by micro-scale fabric evolutions that can be well understood within the framework of existing critical state theories. It is also found that for a given stress path, a unique critical state fabric norm is dependent on the particle shape but is independent of critical state void ratio.     

Thermal Conductivity and Thermal Boundary Resistances of ALD Al$$_{}$$O$$_{3}$$3 Films on Si and Sapphire

On Si and sapphire substrates, 6–45 nm thick films of atomic layer-deposited Al\(_{2}\)O\(_{3}\) were grown. The thermal conductivity of ALD films has been determined from a linear relation between film thickness and thermal resistance measured by the 3\(\omega \) method. ALD films on Si and sapphire showed almost same thermal conductivity in the temperature range of 50–350 K. Residual thermal resistance was also obtained by extrapolation of the linear fit and was modeled as a sum of the thermal boundary resistances at heater–film and film–substrate interfaces. The total thermal resistance addenda for films on sapphire was close to independently measured thermal boundary resistance of heater–sapphire interface. From the result, it was deduced that the thermal boundary resistance at ALD Al\(_{2}\)O\(_{3}\)–sapphire interface was much lower than that of heater–film. By contrast, the films on Si showed significantly larger thermal boundary resistance than films on sapphire. Data of \(< 30\) nm films on Si were excluded because an AC coupling of electrical heating voltage to semiconductive Si complicated the relation between 3\(\omega \) voltage and temperature.     

DEM simulations of the small strain stiffness of granular soils: effect of stress ratio

DEM (discrete element method) simulations are carried out to evaluate the small strain stiffness (i.e. Young’s modulus and shear modulus) of a granular random packing with focus on the effect of stress ratio (SR). The results show that the Young’s modulus in a given direction generally depends on the stress component in that direction. The Young’s modulus normalized by the related stress component remains nearly constant when SR is less than a threshold value $SR_\mathrm{th}$ . When SR is larger than $SR_\mathrm{th}$ , the normalized Young’s modulus decreases, particularly in the minor principle stress direction. Moreover, the Young’s modulus during unloading is always smaller than the one during loading at the same stress state, which indicates that the microstructure of the specimen has been modified by the historical shearing process. The shear modulus mainly depends on the mean effective stress and shows similar evolution trend as the Young’s modulus. This study finds that the macroscopic stiffness of the specimen is closely related to the evolutions of particle contact number and contact force during shearing. When SR is less than $SR_\mathrm{th}$ , the specimen only adjusts the distribution of contact forces to resist the external load, without any apparent change of contact number. When SR is larger than $SR_\mathrm{th}$ , however, the specimen has to adjust both contact number and contact forces to resist the external load. The study also illustrates that there is a good relationship between the macroscopic stiffness anisotropy and fabric anisotropy, and therefore the stiffness anisotropy may be used as an indicator of fabric anisotropy.     

Phase transformation kinetics and microstructure of NiTi shape memory alloy: effect of hydrostatic pressure

The effect of hydrostatic pressure on the behaviour of reverse and forward transformation temperatures and physical properties of NiTi shape memory alloy has been investigated. The transformation temperatures and physical properties of the alloy change with applied pressure. It has been clearly seen from differential scanning calorimetry that with the increase of applied pressure, while \(A_\mathrm{s},\, A_\mathrm{f}\) and \(M_\mathrm{f}\) transformation temperatures decrease, \(M_\mathrm{s}\) value increases. Moreover, it is obvious that with the increase of applied pressure, Gibbs free energy increases by 5.2883 J, while elastic energy increases by 1.4687 J. In addition, entropy of the alloys decreases by 0.2335 J \((\hbox {g }{^{\circ }}\!\hbox { C})^{-1}\) with applied pressure. Additionally, it is evident from the scanning electron microscopy images of the samples that there is an obvious difference in the grain sizes of the unpressured sample and the samples on which pressure is applied, the sizes being 10–100 and 30–150 \(\upmu \!\hbox {m}\), respectively.