Long rod penetration models—Part I. A flow field model for high speed long rod penetration

A semi-infinite solenoid in a uniform velocity flow field is used as a model for the quasi-steady primary phase of long rod penetration. Assuming the materials are perfectly plastic and that the Lévy-Mises equations hold leads to a modified Bernoulli equation. Relationships between the strength factors R_t and Y_p and the dynamic yield strengths of the materials are indicated. The effects of unsteady motion are briefly examined.     

Application of Hill's new yield theory to sheet metal forming—Part II. A numerical study of hydrostatic bulging using Hill's 1979 yield criterion

Four special cases of Hill's new yield theory (1979) are introduced into a rigid-plastic finite element method (FEM). Comparison between numerical results and experiment shows that the FEM formulation is appropriate for simulating the bulging process of sheet metals. A numerical study of the effects of yield function shape on bulging deformation is carried out. It is found that these effects can be expressed by two characteristic parameters, α and β. Bulging pressure is found to increase linearly as α increases, and the uniformity of strain distribution decreases as β increases.     

Machining with applied chip tension—Part II: Experiments

Machining with applied chip tension is the basis of a process, strip peeling, for making small batches of metal special strip products. An approximate slip-line field numerical analysis of the process, related to the matrix method, is presented which shows how pulling stress and its direction affect chip thickness and curvature and tool forces. Pulling parallel to, or within 5° of, the rake face produces straight chips but results in less reduction of chip thickness and tool forces than pulling at more than 5° to the rake face. In the latter case chips are formed curled and are subsequently plastically straightened by the pulling force. Chip failure by plastic straightening and other causes is discussed and it is recommended that the pulling direction should be between 5 and 20° from the rake face. Influences of rake angle and friction stress are also considered.     

On the theory of optimal, constant thickness fibre-reinforced plates—II

The investigation of optimal fibre reinforcement layouts begun earlier¹ is continued and extended to another important combination of support conditions. It is also shown that all the deflected shapes for the slabs discussed in the previous paper are everywhere both displacement and slope continuous, and hence are global optima.     

Performance of synthetic oils in the hydrodynamic regime — 1. experimental

An investigation of the performance of environmentally adapted synthetic oils in the hydrodynamic lubrication regime has been carried out. Four oils have been tested: polyalphaolefin and ester based ISO VG46 oils as well as mineral ISO VG68 and VG46 oils. Tests were conducted in a facility containing two identical tilting‐pad thrust bearings typical of the design in general use. The differences between the mineral and synthetic oils in terms of maximum operating temperature, minimum oil film thickness, and bearing power loss have been examined. Substitution of the mineral ISO VG68 oil with an ISO VG46 oil slightly reduces the bearing operating temperature. This is due to a decrease in the basic viscosity. It is concluded that the ester base ISO VG46 oil can be used as an environmentally adapted replacement for the mineral ISO VG68 oil without sacrificing bearing safety. Such a change also offers noticeable energy savings. If the ester based oil is used instead of a mineral oil of the same viscosity grade, bearing reliability is improved by the increased oil film thickness.     

Extended exact least-weight truss layouts—Part II: Unsymmetric cantilevers

In Part I of this study, the optimal bar layout and adjoint displacement fields were derived for cantilever trusses that are symmetric about a horizontal axis. In this paper, the above results are generalized to unsymmetric trusses and a number of further extensions to other support and load conditions are outlined briefly. Most results are verified by comparisons with discretized optimal layouts of trusses and perforated plates.     

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.     

Extensions to the theory of balancing frame forces in planar linkages

This paper presents extensions to the theory of force-balancing planar linkage mechanisms given in [1]. It incorporates (i) a technique for checking whether a linkage can be fully force-balanced using counterweights alone, (ii) a formula that defines the minimum number of counterweights needed for a full force-balance, and (iii) a criterion for selecting what is likely to be the optimum counterweight set. The linkages may be multi degrees-of-freedom and may contain both revolute and prismatic joints.     

The weight vector theory of Coriolis mass flowmeters — Part 2. Boundary source of secondary vibration

The purpose of this short paper is to draw attention to a boundary source of secondary vibration in Coriolis mass flowmeters. This is important in the calculation of meter sensitivity using the weight vector theory if the effect of fluid viscosity is to be taken into account in the vibrational flow.     

Performance of synthetic oils in the hydrodynamic regime ‐ II. Generalisation

In Parti I the results of an extensive experimental investigation of the performance of environmentally adapted oils in the hydrodynamic regime were reported. Four oils were tested in a tilting‐pad thrust bearing for different combinations of load, shaft speed, and supply oil temperature. In this second part, details of a generalisation procedure are described. A number of parameters representing the physical properties of an oil, such as viscosity and viscosity‐temperature coefficient, are adopted. The influence of each of these parameters on minimum oil film thickness, maximum temperature rise, and bearing power loss is then analysed. It is shown that viscosity measured at the supply oil temperature is the most important parameter. The effects of the viscosity‐temperature coefficient and oil thermal conductivity are less pronounced and yet significant. It is also shown that it is not possible to select an optimum oil that yields maximised oil film thickness, minimised temperature rise, and minimised power loss at the same time.     

The response of wire rope strands to axial tensile loads—Part II. Comparison of experimental results and theoretical predictions

Carefully instrumented tests were performed on straight single steel strands of seven-wire construction subjected to axial loads and with various end restraints. The strands have a practical range of lay angles between 9.2 and 17.0° with core and helical wire diameters of 3.94 and 3.73 mm, respectively. A mathematical model of a strand was developed to explore the change of helix angle under load, Poisson ratio effects in wires, wire flattening under interwire pressure and the effect of friction between the core and helical wires. A companion article (Part II) [Int. J. Mech. Sci. 29, 621–636 (1987)] compares the theoretical predictions with previously published analytical work and with the corresponding experimental results reported in this article.     

Conjectures relating to rigid-plastic plate bending—II

The first paper of this title [P. G. Lowe, Conjectures relating to rigid-plastic plate bending. Int. J. Mech. Sci.30, 365–370 (1988)] restated two conjectured general results relating to plate collapse and went on to apply them to finding accurate lower bound collapse load estimates, as well as the extent of the plastically deforming regions, for a series of clamped plates with regular polygonal shapes.The main geometrical results used there are applicable only to polygonal shapes of plate which have an in-circle. In this paper the geometrical procedures are generalized to apply to any polygonal shape of plate, including non-convex shapes. These more general geometrical results enable additional shapes of plate to be analysed and further evidence is collected which is consistent with the conjectured general results being true.     

Shear-torsion of large curvature beams—Part I. General theory

The shear-torsion problem for an elastic circular beam with large curvature and multiconnected cross section is analysed using warping function and potential stress function approaches. The resultant forces and the shear-torsion modulus are computed.The circulation of the shear stress along a curve is defined and consequently the compatibility equations for solving the problem in multi-connected cross section are presented.The positivity of the potential function is established as a consequence of a general theorem on a Boundary Value Problem (BVP). The maximum shear stress is proved to be attained at the boundary and a lower bound of its value is also given.     

Cross-sectional deformations of rectangular hollow sections in bending: Part II — analytical models

In this part, analytical models to predict the deflection of cross-sectional members such as flanges and webs are developed. The models are based on the deformation theory of plasticity along with the energy method, using appropriate shape functions capable of including the restraining effect of adjacent members. The present method provides explicit solutions of cross-sectional deformations prior to buckling, onset of buckling, as well as post-buckling deformations at different stages of bending. The predictions show that the suck-in of the tensile flange is closely related to geometry parameters, particularly the flange width. Plastic anisotropy appears to be the most significant material parameter. The width-to-thickness ratio tends to be the governing parameter with respect to buckling of the inner (compressive) flange. Also, the strain hardening of the material has a major effect on onset of buckling as well as post buckling deformations. Upon continued bending after buckling, the wavy deformation of the inner flange develops more rapidly than the more uniform deformation of the outer (tensile) flange. For relatively compact sections, however, the deformation mode of the compressive flange resembles that of the tensile flange without any typical buckling waves. There are also obvious interactions between deformations of different members. Comparing the theoretical predictions with the experimental results presented in Part I, a reasonably good agreement was found.     

On the compressive behavior of sintered porous coppers with low-to-medium porosities—Part II: Preparation and microstructure

A polymer space-holder method was used in this study to prepare porous coppers with low-to-medium porosity within the range 5–50%. This provides the possibility to control the pore size, distribution and structure. Optical microscopy and scanning electron microscopy (SEM) with energy dispersion spectrum (EDS) were utilized to characterize the porous samples. Two different sizes of copper powders, 5 and 45 μm, were used to investigate the effect of raw materials powder size. Microstructure results have shown that there exist two different types of pore in the sintered samples: round-shaped macro-pores left over by the burnout of the space holder and irregular micro-pores or the intervals among metal powders. No matter which size powder was used, the size of the macro-pore falls into a range 200–500 μm, but the pore structures are different in the two cases, interconnected or open pores for the 45 μm raw powders and closed pore for the 5 μm powders. The sizes of the micro-pores among the copper powders in the two cases are also different, several microns for the 5 μm powders and 10–20 μm for the 45 μm powders, though all micro-pores are interconnected for both powder sizes. From the viewpoint of pore structure, it is concluded that the 45 μm powder is more appropriate for use to prepare the porous metal. In addition, the effect of the binder was also investigated. It is suggested that a binder that can be easily and completely removed should be used in order to induce the residue. This paper, as Part II of the publication, focuses on the fabrication of the porous samples where Part I [Lemons JE, editor. Quantitative characterization and performance of porous implants for hard tissue application. ASTM STP 953; 1985] has been published earlier for the mechanical properties of the material.     

Machining with tool–chip contact on the tool secondary rake face—Part II: analysis and discussion

The forces, chip thickness, and natural tool–chip contact length in machining with a double-rake-angled tool are predicted in Part II of the present study. It is revealed that in comparison with a single-rake-angled tool, a double-rake-angled tool increases the forces, especially the thrust force. However, the increase in chip thickness and tool–chip contact length is not significant under the input conditions specified in the present study. The effect of seven input variables of the proposed model is quantitatively investigated. The predicted variations of forces, chip thickness, and natural tool–chip contact length are in good agreement with theoretical and experimental results obtained by other researchers. The interrelationships among the resultant force, the chip thickness, and the natural tool–chip contact length are established, which provides a new and promising method to estimate the tool–chip contact length by employing the resultant force. It is demonstrated that the model can also be extended to study the problem of machining with a groove-type chip breaker tool.     

Thermal modeling of the metal cutting process — Part II: temperature rise distribution due to frictional heat source at the tool–chip interface

Heat partition and the temperature rise distribution in the moving chip as well as in the stationary tool due to frictional heat source at the chip–tool interface alone in metal cutting were determined analytically using functional analysis. An analytical model was developed that incorporates two modifications to the classical solutions of Jaeger's moving band (for the chip) and stationary rectangular (for the tool) heat sources for application to metal cutting. It takes into account appropriate boundaries (besides the tool–chip contact interface) and considers non-uniform distribution of the heat partition fraction along the tool–chip interface for the purpose of matching the temperature distribution both on the chip side and the tool side. Using the functional analysis approach, originally proposed by Chao and Trigger (Transactions of ASME, 1951; 73:57–68), a pair of functional expressions for the non-uniform heat partition fraction along the tool–chip interface — one for the moving band heat source (for the chip side) and the other for the stationary rectangular heat source (for the tool side) were developed. Using this analysis, the temperature rise distribution in the chip and the tool were determined for two cases of machining, namely, conventional machining of steel with a carbide tool at high Peclet number (N_Pe≈5–20) and ultraprecision machining of aluminum with a single-crystal diamond tool at low Peclet number (N_Pe–0.5). The calculated temperature rise distribution curves on the two sides of the tool–chip interface are found to be well matched for both cases. The analytical method developed was found to be much faster, easier to use, and more accurate than various numerical methods used earlier. Further, the model provides a better physical appreciation of the thermal aspects of the metal cutting process.     

Ideal forming—II. Sheet forming with optimum deformation

A method is proposed for the design of ideal forming processes. The objective is to directly determine ideal configurations for both the initial and the intermediate stages that are required to form a specified final shape. At the start, it is assumed that formability of local material elements is optimum when they deform in minimum work paths. The ideal global process is then defined as the one having such local deformations optimally distributed in a final shape. Mathematical procedures for implementing these conditions are derived. Primary emphasis is placed upon forming of sheet (membrane) materials under plane-stress conditions, although many of the ideas are applicable to more general forming processes. Sample results illustrate optimum process parameters which the ideal forming theory can provide.     

Hybrid analytical–numerical solution for the shear angle in orthogonal metal cutting — Part II: experimental verification

The hybrid analytical–finite element model described in Part I is applied to predict the shear angle for a range of cutting velocity, uncut chip thickness, and two tool orthogonal rake angles. Experimental results and an empirical equation are also presented for the influence of the cutting conditions and cutting tool geometry on the chip–tool contact length. It is shown that there is a linear dependence between the chip–tool contact length/uncut chip thickness ratio and chip thickness/uncut chip thickness ratio over the range of cutting conditions assumed. The increase of the shear angle with the tool orthogonal rake is mostly due to the reduction of the specific shear energy in the primary shear zone and the specific friction energy in the secondary shear zone accompanied by a reduction of the chip–tool contact zone. The uncut chip thickness and cutting velocity influence the shear angle through their effect on the interface temperature and hence on the material flow stress in the secondary shear zone. The change in both parameters does not change significantly the specific shear energy in the primary shear zone. The model results are compared with the experimental results for a work material 0.18% C steel. The agreement between the predicted and experimental results is seen to be exceptionally good.