Force Balance Method Research Articles

Geometric correction factors for center cracked specimens subjected to nonlinear bridging stresses in the shear lag model

Fiber bridging plays an important role in the fracture mechanism of fiber-reinforced composites. The determination of the geometric correction factors for finite-width specimens subjected to complex bridging stresses is vital for the practical application of various bridging models. An approximate approach named the force balance method (FBM) was recently reported in the literature to evaluate such geometric factors. The main purpose of this study is to assess the effectiveness of the FBM by using the well-established boundary element method. The case of a center cracked specimen subjected to a nonlinear fiber bridging stress in the shear lag model in fiber-reinforced composites is considered. The geometric correction factors computed by the boundary element method are compared with those deduced by the FBM.

Ultrasonic Power Measurement by the Radiation Force Balance Method –Experimental Results using Burst Waves and Continuous Waves–

Results of ultrasonic power measurements using a radiation force balance system constructed at National Institute of Advanced Industrial Science and Technology (AIST) are described. The aim of this research is to establish the ultrasonic power standard for medical ultrasonics. The experimental results of the linearity of the system under 1 mW to about 60 mW for the continuous and the burst waves are presented. It is also confirmed that the measured ultrasonic power is not affected by the repetition rate of the burst wave.

Statistical control of ultrasonic power measurements using hypothesis testing

The measurement in the calibration of ultrasonic power was controlled using hypothesis testing. The ultrasonic power measurement system is based on the radiation force balance method according to IEC 61161 (1998). To assess the uncertainty in the measurement, the experimental variance needs to be estimated. Having a well-characterized measurement with statistical method in accordance with the Guide to the Expression of Uncertainty in Measurement (4.2.4 and the note of H.3.6), a pooled estimate of the experimental variance that characterizes the measurement is obtained. During an acoustical calibration and measurements over a period of 6 weeks, hypothesis testing was applied to the measurement data to ensure the validity of the pooled experimental variance. The measurement data were divided into data blocks with a sliding window to form five independent consecutive observations. Hypothesis tests were then applied to the data blocks to examine the variability of the value of a measurand. Good measurement reproducibility was observed that resulted in the confidence of the measurement.

Stress Ahead of the Tip of a Finite-Width Center-Crack in Fiber-Reinforced Composite Specimen: Subjected to Non-Linearly Distributed Bridging Stresses

The force balance method (FBM) is a simple and effective way to calculate geometric correction factors for the stress distribution ahead of the tip of finite-width center crack specimen. In this paper, the accuracy and effectiveness of the FBM is shown by means of a numerical evaluation of the stress distribution ahead of the tip of finite-width center-cracked specimens subjected to nonlinearly distributed bridging stresses in fiber-reinforced composites. The finite element method is used for this purpose.

Model-based method for improvements in the calibration of ultrasonic power measurements at low-power levels

The measurement uncertainty in the calibration of ultrasonic power measurements at low-power levels was reduced by a model-based signal-processing method. The ultrasonic power measurement system is based on the radiation force balance method according to IEC 61161. Outputs of an electronic balance and the excitation voltage were simultaneously sampled and recorded. A computer-controlled coaxial switch that utilizes data lines of the parallel port of a desktop computer was used for power-on and power-off control. Power-on and power-off intervals were finely controlled by the desktop computer. The Electroacoustic radiation conductance, defined as the ratio of the ultrasonic power of a transducer and the square of the rf voltage at its input, was calculated from the recorded data. During data processing, a simple model for drifting and switching was proposed and a least-mean-squares algorithm was used to estimate parameters of the model. Good measurement reproducibility was also observed that resulted in the reduction of total measurement uncertainty.

Improved Dynamic Friction Models for Simulation of One-Dimensional and Two-Dimensional Stick-Slip Motion

In many mechanical systems, the tendency of sliding components to intermittently stick and slip leads to undesirable performance, vibration, and control behaviors. Computer simulations of mechanical systems with friction are difficult because of the strongly nonlinear behavior of the friction force near zero sliding velocity. In this paper, two improved friction models are proposed. One model is based on the force-balance method and the other model uses a spring-damper during sticking. The models are tested on hundreds of lumped mass-spring-damper systems with time-varying excitation and normal contact forces for both one-dimensional and two-dimensional stick-slip motions on a planar surface. Piece-wise continuous analytical solutions are compared with solutions using other published force-balance and spring-damper friction models. A method has been developed to set the size of the velocity window for Karnopp’s friction model. The extensive test results show that the new force-balance algorithm gives much lower sticking velocity errors compared to the original method and that the new spring-damper algorithm exhibits no spikes at the beginning of sticking. Weibull distributions of the sticking velocity errors enable maximum errors to be estimated a priori.

Applications of colloidal force measurements using a microcollider apparatus to oil sand studies

Two colloidal force measurement techniques have been applied to oil sand studies both using the same apparatus called the microcollider. The techniques are colloidal particle scattering method for repulsion-dominant systems and hydrodynamic force balance method for attraction-dominant systems. The former is based on calculating the colloidal forces from the magnitude of particle–particle collision trajectory deflections. The latter is based on separating a colloidal doublet with increasing shear and calculating the maximum attractive force at the onset of the doublet breakup. Both methods involve the microscopic observation on two individual particles. The methods are also well suited to emulsion systems where the interaction forces as small as 10 −13 N between two droplets can be detected. In oil sand research, two stable emulsions: water-in-diluted bitumen and bitumen-in-water have been receiving considerable attention because of their detrimental effects on the industrial process. The droplet–droplet forces and the emulsion stability mechanism were determined for both emulsions using either one of the techniques. For the w/o emulsion, steric repulsion is the main contributor to the emulsion stability. For the o/w emulsion, all interactions are exclusively DLVO-type forces and the electrostatic force plays a major role in stabilizing the emulsion. Isolated protrusions of tens of nanometers in thickness have also been detected on bitumen surfaces. The protrusions enhance the repulsive force at a long distance but reduce it near the energy barrier, a useful feature that might help in destabilizing the system.

Ultrasonic Power Measurements by Radiation Force Balance Method –Characteristics of a Conical Absorbing Target–

In this study, the authors proposed a conical absorbing target for ultrasonic power measurements using the radiation force balance method. We have compared three types of targets, i.e., a conical reflecting target, a plane absorbing target and a conical absorbing target. As the result of these experiments, the conical absorbing target showed some good characteristics for a precise ultrasonic power measurement system.

Summary of a European comparison of ultrasonic power measurements

A summary is given of the results of a European comparison of ultrasonic power measurements. Three national metrology institutes participated. All measurements were carried out using the radiation force balance method according to International Electrotechnical Commission Standard IEC 61161, with minor differences in certain experimental details. Five standard transducers were circulated, with nominal resonance frequencies between 1 MHz and 10 MHz. The measurements covered the power range from 10 mW to 200 mW, which roughly corresponds to the output of medical diagnostic equipment. The results obtained by the participants agreed within the estimated uncertainties.

A simple closed form force balanced solution for pore pressure, overburden and the principal effective stresses in the Earth

Force balance in the Earth occurs through minerals and fluid, the constituents of the Earth. A simple set of equations rigorously defines the relationships between pore pressure, external confining loads, the principal effective stresses, mineralogy and strain in the Earth. The closed form solution applies The Effective Stress Theorem force conservation law through linkage of force balance definitions with granular mineral and fluid physical properties to a single absolute strain definition. Force balance for solids in the Earth is vectorial within volumetric. Volumetric effective stress is therein directly related to volumetric in situ strain. Force balanced means that all the static solid vectors and the fluid scalars individually and collectively sum to zero. All three principal confining loads, opposing effective stresses and strain are rigorously defined in the closed mathematical form. This set of equations represents a special case of Newtonian physics that applies in the Earth's sedimentary crust. The mathematical closure of the force balance and strain definitions has the fewest possible coefficients. The closed form involves only the density and compressibility coefficients of the minerals and fluid, which bear the external loads. Loading limb mineralogic stress/strain coefficients for the Newtonian closed form solution were measured in the Earth in sedimentary basins that closely fit the Newtonian gravitational biaxial idealization. More than half of the sedimentary basins of the world are extensional, dominated by normal faults and involving an approximately biaxial normal fault regime stress field. Assuming that continental drift is due to mantle convection, and that the Earth's volume is constant, all the horizontal stresses on the surface of the Earth's upper brittle crust would average to zero. Restating these assumptions more briefly, the average stress field of the Earth is biaxial with the maximum principle stress being vertical toward the Earth's center. The closed form equations exactly represent the average governing physics of the Earth. The closed form solution has been inverted and implemented to predict pore pressure and fracture pressure in hundreds of wells in several extensional basins. Wherever it was statistically tested in comparison to empirical methods to predict pore pressure and fracture pressure, the closed form force balanced method was found to be the most accurate. The physical conservation laws—rock properties relationships embodied in the closed form solution—touch every science and technology that deals with the Earth's sedimentary crust.

Numerical evaluation of the stress distribution ahead of a crack tip for a finite‐width centre‐cracked specimen loaded by stresses along a portion of the crack

Recently, the force balance method (FBM) has been proposed to calculate geometric correction factors for the stress distribution ahead of a crack tip. In this paper, the effectiveness of the FBM is proved by means of a numerical evaluation of the stress distribution ahead of a crack tip in finite‐width centre‐cracked specimens loaded by stresses along a portion of the crack. The finite element method is used for this purpose.

ANALYTICAL COMPARISON OF FORCE AND ENERGY BALANCE METHODS FOR CHARACTERIZING SPRAYS FROM HYDRAULIC NOZZLES

Theoretical approaches for characterizing sprays include the application of force balance (FB) and energybalance (EB) principles to a droplet separating from a liquid sheet. Although both methods are within the domain ofclassical fluid dynamics, their prediction equations for the droplet size (d) are quite different. The objective of this studywas to analytically compare the FB and EB methods for characterizing sprays. Revised equations for d were developedbased on the EB and FB principles. Droplets were assumed to separate (from a liquid sheet) radially while deceleratingunder the combined effect of viscosity, surface tension, and effective-drag (accounts for the combined effect of viscousdrag, air entrainment, and mutual interaction of droplets). Compatibility of the FB and EB equations requires a dropformation process to be completed at a radial distance ( .r from the liquid sheet breakup region) equal to d. Thisrequirement is automatically relaxed in the EB equation. The calculated effect of effective-drag (for .r = 0-25d) on dropvelocities was negligible for a water spray. Further analysis revealed that the previous FB equations represent a verylimited and special case of the revised equations.

Stress fields in general composite laminates

A direct approach is employed to obtain a general boundary integral formulation for the analysis of composite laminates subjected to uniform axial strain. The integral equations governing the problem are directly deduced from the reciprocity theorem, employing the generalized orthotropic elasticity fundamental solutions expressly inferred. The solution is achieved by the boundary element method, which gives, once the traction-free boundary conditions and the interfacial continuity conditions are enforced, a linear system of algebraic equations. The formulation does not present restrictions with regard to the laminate stacking sequence and it does not require any aprioristic assumption. The interlaminar stress field near the free edge of generally stacked composite laminates subjected to uniaxial extension is investigated through this boundary integral equation formulation. The numerical applications show good agreement with those already available in literature, and they demonstrate the accuracy and the efficiency of the proposed method. approach where a complete three-dimensional analysis is performed was presented by Pipes and Pagano,1 who employed the finite dif- ference technique to obtain the solution of the governing elastic- ity equations. Many solutions obtained by using the finite element method are available.21() These differ from each other in the formu- lation, in the kind of employed elements, and in the discretization schemes. In the literature analytical solutions of approximate the- ories are also present. The techniques employed to achieve these solutions include the perturbation method,11 series solution,12'13 Lekhintskii's complex stress potentials coupled with an eigenfunc- tion expansion14'15 or a polynomial expansion,16'll the extension of Reissner's variational principle,18'19 and the force balance method coupled with the minimum complementary energy principle.20'21 The stress distributions obtained with these approaches show good agreement between them for points away from the free edge. Con- siderable disagreement exists instead for points near the free edge location among the various numerical and analytical solutions. This is to be expected as a result of a priori assumptions or because the boundary conditions of the continuum problem have been trans- formed into conditions on the generalized data. Actually the numer- ical solution techniques are not able to predict the singular trend in the stress field at the free edge, and hence, to achieve satisfactory solutions a lengthy extrapolation procedure is required. On the other hand, the analytical approximate solutions often rest on assumptions about the problem unknowns that enforce the free edge stress field structure. In the present paper, the stress field in multilayered composite laminates under uniform axial extension is analyzed on the basis of the integral equation theory.22'23 The laminate is considered as composed by prismatic elements having different elastic proper- ties. The generic element or ply is treated as homogeneous, and in terms of constitutive equations it is described by a generalized orthotropic law. The integral equations governing the exact elastic- ity solution of the problem are directly obtained by applying the reciprocity theorem with the fundamental solutions of the general- ized orthotropic elasticity.2427 The

Simple considerations on forces driving plate motion and on the plate-tectonic contribution to the long-wavelength geoid

SUMMARY In order to gain some insights into the role of deep mass anomalies on surface velocity and geoid anomalies, Cartesian models involving strong lateral viscosity contrasts and where plate boundaries are mimicked by zones of very low viscosity are performed. The response of the system to mass anomalies at various depths and various distances from the plate boundary is computed. It is compared with the responses obtained using the three other methods used in global geoid models for mimicking the mobility of the lithosphere: models with layered viscosity and a uniform low-viscosity lithosphere; models computing plate velocities from horizontal force balance; and models where the surface velocities are set equal to the observed ones with plates ‘moved by the hand of God’. Contrary to what occurs in models with layered viscosity, the geoid response for the weak-zone model proposed here changes drastically from positive to negative, depending upon the position of the mass anomaly with respect to the plate boundary. This arises from the fact that only mass anomalies situated close to the plate boundary are able to move the plates efficiently. Changing the location of an upper-mantle mass anomaly by a few hundred kilometres considerably modifies the amplitude of the predicted plate velocities and geoid anomalies. Consequently, upper-mantle density anomalies deduced from global tomography analysis, or density anomalies assumed to be known a priori (subducted slabs) but truncated by a spherical harmonic decomposition should not be used in models aimed at computing plate motions and the associated geoid. When a mass anomaly is situated just below a plate boundary, the sign of the predicted geoid anomalies can be the same as for models with a layered viscosity and a low-viscosity lithosphere. However, the shape of the predicted geoid anomaly and its amplitude as a function of the depth of the mass anomaly cannot be mimicked by models with a uniform-viscosity lithosphere, whatever the lithospheric viscosity. For mass anomalies situated at a large distance from the plate boundaries, the induced plate velocities are small and the geoid is equal to that computed for a highly viscous continuous lithosphere. The ‘force-balance method’ is strongly affected by the cut-off in the harmonic decomposition. Only models with a lithospheric layer below the surface reproduce the geoid successfully for mass anomalies situated away from a plate boundary. The plate velocities for the force-balance method and for the weak-zone model proposed here are not proportional, due to differences in the structure of the plate boundary. In short, only mass anomalies very close to a plate boundary are able to influence the plate velocities, but these velocities depend strongly on the mechanical details of the plate boundary. As a consequence, we believe that it is impossible to compute plate velocities from what we know from mass anomalies in the Earth precisely enough to include them in a geoid model. On the other hand, actual plate velocities are known. We show that an accurate geoid can be computed by imposing the observed plate velocities onto the Earth's surface, even if the details of the mechanical structure of the lithosphere are not respected. It is this method that is suggested for introducing the effect of plate tectonics in global geoid models.

Bragg scattering and effective force-balance equations in superlattice miniband transport

The two existent balance-equation methods for electron transport, which incorporate Bragg scattering and give rise to bulk negative differential mobility, are further investigated using the Boltzmann transport equation for Bloch electrons. We point out that the ansatz employed in the earlier Büttiker–Thomas (BT) scheme to relate the average drift velocity and the average momentum, should be modified for a general energy band. Numerical calculation of superlattice miniband conduction shows that the modified BT force-balance method yields a velocity–field behavior almost equivalent to that predicted by the acceleration-balance method of Lei, if the appropriate momentum function is used in the calculation of the BT frictional force, such that Bragg scattering is properly taken into account in the process of electron scattering.

Assessment of force balance method used to calculate stress intensity factors for center cracked finite strips

Based on the results obtained from the weight function method, the basic assumptions and the accuracy of the force balance method are discussed

A force-balance study of ice flow and basal conditions of Jutulstraumen, Antarctica

AbstractStresses and velocities at depth are calculated across Jutulstraumen, an ice stream in Dronning Maud Land, draining about 1% of the Antarctic ice sheet. The force-balance study is based on data from kinematic GPS measurements on three strain nets, each consisting of 3 × 3 stakes. The maximum measured velocity is 443 m a−1 and the velocity variation over short distances is large compared with studied ice streams in West Antarctica. The surface topography together with the measured velocities across the profile indicate that the bottom topography has a great influence on the flow direction, even where the ice thickness is more than 2000 m. The basal shear stresses are calculated as 180, 227 and 146 kPa in the three Strain nets, while the corresponding driving stresses are 180, 122 and 111 kPa (±5%). The heat produced by sliding and internal deformation is sufficient to keep the base at the pressure-melting point. The annual basal melting is estimated to be about 60 mm. Investigations on the effect of temperature softening show that the flow parameter’s influence on the effective strain rate is more important than the flow parameter’s direct softening in the flow low alone. The mass flow calculated by the force-balance method is between 87 and 96% of pure plug flow and total discharge is calculated to be 13.3 ± 10 km3a-1.

A force-balance study of ice flow and basal conditions of Jutulstraumen, Antarctica

Abstract Stresses and velocities at depth are calculated across Jutulstraumen, an ice stream in Dronning Maud Land, draining about 1% of the Antarctic ice sheet. The force-balance study is based on data from kinematic GPS measurements on three strain nets, each consisting of 3 × 3 stakes. The maximum measured velocity is 443 m a−1 and the velocity variation over short distances is large compared with studied ice streams in West Antarctica. The surface topography together with the measured velocities across the profile indicate that the bottom topography has a great influence on the flow direction, even where the ice thickness is more than 2000 m. The basal shear stresses are calculated as 180, 227 and 146 kPa in the three Strain nets, while the corresponding driving stresses are 180, 122 and 111 kPa (±5%). The heat produced by sliding and internal deformation is sufficient to keep the base at the pressure-melting point. The annual basal melting is estimated to be about 60 mm. Investigations on the effect of temperature softening show that the flow parameter’s influence on the effective strain rate is more important than the flow parameter’s direct softening in the flow low alone. The mass flow calculated by the force-balance method is between 87 and 96% of pure plug flow and total discharge is calculated to be 13.3 ± 10 km3a-1.

Geometric correction factors determined by force balance method for center cracked specimens. X.

acad sinica,inst met res,state key lab fatigue & fracture mat,shenyang 110015,peoples r china.;chen, dl (reprint author), univ vienna,inst phys chem mat sci,waehringer guertel 18,a-1090 vienna,austria

Discrete element simulation of granular flow in 2D and 3D hoppers: Dependence of discharge rate and wall stress on particle interactions

Discrete element Newtonian dynamics simulations have been carried out of filling and discharge under gravity of non-cohesive discs (in two dimensions) and spheres (in three dimensions) from model hoppers. The current model improves that developed previously by us (Langston et al., 1994) in several respects. We introduce a continuous and gradual hopper filling method, a more realistic normal-tangential interaction between the particles, particle size polydispersity, and the model is extended from two to three dimensions (3D). The hopper discharge rate has been computed as a function of material head height, outlet size and the hopper half-angle. The model results are, in general, in very good agreement with established literature empirical predictions. The hopper wall stresses have been compared in the static state after filling and in the dynamic state during discharge. Generally there is encouraging agreement with predictions from the continuum differential slice force balance method, with significant improvements over our previous work. We have also observed, for the first time in a discrete element simulation of hoppers, the appearance of rupture zones within the material and associated wall stress peaks where the rupture zones intersect with the hopper wall. We consider that the current model is more successful than the previous one because the particle interactions include a much greater level of frictional “engagement” at low loads, with less variation at high loads.