Showing papers on "Necking published in 1991"

Tensile ductility of superplastic ceramics and metallic alloys

Abstract: Superplastic ceramics and metallic alloys exhibit different trends in tensile ductility in the range where the strain-rate-sensitivity exponent, m, is high (m⩾0.5). The tensile ductility of superplastic metallic alloys (e.g. fine-grained zinc, aluminium, nickel and titanium alloys) is primarily a function of the strain-rate-sensitivity exponent. In contrast, the tensile ductility of superplastic ceramic materials (e.g. zirconia, alumina, zirconia-alumina composites and iron carbide) is not only a function of the strain-rate-sensitivity exponent, but also a function of the parameter ⋗e exp (Qc/RT) where ⋗e is the steady-state strain rate and Qc is the activation energy for superplastic flow. Superplastic ceramic materials exhibit a large decrease in tensile elongation with an increase in ⋗e exp (Qc/RT). This trend in tensile elongation is explained based on a “fracture-mechanics” model. The model predicts that tensile ductility increases with a decrease in flow stress, a decrease in grain size and an increase in the parameter (2γs−γgb), where γs is the surface energy and γgb is the grain boundary energy. The difference in the tensile ductility behavior of superplastic ceramics and metallic alloys can be related to their different failure mechanisms. Superplastic ceramics deform without necking and fail by intergranular cracks that propagate perpendicular to the applied tensile axis. In contrast, superplastic metallic alloys commonly fail by intergranular and transgranular (shearing) mechanisms with associated void formation in the neck region.

Effect of strain gradient and curvature on forming limit diagrams for anisotropic sheets

Abstract: Recent work on sheet metal formability had shown that the position of forming limit diagrams (FLDs) in punch stretching is higher than that in in-plane stretching because of a strain gradient effect resulting from bending a flat sheet into a curved sheet by punch stretching. To our knowledge, none of the developed theoretical models in the study of localized necking can be used to predict this phenomenon accurately so far. In this study, a new model, using Barlat and Lian’s new nonquadratic anisotropic yield criterion, is proposed by introducing a strain gradient term in the constitutive equation to consider the effect of the first order strain gradient (curvature), in the thickness direction resulting from bending, on the localized necking in anisotropic sheets. The developed model is used to study the effects of curvature on FLDs and to predict FLDs in punch stretching and inplane stretching for various materials. It is found that the theoretical predicted results are in good agreement with experimental data.

The energy criteria of instability in time-dependent inelastic solids

Abstract: CONDITIONS sufficient for instability of deformation are examined for a class of incrementally non­ linear, time independent inelastic solids. Instability of a quasi-static deformation process (path) at varying loading is distinguished from a narrower concept of an unstable equilibrium state. The en­ ergy criterion is extended to deformation paths under generał assumptions which ensure that the incrementa) boundary value problem can be given a variational formulation. For a discretized prob­ lem, fulfilłment of the instability condition along a path is shown to imply either instability of the traversed equilibrium states in a dynamie sense or persisting possibility of quasi-static bifurcation at varying loading. For a continuum, instability at varying loading is interpreted as sensitivity of the incremental deformation to arbitrarily small perturbmg forces.

On Some Issues in Triaxial Extension Tests

Abstract: Results of triaxial extension tests on dry sand are presented. Special attention is paid to the factors influencing the results in triaxial extension tests. It is found that factors such as accuracy of the axial force measurement, axial force carried by the rubber membrane surrounding the specimen, gravity, and inhomogeneous deformation have a much larger influence on the results in triaxial extension tests than in triaxial compression tests. Accurate measurement of the axial force is achieved by placing the load cell inside the pressure chamber. The influence of the confining pressure on the axial force measurement is avoided through a proper construction. The force carried by the rubber membrane is corrected with reference to the result of a tension test on a strip of rubber membrane. The effect of gravity is accounted for by adding the axial stress due to gravity to the applied axial stress. The inhomogeneous deformation is traced by three lateral strain collars placed along the specimen height. Results of triaxial extension tests cannot be appreciated if these influential factors are not taken into account. The failure mode of the specimen is found to be influenced largely by the initial density. Inhomogeneous deformation in the form of necking develops in the upper part of dense specimens and in the middle of loose specimens. For dense specimens, the necked region becomes wider with advanced deformation and develops into one single or two intersecting shear bands. For loose specimens, however, no shear bands can be observed.

Method for necking a metal container body

Abstract: The present invention is directed to a novel processing for necking metal container bodies. The process comprises die-necking a container body to a first necked plug diameter, employing one or more operations, and thereafter spin-flow necking the container body to a second reduced plug diameter. The utilization of die-necking advantageously reduces plug diameter variability, thereby enhancing and complimenting the spin-flow necking operation.

Computational coupled non-associative thermo-plasticity

Abstract: Computationally oriented formulation of the isothermal, rate-independent theory of non-associative elasto-plasticity is extended in this paper to describe coupled thermo-elastic-plastic and thermo-elastic-visco-plastic behaviour of materials. This is done by additionally considering thermal strains, assumming all material properties to be temperature dependent and accounting for the mechanical coupling terms in the non-stationary heat conduction equation. The finite deformation effects are included in the analysis. The theory is employed for the analysis of thermo-mechanical response of ductile metals with damage effects modelled by a generalization of the so-called Gurson approach. This constitutive model is known to generate equations typical of non-associative plasticity and hence it can be consistently incorporated into the present more general considerations. The finite element assessment of combined thermal and damage effects on the axisymmetric necking process illustrates the paper. Numerical aspects such as a ‘tangent’ stiffness for rate-dependent thermo-plasticity and the algorithmic (or consistent) tangent stiffness matrix for non-associative plasticity are discussed as well.

On the numerical integration of a class of pressure‐dependent plasticity models with mixed hardening

Abstract: Radial return algorithms, for both three-dimensional and plane stress situations, are developed for a class of pressure-dependent plasticity models (formulated in state variables) with mixed hardening. The consistent tangent matrix has been developed which, among other advantages, does not require numerical inversion. The algorithms, for Gurson's mixed hardening model, are incorporated in a finite element program to solve several simple uniaxial tension problems. When compared with numerically integrated solutions, the results from the finite element analysis show excellent agreement. Finally, results of the axisymmetric necking problem, using Gurson's mixed hardening model, are presented as an example of application.

The stress-whitened damage zone of PVC blends

Abstract: The stress-whitened damage zone that formed ahead of a semicircular notch during slow tensile loading has been measured from optical micrographs of translucent blends of poly(vinyl chloride) (PVC) with experimental chlorinated polyethylene (CPE) resins. When the zone was small, the plane strain condition applied and from the elastic stress distribution a constant mean stress condition was found at the boundary of the crescent-shaped zone. The critical mean stress did not depend on the chlorine content or the chlorine distribution of the experimental CPE resin used in the blend. While the critical mean stress decreased as the amount of CPE in the blend was increased, the critical volume strain, calculated from the bulk modulus, was independent of composition and was thought to be the controlling parameter for stress-whitening. When the zone was larger, the shape was qualitatively described by concepts of stress redistribution in the presence of a plastic zone ahead of the notch. Macroscopic flow and necking were only detected near the maximum in the stress-displacement curve.

On the relationship between neck length and bond radius during compression of snow

Abstract: In an earlier study on the variations in micro-structure during large volumetric deformations of snow, the authors observed that, contrary to expectations, the length of necked regions connecting adjacent grains did not necessarily decrease during compression. Rather, there was no discernible or predictable change in neck length, in some cases increasing and in others decreasing. Further evaluations of the data and an analysis of the mechanics of neck deformation determined that the process is complicated by three different effects: (1) increase in coordination number (number of bonds per grain), (ii) plastic deformation of the neck, and (iii) a geometric effect determined by bond growth and grain geometry. It is found that the first two effects tend to decrease the neck length and that the third produces an increase in mean neck length. A set of coupled differential equations is developed describing the variation of neck length and bond radius, and solved numerically for conditions consistent with the experimental data. Calculated results agree well with the data for the bond radius but the results for the neck length are less satisfactory. Reasons for this lie with difficulty in making accurate measurements of mean neck length from two-dimensional surface-section data and in the criteria for the definition of necks.

Lithospheric breakup in three dimensions: Necking of a work‐hardening plastic plate

Abstract: Lithospheric breakup is, in general, oblique to the principal strain axes, with shortening in one horizontal axis (eh < 0). Local necking of the plate, including the mantle part of the lithosphere, is necessary for the creation of a divergent plate boundary. The necking develops as a mechanical instability that decreases the resistance of the plate to extension despite the intrinsic hardening of the material. We model the flow that precedes breakup stressing two aspects that have been overlooked before: (1) three-dimensional flow, and (2) strain dependent strength of the lithosphere. The model mimics spatial and temporal features of the most extensively documented rift systems. The neck is oblique to the direction of principal extension, and the transition from diffuse stretching to local necking is abrupt at 5–10% strain. The critical strain for local necking in the model appears to be independent of the intrinsic strength. Therefore various rheological layers (brittle upper crust, ductile lower crust, and stiffer but hotter mantle lithosphere) may neck concomitantly to form a rift.

The effect of rate sensitivity on history dependent forming limits of anisotropic sheet metals

Abstract: history dependent forming limits of sheet metals are computed by examining the role of rate sensitivity of flow stress in forming limits for anisotropic materials. Assuming that necking or nonuniform deformation is caused by initial heterogeneity, the forming limits are computed by considering the flow theory and incorporating an isotropic hardening model for anisotropic materials. Representative results show some of the trends for changing forming limits with different parameters under complex nonproportional loading histories. The computed results agree well with published experimental data for different loading history, anisotropy, and rate sensitivity of sheet materials.

On the long time creep and lifetime behavior in uniaxial extension of a linear low density polyethylene

Abstract: This paper describes uniaxial creep measurements done on a linear low density polyethylene over a wide range of temperatures and applied stresses. It is found that the creep behavior overall is quite complex and that the one quantity which can best be used to predict useful lifetime of this material is the time at which necking is observed. The time to neck data has been used to generate a composite curve which can serve as an upper bound to lifetime prediction.

Effects of strain rate on plastic flow and fracture in pure tantalum

Abstract: This paper describes the strain rate effects on flow and failure properties of pure tantalum. The strain rate dependent plastic behavior was determined from both quasistatic and split Hopkinson bar (SHB) tests. The competing effect of strain rate and inertia on the onset of necking, post-elongation, and strain to failure (ductility) was investigated. The quasistatic tests were performed at strain rates 0.001, 1, and 10/sec. The strain rates in the SHB tests ranged between 700 and 1600/sec. Under quasistatic loading, the strain hardening in tantalum was found to be rate sensitive. The strain hardening coefficient (n) decreased continually from a maximum value of about 0.28 to almost 0 in the quasistatic loading regime. In the SHB tests, it was not possible to determine the shape of the stress-strain curves for strains less than 5% due to spurious wave reflections. Nonzero positive values forn at high strain rates were obtained through viscoplastic, constitutive modeling. The flow stress at SHB strain rate levels was almost twice the quasistatic value at a strain rate of 0.001/sec, indicating significant strain rate sensitivity in tantalum. Both the ductility and ultimate strain decreased with increasing strain rate under the quasistatic loading regime reaching a minimum of 0.36 and about 0.02, respectively, at 10/sec. While the ductility remained at this level in the SHB (dynamic) loading regime, the ultimate strain (at the onset of necking) increased to values greater than 0.1, indicating deformation stability due to inertia.

Molecular mechanism for elongation : poly(vinylidene fluoride) form II

Abstract: Elongation of an unoriented sample of poly(vinylidene fluoride) form II at high temperature (above 140 °C) results in a uniaxially oriented sample of form II during so-called necking The short-range and long-range order parameters of poly(vinylidene fluoride) form II and measures of the structural order on thec-projection are characterized by the intensity and half-width of the 120 reflection The elongation under the same condition gives almost the same order parameters, independent of the order parameters before the elongation Furthermore, the dependence of the order parameters on the elongation temperature behaves in the same way as the dependence of the quenched unoriented sample on the annealing temperature This suggests that the elongation of the sample during necking corresponds to the crystallization or recrystallization after a much disordered state, approximately molten state; this supports the mechanism proposed by Yoon and Flory

Effect of two-stage strain-rate test on the superplastic behavior of an Al-Li-Cu-Mg-Zr alloy—Mechanical behavior

Abstract: Fine grain size is one of the essential conditions for obtaining superplasticity in polycrystalline materials. Several methods are available for grain refinement, including phase transformation, recrystallization, working of duplex alloys, and phase separation in duplex alloys. Recrystallization has been extensively used for grain refinement of superplastic quasi-single phase aluminum-base alloys. There are two kinds of superplastic Al-base alloys. In one of them, a fine grain size microstructure is obtained by static recrystallization microstructure is obtained by deformation-induced recrystallization during the initial stage of superplastic deformation. In the case of Al-Li base alloys, either method can be adopted for obtaining superplasticity. However, the deformation-induced recrystallization method can make the alloy more superplastic at higher strain-rates, which is more attractive for industrial applications. The paper examines the effect of two stage strain rate tests on stress-strain curves and superplasticity of an Al-Li-Cu-Mg-Zr alloy in detail. The results show that the proper combination of deformation parameters in a two-stage strain rate test results in higher elongation than that in a single strain-rate test. The optimum deformation condition corresponds to the proper combination of strain rate hardening and strain hardening in the second stage of superplastic deformation, which keeps the engineering stress constant ormore » slightly increasing and provides a high necking resistance.« less

Three‐dimensional finite element analysis of thin‐film stresses using algor personal‐computer‐based software

Abstract: algor, a commercially available, personal computer‐based, finite element software package was used to study three‐dimensional stress–strain relations in both free standing and adherent thin films. The accuracy of the analyses was verified by comparison to tensile tests and analytical calculations of radius of curvature. The results also agree with earlier two‐dimensional calculations. The program was used to simulate tensile testing in order to establish limits on film dimensions to yield Young’s modulus upon the application of a uniaxial stress approximation. Stress contours and deflections arising from submicroscopic elastic Poisson effects (necking) were determined for different film dimensions. In addition, the effect of using adhesives in sample mounting for tensile testing was studied, and the three dimensional models and results are compared to similar two‐dimensional calculations.

Method and apparatus for the aftertreatment of metal bodies, preferably round, thin-walled metal bodies, of two- or three-piece cans

Abstract: A method for the aftertreatment of metal bodies R, preferably round, thin-walled metal bodies, of two- or three-piece cans (tins) is characterized in that the area of transition 10, 10' to the necking area 2, 2' is reinforced by longitudinal ridges 5, 5'.

Near-crack-tip deformation in copper single crystals

Abstract: Cracked Cu specimens, made by diffusion bonding two halves of a single crystal, were 3-point bend tested, and the surfaces near the crack tips were examined by an optical microscope and a stylus profilometer. The plastic zone developed as assembled fan-shaped sectors, the details of which depended on the crystal orientation. A sector was often characterized by a family of dominant slip lines, and operations of slips on coplanar slip planes (CSP) were mutually exclusive. The through-thickness displacement changed gradually across sector boundaries but its gradient did not, suggesting a constant plastic strain within a sector but strain discontinuites at sector boundaries. The degree of necking depended mostly on the operation of slips on non-CSP, but operation of CSP caused either local necking or protrusion depending on the crystal orientation.

Experimental Analysis of Thermomechanical Coupling by Infra-Red Thermography

Abstract: In the first part we consider the energy balance form in case of thermoelastoplastic material. The relationships between the dissipation, the stored energy of cold work and the state variables are reviewed through the heat equation. Then, an experimental set-up consisting of an infra-red camera placed directly on the crosshead of a testing machine is introduced. Its numerization system allows recording thermal pictures on the surface of the sample during the deformation process. The numerical data analysis allows us to estimate the mechanical heat sources: plastic dissipation and the isentropic term due to thermoelastic effects. In the case of homogeneous mechanical tests performed at room temperature under several uniaxial loading paths, energy balances are shown. Finally, in the case of heterogeneous experiments, the performances of such an approach are tested to observe shear band evolution or to detect localized necking.

Characterization of commercial polybutylenes. part II. Crystallinity and tensile properties

Abstract: A series of previously characterized polybutylenes were compression molded using various cooling conditions. Crystallinity decreased as cooling rate increased. The samples exhibited three types of tensile behavior. The crystallinity of samples containing around 5% ethylene was about 40%. These behaved as elastomers, exhibiting typical entropic elasticity. For the remaining samples, crystallinities between 55% and 70% were observed, depending on grade, and more particularly on cooling conditions. For these, lower crystallinity levels favor sample necking and stress-induced orientation, producing high elongation at break and high tensile strength values, while the higher crystallinity samples show high moduli and elasticity values coupled with uniform deformation. In the former case, significant crystalline deformation—causing alignment of the c axes of the crystallites towards the stretching direction, and thereby reinforcing the sample—is responsible for the high elongations and tensile strength ...

Method for preventing necking of hot strip

Abstract: PURPOSE:To surely prevent necking by measuring the position of the transformation temp. of the present strip in the direction of line with plural transformation rate sensors and predicting the generating position of necking based on that result. CONSTITUTION:The plural transformation rate sensors 4 are arranged on run out tables 3 to measure the position of transformation temp. of the present strip 5 and the position of transformation temp. of the strip 5 can be measured with these transformation temp. rate sensors 4. And, because the generating position of necking is predicted based on the position in the direction of rolling process line, the generating position of necking can be predicted with high accuracy. Therefore, the generation of necking can be surely prevented.