Failure surfaces for cellular materials under multiaxial loads—II. Comparison of models with experiment

The behaviour of cellular materials under multiaxial loads was modelled in the previous companion paper. Here we present data for the failure of foams by elastic buckling and plastic yielding and compare them to the results of the models. The models describe the main features of the multiaxial behaviour of foams well.     

Simplified theories of flat rolling—II. Comparison of calculated and experimental results

A simplified inhomogeneous solution for the roll pressure has been used as the basis for computing consistent precise estimates of roll force and roll torque from the theory of cold flat rolling. The accuracy of the new method is established in this paper by re-analysing previous data for the rolling of prestrained copper, data for the rolling of annealed mild steel and results for the rolling of low carbon steel with lubrication. Both Swift's stress-strain law and a polynomial function are used to represent the experimental yield data for the rolled materials.     

Long rod penetration models—Part II. Extensions to the hydrodynamic theory of penetration

The modified hydrodynamic theory of penetration is extended to take account of the transient, plastic-wave dominated and after-flow phases of penetration. It is also indicated how a more detailed flow field model of the primary phase of penetration leads to the modified Bernoulli equation and a relationship between the dynamic yield strength and the strength factors R_t and Y_p. The effect of the decelerative motion on the modified Bernoulli equation is also briefly examined. Finally, the theory is compared with experimental results of previous papers.     

An approach to the study of elasto-plastohydrodynamic lubrication in the wire drawing process. Part 2: Theoretical predictions

The generalised Reynolds' equation for Newtonian and non-Newtonian fluids, as applied to the wire-drawing process, together with the plasticity and energy equations have been adopted in solving the elasto-plastohydrodynamic lubrication problem in the wire-drawing process. The equations have been solved numerically using a finite difference technique with Gauss-Siedel iterative scheme to predict hydrodynamic behaviour and to correlate the forming parameters to the lubrication behaviour in an endeavour to find the optimum operating conditions for maximum precision and productivity. The effect of using either Newtonian or non-Newtonian lubricants on the process parameters has been also studied, to predict the most suitable lubricant type. The results indicate that the increase in the flow behaviour index increases the pressure gradient in the work zone, with a consequential reduction in oil film thickness. Also the minimum film thickness is highly influenced by the drawing speed. It can be concluded that the isothermal solution renders lower drawing stress than the adiabatic solution. The maximum shear stress, and hence the power loss, increases with the increase in die convergence angle.     

The complex buckling of flexible sheet materials—Part II. Experimental study of three-fold buckling

This paper reviews the technological importance of the problems of complex buckling of textile fabrics and other sheet materials and the reasons why conventional shell theory is of little value. It stresses the importance of the occurrence of membrane strains in double curvature over finite areas, reviews earlier work on the subject, discusses briefly the characterization of the properties of sheet materials and shows the approach to the problem through simple three-fold buckling. A major section of the paper relates to order-of-magnitude estimates of bending, membrane and gravitational energies and introduces two important dimensionless groups, J₁ = Yl²/D and J₂ = γgl³/D, in terms of which deformed shapes can be calculated. A mathematical model for three-fold buckling is described and the contributions of different energies during deformations are presented.     

Dynamic response of bars subjected to longitudinal impact—An experimental approach

The response of structure to shortduration impact is studied experimentally by employing explosively induced stress pulses in long aluminum bars containing central circular holes. The amplitude of the strain is measured in all cases. The effect of the direction of loading on the existing strain is also studied.It is concluded that the addition of more holes will decrease the dynamic stress concentration, especially if the direction of loading is from the smaller to the larger diameter holes.     

A theoretical and experimental study of hemispherical shells subjected to axial loads between flat plates

The quasi-static loading of an open hemispherical shell along its axis of symmetry through a rigid flat plate is considered with particular reference to large deformations and buckling.Deformation patterns which are symmetric and non-symmetric about the axis are studied analytically and experimentally for models of different materials and radius to thickness ratios varying between 36 and 460.     

The plane-strain general yielding of notched members due to combined axial force and bending—II: Deep circular notches

The slip-line fields proposed by Green for the plane-strain general yielding of notched plates in pure bending are generalized to provide solutions for notched plates subjected to combined axial force and bending. Deep symmetrical circular notches and single circular notches are considered. For notched plates subjected to arbitrary combinations of axial force and bending, two constraint factors are obtained, T₁ due to the axial force and M₁ due to the bending moment. These constraint factors are shown to have characteristic relationships on the T₁−M₁ plane for the single notched plate and the symmetrically notched plate. The derivations of these general yielding loci are described in detail and the statical and kinematical limitations of the slip-line fields are discussed. Finally it is demonstrated that the corresponding strain-rate vectors are normal to these loci and that, therefore, these loci can be regarded as plastic potentials.     

The plane-strain general yielding of notched members due to combined axial force and bending—III: Comparison of theories with experiment

The plane-strain general yielding of plates with deep single notches is studied using slip-line field analysis, Rice's upper bound solution and finite element analysis. When the plates are subjected to arbitrary combinations of axial force and bending moment, it is possible to calculate the corresponding constraint factors and to map them on the constraint factor plane.It is shown that there is a change in the mode of general yielding from that predicted by slip-line field analysis to that predicted by Rice's upper bound solution. This mode transition occurs when the axial force becomes dominant in the first and third quadrants of the constraint factor plane. The transition is confirmed by finite element analysis and also experiments on notched steel plates.     

Cutting tool strategies for multifunctional part configurations: Part II—Discussion of experimental and analytical results

The analytical models, developed in Part I [Int J Adv Manuf Technol (1992)7: 59–69] for the optimisation of multistep cutting tools, are evaluated using experimental data. The effectiveness of the proposed approaches utilising the mathematical models from Part I for multifunctional tools, including both multi-step and combination tools, are demonstrated through simulations. The solution schemes and heuristic algorithms used for optimising the aforementioned cutting tool designs are described and explained through simulation examples which involve several tool configuration situations often applicable in a production environment. When the aforementioned cutting tools are utilised in mass production applications, the advantages of lower production cycle time and cost, become obvious through the tutorial of the examples. These simulations clearly demonstrate the benefits obtained when the mathematical models and analytical schemes, developed in Parts I and II, are incorporated in the manufacturing process and system design optimisation analytical tools or expert systems for justifying the use of multi-functional cutting tools.     

An investigation into upheaval buckling of buried pipelines—II. Theory and analysis of experimental observations

This paper and its companion describe an experimental study of some aspects of the upheaval buckling of buried pipelines by means of a small-scale model apparatus. After a discussion of relevant literature, the experimental apparatus is described in detail: it involves a thin-walled steel pipe of diameter 6 mm and length 5 m, buried in a bed of artificial soil. The horizontal and vertical profiles of the pipe are measured by an electrical remote-sensing device. Axial load is imparted to the pipe by a screw arrangement and/or by interior oil pressure; and transverse horizontal loading may be applied through a string and pulley. The arrangements for assaying the resistance of the soil to transverse motion of the pipe are described. Results are presented for several tests involving both axial and transverse loading, and cyclic axial loading. The paper concludes with a short discussion.     

The probabilistic characteristics of estimation of the residual strength and operation lifetime of steel wire rope based on the results of non-destructive testing

This article describes a procedure for the probabilistic estimation of the strength indices of steel wire ropes on the basis of the data of magnetic non-destructive testing. The proposed method for the determination of probabilistic characteristics undetection an existing fault of a heterogeneous wire rope structure and the false detection of a fault. The obtained probabilistic estimates of errors of nondestructive testing have been applied for calculations of high-risk and conservative scenarios of the variation of the strength and remaining lifetime of wire rope during its non-fault operation lifetime.     

Steady state characteristics of a tilting pad journal bearing with controllable lubrication: Comparison between theoretical and experimental results

This paper is aimed at presenting results regarding the static and thermal behavior of a tilting-pad journal bearing operating under controllable regime. The bearing is rendered controllable by injecting high pressure oil into the clearance using holes drilled across the bearing pads in the radial direction. The modification of the injection pressure enables to modify the bearing static and dynamic properties according to the operational needs. The results presented are obtained using a theoretical model, which considers all the effects that determine the bearing behavior (controllable elastothermohydrodynamic lubrication regime), as well as using a test rig designed and built to this effect. The comparison between experimental and theoretical results provides solid ground to determine the accuracy of the available model for the the prediction of the steady-state behavior of the tilting-pad bearing with controllable lubrication. Among the parameters considered for the study are: oil film temperature field, resulting forces over rotor and pads, and rotor equilibrium position. The results obtained show good agreement between theory and experiment, as long as the assumptions on which the model is based are respected. Also, it is shown that some improvements are possible when it comes to model the steady-state behavior of the controllable bearing with the injection system turned off.     

Comparison of experimental and theoretical residual stresses in welds: The issue of gauge volume

Welding residual stresses have an effect on many aspects of the integrity of structures but are normally one of the largest unknown stresses. Residual stresses are difficult to measure and to estimate theoretically but are often significant when compared with the service stresses on which they superimpose. High tensile residual stresses can lead to loss of performance in corrosion, fatigue and fracture.In this research, measurement of residual stresses by the neutron diffraction technique is compared to an analysis of a sample geometry by theoretical finite-element procedures. The results indicate good qualitative agreement. One of the key issues in this comparison relates to what is termed “gauge volume” in the measurement technologies and what might be described as a “calculation volume” in theoretical approaches.     

Systematic investigation of pipe flows and installation effects using laser Doppler anemometry—Part II. The effect of disturbed flow profiles on turbine gas meters—a describing empirical model

For systematic investigations of installation effects and for finding efficient ways to minimise these effects, a research project was initiated at the PTB. It covers the design of an automated test facility using a laser Doppler anemometer, the measurement of velocity profiles downstream of several pipe configurations and flow conditioners, as well as the measurement of the change in the gas meter behaviour, namely the shift of the error curve due to the disturbed velocity profiles.

Part I of this paper (presented in this issue) describes the test facility for the investigation of installation effects and shows the relation between pipe configuration and disturbed flow profile for a wide variety of pipe configurations and flow conditioners.

The second part compares the error shift of turbine meters with the characteristic of disturbed flow profiles. For this, three flow field parameters are used to quantify the disturbances of the velocity profiles such as the swirl intensity, flatness and asymmetry of the profile. Considering this, an empirical model is presented to explain the error shift of a turbine meter as a function of these three flow field parameters. The model will be verified for three types of turbine meters and the results will be discussed.     

Indentation of ring-stiffened cylinders by wedge-shaped indenters—Part 1: An experimental and finite element investigation

This is the first of a two part account of the indentation of ring-stiffened cylinders with fully fixed ends loaded centrally at mid-span by a wedge-shaped indenter. In this paper, the results of experimental tests on three similar cylinders of 315 mm outer diameter are presented and discussed. The cylinders were stiffened internally with rectangular sectioned rings and deep frames (bulkheads). Strains and deformations were determined in the dent-affected zone particularly along the top generator and around the circumferential mid-section. The cylinders were loaded up to failure, i.e. until rupture of the shell occurred. A finite element analysis for a geometrically identical specimen is also presented and compared to the experimental results.     

Elastodynamic analysis of a gear pump. Part II: Meshing phenomena and simulation results

A non-linear lumped kineto-elastodynamic model for the prediction of the dynamic behaviour of external gear pumps is presented. It takes into account the most important phenomena involved in the operation of this kind of machines. Two main sources of noise and vibration can be considered: pressure and gear meshing. Fluid pressure distribution on gears, which is time-varying, is computed and included as a resultant external force and torque acting on the gears. Parametric excitations due to time-varying meshing stiffness, the tooth profile errors (obtained by a metrological analysis), the backlash effects between meshing teeth, the lubricant squeeze and the possibility of tooth contact on both lines of action were also included. Finally, the torsional stiffness and damping of the driving shaft and the non-linear behaviour of the hydrodynamic journal bearings were also taken into account. Model validation was carried out on the basis of experimental data concerning case accelerations and force reactions. The model can be used in order to analyse the pump dynamic behaviour and to identify the effects of modifications in design and operation parameters, in terms of vibration and dynamic forces.Part I is devoted to the calculation of the gear eccentricity in the steady-state condition as result of the balancing between mean pressure loads, mean meshing force and bearing reactions, while in Part II the meshing phenomena are fully explained and the main simulation results are presented.     

Stochastic simulation of electron-hole recombination in two-dimensional and three-dimensional inhomogeneous semiconductors. Part II. Simulation results

This paper describes the stochastic models of electron-hole recombination in inhomogeneous semiconductors in two-dimensional and three-dimensional cases, which were developed on the basis of discrete (cellular automaton) and continuous (Monte Carlo method) approaches. The particle recombination kinetics in pure diffusion and diffusion with tunneling is studied. There is a certain difference revealed between the behavior of electron-hole spatial correlations calculated by discrete and continuous models and the nature of segregation formation in three-dimensional semiconductors associated with that behavior. The comparative analysis of the simulation characteristics determined via cellular automaton and continuous recombination models is carried out.     

Large deflexion elastic-plastic response of certain structures to impulsive load Numerical solutions and experimental results

A theoretical and experimental study of the elastic-plastic response of certain structures to impact and impulsive load is described. Lead rings were allowed to fall freely on to a flat and pointed sharp anvil, aluminium rings were subjected to the impact of a free falling sharp indenter and thin aluminium cantilevers, rectangular and triangular frames and semicircular arches were subjected to magnetomotive and explosive impulse.

A numerical solution based on a finite difference approximation was developed to describe the response of an equivalent lumped parameter model for each of the above structures. This method, although restricted to two-dimensional structures, can be applied to a variety of structural elements.

High-speed photographs were taken for each of the loading events and the experimental data obtained were compared with the theoretical plastic response predicted by the numerical method.     

Modeling of transport phenomena and solidification cracking in laser spot bead-on-plate welding of AA6063-T6 alloy. Part II—simulation results and experimental validation

As the mathematical model has been developed in part I, the simulation results of the transport phenomena and solidification cracking in laser spot bead-on-plate welding of AA6063-T6 aluminum alloy and the experimental validation are presented in this paper. Modeling results showed that the solute concentration in the solidified region continuously increases during the solidification process. As the temperature is lower than the coherent temperature (i.e., the temperature at which the coherent mushy zone is just formed), the strains accumulated in the coherent mushy zone increase with the increasing solid fraction. The amount of strain in the mushy zone is primarily determined by the life (i.e., time span) of the coherent mushy zone, which is determined by the solidification range and solidification time. The increased solidification range and consequently solidification time extend the life of the coherent mushy zone, which increases the amount of strain and thus increases the likelihood of solidification cracking. The modeling results are in agreement with the experimental results. Both the experimental and modeling results exhibited that solidification cracking is prone to occurring near the top surface and middle part of the weld bead and an increase of laser power leads to the higher cracking susceptibility.