Showing papers on "Necking published in 1978"

Limits to ductility set by plastic flow localization

Abstract: The theory of strain localization is reviewed with reference both to local necking in sheet metal forming processes and to more general three dimensional shear band localizations that sometimes mark the onset of ductile rupture. Both bifurcation behavior and the growth of initial imperfections are considered. In addition to analyses based on classical Mises-like constitutive laws, we discuss approaches to localization based on constitutive models that may more accurately model processes of slip and progressive rupturing on the microscale in structural alloys. Among these non-classical constitutive features are the destabilizing roles of yield surface vertices and of non-normality effects, arising, for example, from slight pressure sensitivity of yield. We also discuss analyses based on a constitutive model of a progressively cavitating dila- tional plastic material which is intended to model the process of ductile void growth in metals. A variety of numerical results are presented. In the context of the three dimensional theory of localization, we show that a simple vertex model predicts ratios of ductility in plane strain tension to ductility in axisymmetric tension qualitatively consistent with experiment.. We also illustrate the destabilizing influence of a hydrostatic stress dependent void nucleation criterion. In the sheet necking context, and focussing on positive biaxial stretching, it is shown that forming limit curves based on a simple vertex model and those based on a simple void growth model are qualitatively in accord, although attributing instability to very different physical mechanisms. These forming limit curves are compared with those obtained from the Mises material model and employing various material and geometric imperfections.

Conditions for shear localization in the ductile fracture of void-containing materials

Abstract: This paper investigates the possibility that ductile fracture occurs by the McClintock-Berg mechanism of localization of deformation within a narrow shear band, owing to the progressive softening of the material by increasing porosity due to void growth. The ductility predicted for a macroscopically homogeneous sample of a voided material is shown to be unrealistically large and hence an initial inhomogeneity of properties is considered, in the sense of an analysis by Marciniak and Kuczynski in the related problem of local necking in sheet metals. General conditions for a localization bifurcation with an initial inhomogeneity (imperfection), concentrating deformation to allow localization within it, are derived. The initial imperfection is taken in the form of a void-containing, thin slice of a material and is assumed to have a void volume fraction slightly larger than the outside of the imperfection. Elastic-plastic constitutive rate relations for void-containing materials proposed by Gurson are adopted to the conditions for the localization bifurcation. The critical conditions are analyzed numerically to discuss the sensitivity of localization conditions to an initial imperfection, in consideration of the implications for the theory of ductile fracture. The results suggest that the existence of an initial imperfection makes it possible for localization to occur at a reasonable strain, and the predictions from this analysis seem broadly consistent with reported experimental observations.

Sheet Necking-II. Time-Independent Behavior

Abstract: Various factors affecting the prediction of limit strains in biaxially-stretched sheets are studied. Time-independent material behavior is assumed, and both the flow theory of plasticity as well as a finite-strain version of deformation theory are considered. A localization-band bifurcation analysis is first carried out. The influence of geometric imperfections is then analyzed using the long-wavelength approximation treated in Part I. We also discuss the predicted forming limit curves and comment on their relation to published experimental data. The main emphasis in this Part, however, is on comparisons between the corresponding predictions of flow theory and deformation theory.

A computer simulation of the tension test

Abstract: A dynamic finite-difference computer program is used to calculate the quasi-static necking deformation of a round tensile bar to 71 per cent reduction in area. Finite strain and rotation are accounted for. We modelled the behavior of A-533 Grade B Class 1 nuclear-pressure-vessel steel as elastic work-hardening plastic material, using J2-flow theory and a flow curve obtained from a simple tensile test. Up to the time of fracture, computed results of neck radius vs load and elongation, load vs elongation, and neck profile vs neck radius compare favorably with experimental results. We present the macroscopic stress and strain state at fracture and compare these results with those of Bridgman and other calculators. Our calculated neck stress shows monotonically decreasing stress in the radial direction and does not show the sharp stress peaks on the axis or the rounder stress peaks off the axis that these earlier calculations show. We find considerable differences from the Bridgman solution. An iterative computer method is introduced to allow correction of simple tension-test data to a universal flow-stress curve valid for large strain.

Sheet Necking-III. Strain-Rate Effects

Abstract: The effect of material strain-rate dependence on necking retardation is examined for biaxially-stretched sheets. Rate-dependent versions of both flow theory and deformation theory are employed in an analysis of the growth of long-wavelength nonuniformities. Material strain-rate sensitivity is seen to substantially increase the predicted limit strains beyond their corresponding values for time-independent material response. We also discuss the influence of strain-rate dependence on imperfection- sensitivity and forming limit curves.

Sheet Necking—I. Validity of Plane Stress Assumptions of the Long-Wavelength Approximation

Abstract: Two special solutions are used to illustrate the errors involved in the analysis of sheet necking from invoking plane stress assumptions. The first is an exact solution for the growth-rate of a small amplitude, sinusoidal thickness variation in a sheet of material characterized by \(\dot \in \) = ασ n in simple tension. The plane stress assumptions become accurate when the ratio of variation wavelength to average thickness exceeds four and otherwise lead to overestimates of the actual growth-rate. When this same ratio is approximately unity the relative size of the thickness variation decays with increasing deformation—an effect not predicted by a plane stress analysis. The second special solution is obtained using a perturbation expansion with the nonlinear long-wavelength solution (i.e., the plane stress solution) as the lowest order contribution. In this way explicit corrections to the plane stress solution are obtained. Selected comparisons with fully nonlinear finite element calculations are made.

The fracture characteristics of a superplastic single phase copper alloy

Abstract: A superplastic single phase copper alloy exhibits a sigmoidal relationship between strain rate and stress at 823 K, dividing the behaviour into three regions. Maximum elongation to fracture (∼380%) occurs at intermediate strain rates at the lower end of region II, and there is a decrease in total elongation at both low (region I) and high (region III) strain rates. No necking is observed in regions I and II, and there is only very slight necking in region III. Internal cavities are formed at all strain rates, but the appearance of the cavities depends critically on the imposed strain rate. At high strain rates, the cavities are small and lie in strings parallel to the tensile axis; but as the strain rate is reduced the cavities become larger, more rounded, and essentially randomly distributed. The mode of failure is ductile rupture in region III, but void growth and interlinkage become increasingly important with decreasing strain rate.

Plastic Flow Properties in Relation to Localized Necking in Sheets

Abstract: Considerable interest exists in understanding the levels of maximum useful strains achievable prior to localized necking (forming limits) and their dependence on the imposed stress-state. Marciniak’s model of imperfection growth has successfully explained the rise in forming limit as the imposed strain-ratio (e2/e1) is increased from zero (plane strain) toward unity (balanced biaxial tension). Experimental studies on formability of various materials have, however, revealed basic differences in behavior, such as the “brass-type” and the “steel type”, exhibiting respectively, zero and positive dependencies of forming limit upon the strain-ratio. Such results cannot be reconciled without proper attention to the details of strain hardening and strain-rate hardening behaviors of these materials, particularly as functions of strain and strain-ratio. A review of these properties for several materials will be presented in an attempt to show their importance on the necking behavior. Furthermore, the dependence of the patterns of behavior upon the mode of stretching (in-plane and punch stretching) is discussed. Some results of a Marci niak-type model of material imperfection are also considered.

Apparatus for closing and sealing containers

Abstract: An apparatus is described for handling a continuous, stuffed, flexible casing and especially stuffed with explosives material. The apparatus includes pairs of split necking plates on either side of a casing path adapted for opposed reciprocal movement for engaging the casing in the path and necking the casing. The necking plates are mounted by a parallelogram linkage suspended from an overhead frame, and linkage means are provided for simultaneously moving the necking plates through said parallelogram linkage to neck the casing. Each pair of necking plates is adapted to move apart in a direction parallel to the axis of the path of the casing such that when the casing is necked by the necking plates, the neck so formed on the casing can be elongated by moving the plates apart. Magazine means are provided for advancing clips overhead of the casing, and a reciprocating plunger removes the clips from the magazine and arranges them on the neck portion of the casing between the necking plates as they are split apart. Die means are pivoted from the overhead frame and adapted for movement to and from a position between the split-apart necking plates below and adjacent the necked portion of the casing for receiving and forming the clips. Cutting means are pivotally mounted to the overhead frame for movement between the split-apart necking plates to cut the casing in the vicinity of the clips.

Deformation Analysis of Large Sized Panels in the Press Shop

Abstract: This paper describes experimental results of forming limits for steel sheets and deformation states in large-sized autobody panels together with examples of applying these results to analysis of actual press forming operations. The forming limit is defined as the amount of strain at which a pronounced roughening in surface finish occurs. This roughening signals the onset of necking as determined by means of stylus instrument measurement and visual observation. Based on this definition, forming limit curves were obtained for both simple and complex deformation paths. An example of using these data in the forming of a new quarter panel is given.

Forming limit criteria - sheets

Abstract: First introduced in 1963, forming limit diagrams (FLDs) have been empirically constructed to describe the strain states, or combinations of major (e1) and minor (e2) principal strains, at which a highly localized zone of thinning or necking becomes visible in the surface of sheet metal. Laboratory rigid-punch and pressshop experiments have shown that a single, gage-corrected FLD — known as the Keller-Goodwin Curve — is applicable to most grades of low-carbon, low-strength, 1008-type steels and is unaltered by normal production variations in material properties and cleanliness. Different FLDs are obtained, however, for steels whose properties differ widely from 1008 steels — such as high-strength or stainless steels — and for nonferrous metals. For some metals, ductile fracture terminates usable deformation and becomes the fracture-forming limit. Distinction is made between FLDs obtained from rigid punch tests and those derived from in-plane stretching of flat sheets in free space. Recently, theoretical calculations of FLDs have achieved some measure of success. Unfortunately, knowledge of the peak strain limit described by the FLD is insufficient to completely characterize the formability of a sheet metal. Equally important is the ability of the sheet metal to distribute the strain as uniformly as possible. Since the level of the FLD is relatively fixed for a given material, control of the strain distribution is the primary practical means available to sheet-metal producers and users to improve formability limits. The goal of current research is to apply forming limit criteria during the design or blueprint stage.

Strain Induced Plastic-to-Rubber Transition of An SBS Block Copolymer and Its Blend with PS.

Abstract: : The strain softening phenomenon in poly(styrene-b-butadiene-b-styrene) and its blends with polystyrenes were investigated by means of electron microscopy and small angle x-ray scattering. Samples were cast from mixed solvents of tetrahydrofuran and methyl ethyl ketone (90/10 by volume). The structure of these samples consist of randomly oriented alternating lamellar domains of the two components. Their mechanical behavior is plastic-like in that they exhibit yielding and necking when first stretched to around 200%. After the necking has propagated throughout, the samples show typical rubber-like behavior. This phenomenon may be called the strain induced plastic-to-rubber transition, and is believed to occur as a result of structural changes from alternating lamellar domains to fragmented PS domains dispersed in a PB matrix.

Method and apparatus for necking stuffed flexible casings

Abstract: An apparatus for handling a continuous, stuffed, flexible casing, including two pairs of necking plates (22). Each pair of necking plates is adapted to move apart in a direction parallel to the casing such that when the casing it necked by the necking plates the neck can be elongated by moving the plates apart. Die means (24) are provided for clipping a pair of clips at the neck and cutting means (26) are provided to cut the casing between the clips.

Tensile deformation of a round bar

Abstract: An approximate mathematical description of the tensile test is given for a material that is strain hardening and strain rate sensitive. Three phases of the deformation are distinguished: (I) nearly homogeneous deformation up to maximum load, (II) gradual localization of the deformation at nearly constant load, and (III) necking. The analysis realistically approximates: load, extension curves; post-uniform elongation; incipient neck size; and neck profiles.

Shear girdling phenomenon in polymers

Abstract: Hollow and solid specimens of polypropylene and solid specimens of polyoxymethylene exhibited an effect under torsional shear which is analogous to the necking usually observed in tensile tests. After reaching some critical shear strain in the postyield region localized shear deformation developed on the gauge length. As twisting was continued a dramatic decrease in the diameter of the cross section was observed. This torsional shear induced phenomenon was named girdling. The superimposition of hydrostatic pressure up to 6 kbar has a significant influence on the extent of girdle formation. Stress whitening, observed on the solid polyoxymethylene specimens was suppressed by the application of pressures greater than 1 kbar. Very large shear strains produced a ratchet-type fracture surface on the solid specimens which indicates the presence of axial, radial, and tangential strains. Qualitatively, these results are supported by the finite deformation theory of elasticity.

The Role of Chain Scission in Homogeneous Deformation and Fracture

Abstract: Section II B of Chapter 2 gave a description of the uniaxial deformation behavior of an unoriented thermoplastic polymer. It was indicated that — depending on experimental and material parameters — failure could occur at any of the different stages of a tensile loading process: as brittle fracture due to crack initiation and propagation during anelastic deformation as a consequence of plastic flow after necking or homogeneous yielding as ultimate failure following plastic deformation with strain hardening.

Transformation-induced plasticity in Fe-17.20% Cr-7.34% Ni steel

Abstract: The characteristics of transformation-induced plasticity of Fe-17.20% Cr-7.34% Ni steel were studied. The maximum value of fracture elongation occurred at 20° C in the temperature rangeMs (−196° C) toMd (75° C), and this maximum elongation was brought about by the delay of necking. The percentage ofα′ martensite per unit tensile strain after the martensite transformation was then 2.20

Unstable Fracture Criteria Under Large Plastic Deformation

Abstract: Publisher Summary If fracture occurs between the yield point and the load predicted by the ultimate tensile strength, then neither the linear fracture mechanics is any longer applicable nor any other conventional fracture criteria. This chapter presents an investigation concerned with unstable ductile fracture criteria, which would complete a whole fracture concept along with linear fracture mechanics. In this study, a crack length is limited to be (a) not so large as the plastic region does not cover entirely the test piece and (b) not so small as a local necking takes place, providing a unfirom uniaxial plastic condition. The chapter presents the model for investigating the unstable fracture criterion.

Superplasticity of alloy V96Ts

Abstract: Alloy V96Ts with a fine-grained structure (grain diameter 5 μ) exhibits superplasticity in tension at strain rates of 2.8·10−4 to 5.5·10−3 sec−1 at 460–470°. In the superplastic condition the samples elongate evenly without necking.

Mathematical models of the most-widespread types of deformation of polyurethane subject to pressworking

Abstract: under those experimental conditions for which no peak is formed. It is a line of intersection between the deformation surface and the (t%, t r) plane, where t Z is the loading time. The region included between this curve and the tr axis corresponds to brittle failure, while the remaining portion of the diagram corresponds to neck formation; in this case, the length of the neck can be determined graphically from the figure. These data apply, of course, only to one size of specimen; it is easy, however, to predict anticipated results, considering the data in Figs. I and 2 for other sizes of specimens and stresses. Thus, it is shown in the study that tensile necking is not a fundamental property of polymers and like all processes that are relaxation in nature, depends on the loading conditions; at least two processes occur in polymers under load -the propagation of microcracks and plastic deformations; in the long run, the relationship between the rates of these processes determines the character of the rupture for different experimental conditions.