Average Normal Stress Research Articles

Development of Finite-Element Modeling of Processing Metals Under Pressure Using Variational Principles of Mechanics Proposed by V. L. Kolmogorov

On the basis of the variational principle of metal virtual stresses and flow rates in high plastic metal deformation with complex processes of hardening and softening, we propose an iterative procedure using finite-element simulation of processing metals under pressure, taking into account the heterogeneity of mechanical properties in the volume of the deformation zone. The proposed method of solving the boundary value problem increases the computational precision for the workpiece shape deformation, satisfying the condition of ideal plasticity for the material particles at any arbitrary point in time, as well as improving the accuracy of determining the field of the average normal stress in the deformation zone.

Asperity generation and its relationship to seismicity on a planar fault: a laboratory simulation

Author(s): Selvadurai, PA; Glaser, SD | Abstract: Earthquake faults, and all frictional surfaces, establish contact through asperities. A detailed knowledge of how asperities form will enable a better understanding of the manner in which they communicate during foreshock failure sequences that are observed, leading to the larger main shock. We present results of experiments where a pressure sensitive film was used to map, size and measure the magnitudes of the normal stresses at asperities along a seismogenic section of a laboratory simulated fault. We measured seismicity acoustically and foreshocks were found to be the result of localized asperity failure during the nucleation phase of gross fault rupture. Since surface roughness plays an important role in how asperities are formed, two Hurst exponents were measured to characterize a highly worn interface using roughness profiles: (i) long wavelength estimates (H ~ 0.45) and (ii) short wavelength estimates (H ~ 0.8-1.2). The short wavelength roughness estimates were computed at the scale of single asperity junction points. Macroscopically, the number of asperities and real contact area increased with additional application of normal force while the mean normal stress remained constant. The ratio of real to nominal contact area was low - ranging from 0.02 l Ar/A0 l 0.05-predicting that the asperities should be elastically independent of each other. Results from the pressure sensitive film showed that asperities were closely spaced and could not be treated as mechanically independent. Larger asperities carried both higher levels of average normal stress and higher levels of normal stress heterogeneity than smaller ones. Using linear stability theorem, the critical slip distance on foreshocking asperities was estimated to be d0 ~ 0.65-3 μm. The critical slip distance d0 was ~1.8-11.5 per cent of the premonitory slip needed to initiate gross fault rupture of the interface (20-40 μm) and the overall slip necessary to initiate gross fault rupture was on the order of the average asperity diameter (52 μm). Foreshocks may be due to a change in the critical slip distance, at localized sections of the fault, caused by the two distinct roughness profiles measured at short and long length scales.

Geometric effects on electrocapillarity in nanochannels with an overlapped electric double layer.

Unsteady filling of electrolyte solution inside a nanochannel by the electrocapillarity effect is studied. The filling rate is predicted as a function of the bulk concentration of the electrolyte, the surface potential (or surface charge density), and the cross sectional shape of the channel. For a nanochannel, the average outward normal stress exerted on the cross section of a channel (P[over ¯]_{zz}^{}) can be regarded as a measure of electrocapillarity and it is the driving force of the flow. This electrocapillarity measure is first analyzed by using the solution of the Poisson-Boltzmann equation. From the analysis, it is found that the results for many different cross sectional shapes can be unified with good accuracy if the hydraulic radius is adopted as the characteristic length scale of the problem. Especially in the case of constant surface potential, for both limits of κh→0 and κh→∞, it can be shown theoretically that the electrocapillarity is independent of the cross sectional shape if the hydraulic radius is the same. In order to analyze the geometric effects more systematically, we consider the regular N-polygons with the same hydraulic radius and the rectangles of different aspect ratios. Washburn's approach is then adopted to predict the filling rate of electrolyte solution inside a nanochannel. It is found that the average filling velocity decreases as N increases in the case of regular N-polygons with the same hydraulic radius. This is because the regular N-polygons of the same hydraulic radius share the same inscribing circle.

A model for tensile strength of polymer/clay nanocomposites assuming complete and incomplete interfacial adhesion between the polymer matrix and nanoparticles by the average normal stress in clay platelets

In this article, a model for tensile strength of polymer/clay nanocomposites (PCN) is suggested assuming perfect and imperfect interfacial adhesion between the polymer matrix and platelets by the average normal stress in clay platelets.

The Third-Order Viscoelastic Acoustic Model Enables an Ice-Detection System for a Smart Deicing of Wind-Turbine Blade Shells

The present work is based on the third-order partial differential equation (PDE) of acoustics of viscoelastic solids for the quasi-equilibrium (QE) component of the average normal stress. This PDE includes the stress-relaxation time (SRT) for the material and is applicable at any value of the SRT. The notion of a smart deicing system (SDS) for blade shells (BSs) of a wind turbine is specified. The work considers the stress in a BS as the one caused by the operational load on the BS. The work develops key design issues of a prospective ice-detection system (IDS) able to supply an array of the heating elements of an SDS with the element-individual spatiotemporal data and procedures for identification of the material parameters of atmospheric-ice (AI) layer accreted on the outer surfaces of the BSs. Both the SDS and IDS flexibly allow for complex, curvilinear and space-time-varying shapes of BSs. The proposed IDS presumes monitoring of the QE components of the normal stresses in BSs. The IDS is supposed to include an array of pressure-sensing resistors, also known as force-sensing resistors (FSRs), and communication hardware, as well as the parameter-identification software package (PISP), which provides the identification on the basis of the aforementioned PDE and the data measured by the FSRs. The IDS does not have hardware components located outside the outer surfaces of, or implanted in, BSs. The FSR array and communication hardware are reliable, and both cost- and energy-efficient. The present work extends methods of structural-health/operational-load monitoring (SH/OL-M) with measurements of the operational-load-caused stress in closed solid shells and, if the prospective PISP is used, endows the methods with identification of material parameters of the shells. The identification algorithms that can underlie the PISP are computationally efficient and suitable for implementation in the real-time mode. The identification model and algorithms can deal with not only the single-layer systems such as the BS layer without the AI layer or two-layer systems but also multi-layer systems. The outcomes can be applied to not only BSs of wind turbines but also non-QE closed single- or multi-layer deformable solid shells of various engineering systems (e.g., the shells of driver or passenger compartments of ships, cars, busses, airplanes, and other vehicles). The proposed monitoring of the normal-stress QE component in the mentioned shells extends the methods of SH/OL-M. The topic for the nearest research is a better adjustment of the settings for the FSR-based measurement of the mentioned components and a calibration of the parameter-identification model and algorithms, as well as the resulting improvement of the PISP.

Timing of water plume eruptions on Enceladus explained by interior viscosity structure

Water plume eruptions on Saturn’s icy moon Enceladus are delayed relative to the peak tidal stresses. Simulations suggest the delay can be explained by the moon’s interior structure and the presence of a subsurface ocean. At the south pole of Saturn’s icy moon Enceladus, eruptions of water vapour and ice emanate from warm tectonic ridges1,2,3,4. Observations in the infrared5 and visible6 spectra have shown an orbital modulation of the plume brightness, which suggests that the eruption activity is influenced by tidal forces. However, the observed activity seems to be delayed by several hours with respect to predictions based on simple tidal models6,7. Here we simulate the viscoelastic tidal response of Enceladus with a full three-dimensional numerical model8,9 and show that the delay in eruption activity may be a natural consequence of the viscosity structure in the south-polar region and the size of the putative subsurface ocean. By systematically comparing simulations of variations in normal stress along faults with plume brightness data, we show that the observed activity is reproduced for two classes of interior models with contrasting thermal histories: a low-viscosity convective region above a polar sea extending about 45°–60° from the south pole at a depth below the surface as small as 30 km, or a convecting ice shell of 60–70 km in thickness above a global ocean. Our analysis further shows that the eruption activity is controlled by the average normal stress applied across the cracks, thus providing a constraint on the eruption mechanism.

Shear strength properties of Dimitrovgrad flysch, Southeastern Serbia

Flysch deposits are common in Serbia. Approximately 15 % of the 250 km of highways currently under construction will be constructed in flysch. In the most southern part of the E80 project, close to the border crossing with Bulgaria, construction of 3-km long cuts, often over 30 m high, is foreseen by the design. The geology of this part of Serbia is mainly characterized by flysch deposits represented by a sequence of sandstone and siltstone, interchanging in different proportions. After excavation of a majority of the cuts, several slopes suffered from global and structural instabilities. This required re-design of one part of the cuts. For this purpose, a geological strength index (GSI) was estimated and the structural features of rock discontinuities were observed on the faces of the surface excavations. This information and data obtained from laboratory testing enabled the determination of five characteristic rock mass types. For every type, shear strength properties were determined based on three criteria: the Hoek–Brown failure criterion; the Mohr–Coulomb criterion; and an hyperbolic nonlinear envelope. During the process of converting the Hoek–Brown parameters to the parameters of hyperbolic envelope, the Levenberg–Marquardt algorithm (LMA) was utilized to solve for the nonlinear regression problem. Verification of the parameters was performed on several examples. The median angle pressure increases exponentially with the GSI value and ranges between the value characteristic for clays and well-graded gravel. The maximum angle difference is obtained for a GSI value of 30. The average normal effective stress acting on the failed slopes, expressed in the form of the stress level ratio (SLR), is below 0.5. This indicates that the curved part of the shear strength envelope is utilized during the shearing. As such, the linear segment overestimates the shear strength.

The interface between fluid-like and solid-like behavior for drops suspended in two-phase Couette flow

The flow of two-dimensional buoyant drops in a horizontal channel is studied by numerical simulations at finite Reynolds numbers. A linear shear flow is assumed inside the channel. The study is similar to that performed by Zhang and Campbell in granular flow regime (Zhang and Campbell in J Mech 237:541–568, 1992). The areal fraction is relatively large (0.72), and the flow is studied as a function of the bulk Reynolds number, a Reynolds number defined based on the acceleration due to gravity, and the capillary number. It is found that for a single drop motion the drop obtains an equilibrium position inside the channel. The equilibrium position is validated by comparing with other efforts. Results at a high areal fraction are compared to the work by Zhang and Campbell. The average velocity profile across the channel is relatively different compared to granular flow regime. The average fluctuation energy shows similar trends across the channel. The fluctuation energy is significantly lower on the average in the present study. The average normal stress (load) is also lower compared to granular flow regime. It is expected that this is due to the effect of interstitial fluid present in the present study.

Atomic-Scale Wear of Amorphous Hydrogenated Carbon during Intermittent Contact: A Combined Study Using Experiment, Simulation, and Theory

In this study, we explore the wear behavior of amplitude modulation atomic force microscopy (AM-AFM, an intermittent-contact AFM mode) tips coated with a common type of diamond-like carbon, amorphous hydrogenated carbon (a-C:H), when scanned against an ultra-nanocrystalline diamond (UNCD) sample both experimentally and through molecular dynamics (MD) simulations. Finite element analysis is utilized in a unique way to create a representative geometry of the tip to be simulated in MD. To conduct consistent and quantitative experiments, we apply a protocol that involves determining the tip-sample interaction geometry, calculating the tip-sample force and normal contact stress over the course of the wear test, and precisely quantifying the wear volume using high-resolution transmission electron microscopy imaging. The results reveal gradual wear of a-C:H with no sign of fracture or plastic deformation. The wear rate of a-C:H is consistent with a reaction-rate-based wear theory, which predicts an exponential dependence of the rate of atom removal on the average normal contact stress. From this, kinetic parameters governing the wear process are estimated. MD simulations of an a-C:H tip, whose radius is comparable to the tip radii used in experiments, making contact with a UNCD sample multiple times exhibit an atomic-level removal process. The atomistic wear events observed in the simulations are correlated with under-coordinated atomic species at the contacting surfaces.

Non-linear behavior of unreinforced masonry walls with different Iranian traditional brick-work settings

The need to preserve and protect the historical buildings around the world has seen the emergence of researches directed toward the analytical modeling of fracture in masonry. The fracturing mechanism in masonry is a complex phenomenon due to existing two brittle materials with distinct material properties. The mechanical behavior of brickwork is strongly affected by the behavior of mortar joints. Mortar joints are the planes of weakness of masonry, especially in old buildings due to the weathering and agedness. On the other hand the orientation of mortar joints affects the fracture pattern of brickwork and causes different types of crack pattern in brickwork settings. Accordingly, the analysis of historical buildings, aimed at structure assessment and restoration, demands an adequate understanding of the mechanical behavior of these different types of brickwork setting and accurate data consisting elastic and inelastic parameters. This paper presents the results of a comprehensive numerical modeling of common types of brickwork settings behavior used in brick-built monuments. Since derivation of an accurate yield criterion for masonry units is usually difficult, there is a higher willingness of using simple plasticity models for practical problems. For better comparison of an-isotropic mechanical behavior of masonry units with these brickwork settings in linear and non-linear phases, numerical modeling of some masonry panels subjected to in-plain compressive and shear loadings are performed using an algorithm based on the Distinct Element Method (DEM). In the DEM modeling, the Mohr–Coulomb failure surface with a tension cut-off is chosen as a constitutive law for both blocks and joints with zero thickness representing mortar bonds. The relations between average normal stress and maximum average shear stress are presented for different brick-work settings taken in this study subjected to monotonic loadings.

The Research on Ceramic Friction and Flow Stress of Plastic Forming

The interface friction is used to evaluate the plastic flow behavior of workpiece material in different conditions such as temperature, pressure, strain rate and strain distribution. It is analyzed that deformation and material flow by the ring compression method during compression, which is contained with the theoretical calculation of different interface friction ring inside diameter and the height of the change. The progressive deformation incremental method is studied to the curve of the friction factor and ring size. It is given that the standard calibration curve of ring friction factor by 6:3:2 size ratio. According to the practical circle deformation ,it is given to the relative average stress, and then to calculate the average normal stress, according to the actual load stress ,it can be concluded that the actual flow stress of material. The change of ring height and diameter is measured by experiment. The results show that the friction factor is relatively stable, the maximum is 0.48, and then the minimum is 0.35.

A Scalar Acoustic Equation for Gases, Liquids, and Solids, Including Viscoelastic Media

The work deals with a mathematical model for real-time acoustic monitoring of material parameters of media in multi-state viscoelastic engineering systems continuously operating in irregular external environments (e.g., wind turbines in cold climate areas, aircrafts, etc.). This monitoring is a high-reliability time-critical task. The work consistently derives a scalar wave PDE of the Stokes type for the non-equilibrium part (NEP) of the average normal stress in a medium. The explicit expression for the NEP of the corresponding pressure and the solution-adequateness condition are also obtained. The derived Stokes-type wave equation includes the stress relaxation time and is applicable to gases, liquids, and solids.

Stresses Within Granular Materials Contained Between Vertical Walls

Arching is an important phenomenon that has to be understood when designing backfilled trenches, storage silos and underground mine stopes supporting granular materials. Here, a significant fraction of the fill load is carried by the wall friction and hence the load transferred to the bottom of the fill is substantially reduced. The objective of this paper is to present three different approaches, namely, analytical, experimental and numerical, to study the vertical normal stresses within a granular material contained between vertical walls. The laboratory model discussed herein is an effective tool in deriving the variation of shear stress on the wall and the average normal stresses with depth. It is shown that the analytical and numerical models that treat the granular material as a continuum suggest an asymptotic vertical normal stress that is reached at certain depths, whereas the laboratory model tests show that the vertical stresses increase continuously even at very large depths.

Effect of fibre curvature on the rheology of particulate suspensions

Rheological properties of non-Brownian straight and curved fibre suspensions in simple shear flow have been investigated by particle-level simulation. An inertialess fibre particle in Newtonian fluid is modelled as a collection of spheres connected with Hookean-type constraint force. The fibre motions are governed by hydrodynamic interaction based on Rotne–Prager correction to velocity disturbance and short-ranged repulsive force. An isolated curved fibre in simple shear flow shows a decrease in the period of rotation with increasing the curvature. Initial stress overshoot is observed as fibres undergo transition from isotropic orientation. Shear viscosity and first normal stress of straight fibre suspensions exhibit scaling with respect to concentration in a manner consistent with comparable literature results. The overall viscosity enhancement with increasing the curvature has been observed over the studied range of aspect ratio and concentration. This is accompanied by the decrease of flow-aligned component of configuration tensor. Straight and curved fibre simulation exhibits an average positive first normal stress difference but the data fluctuation is too large to distinguish curvature effect.

Effect of thermal annealing on the stress and morphology of deposited nanofilms analyzed using molecular dynamics

Molecular dynamics (MD) simulations are used to investigate the surface roughness and intermixing of grown films and to calculate the atomic-level stress before and after the annealing process. The tight-binding second-moment approximation (TB-SMA) many-body potential is employed to model the interaction. The results reveal that the morphology of the film becomes smoother after 900K annealing due to the substrate temperature being lower for the as-deposited film. The results indicate that the annealing decreases the number of vacancies and voids for all thin films. More Al atoms penetrate into the substrate after the annealing process. The interface mixing of annealed film is thus better than that of as-deposited film. The first peak of the radial distribution function (RDF) becomes higher and narrower when the Al–Cu film is cooled from 700 to 300K. This indicates that new grains nucleate and grow to replace those deformed by internal stresses and that recrystallization may occur for the Al–Cu film. In the atomic-level stress analysis, the average normal stress along the thickness direction and the average mean biaxial stress are considered. Both residual stresses decrease for all layers after the annealing process. This implies that internal stress is relieved within the Al–Cu film during the cooling phase.

Soil-Structure Interaction of an Earth Pressure Cell

The output from an earth pressure cell (EPC) is usually related to the normal stress in soil through fluid calibration, where a known pressure is applied to the EPC and the output is recorded. However, distribution of normal stress within a soil is not uniform, and the EPC is not an ideal membrane—bending stiffness affects the response. These factors complicate the performance of the EPC. A calibration procedure for an EPC is reviewed, and it is shown that these controversial sensors can provide an accurate measure of average normal stress if calibrated in soil at a given density. In addition, a soil-structure interaction model is proposed to explain why soil calibration is necessary.

Model of Toner Impaction and Developer Failure

High definition digital imaging is enabled in printers by using small micron and nano toner particles. Use of small particles in a housing presents challenges in particle flow as small particles tend to aggregate, clog and impact either on the wall of the housing or on other surfaces. Solids are known to undergo brittle-ductile transition depending on the size of a particle, elastic plastic behavior and strain rates under which they are deformed.In macromolecules, polymer chain flexibility and shear flow of uniformly sized, spherical particles can be analyzed. Inter-particle attractive forces are considered to influence flow of small particles. Simulations performed for different strengths of cohesion, shear rates, particle stiffnesses, particle volume fractions and coefficients of friction show interesting results. From each simulation, the average normal and shear stresses and the average coordination number have been extracted. Generally small particles are externally mixed with nano-sized particles to improve flow. Hard nano-sized particles reduce cohesiveness of toner particles and reduce its aggregation.Particulate flow can some time result in jamming and has been analyzed using Lattice-Boltzmann (LB) or DEM (Discrete Element Methods) involving deformation from collisions resulting from hydrodynamic forces. Consequence of particle impaction on surfaces is a reduction in particle charge with wider distribution causing shortfalls in electro-photographic development and image quality. A rate equation model is developed for impaction in a cylindrical cavity that depends on the impact parameter, rate of volumetric flow, yield stress (modulus) of the elastic-plastic particle, size of the particle and dynamic coefficient of friction. The model predictions are compared with experimental data on the particle (toner) impaction

Numerical and analytical modeling of orthogonal cutting: The link between local variables and global contact characteristics

The response of the tool–chip interface is characterized in the orthogonal cutting process by numerical and analytical means and compared to experimental results. We study the link between local parameters (chip temperature, sliding friction coefficient, tool geometry) and overall friction characteristics depicting the global response of the tool–chip interface. Sticking and sliding contact regimes are described. The overall friction characteristics of the tool are represented by two quantities: (i) the mean friction coefficient qualifies the global response of the tool rake face (tool edge excluded) and (ii) the apparent friction coefficient reflects the overall response of the entire tool face, the effect of the edge radius being included. When sticking contact is dominant the mean friction coefficient is shown to be essentially the ratio of the average shear flow stress along the sticking zone by the average normal stress along the contact zone. The dependence of overall friction characteristics is analyzed with respect to tool geometry and cutting conditions. The differences between mean friction and apparent friction are quantified. It is demonstrated that the evolutions of the apparent and of the mean friction coefficients are essentially controlled by thermal effects. Constitutive relationships are proposed which depict the overall friction characteristics as functions of the maximum chip temperature along the rake face. This approach offers a simple way for describing the effect of cutting conditions on the tool–chip interface response. Finally, the contact length and contact forces are analyzed. Throughout the paper, the consistency between numerical, analytical and experimental results is systematically checked.

An Experimental Study on Scale Effects in Rock Mass Joint Strength

A series of laboratory tests were conducted on matched rock joint samples, no larger than 16 x 16 cm2 of section, which were extracted from an artificial joint, having 4.32 m2 in area, carved in a porphyritic granite block. These tests (1200 pull tests and 200 trials conducted in a sliding machine) involved the systematic levelling of sample middle planes and lead to conclusions that are discrepant with respect to conventional ideas admitted about rock-mass joint mechanics. Those discrepancies are: a) Larger matched samples showed higher strengths in the dilating phase of the sliding tests rather than those from small matched samples; b) Sample shear strengths probably depend on the transverse widths, when JRC, JCS and n (the average normal stress on the rock mass joint) are high, thus inhibiting the use of stability analysis by common slope stability methods such as Fellenius’; c) At the dilating sliding phases, the mechanics of matched joints is essentially different from that of mismatched joints, as the former brings about inverse scale effects (represented by positive exponential regressions) and the latter involves normal scale effects (represented by negative exponential regressions). The results obtained upon those lab tests do not agree with those reported from in situ experiments, as well as the actual behaviour of natural joints. The obtained moderate correlation coefficients do not allow the consideration of these findings as physical laws, nevertheless they do represent certain types of rock mass joint behaviour, or simply useful generic rules. Thus, the subject is full of surprises, as the authors show in text.

Study on the tribological properties between the aluminum alloy 7050-T7451 and the YG8 cemented carbide

The ball–disc friction experiments are performed by applying the YG8 cemented carbide ball and the aluminum alloy 7050-T7451 plate under high speed and high load, and then the wear depth of the groove was observed using white light interferometer. The average contact normal stress was calculated by the depth of the groove. The relationship between friction coefficient and average contact normal stress as well as sliding velocity is fitted with Minitab. It shows the friction coefficient decreases with the increasing of the sliding velocity and the average contact stress. The results provide certain theoretical basis to build the friction model and finite element model of machining Al alloy.