International Journal of Mechanical Sciences

Published by Elsevier
Online ISSN: 0020-7403
Publications
Conference Paper
The nonlinear problem of large deflection of a simply supported piezoelectric layered plate under initial tension is studied. The approach follows von Karman plate theory for large deflection for a symmetrically layered isotropic case including a piezoelectric layer. The thus derived nonlinear governing equations for the lateral slope and radial force resultant are solved using a numerical finite difference method with the aid of an iteration scheme, by taking the associated linear analytical solution as an initial guess. The case of a nearly monolithic plate under a very low applied voltage across the piezoelectric layer was implemented, first. The results for are found to correlate well with available solutions for a single-layered case under pure mechanical loading and thus the present approach is validated. For three layered symmetric plates made of typical silicon based materials, various initial tension and lateral pressure are considered, and different applied voltages up to a moderate magnitude are implemented. No edge effect was observed, in contrast to the cases of clamped plates in literature. In additions, varying the layer moduli seems to have an insignificant effect upon the structural responses of the layered plate. On the other hand, the piezoelectric effect tends to be apparent only in a low pretension condition. For a relatively large pretension, the effect of initial tension becomes dominant, yielding nearly unique solutions for the structural responses, regardless of the magnitudes of the applied voltage and the lateral pressure.
 
Article
Steel specimens of type 1023 and heat treated 4130 steel of hardnesses, between 257 and 450 HV10, were compressed at strain rates between 3 × 103 and 3 × 104 s−1 using a modified Hopkinson bar. Both steels showed viscous type flow behaviour with a linear increase in flow stress with strain rate. For the 1023 steel there were two linear regions, one from 3 to 12 × 103 s−1 with a macroscopic viscosity of 4·7 kPa s and two from 14 to 27 × 103 s−1 with a viscosity of 0·7 kPa s. These results indicate some change in the controlling mechanism. For the 4130 steel the macroscopic viscosity decreased linearly with increasing hardness from 7·4 kPa s at 257 HV 10 to 2·2 kPa s at 450 HV 10. This was probably due to a decrease in the density of mobile dislocations with increased tempering temperatures. At lower hardness values (257 and 300 HV 10) and higher strain rates, a levelling off of the flow stress occurred but the data were too scattered to give a definite trend. The heat generated due to deformation of the 1023 steel was sufficient to produce steady state flow at strains above about 0·3. In the 4130 steel the thermo-mechanical properties were such that linear work softening was observed at a rate inversely proportional to the square root of the strain rate and independent of the hardness. This suggests that the work softening was a function of properties of the common ferrite matrix. The strain at which the work softening commenced decreased with increasing hardness, because of the more rapid heat generation at higher flow stresses. At higher hardness and higher strain rates 4130 steel failed by shear. Shear failure occurred at lower strain rates with increasing hardness and, for a given hardness, at lower strains with increasing strain rate. This behaviour was consistent with Recht's analysis of catastrophic shear failure.
 
Article
Extensive and accurate numerical results are presented for the critical buckling loads of simply supported, rectangular, laminated composite plates subjected to five types of loading conditions: (1) uniaxial, (2) hydrostatic biaxial, (3) compression-tension biaxial, (4) positive shear and (5) negative shear. Considerably different results are found for the two types of shear loading for angle-ply composites. The Ritz method, along with displacements assumed in the form of a double sine series, is used to solve the problems. Convergence studies are presented to demonstrate the accuracy of the results. Contour plots of the buckled mode shapes are shown for some of the more interesting plate and loading configurations.
 
Article
A series of tests is described in which tubular specimens of a commercially pure polycrystalline aluminum were loaded in torsion at either of two dynamic rates, 300 and 600 sec−1, up to shear strains of about 2 and 4 per cent, respectively, at temperatures in the range −180 to 250°C. The tests were performed in a torsional split-Hopkinson bar. In the past when this apparatus was employed at an elevated or reduced temperature multiple reflections were encountered along the bars due to the temperature gradients. These reflections required elaborate computational corrections. In the present tests the reflections were eliminated by tapering the Hopkinson bars appropriately so their mechanical impedance in torsion remained constant in spite of the temperature gradients. The results, in the form of stress-strain curves, are compared to the corresponding “static” curves obtained by testing similar specimens in torsion at about 10−3 sec−1. The influence of strain rate and of temperature is generally as expected, i.e. the flow stress increases with an increase in strain rate or a decrease in temperature. The strain rate sensitivity parameter varies non-linearly with temperature, and has a minimum value in the neighborhood of room temperature.
 
Article
Deformation by 〈111〉-pencil glide has been analyzed by an upper-bound model which combines a least-shear analysis and Piehler's maximum virtual work analysis. The least-shear analysis gives exact solutions if three 〈111〉 slip systems are active, while the maximum work analysis provides solutions for the case of four active slip systems. Independent checks are used to determine which solution method is appropriate.Computer calculations using this model have been made to determine; (1) the orientation dependence of the Taylor factor for axisymmetric deformation; (2) the yield loci for textured materials having [100], [110] and [111] sheet metals and rotational symmetry; (3) the isotropic yield locus for randomly oriented materials; and (4) flow stresses along critical loading paths for various assumed textures with rotational symmetry. The latter calculations indicate that anisotropic yield loci of textured bcc metals with rotational symmetry are much better approximated by where R is the strain ratio and Y is the tensile yield strength with an exponent a = 6 rather than with a = 2 as postulated by Hill. It is not known how well upper-bound calculations like these represent actual yielding behavior.
 
Article
After describing Robins' ballistic pendulum in general an outline is presented of the contributions to the elementary theory of the impact of translating point masses between the time of Marcus Marci (b.1595) and Christopher Wren (1632–1723). The specific work of Christian Huygens (1629–1695) especially, is described for relevant theory of the compound pendulum. A brief outline of the early lives of Robins and Cassini is given leading to an account of how the latter came to be involved, probably being the first scientist recorded as using a ballistic pendulum.The author's search for a written account of Cassini's work, in French, was located in the Procèsverbaux—the original hand-written record of scientific work as reported to the French Academy—for 1707. An abridgment of the reports was subsequently printed in the Philosophical History and Memoirs of the Academy and the latter eventually rendered into English by Ephraim Chambers (with Professor John Martyn as a co-author) in 1742.The latter may be contrasted with Benjamin Robins' own account of his pendulum design, use and experiments as given in his book, New Principles of Gunnery, published in 1742. Some reference to Euler's reception and reaction to the latter is noticed.Seemingly, Robins was not aware of Cassini's work and in any case used the pendulum to great and, different, purposes. As far as the author is aware no paper or publication, and but one book—and that minimally—in English has ever noticed or assessed the claim of Cassini to a share in the invention of the ballistic pendulum. The purpose of this paper is less to establish a priority than to put on record a truer account of the origins of the ballistic pendulum. (Ballistics: from the Greek βαλλεìv, to throw, and pertaining to the throwing of projectiles.)Several useful Notes about people, apparatus and events, are appended for improving understanding of the background of the times in which Cassini and Robins lived.
 
Article
R. J. Boscovich is a scientifically shadowy figure, see Note 1, to most English-speaking students of 18th century physical science, as is, incidentally, Emmanuel Swedenborg. An attempt to account for this situation is given, followed by a review of Jesuit Boscovich's scientific life during the years in which he wrote his most significant works. The activities of Boscovich for the Pope and as a diplomatist are described and some of his English connections are made clear. Certain impediments to his scientific career as caused by his character are noted, see Note 2. Boscovich's life in Paris, his return to Italy and a mention of his “atomic theory” are given. Specific references to certain of his papers are outlined and attention is called to the probable effect of Boscovich's ideas on Faraday (this being the latter's bicentennial year of birth). That Boscovich was to be taken very seriously by English-speaking students of natural philosophy is evident from the attention given to his work by outstanding British scientists of the last two centuries.
 
Article
The origin of the little known and virtually unread work of well-known polymath William Whewell, The Mechanical Euclid, (1837) seems ascribable to 19th century concern with the exact teaching of Euclid. The book probably initially stimulated the interest of Isaac Todhunter and Charles Dodgson who so loudly championed Euclid a generation later. The main purpose of this Note relates to their concern with Euclid and rigour.In writing about one of Whewell's books we do not neglect to observe that this year is the 200th anniversary of his birth.†
 
Article
An outline of Todhunter's life history is first given and we then consider (unequally however) his contributions to mathematical scholarship through his extensive, weighty books commenting on, to varying degrees, the History of the Calculus of Variations, the Attraction and Figure of the Earth, Probability Theory and the Theory of Elasticity. These are followed by short accounts of some of his score or more well-known textbooks at junior and sophomore level, mostly written in about the middle third of the 19th century. A number of Todhunter's miscellaneous yet mathematics-related books are also discussed and finally, his success as a private tutor and a coach of undergraduates for mathematics degrees at Cambridge in the late 19th century.Today, Todhunter's books have disappeared from library shelves and his activity as a historian of applied mathematics has to be recognised as now more or less forgotten. Todhunter is seen to have been a man of great influence in his time, a highly respected college and university man, greatly honoured at the time of his death but now almost universally neglected. The purpose of this paper is to try to revive appreciation of his contributions in their several dimensions.
 
Article
Some issues about teaching “Euclid” are dealt with in Todhunter's text book of the same name, see Ref. [3] in Ref. [1] and again in the first of his six essays in Ref. [2]. Charles Dodgson's title work above, Ref. [3], also addresses the same topic and in this short article we endeavour to describe the background to Dodgson/Carroll's work and indicate its nature.
 
Article
The theory of the invariant representation for tensor functions in first illustrated by providing a general form of the Hill (1948) orthotropic yield criterion. It is then applied to derive a quadratic yield equation for the case of prismatic monoclinic symmetry, which is induced by simple shear deformation. This new criterion can in turn be approximated by an orthotropic one by choosing the ‘best’ symmetry axes. The above equations are then used to derive the angular dependences of the uniaxial yield stress and strain rate ratio in the plane of a prismatic monoclinic sheet. Finally, it is shown on an example that they are able to predict the axial stresses occurring during torsion testing with a fairly good accuracy.
 
Article
A user-friendly yield criterion was proposed by Hill in 1993, which utilizes five independent material parameters in representing the yield locus. In the present investigation, an attempt is made to analyze forming limits in sheet metals based on this yield criterion and the M–K approach. Comparison of the predicted results with experimental data indicates that Hill’s 1993 yield criterion is able to characterize the localized necking of both aluminum and AK steel. A parametric study is carried out to investigate the influence of material parameters on forming limits, which shows that the shape of the yield locus has a significant influence on limit strains.
 
Article
We first give a resumé of the life of Voltaire with accents on his interests in science and engineering. His writings are broadly categorized and noted for their variety, quality and volume. He was a great man of letters with wide appreciations and sympathies. The impact of his work on the thinking of educated people helped give birth to the Enlightenment. He spanned political and ethical matters with his essays, pamphlets and plays and for these and his histories, satires and novels he is justly remembered. Voltaire spent several years endeavouring to promote a liberating Newtonianism, writing books and pamphlets on pure and applied science. He has received less than his due credit for this latter service, which we here try to make more prominent than is usual.A comparison is made between him and contemporaries Samuel Johnson and Benjamin Franklin, principally. We propose that the closest modern approximation to him, in breadth of general interests, is H. G. Wells.We find, in effect, a celebration of Voltaire's birth in two excellent recent classical analyses of his scientific works, which emanate from the Voltaire Foundation at Oxford with its critical editions of The Elements of the Philosophy of Isaac Newton (published 1992) and Essay on the Nature and Propagation of Fire (1991).
 
Article
A 2008-T4 sheet sample has been characterized and its mechanical behavior and formability have been modeled. Uniaxial tensile and equal biaxial tensile stress-strain data, compressive yield strengths, crystallographic texture, earing and the forming limit curve were experimentally determined. Bulge test specimen shape and thickness profiles were also measured after various amounts of biaxial strain. A recently developed phenomenological constitutive model of anisotropic mechanical behavior was used to predict the directionality of strength, plastic strain ratio (R) and shear strain ratio (Г) values. In addition, this model was used to predict the forming limit curve for this sample. Predictions made with the recent model generally compare favorably with experimental results and with predictions made using the Taylor/Bishop and Hill theory. According to the data obtained in hydraulic bulge testing, the 2008-T4 exhibited apparent isotropic behavior. However, in cup drawing—another axisymmetric deformation mode—this material exhibited anisotropic behavior, as indicated by the formation of ears and troughs.
 
Article
Sheet aluminum alloy (2036-T4) specimens of several geometries were photogrid-ded and pulled in a tensile testing machine while precision photographs were taken of the photogrid. This technique allowed determination of strain distributions and load-displacement points. These results are compared with corresponding results obtained by Finite Element Modeling based on Hill's anisotropic plasticity theory and experimental tensile stress-strain data. FEM predictions and experimental results are in excellent agreement; verifying Hill's model for the case of in-plane deformation of 2036-T4 aluminum alloy between the strain states of plane strain tension and uniaxial tension.
 
Article
This paper explores the relation between the microstructure and the effective properties of cellular solids. Most available models are based on Voronoi structures, giving a limitation in the cell geometry diversity. In this study, circular cylinder packings followed by radical plane determination leads to various 2D structures exhibiting bimodal or multimodal cell size distributions. These structures are then modelled by a network of beams and are used in a finite element analysis (FEA). Macroscopic properties, such as Young's modulus and the yield strength are estimated. The yield strength corresponds to the appearance of the first plastic hinge. The results of the simulations reveal a large influence of the cell geometry on the mechanical properties. In the case of low densities, scaling laws involving pertinent geometrical characteristics such as beam length or proportion of large cells are proposed to describe Young's modulus and the yield strength.
 
Article
This paper is concerned with the development of an analytical model for the calculation of the effective linear elastic stiffness of a 2D triaxial flat braided composite (2DTBC) and the effect of initial unintended microstructural imperfections on the calculated stiffnesses. A representative unit cell (RUC) of the braid architecture is first identified along with its constituents. Tow geometry is represented analytically taking account of tow undulation. Each tow is modeled as a transversely isotropic linear elastic solid and the contribution from each tow to the RUC elastic stiffness is obtained by volume averaging, taking account of the volume fraction of each constituent. Predictions of the elastic constants are compared against experimental data and a fully 3D finite element computation based on the RUC. Effects of the bias tow angle, the angle uncertainty and, the bias tow undulation magnitude on the elastic constants are examined by considering composites with bias tows at 30° and 60°. This latter part, thus, examines the effect of microstructural imperfections on the elastic stiffness of 2DTBCs. It also serves as a tool to assess the most significant parameter that affects composite stiffness.
 
Article
Rolling of an elastic thermoinsulated cylinder on a thermoelastic half-space is investigated. The frictional heating due to the slipping in the contact area is involved. The problem is reduced to a nonlinear system of integral equations which is solved iteratively. The effects of the heat generated on the rolling contact are explored.
 
Article
The present paper extends the classical limit analysis of plane frames to account for 2nd-order geometric nonlinearity. Any specified displacement limits can also be included in the proposed analysis. The effect of combined bending moment and axial force is accommodated in the adopted piecewise linearized yield condition, albeit still assumed as perfectly plastic. The main feature of the novel approach proposed is to compute simultaneously, in a single step, the maximum load and corresponding deformations of the structure under limited displacement conditions. The problem is cast as an instance of the challenging class of (nonconvex and nonsmooth) mathematical programs with equilibrium constraints (MPECs). Various nonlinear programming based algorithms are proposed to solve the MPEC. Four numerical examples are provided to illustrate application of the proposed limit analysis approach and to highlight the necessity of considering geometric nonlinearity for a more realistic assessment of structural behavior.
 
Article
It has been proposed that highly triaxial residual stress fields may be sufficient to promote creep damage in thermally aged components, even in the absence of in-service loads. To test this proposal, it is necessary to create test specimens containing highly triaxial residual stress fields over a significant volume of the specimen. This paper presents results from an experimental and numerical study on the generation of triaxial residual stresses in stainless steel test specimens. Spray water quenching was used to generate residual stress fields in solid cylinders and spheres made from type 316H stainless steel. A series of finite element simulations and measurements were carried out to determine how process conditions and specimen dimensions influenced the resulting residual stress distributions. The results showed that highly compressive residual stresses occurred around the surfaces of the cylinders and spheres and tensile residual stresses occurred near the centre. Surface residual stresses were measured using the incremental centre hole-drilling technique, while internal residual stresses were measured using neutron diffraction. Overall there was good agreement between the predicted and measured residual stresses. The level of triaxiality was found to be very sensitive to the heat transfer coefficient, and could be controlled by adjusting the cooling conditions and changing the dimensions of the steel samples. This differed from other processes, such as welding and shot-peening, where the magnitudes and distributions of residual stresses are ill-defined and the volume of material subjected to a triaxial residual stress state is relatively small.
 
Article
Finite strip methods are presented for the prediction of buckling stresses and natural frequencies of vibration of “long” prismatic plate structures which may be formed of fibre-reinforced, composite, laminated material with very general properties. The finite strip methods are of the single-term type with complex algebra employed to accommodate applied in-plane shear stress and anisotropic material behaviour. The developments, described here follow on very directly from an earlier paper in this Journal ([1] Dawe and Craig, Int. J. Mech. Sci.30, 77, 1988) to which frequent reference is made herein. The first development is the introduction of major improvements and extensions on the earlier work [1] which is based upon the use of first-order shear deformation plate theory to represent the out-of-plane properties of plate flats: the chief advance involves the use of multi-level substructuring procedures, including the introduction of so-called superstrips, but eccentric connections of component plates at their junctions is also included. The second development is the introduction of a new finite strip analysis which is based on the use of classical plate theory and which is complementary to the shear deformation analysis, with similar advanced features. Two computer programs, BAVPAS and BAVPAC, are introduced and description is given of some results of the application of these programs.
 
Article
3D non-axisymmetrical tube (NAT) spinning is a kind of new spinning technology, which breaks through the restriction that only axisymmetrical hollow parts could be produced by traditional spinning technology. The research on the spinning force aims to optimize the machine design and the processing parameters selection. The neck-spinning process of the 3D NAT is simulated by 3D elastic–plastic finite element software, MARC. The characteristics of the neck-spinning force of 3D NAT are compared with that of the axisymmetrical tube (AT) spinning. The effect of the main forming parameters, such as offset amount, oblique angle, nominal reduction of blank radius, feed rate and path direction, on the spinning forces have been studied theoretically and experimentally. It shows that during 3D NAT spinning, the spinning forces varies periodically with the revolution angle of the roller around the blank; the spinning force during backward path spinning is greater than that of forward path spinning. The simulation results conform well to the experimental ones.
 
Article
A three-dimensional (3D) mesoscopic model to simulate the collective dynamic behavior of a large number of curved dislocations of finite lengths has been developed for the purpose of analyzing deformation patterns and instabilities, including the formation of dislocation cell structures. Each curved dislocation is approximated by a piecewise continuous array of straight line segments. The interactions among the segments, including line-tension and self-interactions, are treated explicitly. For longer-range interactions, the space is divided into a regular cellular array and the elastic fields of the dislocations in a remote cell approximated by a multipolar expansion, leading to an order N algorithm for the description of a cell containing N dislocations. For large arrays, the simulation volume is divided into cubical cells. A discrete random starting array is selected for the master cell and its nearest neighbors, which constitute an order 2 cell. Reflection boundary conditions are imposed for near-neighbor order 2 cells and so forth, creating an NaCl-type lattice array. The boundaries between the cells are considered to be relaxed grain boundaries. That is, recovery within the boundaries and rotation across them are considered to occur so that the boundaries have no associated elastic fields. This cell hierarchy, coupled with the multipole expansion, is suitable for the use of massively parallel computation, with individual cells assigned to separate processors.
 
Article
A full three dimensional (3D) heterogeneous approach for FE upper bound limit analyses of in- and out-of-plane loaded masonry walls is presented. Under the assumption of associated plasticity for the constituent materials, mortar joints are reduced to interfaces with a Mohr–Coulomb failure criterion with tension cut-off and cap in compression, whereas for bricks a Mohr–Coulomb failure criterion is adopted. Four-noded tetrahedron elements with linear interpolation of the velocities field are used for bricks discretization, whereas possible jumps of velocities at the interfaces between adjoining elements can occur. Triangular elements with linear interpolation of the jump of velocities field are used both for joints reduced to interfaces and internal bricks interfaces. In this way, an improvement of the numerical model in terms of collapse load is obtained.In order to test the reliability of the model proposed, two examples consisting of an English bond shear panel and a simply supported rectangular stretcher bond slab are discussed. Results obtained are compared with experimental data available and previously presented numerical models. The comparisons show both that reliable predictions of collapse loads and failure mechanisms can be obtained by means of the numerical procedure proposed and that full 3D models should be employed in presence of loads eccentricities and/or multi-leaf walls out-of-plane loaded.
 
Article
To reduce the computational time of finite element analyses for sheet forming, a 3D hybrid membrane/shell method has been developed and applied to study the springback of anisotropic sheet metals. In the hybrid method, the bending strains and stresses were calculated as post-processing, considering the incremental change of the sheet geometry obtained from the membrane finite element analysis beforehand. To calculate the springback, a shell finite element model was used to unload the sheet. For verification purposes, the hybrid method was applied for a 2036-T4 aluminum alloy square blank formed into a cylindrical cup, in which stretching is dominant. Also, as a bending-dominant problem, unconstraint cylindrical bending of a 6111-T4 aluminum alloy sheet was considered. The predicted springback showed good agreement with experiments for both cases.
 
Article
A heterogeneous full 3D limit analysis model for the evaluation of collapse loads of FRP-reinforced multi-layer masonry structures loaded in- and out-of-plane is presented. Four-noded rigid infinitely resistant tetrahedrons are used to model bricks, stones and filler. Three-noded rigid infinitely resistant triangles are used to model FRP strips. Plastic dissipation is allowed only at the interfaces between adjoining elements, i.e. on mortar joints reduced to interfaces, on brick–brick interfaces and on filler. A possible dissipation at the interfaces between FRP triangles and masonry wedges is also considered in order to take into account, in an approximate but effective way, the possible delamination of the strips from the supports. Italian code CNR-DT200 formulas are used as a reference to evaluate peak interface tangential strength. While the delamination from the support can be modeled only in an approximate way within limit analysis, the aim of the paper is to accurately reproduce the change in the failure mechanism observed in experiments due to the introduction of strengthening elements.
 
Article
Hot extrusion of Ti–6Al–4V alloy has been studied using finite element simulation and the results are compared with those obtained experimentally. First, the constitutive behavior of the material and friction at the extrusion temperatures are established based on the results obtained through cylindrical and ring compression tests, respectively. While the flow stress below β transus temperature is expressed as a strain-dependent function, it is taken as strain-independent one at higher temperatures. The distribution of strain, temperature and effective stress has been simulated under different design and processing conditions. Simulation results show that heat generation due to deformation is significant (as much as 160°C) in the hot extrusion of Ti alloys, and it mainly occurs at the beginning of the extrusion process. This leads to reduction in flow stress which, in turn, leads to enlarged deformation zone. A fair agreement has been found between the experimental results and those obtained through simulations.
 
Article
Characteristics of localized necking in sheet metals are examined with anisotropic plasticity as well as anisotropic damage developed progressively after load application. The vertex theory is employed to describe basic mechanisms of localized necking. Anisotropic plasticity is accounted for by Hill's quadratic yield criterion. An anisotropic damage model based on Continuum Damage Mechanics is reviewed and expanded. The anisotropic damage model is combined with a modified vertex theory to generate damage-coupled localized necking criteria on both sides of forming limit diagram (FLD). The criteria lead to explicit expressions of critical hardening modulus on both sides of FLD. It is shown that the damage-coupled FLD model can be readily reduced and used to predict the forming limit strains of damage-free materials satisfying power hardening law given by other researchers (Hill, J. Mech. Phys. Solids. (1952)1,19; Zhu et al., ASME J. Eng. Mater. Tech. (2001) 123, 329). Critical damage value at localized necking can be computed from the damage-coupled localized necking criteria as a function of stress/strain states and strain paths. Tests on the formability and material properties of Al 6022, such as hardening and damage law, anisotropic plasticity parameter, have been performed. The measured FLD of the material are compared with the predictions based on the damage-coupled localized necking criteria for validation of the proposed FLD model. Material damage is observed to have a definite effect on the forming limits of Al 6022, thus providing a more accurate prediction than that of the conventional models.
 
Article
In order to evaluate the formability of friction stir welded (FSW) automotive TWB (tailor-welded blank) sheets with respect to base material direction, the aluminum alloy 6111-T4 sheet was joined with three different types of combination: RD||RD, TD||RD, TD||TD (Here, RD and TD mean the rolling direction and transverse direction, respectively). Formability performance was experimentally and numerically studied in three applications including the simple tension tests, hemisphere dome stretching and cylindrical cup drawing tests. For numerical simulations, the non-quadratic orthogonal anisotropic yield function, Yld2004-18p and the isotropic hardening law were implemented into the material constitutive model. As for the failure criterion, the forming limit diagram (FLD) was utilized to determine the failure strain.
 
Article
The effects of changing strain-paths on forming limits of aluminum alloy 6111 T4 have been investigated by determining forming limit diagrams (FLDs) of specimens prestrained to several levels in uniaxial, plane strain and biaxial tension, parallel and perpendicular to the prior rolling direction. Prestraining in biaxial tension generally lowers the entire FLD, whereas prestraining in uniaxial tension raises the limits on the right hand side of the FLD without much effect on the left hand side, when the direction of the largest principal strain does not change. If the directions of the principal strains are rotated, prestraining in uniaxial or plane strain tension lowers the forming limits for most of the FLD range.A general finding was that, after prestraining, the amount of the additional plane strain deformation possible before failure depends on the effective strain during prestrain, regardless of the original strain-path. Finally, an example of the importance of strain-path changes in a stamping of an aluminum automobile part is presented.
 
Article
In this paper, the surface generation in ultra-precision diamond turning of Al6061/15SiCp metal-matrix composites was investigated based on different analytical approaches which include parametric analysis, cutting mechanic analysis, finite element method (FEM) analysis and power spectrum analysis. Parametric analysis was performed to explore the in situ inter-relationships between the process parameters and the surface roughness. The surface properties of the diamond turned surface were extracted and analyzed by the power spectrum analysis of the surface roughness profiles. Different surface generation mechanisms were deduced based on the cutting mechanics and FEM analysis. The results of the theoretical analyses were verified through a series of cutting tests conducted under various cutting conditions and a good correlation between the theoretical and experimental results was obtained.
 
Article
Acoustic scattering from an infinitely long fluid-saturated porous elastic circular cylinder located near a planar boundary with locally varying surface impedance is studied. The formulation utilizes the novel features of Biot dynamic theory of poroelasticity, the appropriate wave field expansions, the classical method of images and the translational addition theorem for cylindrical wave functions along with a simple local surface reaction model involving a complex amplitude wave reflection coefficient applied to develop a closed-form solution in the form of infinite series. The analytical results are illustrated with a numerical example in which a cylindrical plastic foam absorber is located near a layer of foam material set on an impervious rigid wall. The numerical results reveal the important effects of incident wave frequency, angle of incidence, interface local surface reaction, cylinder poroelasticity and position on the acoustic field quantities. The proposed model can lead to a better understanding of acoustic scattering from two-dimensional near-interface porous absorbers or targets which are commonly encountered problems in outdoor acoustics, noise control engineering, and ocean engineering. The presented solution could eventually be used to validate those found by numerical approximation techniques.
 
Article
The characteristics of a number of metal components proposed as impact energy absorbers are reviewed, attention being focussed on to modes of deformation which stem from the axial compression of metal tubes. Progressive buckling, inversion and splitting are discussed and areas for future work identified. The buckling of thin-walled square section tubes filled with polyurethane foam is also described. Reference is also made to recent work on cellular materials which highlights the influence of inertia in axially compressed tubes and tubular arrays.
 
Article
This paper is focused on the behavior of boring bars with a passive dynamic vibration absorber (DVA) for chatter suppression. The boring bar was modeled as a cantilever Euler–Bernoulli beam and only its first mode of vibration was considered. The stability of the two-degree-of-freedom model was analyzed constructing the stability diagram, dependent on the bar characteristics and on the absorber parameters (mass, stiffness, damping, and position). Two analytical approaches for tuning the absorber parameters were compared. The selection criterion consisted on the maximization of the minimum values of the stability-lobes diagram. Subsequent analysis performed in this work, allowed formulating of new analytical expressions for the tuning frequency improving the behavior of the system against chatter.
 
Article
In this paper, the sound absorptions of flexible curved micro-perforated panels that are backed by an air cavity are studied in detail. A theoretical model that is based on the classical plate equation coupled with an acoustic wave equation is developed for the prediction of sound absorption. This model considers both symmetrical and antisymmetrical structural acoustic responses. Using the electro-acoustic analogy approach, another model is developed that only considers single structural and acoustic modes. It is proposed to make use of panel and cavity resonances to widen the absorption bandwidth of a single/double perforated absorber. The absorption of a flexible micro-perforated panel can be further enhanced by adjusting its curvature to bring the resonant frequencies closer together. The effects of various parameters such as boundary condition, incidence angle, and curvature on the absorption are studied. Predicted results for the single and double layer absorbers show good agreement with measurements.
 
Article
This paper describes a tunable vibration absorbing isolator. The device is based on the liquid inertia vibration eliminator, which is modified so that the frequency at which maximum isolation occurs can be changed in real time. This is achieved by using adjustable pneumatic springs. A theoretical model describing the device is derived using Lagrange's equations. The model is used to design a practical device and experimental results confirm the validity of the model. With the experimental device a roll-off of about 90 dB/decade over a 12 Hz frequency band was achieved.
 
Article
A theoretical model to predict the energy absorption capabilities of aluminum foam filled braided stainless steel tubes under tensile loading conditions has been developed and is presented. Experimental testing was completed on braided tubes, with a nominal diameter of 64.5 mm and woven from 304 stainless steel wires with a diameter of 0.51 mm, filled with rectangular prisms of closed cell aluminum foam with densities ranging from 248 to 373 kg/m3. Based upon observations from experimental testing and applying a unit cell concept to the braided tube, a theoretical model which incorporates two stages of deformation was developed. Within the first stage of deformation, which occurs prior to tow lockup of the braided tube, energy absorption is primarily due to compression of the aluminum foam core. After tow lockup has occurred the energy absorption behavior of the assembly is a sole result of the deformation of the braided tube. Comparisons between the energy absorption predictions of the analytical model and experimental observations were found to be in good agreement for assembly lengths of approximately 400 mm. For the tensile loading conditions and geometry of aluminum foam filled braided tubes considered in this research energy absorption ranged from approximately 5.2 to 7.9 kJ with corresponding tube elongations of 400 mm.
 
Article
Tapered tubes have been considered desirable impact energy absorbers due to their relatively stable mean load–deflection response under dynamic loading. Relatively few studies have been reported on the energy absorption performance of tapered tubes compared with straight tubes. This paper compares the energy absorption response of straight and tapered thin-walled rectangular tubes under both quasi-static and dynamic axial impact loading, for variations in wall thickness, taper angle, impact mass and impact velocity. It is found that the dynamic response of tapered tubes is more sensitive to impact velocity and wall thickness than taper angle for lower impact velocities. Inertia effects influenced the dynamic response for both straight and tapered tubes, yet were less significant for the latter. Overall, the results indicate that the energy absorption response of tapered tubes can be controlled via their wall thickness and taper angle, and this highlights their potential for use as energy absorbers. Analysis has been undertaken using a finite element model, validated using existing theory.
 
Article
The plastic collapse response of aluminium egg-box panels subjected to out-of-plane compression has been measured and modelled. It is observed that the collapse strength and energy absorption are sensitive to the level of in-plane constraint, with collapse dictated either by plastic buckling or by a travelling plastic knuckle mechanism. Drop weight tests have been performed at speeds of up to , and an elevation in strength with impact velocity is noted. A 3D finite element shell model is needed in order to reproduce the observed behaviours. Additional calculations using an axisymmetric finite element model give the correct collapse modes but are less accurate than the more sophisticated 3D model. The finite element simulations suggest that the observed velocity dependence of strength is primarily due to strain-rate sensitivity of the aluminium sheet, with material inertia playing a negligible role. Finally, it is shown that the energy absorption capacity of the egg-box material is comparable to that of metallic foams.
 
Article
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.
 
Article
The behavior of sloshing dynamics modulated fluid systems driven by the orbital accelerations including gravity gradient and jitter accelerations with partially-filled rotating fluids has been studied. Present study is applicable to a full-scale Gravity Probe-B Spacecraft dewar tank with and without baffle. Results of slosh wave excitation along the liquid—vapor interface induced by jitter acceleration-dominated orbital accelerations provide a torsional moment with an up-and-down movement of bubble oscillations in the rotating dewar. The results show rightward and leftward movement of bubble oscillations transverse to the rotating axis, and up-and-down movement of bubble oscillations longitudinal to the rotating axis of dewar container. The orbital accelerations also induce an eccentric contour of bubble oscillations in a horizontal r—θ plane. As viscous force between liquid—solid interface, and surface tension force between liquid—vapor—solid interface can greatly contribute to the damping effect of slosh wave excitation, the rotating dewar with baffle provides more areas of liquid—solid and liquid—vapor—solid interfaces than that of a rotating dewar without baffle. Results show that the damping effect provide by a baffle reduce the amplitude of slosh wave excitation and reduce the degree of asymmetry in liquid—vapor distribution. Computation of bubble (helium vapor) mass center fluctuations also verifies that a rotating dewar with baffle produces less fluctuations than that of a rotating dewar without baffle.
 
Article
Trabecular bone, a porous, cellular type of bone found at the ends of the long bones and within the vertebrae, is subject to cyclic compressive loading resulting from the activities of daily living. Such fatigue loading can result in fracture, especially in vertebrae of patients with osteoporosis. As an initial step in understanding compressive fatigue of trabecular bone we previously used finite-element analysis to model the progressive damage and failure of a simple, two-dimensional hexagonal honeycomb. In this study, the analysis is extended to a random, Voronoi honeycomb. Bending of the cell walls induces tensile stresses even when the overall loading is compressive. The cell walls are assumed to have a distribution of crack lengths in their tensile zones. The cracks are assumed to grow according to a Paris law and fail when the cracks reach 75% of the cell wall thickness. Failed cell walls are removed from the structure, the stress distribution recalculated and the next increment of fatigue loading are simulated. The Young's modulus of the honeycomb is calculated after each cell wall failure. Overall failure of the Voronoi structure is assumed to occur when the modulus is reduced by 5%; further loading reduces the modulus sharply. The slope of the S–N curve for the Voronoi honeycomb is the same as that for the hexagonal honeycomb. The model suggests that a random honeycomb is more sensitive to fatigue than a regular one.
 
Article
A new design of the uniaxial creep testpiece with slit extensometer ridges is proposed, to improve the accuracy of strain measurement during creep testing. Numerical techniques were developed for finite element analysis of the creep-rupture behaviour and of the accuracy of the measured strain of the new testpiece. Physically based constitutive equations with the stress sensitivity described by both hyperbolic sine and power-law relationships were used in the numerical computation. The technique models the formation and evolution of damaged material and determines the accuracy of strain measurement during testing. It is shown that the distribution of axial stress in the gauge area for the new testpiece is more uniform than that for the standard uniaxial creep testpiece presently used with unslitted extensometer ridges. Variations in the accuracy of the measured strain with life fraction, gauge length and stress level for the testpiece with slit extensometer ridges are presented and compared with those computed by Lin et al. [2] for the standard testpiece. The maximum error of the measured strain obtained from the new testpiece is only half that found for the traditional one. It is concluded that reliable test results can be obtained with shorter testpiece gauge lengths when slit extensometer ridges are used; this may be an important advancement for low-cycle fatigue testing where the use of short gauge lengths is desirable to avoid buckling.
 
Article
The buckling of thin rectangular plates with nonlinearly distributed loadings along two opposite plate edges is analyzed by using the differential quadrature (DQ) method. The problem is considerably more complicated since it requires that first the plane elasticity problem be solved to obtain the distribution of in-plane stresses, and then the buckling problem be solved. Thus, very few analytical solutions (the only one available in the literature is for rectangular plates with all edges simply supported) have been available in the literature thus far. Detailed formulations and solution procedures are given herein. Nine combinations of boundary conditions and various aspect ratios are considered. Comparisons are made with a few existing analytical and/or finite element data. It has been found that a fast convergent rate can be achieved by the DQ method with non-uniform grids and very accurate results are obtained for the first time. It has also been found that the DQ results, verified by the finite element method with NASTRAN, are not quite close to the newly reported analytical solution. A possible reason is given to explain the difference.
 
Article
In general, this paper deals with general nonlinear oscillations of a nonconservative and single degree-of-freedom system with odd nonlinearity and, in particular, it presents accurate higher-order analytical approximate solutions to van der Pol damped nonlinear oscillators having odd nonlinearity and the Rayleigh equation. By combining the linearization of the governing equation with harmonic balancing and the method of averaging, we establish accurate analytical approximate solutions for the general weakly damped nonlinear systems. Unlike the classical harmonic balance method, simple linear algebraic equations instead of nonlinear algebraic equations are obtained upon linearization prior to harmonic balancing. The combination of these two methods results in very accurate transient response of the periodic solution. In addition and for the first time, this paper also presents a method for deducing fourth-, fifth- and higher-order linearized governing equations from the lower-order equations without the requirement of formulating the problem from the first principle. Three examples including the van der Pol damped nonlinear oscillator are presented to illustrate the excellent agreement with approximate solution using the exact frequency.
 
Article
An acoustic emission and force-based sensor fusion system involving pattern recognition analysis has been used to detect tool breakage, chip form and a threshold level of tool flank wear in turning. When normalized with the resultant force, the force components in the cutting, radial and feed directions were found to be highly sensitive to variables such as feedrate, material hardness, tool coating and tool wear, depth of cut, and speed in fractional factorial experiments. A three-dimensional analytical force model was extended to include the effect of flank wear in order to interpret the experimental findings. Subsequently, using an empirical bilinear relationship between the machining variables and forces, a filter was designed to eliminate the variable effects such that pattern recognition of tool failure under varying conditions was feasible. Results of the sensor fusion approach involving testing the system with the same data used in designing it when using AE and force signals indicate a 94% accuracy for sensing tool wear alone, whereas using only AE for detecting chip form and tool breakage indicate a 99 and 96% accuracy respectively.
 
Article
Gearbox power transmissions are widely used in the automotive industry. They have a complex vibro-acoustic behaviour that is influenced by the various acoustic–structural interaction mechanisms. This paper concentrates on modelling these systems using a three-dimensional finite-element (FE) approach for the structure combined with a Rayleigh integral (RI) method for the acoustic radiation process. A modal analysis method is used to evaluate the elasto-acoustic modal characteristics for the coupled system. Effect of the fluid inside the gearbox on the vibration response is discussed. The combined use of this FE/RI model enables evaluation of the acoustic response. A case study of a simplified gearbox internally excited with gear mesh stiffness fluctuation is presented. Vibratory analysis allows concluding that the vibro-acoustic coupling between elastic housing, air-cavity and free acoustic field have not to be neglected.
 
Article
The theory of acoustic emission and the analysis of emission signals is reviewed as it applies to generation of acoustic emission in metal cutting. Based upon the mechanics of the orthogonal cutting operation a relationship is developed between the root mean square (RMS) voltage of the acoustic emission and fundamental cutting parameters. The validity of this relationship is evaluated by a series of tests varying cutting speed, feed and rake angle for orthogonal machining. Strong dependence of the RMS voltage of the emission on both strain rate and cutting velocity was observed. The sources of acoustic emission in metal cutting are discussed and areas of additional work in the study of acoustic emission from metal cutting are identified.
 
Article
An experimental investigation was undertaken to examine the effect of cavity length on flow oscillations produced by an open cavity placed within a subsonic turbulent boundary layer. A narrow rectangular cavity with a constant width to depth ratio, W/D, of 1 was placed within a thick fully developed turbulent boundary layer with a corresponding Reθ=10.5×103. Pressure time histories were acquired for six separate cavity lengths (or L/D values) using microphone type pressure transducers. The spectral character of these signals was analyzed in terms of their magnitude and frequency content. This study indicates that large changes in the fluctuating pressure level can occur as L/D is varied from 1.47 to 8.73. A state of acoustic resonance was only observed at L/D=1.47, while fluid-acoustic resonance occurred at L/D between 1.47 and 8.73. Relative SPL calculations indicate that energy within the cavity was increased by approximately 60% over this L/D range. It is also suggested that this increase was a result of vortical structure shedding and growth. In addition, the location of maximum unsteadiness was estimated to coincide with the location of vortical structure saturation.
 
Article
The acousto-ultrasonic (AU) input–output characteristics for contact-type transmitting and receiving transducers coupled to composite laminated plates are considered in this paper. Combining a multiple integral transform method, an ordinary discrete layer theory for the laminates and some simplifying assumptions for the electro-mechanical transduction behaviour of the transducers, an analytical solution is developed which can deal with all the wave processes involved in the AU measurement system, i.e. wave generation, wave propagation and wave reception. The spectral response of the normal contact pressure sensed by the receiving transducer due to an arbitrary input pulse excited by the transmitting transducer is obtained. To validate the new analytical–numerical spectral technique in the low-frequency regime, the results are compared with Mindlin plate theory solutions. Based on the analytical results, numerical calculations are carried out to investigate the influence of various external parameters such as frequency content of the input pulse, transmitter/receiver spacing and transducer aperture on the output of the measurement system. The results show that the presented analytical–numerical procedure is an effective tool for understanding the input–output characteristics of the AU technique for laminated plates.
 
Top-cited authors
K. M. Liew
  • City University of Hong Kong
T. X. Yu
  • The Hong Kong University of Science and Technology
Guoxing Lu
  • Swinburne University of Technology
S.R. Reid
  • The University of Manchester
Yoshihiro Tomita
  • Kobe University