The determination of plough draught—Part I. prediction from soil and meteorological data with cone index as the soil strength parameter

Using cone index as an indication of soil strength, empirical equations are developed in accordance with soil mechanics theory to relate soil moisture content to plough draught. The plough draught equation comprises a quasi-static component dependent on cone index and a dynamic component which is a function of the soil specific weight, plough speed and mouldbard tail angle. It is further argued that the cohesive and frictional components of the cone penetration resistance can be predicted by means of a simple equation comprising a reciprocal function of the square of the soil moisture content and a linear function of the soil specific weight. The cone index equation explained 98% of the experimental data for threthree soils over a wide range of moisture contents. These empirical equations, together with a soil moisture model, provide a method of predicting plough draught directly from soil and meteorological data.     

Stress intensity factors for two offset parallel circular cracks: Part II — Semi-infinite solid

With the aid of the formulation in [1] (R. Muki, Progress in Solid Mechanics (North-Holland, 1961)) for general three-dimensional asymmetric problems and the superposition principle, Part II of this work makes use of the method in Part I (G.A.C. Graham and Q. Lan, J. Theor. Appl. Fract. Mech. 20, 207–225 (1994) [2]) to examine the interaction of arbitrarily located penny-shaped cracks in an infinite elastic solid to the case of a semi-infinite solid. As in Part I for the infinite body, the problem of a semi-infinite solid containing two penny-shaped cracks is reduced to a system of Fredholm integral equations of the second kind. These integral equations are then solved for some special cases when cracks are far apart and far away from the boundary. Some asymptotic solutions are presented and comparisons are made with the results for the special case where there is only one crack under axisymmetric loading.     

Working processes of cyclic-action machinery for soil deformation—Part III

The analysis deals with a system consisting of a main unit, moving with uniform velocity and generating the necessary tractive force, and an impactor which periodically transmits to the tool a specified amount of energy expanded in the soil at the loading stage.

It is established that the working process is characterized by a specific set of uniquely defined parameters, a change in any of which necessitates corresponding ajustment of all the others; otherwise, the process becomes continuous instead of cyclic or else breaks down altogether. Quantitative values of the parameters are obtainable from the present experimental data. It is also shown that the role of the tractive force consists in permitting uptake of the unloading energy and its recovery by the tool. The force acts only over a certain part of the cycle, preceding the loading stage; its value may vary widely, but in practical cases is considerably lower than its counterparts in continuous processes.

Analytical relationships are desired for minimizing the energy requirement of the process, as the basis for optimizing its parameters.     

Working processes of cyclic-action machinery for soil deformation—Part IV

The analysis deals with a system consisting of a main unit-moving with uniform velocity and generating the necessary tractive force- and a centrifugal vibrator, connected to the main unit by means of a spring and oscillating together with the tool as a single subsystem. The working process is described through piecewise-linear approximation of the frontal resistance force of the soil, as a function of the tool displacement. By this means interrelationship is established between the system parameters (with the possibility of their effective control) and the mechanical characteristics of the soil. It is shown that the process is feasible for a definitive set of the parameters, a change in one of them affecting the others.Special attention is devoted to the tractive force, whose role consists mainly in permitting uptake of the unloading energy and braking of the vibrator-tool subsystem during its backward motion. The latter is accompanied by compression of the spring, which, on being released, restores to the tool the energy expended during loading. The maximum tractive force in a cycle may be varied effectively over a fairly wide range through variation of the system parameters, each of which may be considered as definitive. A methodology for their determination is presented.Analytical relationships are derived for minimizing the energy requirement of the process, so as to optimize its parameters.     

Working processes of cyclic-action machinery for soil deformation—Part I

An analysis is presented of the working process in cyclic-action shaping of horizontal boreholes in soil. Advance of the tool in the required direction is effected through asymmetric vibrational displacements induced by a pneumatic mechanism. The machine is incapable of utilizing the unloading energy of the soil as part of the input. The analysis is based on approximative characterization of resistance force of the soil and the air pressure in the pneumatic mechanism. As regards the influence of external friction on the process, it was established that increase of the former up to a certain level results in considerable saving in the energy requirement, combined with a significant increase in output. The expressions obtained in this context yield the conditions under which the energy requirement is minimized.     

Unleashing a Microcomputer in the Laboratory, Part II Second in a series of three articles

This is the second article in a series discussing the use of the microcomputer in the laboratory. Part I examined the features of the PET* microcomputer which make it a useful partner in the laboratory. It showed how the microcomputer can be used to control four types of devices: (1) the devices which only require control signals, (2) the devices which talk only, (3) the devices which listen only, and (4) the devices which both talk and listen.     

Working Processes of cyclic-action machinery for soil deformation—part II

The analysis deals with machinery for horizontal boring, consisting of a main unit moving with constant velocity and a slider-crank mechanism providing reciprocating motion of the tool. Special emphasis is placed on the force and energy aspects of the working process. It is established that the basic parameters of the process, including the velocity of the main unit, the maximum tractive force in the working cycle, the crank throw, the energy consumption and other, are largely dependent on the displacement of the tool in the loading stage (‘displacement per cycle’ for short). Each value of this displacement is associated with a set of the above parameters, a change in one of which affects the others. The optimal value is determined here, corresponding to the minimum energy consumption, which is considerably lower than that of the corresponding continuous (quasistatic) process. The reduction of the tractive force, compared with the latter, is attributable to the toughening effect of non-recoverable deformation at prelimiting levels of the frontal resistance force of the soil.     

Rigid-plastic and damage behavior in metal forming: Part II—model prediction

Indeterminacy of the Lévy-Mises relations in plane strain rigid-plasticity is overcome by considering change in plastic strain rate due to triaxiality. Better agreement is achieved on the coincidence of uniaxial data with the effective stress and effective strain in addition to the removal of ill conditions associated with necking stresses derived from other theories of rigid plasticity. The formulation accounts for material compressibility and makes use of the variational principle when applied to discrete locations of the continuum. These physical refinements provide the necessary accuracy for predicting potential damage sites and establishing design limits on metal forming products. Developed are damage thresholds for defining the integrity of rigid-plastic materials with nonlinear behavior. Distortion and dilatation of the material elements are mutually interactive and their proportion changes with the local strain rates in the metal forming process. Only the stationary values of the volume energy density could automatically account for the nonlinear relationship between distortion and dilation. Completed in Part I is the development of a modified theory of rigid-plasticity that better describes the yield and fracture behavior of metals. Numerical results for the permanent deformation of sheet metals are provided in Part II; they are compared with those obtained from other theories of rigid-plasticity.     

Fatigue damage in polycrystals – Part 1: The numbers two and three

The fundamental difference between the cyclic yield stress and the fatigue limit is scale. The basic rate of slip mismatch towards a saturated condition, representing polycrystalline behaviour, is a material property embedded into the grain size distribution. Deviations from its basic rate will depend on the shape of the crack and the selected crack path. This work concludes that during the first loading cycle, and for stresses equal and above the fatigue limit, the surface will always been deformed plastically.     

A new volume of fluid method in three dimensions—Part II: Piecewise‐planar interface reconstruction with cubic‐Bézier fit

A new interface reconstruction method in 3D is presented. The method involves a conservative level‐contour reconstruction coupled to a cubic‐Bézier interpolation. The use of the proposed piecewise linear interface calculation (PLIC) reconstruction scheme coupled to a multidimensional time integration provides solutions of second‐order spatial and temporal accuracy. The accuracy and efficiency of the proposed reconstruction algorithm are demonstrated through several tests, whose results are compared with those obtained with other recently proposed methods. An overall improvement in accuracy with respect to other recent methods has been achieved, along with a substantial reduction in the central processing unit time required. Copyright © 2008 John Wiley & Sons, Ltd.     

Prediction of failure in weldments — Part II: Joint with initial notch and crack

This investigation is concerned with predicting failure initiation sites ina butt weld joint under bending. The nonuniform load transmission characteristics through the weld metal, heat-affected zone and base material resulting from alteration in their microstructure are reflected through the macroscopic yield strength parameter. Elastic-plastic stress and strain redistribution is obtained for each increment of load increase. Analyzed in detail are the contours of constant strain energy density for determining the local and global stationary values which are assumed to be related to failure and stability of the system. Failure is predicted to initiate in the heat affected zone at the site of maximum of the minimum local strain energy density function. This corresponds to the experimental observation where cracking starts from the side of the butt joint where local stretching is maximum.     

The moving-load problem in soil dynamics—the vertical displacement approximation

The moving point load problem in soil dynamics is analyzed in the vertical particle displacement approximation. Prior to its motion, the load is stationary. From the instant at which it is set into motion it moves, with constant speed, along a straight path on the (horizontal) planar surface of a semi-infinite elastic medium. The modified Cagniard method for solving transient wave problems is used to determine closed-form expressions for the vertical component of the particle displacement from the elastodynamic wave equation of which only the vertical component is taken into account. The relevant approximation is standard in soil dynamics. Both the cases of “subsonic” and “supersonic” surface load speeds are considered. Methods to include losses in the model are briefly discussed. The study has been initiated with a view to the application of the results to the analysis of the ground motion generated by high-speed trains traveling on a poorly consolidated soil.     

Generalized fourier analyses of the advection–diffusion equation—Part II: two‐dimensional domains

Part I of this work presents a detailed multi‐methods comparison of the spatial errors associated with the one‐dimensional finite difference, finite element and finite volume semi‐discretizations of the scalar advection–diffusion equation. In Part II we extend the analysis to two‐dimensional domains and also consider the effects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and artificial diffusivities. The observed dependence of dispersive and diffusive behaviour on propagation direction makes comparison of methods more difficult relative to the one‐dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control‐volume finite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out‐perform their lumped mass counterparts and finite‐difference based schemes. While this work can only be considered a first step in a comprehensive multi‐methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework. Published in 2004 by John Wiley & Sons, Ltd.     

A new volume of fluid method in three dimensions—Part I: Multidimensional advection method with face‐matched flux polyhedra

A multidimensional advection scheme in 3D based on the use of face‐matched flux polyhedra to integrate the volume fraction evolution equation is proposed. The algorithm tends to reduce the formation of ‘over/undershoots’ by alleviating the over/underlapping of flux polyhedra, thus diminishing the need to use local redistribution algorithms. The accuracy and efficiency of the proposed advection algorithm, which are analyzed using different tests with prescribed velocity field, compare well with other multidimensional advection methods proposed recently. The algorithm is also applied, in combination with a Navier–Stokes solver, to reproduce the impact of a water droplet falling through air on a pool of deep water. The interfacial curvature is calculated using a height‐function technique with adaptive stencil adjustment, which provides improved accuracy in regions of low grid resolution. The comparison of the numerical results with experimental results shows a good degree of agreement. Copyright © 2008 John Wiley & Sons, Ltd.     

Material symmetry and the evolution of anisotropies in a simple material—II. The evolution of material symmetry

A proper evolutionary definition of material symmetry is presented. The evolution of a material's symmetries as the material undergoes a deformation history is followed, and a procedure for the identification of those changes which are common to all simple materials is provided. Explicit results are presented for initially isotropic, transversely isotropic, and orthotropic materials undergoing simple deformation histories.     

Theoretical and practical aspects of the ride dynamics of off-road vehicles — Part 1

Recent work on the ride vibration behaviour of off-road vehicles is reviewed. The contributions to this subject presented at the 8th ISTVS Conference in Cambridge, 1984, form the main part of the review, but these are discussed in the context of other developments which have been presented recently. It is concluded that ride vibration studies have entered a period in which refinement and optimisation are the main goals. The basic techniques of mathematical modelling and measurement procedures are well understood at most of the major research and manufacturing centres of off-road vvehicles. In the military industry, further improvements in suspension design and ride quality are evolving gradually as a result of detailed refinements. In the agricultural industry, some major decisions still remain. There is little further scope for improvement of the unsprung tractor with passive seat suspension, and so the next improvements will come from active seat suspensions, cab suspensions or axle suspensions. Although work continues in all these areas, axle suspensions currently offer the most potential.