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Showing papers on "Necking published in 1987"


Journal ArticleDOI
TL;DR: In this paper, an unconditionally stable algorithm for the numerical integration of elastoplastic pressure-dependent constitutive relations is analyzed in detail, and the application of the method to plane stress problems, in which the out-of-plane strain component is not defined kinematically, is discussed.
Abstract: An unconditionally stable algorithm for the numerical integration of elastoplastic pressure-dependent constitutive relations is analysed in detail in this paper. The application of the method to plane stress problems, in which the out-of-plane strain component is not defined kinematically, is discussed. The tangent moduli resulting from this integration algorithm are obtained by consistent linearization of the elastoplastic constitutive equations. The algorithm is applied to Gurson's constitutive model, some one-dimensional problems are solved, and comparisons with exact solutions are made. The paper closes with a numerical study of the necking of an axi-symmetric specimen using Gurson's plasticity model to describe the constitutive behaviour of the material.

429 citations


Journal ArticleDOI
Frédéric Barlat1, Owen Richmond1
TL;DR: In this article, a theoretical procedure for calculating the tricomponent plane stress yield surfaces and forming limits of textured f.c. polycrystalline metal sheets is presented.

189 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of void nucleation is incorporated in a recently proposed material model that accounts for a combination of kinematic hardening and isotropic hardening of a porous ductile material.
Abstract: The effect of void nucleation is incorporated in a recently proposed material model that accounts for a combination of kinematic hardening and isotropic hardening of a porous ductile material. Since each of plastic dilatancy, void nucleation and yield surface curvature have a strong influence on predictions of plastic flow localization, the present material model can be used to study the interaction of these effects. Nucleation controlled by the plastic strain as well as nucleation controlled by the maximum normal stress on the particle-matrix interface are modelled. The predictions of the material model, for various combinations of parameters, are illustrated by analyses of shear band formation under plane strain or axisymmetric conditions, and by analyses of necking in biaxially stretched sheets.

153 citations


Patent
02 Jul 1987
TL;DR: In this article, a rotatable necking turret is used to produce a smooth tapered wall between the container side wall and a reduced diameter neck, and the necked-in portion is reformed in each succeeding turret by dies.
Abstract: A die necking method and apparatus for producing a smooth tapered wall between the container side wall and a reduced diameter neck includes a plurality of rotatable necking turrets that each have a plurality of identical necking substations each having a necking die. The necking dies in the respective turrets have an internal configuration to produce a necked-in portion on the container which has a first arcuate segment integral with the container side wall and a second arcuate segment integral with the reduced diameter neck. The necking substations also have a floating form control element that engages the inner surface of the container to control the portion of the container to be necked. The necked-in portion is reformed in each succeeding turret by dies to produce a smooth tapered wall between the arcuate segments.

83 citations


Journal ArticleDOI
TL;DR: In this article, the average local surface strain in martensite and alloy was evaluated microscopically during tensile deformation of several step-quenched steels by means of a fine grid applied by photolithography.

70 citations


Journal ArticleDOI
01 Aug 1987-Polymer
TL;DR: In this paper, the application of a semi-empirical equation to the true stress-strain curve in the tensile deformation of plastics is discussed, and the applicability of the equation is further demonstrated using three further sets of published experimental results.

56 citations



Journal ArticleDOI
TL;DR: In this paper, it was shown that when an imperfection is along the zero-extension direction, both the homogeneous zone a and the heterogeneous zone b have the same stress states, which greatly simplifies the theory of Marciniak and Kuczynski, enabling the equation of plane stress which they obtained to be expressed in a one-dimensional form.

44 citations


Journal ArticleDOI
05 Oct 1987
TL;DR: In this article, an experimental-computational procedure is demonstrated, which generates material constitutive parameters valid at strains beyond those at the onset of necking, in the context of an incremental elastic-plastic constitutive formulation, by this procedure.
Abstract: Direct observation of solid deformation at all points in a material test specimen is generally not possible. This becomes important when an internal point experiences the maximum effective deformation of the entire specimen. The simple reduction of load-displacement data to material constitutive parameters, as for inelastic tensile specimen necking, is precluded. Although the mechanics of necking has received considerable attention, the complementary issue of constitutive parameter determination from inelastic specimen experimental data has not. This investigation addresses both aspects of the problem for HY-100 steel. An experimental-computational procedure is demonstrated, which generates material constitutive parameters valid at strains beyond those at the onset of necking. Neck deformation, specimen size and specimen geometry effects are used to ensure the uniqueness of the parameters in the sense that a single uniaxial continuum true-stress–true-strain curve predicts the behaviour of laboratory specimens with different geometries. The solution parameters for HY-100 steel are developed, in the context of an incremental elastic–plastic constitutive formulation, by this procedure. These results support the view that tensile specimen necking is the result of the interaction between imperfection-free specimen geometry, material behaviour and applied load for relatively unsophisticated constitutive formulations if the constitutive parameters are accurately determined. In addition, broken symmetry of specimen deformation is computationally predicted and experimentally confirmed for long, slender specimen geometries.

40 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of heat transfer conditions on the temperature increase of a sheet tensile specimen has been calculated by the finite difference method for a plain-carbon steel at various strain rates and in several environments.
Abstract: The temperature rise in a sheet tensile specimen has been calculated by the finite difference method for a plain-carbon steel at various strain rates and in several environments. Prior to necking, a uniform heat generation function is used with the governing flow equation while during the post-uniform strain, an empirical heat generation function is used. The empirical function is based on a strain distribution equation generated by curve fitting of experimental data. The effect of heat transfer conditions on the temperature increase has been discussed. The maximum temperature rise in air may reach 42 K at the center of an I.F. steel specimen at a strain rate of 10-2/s. The instability strain during tensile testing has been predicted by taking into account strain hardening, strain-rate hardening, and deformationinduced heating. The results show that significant deformation heating can occur during tensile testing in air at “normal” strain rates near 10-2/s, and that the uniform elongation can be affected markedly. Predictions for other alloys based on tabulated data are also presented.

35 citations


Journal ArticleDOI
TL;DR: In this paper, a numerical method for analyzing non-isothermal viscoplastic deformation problems has been developed, where a modified Bishop's method is used to solve the thermo-plasticity problem in decoupled form at each time step.

Journal ArticleDOI
TL;DR: In this article, a quasi-static neck propagation along an infinitely long specimen is analyzed for plane-strain tensile loading and the entire load-deformation behavior of finite length specimens is computed using the finite element method.

Journal ArticleDOI
TL;DR: In this paper, the emergence of instabilities in clad sheet metals subjected to rolling is modeled as bifurcations from a state of homogeneous strain into periodic non-uniform deformations, and it is demonstrated that while a maximum load criterion is valid for diffuse necking in uniaxial tension, it is inappropriate for rolling.
Abstract: The emergence of instabilities in clad sheet metals subjected to rolling is studied theoretically. These instabilities are modelled as bifurcations from a state of homogeneous strain into periodic non-uniform deformations. With this model, a sharp distinction may be drawn between the instabilities observed in rolling, which are not diffuse, and the diffuse necking observed in uniaxial tension. It is demonstrated that while a maximum load criterion is valid for diffuse necking in uniaxial tension, it is inappropriate for rolling. Various aspects of the predictions made here compare favorably with experiments by Semiatin and Piehler1,2,3

01 Mar 1987
TL;DR: In this paper, the authors examined the relationship between tensile properties and microstructural features of variable polarity plasma arc (VPPA) weldments of 2219-T87 aluminum.
Abstract: This study examines the relations between tensile properties and microstructural features of variable polarity plasma arc (VPPA) weldments of 2219-T87 aluminum. Crack initiation and weld failure of transverse tensile specimens of single and multipass weldments were studied. The specimens fractured on the rising portion of the stress-strain curve prior to necking, signifying that an increase in strength would accompany an increase in ductility. Of particular interest is a shallow, typically 0.001-0.003-in. (0.03-0.08-mm) deep, copper-rich region located in the crown and root corners of the weld. This region is a primary source of crack initiation and growth, due to its brittle nature and highly strained location. The brittle regions were removed by electropolishing and machining to determine their effect on weld tensile properties. The removal increased the ductility of the weld specimens, and in the case of single pass welds, actually increased the load carrying capacity. Local strain measurements and metallographic and chemical analyses are presented.

Journal ArticleDOI
TL;DR: In this paper, the influence of material strain-rate sensitivity on neck propagation during the cold drawing of polymeric films is examined and the entire load-deformation behaviour of a rectangular specimen as well as the evolution of the specimen profile and the stress and strain distributions at various stages of the deformation process are computed.

Journal ArticleDOI
TL;DR: In this article, a noncontacting experimental procedure has been used for characterizing the high-temperature large-strain uniaxial behavior of polycarbonate (PC), polyetherimide (PEI), and poly(butylene terephthalate) (PBT), through controlled tests on flat specimens cut from extruded sheet.
Abstract: A noncontacting experimental procedure has been used for characterizing the high-temperature large-strain uniaxial behavior of polycarbonate (PC), polyetherimide (PEI), and poly(butylene terephthalate) (PBT), through controlled tests on flat specimens cut from extruded sheet. While each of these polymers exhibits stable necking over a broad temperature range, the transition to the necked state is shown to be more gradual at higher temperatures, resulting in a less sharply defined neck transition region during the drawing process. These trends in necking behavior, and other phenomena such as double necking, which only occur at high temperatures, are illustrated through contour plots of the Cauchy-Green deformation tensor. Elevated temperature true-stress versus stretch data are given for each of these polymers.

Journal ArticleDOI
TL;DR: In this paper, the structural changes in the lamellar structure of polypropylene during biaxial orientation by hydrostatic extrusion have been examined, and morphological observations confirm the previous interpretation of SAXS and permit a more detailed model of the hierarchical structure to be proposed.
Abstract: Changes in the lamellar structure of polypropylene during biaxial orientation by hydrostatic extrusion have been examined. Examination of etched surfaces in the transmission electron microscope has revealed that up to a draw ratio of about 1.5 × 1.5 the primary mechanism is lamellar rotation into the plane of orientation, At higher draw ratios breakup of the lamellae is observed with formation of a granular structure. Thermal measurements suggest that localized melting and recrystallization may accompany the process of lamellar breakup. These morphological observations confirm the previous interpretation of SAXS and permit a more detailed model of the hierarchical structure to be proposed. Stress strain measurements show a gradual change from sharp necking to uniform deformation as the draw ratio is increased. On the other hand, the structural change at a draw ratio of about 1.5 × 1.5 Is accompanied by a large increase in the tensile impact strength.

Journal ArticleDOI
F. De Candia1, G. Romano1, R. Russo1, V. Vittoria1
TL;DR: In this article, a drawing of isotactic polypropylene was performed at room temperature in monoaxial drawing, and the results showed that the initial structure strongly affects the drawing behavior.
Abstract: Quenched films of isotactic polypropylene were obtained in different quenching conditions; the films structure was analyzed in terms of phases composition and gross morphology. The mechanical behaviour, analyzed at room temperature in monoaxial drawing shows that the initial structure strongly affects the drawing behaviour. The drawing occurs by necking propagation in all the samples, but the deformation in the neck depends on the gross morphology while the drawing load depends on crystallinity. The obtianed results are discussed on the basis of the molecular and structural model of the fibers formation by drawing of crystalline polymeric films.

Journal ArticleDOI
TL;DR: In this article, a quantitative experimental study of shear band formation during plane strain extension of ferrite-austenite sheet is presented. But the authors focus on the formation of short shear bands at the location of surface grain separation.

Journal ArticleDOI
TL;DR: In this article, an on-line study of structure development during poly(butylene terephthalate) melt spinning was carried out, and the phenomenon of diameter thinning (necking) was observed for both polymers at take-up velocities of 3500 and 4500 m/min with a mass throughput of 4 g/min.
Abstract: An on-line study of structure development during poly(butylene terephthalate) melt spinning was carried out. Two polymers with different molecular weights (intrinsic viscosities of 0.75 and 1.0 dL/g) were used. The range of take-up velocities studied was 1500 to 4500 m/min. On-line measurements included diameter, temperature, birefringence, and tension. The phenomenon of diameter thinning (necking) was observed for both polymers at take-up velocities of 3500 and 4500 m/min with a mass throughput of 4 g/min. At a constant mass throughput, the distance from the spinneret at which the necking occurred varied with take-up velocity and molecular weight of the polymer. Increasing the take-up velocity at constant mass throughput caused an increase in cooling rate and a slight increase in the rate at which the temperature decreased with distance from teh spinneret. A small but detectable change in the rate of temperature decrease was observed at a position near or just beyond the formation of the neck. It is suggested that this effect is due to the increased heat transfer caused by the rapid increase in filament velocity and increased surface to volume ration in the neck. Increased take-up velocity also caused necking to occur at higher temperature, as did an increase of polymer molecular weight. Birefringence increased with distance from the spinneret and indicated substantial molecular orientation was developed in the filament prior to the necking zone. A sharp increase of birefringence in the necking zone was observed for take-up velocities of 3500 and 4500 m/min. A discussion of the mechanism of neck formation is presented, and it was concluded that necking is intimately associated with stress-induced crystallization in PBT. An increase of spinline stress resulting from either an increase of take-up velocity or an increase of molecular weight can cause stress-induced crystallization and, hence, necking to occur nearer the spinneret and at higher temperature. For a given polymer this leads to filaments with higher levels of crystallinity, crystalline orientation, and crystalline perfection (greater crystal size). These changes in morphology result in changes in the filament mechanical properties. The effect of molecular weight change on the structure and properties is complicated by the fact that the development of crystallinity seems to be affected by the molecular weight independent of the spinline stress.

Journal ArticleDOI
TL;DR: In this paper, the topography of the fracture surfaces of several high strength, low alloy (HSLA) steels was determined using scanning electron microscopy, and the distribution of the dimple size from both types of specimens was determined.

Journal ArticleDOI
TL;DR: In this paper, Al-4.4.Mg-0.4% polycrystalline sheet is studied and it is shown that zones of intense shearing flow develop across large dimensions of microstructure during plane strain extension.

Journal ArticleDOI
TL;DR: In this article, a tensile test specimens under constant load creep failure is analyzed, based on constitutive relations that account for the nucleation and growth of grain boundary cavities in polycrystalline metals at high temperatures.



Journal ArticleDOI
TL;DR: In this article, the geometry of plastic flow localization during sheet necking and formation of sample-scale shear bands within the neck is described. But the authors focus on identifying three-dimensional, solid element models that correctly describe the heterogeneous initiation of simple shearing flow, inside a band that occupies just a small fraction of the sheet thickness.
Abstract: This paper systematically presents geometric models for describing internal shape change during plane strain extension of sheet. The models describe the geometry of plastic flow localization during sheet necking and formation of sample-scale shear bands within the neck. The emphasis is toward identifying three-dimensional, solid element models that correctly describe (1) the heterogeneous initiation of simple shearing flow, inside a band that occupies just a small fraction of the sheet thickness, (2) the gradual growth of bands of simple shearing across the sheet cross section, and (3) the development of a variety of patterns of sample-scale shear bands before sheet fracture. Models are identified that agree with experimental evidence. The geometry of these models provides quantitative links between flow localization throughout a deforming sample and changes in microscopic or crystal-scale flow behavior.

Journal ArticleDOI
TL;DR: An anomalous decrease in the speed of sound, which is attributed to amorphous phase loosening processes is observed in the necking region as mentioned in this paper, where the straight chains are extended to the maximum extent.
Abstract: An anomalous decrease in the speed of sound, which is attributed to amorphous phase loosening processes is observed in the necking region. Isometric holding of the material is accompanied by “healing” of these defects. In the formation of a fibrillar structure the elastic modulus and the mean orientation are markedly dependent on the appearance, under the action of the applied stress, of sections where the straight chains are extended to the maximum extent. Isometric annealing of the material at high deformations is accompanied by relaxation of some of the straight chains of the amorphous phase which are extended to the maximum extent.

Journal ArticleDOI
TL;DR: In this paper, the elastic moduli of porous materials represented as a combination of spherical, cylindrical or disk shaped holes or solid elements was calculated using a self consistent method and a yield criterion was found by stating that the elastic distortion energy evaluated with these moduli was equal to a critical value.

Journal ArticleDOI
TL;DR: The shear yielding processes in the deformation of biaxially oriented styrene-acrylonitrile (SAN) copolymer films (machine oriented with draw ratio = 6.9 and transverse direction = 2.9) were studied in this paper.
Abstract: The shear yielding processes in the deformation of biaxially oriented styrene-acrylonitrile (SAN) copolymer films (machine oriented with draw ratio = 6.9 in the machine direction and 2.9 in the transverse direction) were studied. In the transverse direction, two sets of shear bands with an intersection angle of about 123.6 degrees (61.8 degrees with the tensile axis) were developed. When necking occurred, the bands in the necked region were thin and discontinuous with an intersection angle of about 81 degrees. In the machine direction, shear bands appeared to be short and diffused with an intersection angle of about 119.2 degrees. Only a slight necking effect was observed. The Luders strain in the transverse direction was about 0.56 and in the machine direction, about 0.16. The shearstrain-volume of activation obtained from the strain rate dependence of shear stress was about 3440 ± 400 A3 in the machine direction and 2700 ± 500 A3 in the transverse direction. The work hardening behavior in both directions seemed to follow a linear relationship between 1n (tensile stress) and tensile strain at large strains. From a consideration of localized shearing toward tensile axis, the fraction of deformed materials was calculated. These observations indicated that (1) a strong orientation hardening effect existed in unbalanced biaxially oriented films, resulting from the difference of the amount of deformable materials between individual directions; and (2) deformation proceeded by shear banding with the high orientation direction involved more correlated molecular segments than the low orientation direction during the activation process.

Book ChapterDOI
01 Jan 1987
TL;DR: In this paper, a fully reversed strain-controlled push-pull test was performed on polycrystalline specimens of commercially pure aluminum to investigate the influence of specimen geometry and strain amplitude in promoting inhomogeneous cyclic deformation.
Abstract: Fully reversed strain-controlled push-pull tests were performed on polycrystalline specimens of commercially pure aluminum to investigate the influence of specimen geometry and strain amplitude in promoting inhomogeneous cyclic deformation. The specimens were cylindrical with an effective gauge section 10 mm in diameter and 20 mm long. The radius of the specimen shoulder was systematically varied between 20 mm and 60 mm. The fatigue tests were run under constant strain amplitude in air and room temperature using a symmetrical sawtooth waveform. The longitudinal strain amplitudes used for the testing were 0.10, 0.18, and 0.40% with a constant strain rate of 0.004 sec−1. The results show that instability, in terms of off-center necking or off-center barelling, is a strong function of the geometry and, to a lesser degree, of the strain amplitude. The tested specimens which did not exhibit shape instability showed intense localization of the deformation, i.e. shear bands uniformly distributed in the gauge section. It is shown that the general condition that appears necessary for shape instabilities and/or localized deformation in shear bands, is a positional variation in the cyclic stress-strain field caused by geometry and material microscopic variations. The observed behaviors are also shown consistant with the hypothesis that localization of deformation into shear bands results form an instability in the constitutive description of an homogeneous deformation field.