Concluding note about a university at Stamford and Francis Peck's academia tertia anglicana: The antiquarian annals of Stamford [1]

The author herewith concludes his work [Int. J. Mech. Sci.33, 675 (1991); 34, 831 (1992)] on the subject of a university at Stamford—a university which “there never was”—but an institution of which there was promise in the early 14th Century. When one did seem likely to be realized, it was suppressed by the then-King of England. This association, mostly in “halls”, was within 13 miles of Newton's birthplace, Colsterworth, Lincolnshire and so might well have been attended by him had it existed in the mid-17th Century. Reliable details of this potential centre of learning are difficult to come by, but a major source of information chanced upon by the writer has the title given above and is a large volume of several hundred pages, Academia tertia Anglicana (The Third English Academy), composed by Francis Peck in 1727. The author gives, briefly, some items from the latter work which should help those who might henceforth wish to penetrate more deeply into this subject; for the mass of readers it provides a simple though partial picture of how some European universities started early in this millenium.     

Closed-form solution for wedge cutting force through thin metal sheets

A simple kinematic model is developed which describes the main features of the process of the cutting of a plate by a rigid wedge. It is assumed in this model that the plate material curls up into two inclined cylinders as the wedge advances into the plate. This results in membrane stretching up to fracture of the material near the wedge tip, while the “flaps” in the wake of the cut undergo cylindrical bending. Self-consistent, single-term formulas for the indentation force and the energy absorption are arrived at by relating the “far-field” and “near-tip” deformation events through a single geometric parameter, the instantaneous rolling radius. Further analysis of this solution reveals a weak dependence on the wedge angle and a strong dependence on friction coefficient. The final equation for the approximate cutting force over a range of wedge semiangles 10° ≤ θ ≤ 30° and friction coefficients 0.1 ≤ μ ≤ 0.4 is: F = 3.28σ₀(δ_t)^0.2l^0.4t^1.6μ^0.4, which is identical in form and characteristics to the empirical results recently reported by Lu and Calladine [Int. J. Mech. Sci.32, 295–313 (1990)].This analysis is believed to resolve a controversy recently developed in the literature over the interpretation of plate cutting experiments.     

Voltaire's contribution to the spread of Newtonianism—II. Élémens de la philosophie de Neuton: The elements of the philosophy of sir Isaac Newton

Continuing from Part I [Int. J. Mech. Sci.32, 423, 1990]^§, we mainly summarise the contents of, and make comments on, the 25 chapters of Voltaire's Élémen, published in 1738. Mme du Châtelet was the constant companion of Voltaire for 10 years and was very influential during the writing of the latter volume (worthy of being designated a co-author say some), so that space is given over to describing their life and work together during that period, mostly at Cirey, in Montjeu, Lorraine. We include an account of her writing of a translation of Newton's Principia, widely published in France in 1759, and of her early death. Voltaire (and Mme du Châtelet) expended very considerable efforts to spread Newton's philosophy through France.We also outline John Locke's Elements of 1720—hitherto undescribed we believe—Henry Pemberton's A View of Sir Isaac Newton's Philosophy of 1728, and we mention Algarotti's book of 1737. The latter two authors, Voltaire (and Mme du Châtelet) were the major popularisers of Newton's work in Europe though others, s'Gravesande and Keil, for instance, have been held to be more influential in doing so.     

Applications of the singularity function method to orthotropic plate problems

The singularity function method is applied to solve structural problems of orthotropic rectangular and circular plates. Except in the work of Conway (Int. J. Mech. Sci.22, 209, 1980) and Selek et al. (Int. J. Mech. Sci.25, 397, 1983), which considered the tapered circular plate, previous attempts at applying the singularity function method have always assumed material isotropy. In this work extensive results for displacements and moments are presented for material rigidities different in two orthogonal directions. In particular, Conway's isotropic plate results [7] are obtained as a special case from the present work.     

A three-dimensional rigid-plastic finite element analysis of bevel gear forging by using a remeshing technique

A three-dimensional remeshing scheme implemented by using a modular concept is proposed for the finite element analysis of a complicated forging process. In order to show the effectiveness of the scheme, forging of a bevel gear is simulated by using several basic modules in the general rigid-plastic finite element code (Yoon and Yang, Int. J. Mech. Sci.30, 887, 1988; Yang et al., Int. J. Mech. Sci.31, 145, 1989) developed for cold forging. Criteria for remeshing as well as a scheme for the mapping of state variables are proposed for three-dimensional remeshing. The computational results are compared with experimental data in order to check the validity of the simulation. The computational results show that the computation can be effectively carried out by using the proposed remeshing scheme and that it can be extended to other more complicated product geometry.     

On the number of cracks in the axial splitting of ductile metal tubes

An analysis is given for the number of cracks which propagate in experiments on the splitting of ductile metal tubes when the ends are flared out. The number of cracks depends on the diameter of the tube (2r₀), the strength-to-toughness ratio of the metal ( ) and its hoop fracture strain _θ∫ (which may be related to microstructure via models of microvoid growth and coalescence). Since the expression for the number of cracks contains the product of ( ) and _θ∫, approximately the same number of cracks is predicted whether the tubes are annealed or work-hardened. Experiments by Reddy and Reid [Int. J. Mech. Sci. 28, 111 (1986)] give support to the predictions.     

Deformation processing of metal powders: Part I—Cold isostatic pressing

Analytical and numerical techniques are used to analyze in detail the stage I Cold Isostatic Pressing (CIPing) of metal powders. Plastic yielding is considered to be the only densification mechanism and the constitutive model developed recently by Fleck, Kuhn and McMeeking [(J. Mech. Phys. Solids40, 1139 (1992)] is used to describe the elastoplastic behavior of the metal powder. It is shown that, for the case of powder consolidation in a long cylindrical tube, a change in length is not possible, unless it is accompanied by some distortion (“shape change”) of the CIPed specimen. The numerical implementation of the constitutive elastoplastic equations in a finite element program is discussed. The finite element method is used to analyze the CIPing of titanium powder. The predictions of the finite element solution agree well with available experimental data.     

Numerical construction of axisymmetric slip-line fields for indentation of thick blocks by rigid conical indenters and friction at the tool-metal interface

A general form of axisymmetric slip-line field solutions using numerical methods is given for cases of axisymmetric smooth and partially rough conical punch indentation of a rigid-perfectly plastic ductile material of semi-infinite thickness, where the cone semi-angle α varies from 15° to 90°. The basic problem of indetermination of the field and pressures near the apex of the conical punch experienced earlier by Locket (J. Mech. Phys. Solids 11, 345 (1963), [1]) for small cone angles was overcome by treating small segments of the curvilinear slip lines as arcs of circles of varying radii and assuming a straight boundary to the deformed lip. The numerical method outlined in detail by Chitkara and Butt (Int. J. Mech. Sci. 34, 833 (1992), [2]) allows the construction of axisymmetric slip-line fields for cone indentation, with varying frictional conditions at the tool-metal interface. The computer program developed requires only the cone semi-angle α and the frictional conditions at the tool-metal interface as the data set. It includes graphical plotting subroutines to plot the calculated slip-line field on a Hewlett-Packard 7550 plotter. A computographic plot of the associated velocity field for a typical case of conical punch indentation is also included.     

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.     

Temperature transients on engine combustion chamber walls—IV. Application of the finite-difference model to surface thermocouples and wall deposits

The FD computational code developed in Part I (Int. J. Mech. Sci. 33, 775 (1991) [1]) has the capability of handling composite walls having different material layers. This characteristic of the FD model is used to study the effects of thermocouple thickness and material type, as well as substrate material type on surface thermocuple readings. Later, the effects of wall deposits on surface thermocouple readings and engine heat transfer are explained.     

Application of a comprehensive dynamic cutting force model to orthogonal wave-generating processes

The dynamics of a cutting process are very complex in nature. They involve not only the changes of plastic state in the intensive shear zone of the chip formation process but also the elastic behaviour of work material surrounding the plastic deformation zone, especially in the vicinity of the tool nose region. As an extension to the previous developments in formulating the shear angle oscillation in dynamic cutting (D. W. Wu, Development of dynamic shear angle model for wave-generating processes based on work-hardening slip-line field theory. Int. J. Mech. Sci. 29, 407–424, 1987; D. W. Wu, Governing equations of the shear angle oscillation in dynamic orthogonal cutting. Trans. ASME J. of Engng for Indust. 108, 280, 1986), a comprehensive dynamic cutting force model has been developed from the mechanics of the cutting process by taking into account the equilibrium of forces in the primary and secondary plastic deformation zones and the redistribution of the contact stress inside the workpiece in the vicinity of the tool nose region.The model has been tested through a computer simulation for orthogonal wave-generating processes. By reference to existing experimental evidence, the theoretical predictions show generally good agreement with the test results.     

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.     

Examination of Hill's latest yield criterion using experimental data for various anisotropic sheet metals

Using experimental data published earlier [Vial et al., Int. J. Mech. Sci. 25, 899 (1983)], values of the exponent m in the Hill (1979) yield criterion [Hill, Math. Proc. Cambridge Phil. Soc. 85, 179 (1979)] are calculated for each of the four special cases suggested. With these findings, stress-strain relations for plane-strain compression are derived and predictions using these derived equations are compared with experimental results. Comparisons between prediction and experiment are reasonable in all cases and it is suggested that the discrepancies could arise because of the assumption of planar isotropy (via the use of an average r-value) and because the exponent m apparently varies with induced strain.     

Some single zone scavenging models for two-stroke engines

The paper proposes a simplified version of the various multi-zone models which have been proposed for diesel engines to represent the pure air, mixing and residual zones of the real process, with or without short circuiting. [Benson, Int. J. Mech. Sci.19, (1977); Baudequin and Rochelle, Proc. Instn Mech. Engrs.194, (1980); Chen and Wallace, SAE paper 871657 (1987).]These models use flow coefficients defining the division of the air-flow entering, and of the outflow leaving, the cylinder between the various zones. The choice of these coefficients is rendered more difficult by the absence of direct experimental evidence.The present model in which the cylinder contents are represented by a single zone uses two coefficients which directly define the nature of the scavenging process.

1. (a) The fraction x of the initial cylinder contents subject to displacement scavenging during phase 1, and

2. (b) the short circuiting fraction y of the entering air during the mixing dominated phase 2.

Single zone representation of the cylinder contents is made possible by the use of a residual filter during phase 1 and an air filter during phase 2, the former allowing pure residuals, and the latter pure air, to be exhausted while the cylinder gases are undergoing a pure mixing process.The model is applied to typical scavenging situations for uniflow, cross flow and loop scavenged diesel engines, both for the idealized isobaric, isochoric case and for the ‘real’ engine using a full cycle simulation program.     

Upper-bound limit analysis of a rigid-plastic body with frictional interfaces

A finite element formulation of the upper-bound theorem for rigid-plastic solids, generalized to include interfaces with finite friction, is described. As proved by Collins [J. Mech. Phys. Solids 17, 323 (1969)], the usual definition of a kinematically admissible velocity field is unnecessarily restrictive when the upper-bound theorem is applied to many practical problems. This paper shows that a relaxed inequality can be used successfully to derive upper bounds in the presence of Coulomb friction on interfaces, provided one considers a wide enough class of “admissible” velocity fields.One of the major advantages of using a numerical formulation of the upper-bound theorem is that both complex loading geometry and inhomogeneous material behaviour can be easily dealt with. Using a suitable linear approximation of the yield surface, the application of the necessary boundary conditions, the plastic flow rule and the yield criterion lead to a large linear programming problem. The numerical procedure uses constant-strain triangular elements with the unknown velocities as the nodal variables. An additional set of unknowns, the plastic multiplier rates, is associated with each element. Kinematically admissible velocity discontinuities are permitted along specified planes within the finite element mesh. During the solution phase, an active set algorithm is used to solve the linear programming problem.     

Rapid prototyping and testing of 3d micro rockets using mechanical micro machining

The trend of miniaturization has been applied to the research of rockets to develop prototypes of micro rockets. In this paper, the development of a web-integrated prototyping system for three-dimensional micro rockets, and the results of combustion tests are discussed. The body of rocket was made of 6061 aluminum cylinder by lathe process. The three-dimensional micro nozzles were fabricated on the same aluminum by using micro endmills with φ100μm~φ500 μm diameter. Two types of micro nozzle were fabricated and compared for performance. The total mass of the rockets was 7.32 g and that of propellant (gun powder) was 0.65 g. The thrust-to-weight ratio was between 1.58 and 1.74, and the flight test with 45 degree launch angle from the ground resulted in 46 m~53 m of horizontal flight distance. In addition, ABS housing for the micro machined rocket was fabricated using Fused Deposition Modeling (FDM). A web-based design, fabrication, and test system for micro nozzles was proposed to integrate the distributed hardware resources. Test data was sent to the designer via the same web server for the faster feedback to the rocket designer.     

Investigation of sheet metal forming by bending—Part IV: Bending and wrinkling of circular sheets pressed by a hemispherical punch

This paper reports on an investigation of the bending forming processes in circular sheets pressed by a hemispherical punch into a conical die. Both theoretical and experimental considerations are provided. It is pointed out that the deformation mechanism of such a circular plate is different from that of the workpiece in the conical die cup test studied previously in part III of this series [Int. J. Mech. Sci.31, 327–333 (1989)]. The theoretical analysis shows that a central gap appears between the plate and the hemispherical punch at small deflections and disappears when the punch force increases beyond a certain magnitude. It is then shown that the previous approximate analytical treatment of the distribution of punch force is no longer appropriate to the wrinkling of the plate. It is shown that, as in the case of the conical die cup test, the circumferential wave number for the wrinkling mode corresponding to the critical wrinkling load of the present workpiece is four. In addition, the paper reveals that a doubling of the wrinkling wave may occur in the first stage of the forming process.     

Forming limit predictions with the perturbation method using stress potential functions of polycrystal viscoplasticity

Plastic potentials of polycrystalline materials are calculated for plane stress states using viscoplastic crystallographic slips and the Taylor approach. The derivation process of these potentials and their development during large plastic deformation of textured aluminium sheets are discussed. These potentials are then used to predict the forming limits of sheet metals. The approach employed was that of the perturbation technique developed by Dudzinski and Molinari [Int. J. Solids Struct. 27, 601 (1991)]. The perturbation method is analytic if Hill-type yield potentials are used. Therefore, to facilitate the use of the polycrystal plastic potentials in the perturbation approach, the polycrystal stress potentials were approximated locally at the loading point by Hill-ellipsoids. In this way even the development of anisotropy during stretching could be taken into account. The effect of initial texture as well as the changes in the anisotropy during deformation are discussed. It has been found that the development of anisotropy influences strongly the predicted limit strains in the vicinity of equibiaxial stretching.