Showing papers on "Necking published in 1999"

Network Stretching, Slip Processes, and Fragmentation of Crystallites during Uniaxial Drawing of Polyethylene and Related Copolymers. A Comparative Study

Abstract: When polyethylene (PE) is deformed to large strains, the stress originates from both the viscous forces associated with the plastic deformation of the crystallites by slip and fragmentation processes and the entropic elastic forces arising from the stretching of the entangled amorphous regions. Relative weights of the different processes change with the crystallinity. The dependencies were analyzed in a comprehensive study on a series of samples encompassing a large range of crystallinities: PE, low-density PE (LDPE), and ethylene−vinylacetate copolymers. The comparison was based on measured true stress−strain curves for constant strain rates. For the samples with higher crystallinity, which show a necking, this was achieved by employing a video-controlled tensile testing machine. Recovery properties of the sample were studied in step-cycle runs, where the load was applied stepwise and interrupted after each step by an unloading−reloading loop. Simultaneous with the mechanical testing, the related textur...

Mechanical Properties and Deformation Behavior of the Double Gyroid Phase in Unoriented Thermoplastic Elastomers

Abstract: The mechanical properties of the double gyroid (DG) cubic phase in glassy−rubbery block copolymer systems are examined. The stress−strain properties of an isoprene-rich polystyrene/polyisoprene/polystyrene (SIS) triblock and a polystyrene/polyisoprene (SI) starblock DG, both comprised of two separate interpenetrating glassy networks embedded in rubbery matrices, are compared to those of the sphere, cylinder, and lamellar morphologies. This 3-dimensionally interpenetrating periodic nanocomposite is found to have superior properties over those of its classical counterparts, attributable to the morphology rather than to the volume fraction of the glassy component, the architecture of the molecule, or the molecular weight. The DG is the only polygranular/isotropic thermoplastic elastomer morphology which exhibits necking and drawing and which requires considerably higher stresses for deformation up to 200% strain than any of the three classical microdomain morphologies. The deformation behavior of the DG is f...

The Considère condition and rapid stretching of linear and branched polymer melts

Abstract: We analyze the onset of “necking” and subsequent filament failure during the transient uniaxial elongation of viscoelastic fluid samples in extensional rheometers. In the limit of rapid elongation (such that no molecular relaxation occurs), the external work applied is all stored elastically and the Considere criterion originally developed in solid mechanics can be used to quantitatively predict the critical Hencky strain to failure. By comparing the predictions of the Doi–Edwards model for linear homopolymer melts with those of the “Pom-Pom” model recently proposed by McLeish and Larson [J. Rheol. 42, 81–110 (1998)] for prototypical branched melts we show that the critical strain to failure in rapid elongation of a rubbery material is intimately linked to the molecular topology of the chain, especially the degree of chain branching. The onset of necking instability is monotonically shifted to larger Hencky strains as the number of branches is increased. Numerical computations at finite Deborah numbers also show that there is an optimal range of deformation rates over which homogeneous extensions can be maintained to large strain. We also consider other rapid homogeneous stretching deformations, such as biaxial and planar stretching, and show that the degree of stabilization afforded by inclusion of material with long-chain branching is a sensitive function of the imposed mode of deformation.

Thickness dependence of cracking resistance in thin aluminium plates

Abstract: The influence of thickness on the fracture toughness of aluminium 6082T0 thin plates of 1-6 mm thicknesses was investigated experimentally and numerically from tensile testing of cracked DENT specimens. The critical J-integral, J(c), critical CTOD, delta(CTODc), and essential work of fracture, w(e), are found to increase with thickness and to constitute equivalent measures of fracture toughness at small thickness. For larger thickness, J(c) and delta(CTODc) increase non-linearly with thickness and reach a maximum for 5-6 mm thickness Whereas iv, keeps increasing linearly with thickness. This difference is related to a more progressive development of the necking zone in front of the crack tip when thickness increases: at large thickness, cracking initiates well before the neck has developed to its stationary value during propagation, w(e) is more directly related to the steady-state crack growth resistance. A linear regression on the fracture toughness/thickness curve allows further separation of the two contributions of the essential work of fracture: the necking work and the fracture work spent for damaging. The maximum of the stress triaxiality ratio is shown to constitute a pertinent parameter for characterising how constraint affects cracking initiation in the present context where out-of-plane constraint dominates in-plane constraint. It allows justifying the shape of the J(c)/thickness relationship and results in the proposal of a 3D J(c)/thickness/triaxiality fracture locus. As fracture profiles are macroscopically flat with microscopic dimples and with only very small shear lips along the edges, a local criterion based on the growth and coalescence of voids has been used in order to predict fracture initiation. (C) 1999 Elsevier Science Ltd. All rights reserved.

Sheet Metal Forming: A Review

Abstract: Developments in the numerical modeling of stamping processes and experimental measurements now make it possible to design stamping processes using sound engineering principles. This article shows how experimental and theoretical contributions have led to the concept of a forming window in strain space that identifies the strains that can be developed safely in a sheet element. It is bounded by failure limits corresponding to localized necking, shear fracture, and wrinkling. A robust stamping process is one in which the strains in the part lie well within the forming window. The nature of the window and the influence of material behavior on its shape can be predicted.

Necking bifurcations during high strain rate extension

Abstract: Dynamic necking bifurcations which occur during rapid plane strain extension of a block of strain hardening plastic material are investigated. The block is presumed to be a portion of a plate or thin-walled shell deforming at high strain rate. It is found that the rates of growth of both very long and very short wavelength modes of nonuniform deformation are suppressed by inertia, thus promoting a necking pattern at an intermediate wavelength. The analysis indicates that, for blocks of small aspect ratio, the number of necks formed per unit length is proportional to the square root of the mean extensional strain rate of the block. The results of the analysis agree with necking patterns observed in high velocity ring expansion experiments and in detailed numerical simulations.

Factors affecting work of fracture of uPVC film

Abstract: Essential work of fracture (EWF) approach was used to evaluate the fracture toughness of uPVC film. It was found that the specific essential work of fracture, (we) is independent of specimen width, specimen gauge length, loading rate and test temperature, but dependent on the geometry of the test specimens. Test temperature and geometry were the only testing parameters affecting the specific non-essential work of fracture (βwp) in a very significant way. The plastic zone shape factor (β) was found to be very sensitive to both the geometry and temperature. It was established that both we and βwp could be partitioned into components that are linked to yielding (i.e. we,y and βywp,y) and necking/tearing (i.e. we,nt and βntwp,nt) processes. The only testing parameter that affected we,y was test temperature, whereas we,nt was affected by test temperature as well as geometry. All testing parameters used in this study affected the values of βywp,y and βntwp,nt.

Determination of the Forming Limit Diagrams Using Image Analysis by the Corelation Method

Abstract: This paper deals with a new method of strain measurement applied to the experimental determination of the forming limit diagrams of thin steel sheets. This method uses the correlation technique to determine the displacement field between two images taken on the same area of the sample at two different strain levels. The strains are calculated from this field. The range of strains determined between two images may be very wide. This allows to compare the initial image to one before the sample fracture or two successive images during the straining. This method shows that the strain localization may occur early during the forming process and so the onset of localized necking is not a sudden phenomenon. A method is proposed to draw the forming limit diagrams for necking.

A computational method for generating the free-surface neck-down profile for glass flow in optical fiber drawing

Abstract: A combined analytical and numerical approach, based on the transport equations and surface force balance, has been developed for the generation of the neck-down profile of an optical fiber during the drawing process. This is a fairly complex but important circumstance, which involves modeling the flow of glass under large temperature differences and large changes in viscosity and cross-sectional area. An axisymmetric, laminar flow is assumed in the glass and in the circulating inert gases. The governing transport equations are solved employing a finite difference method. The radially lumped axial velocity, the normal force balance, and the vertical momentum equations are used to obtain a correction scheme for the neck-down profile. After a new corrected profile is obtained, the full governing equations are solved for the flow and heat transfer, considering both radiation and convection transport. This process is continued until the necking shape does not change from one iteration to the next. The necking ...

Necking in rectangular tensile bars approximated by a 2-D gradient dependent plasticity model

Abstract: Necking and post-necking of a uniaxially stretched tensile test specimen with a rectangular cross-section is investigated. The analysis is based on an enhanced 2-D plane stress finite element model, where the third dimension (the thickness effect) is taken into account by an incorporated length scale. The length scale, fixed with respect to the current deformed state, is incorporated in the continuum description by a finite strain version of a gradient dependent J 2 -flow theory. A convincing agreement with the true 3-D post-necking behaviour is obtained by this approximative 2-D plane stress model. The model gives a realistic prediction of the development of the post-necking zone in the tensile bar. Furthermore, the model is found to capture the transition from a dominating diffuse necking mode for a tensile bar with a square cross section to a dominating oblique localised necking mode for a wide strip; effects which can not be captured by an analysis based on a conventional (local) plane stress model.

High-temperature large strain viscoelastic behavior of polypropylene modeled using an inhomogeneously strained network

Abstract: The effects of microstructural rearrangements during the stretching of semicrystalline polymers and the resultant inhomogeneous strains are modeled by rigid spheres embedded in a polymer network. This results in strain concentrations in the network, which is then caused to yield at realistic overall strains. To simulate the collapse of the original spherulitic morphology, the radii of the spheres decrease at a rate dependent on the shear stress imposed on them by the surrounding network. This results in time-dependent behavior. The resultant large strain viscoelastic model is implemented in a commercial finite element code and used to predict shapes of necking polypropylene sheet specimens at 150°C. Rate dependence of stress and stress relaxation are also predicted, and the model is shown to be generally effective in its predictions of shapes and forces up to large deformations.

Effects of injection molding–induced morphology on the work of fracture parameters in rubber‐toughened polypropylenes

Abstract: The effects of the injection-molding induced skin-core morphology on the fracture behavior of rubber-toughened polypropylene (RTPP) systems were studied by employing the essential work of fracture (EWF) method. RTPP with 31 wt% ethylene/ propylene rubber (EPR) showed no skin-core structure after molding and the EWF approach worked well in this case. In contrast, RTPP with 10 wt% EPR exhibited a pronounced skin-core morphology: EPR depletion and enrichment was observed in the skin and core region, respectively. This morphology caused necking instead of crack growth in deeply double edge-notched (DDENT) specimens under tensile loading along the mold filling direction (MFD). The necking process not only was accompanied by a large scatter but also yielded highly unrealistic specific essential work of fracture (w e ) values. This skin-core structure was also the reason for an anistropic EWF response of this system observed by loading the specimens both in longitudinal (L) and transverse (T) directions to the MFD. The failure sequence and its characteristics were studied by light microscopy (LM) and infared thermography (IT). It was concluded that the EWF approach cannot be applied for RTPP with a prominent skin-core structure. Since yielding preceded the limited crack growth prior to necking in the loading direction for the DDEN-T specimen of RTPP with 10 wt% EPR, the yielding-related specific essential work (w e,y ) was used for toughness comparison. In case of RTPP with 31 wt% EPR, where yielding was less pronounced prior to the crack growth, the work of fracture until the maximum load was assigned to the yielding-related work of fracture (w f,y ) used for computing w e,y . The latter value seems to be closely matched to the plane-strain essential work of fracture value.

Fracture characterization of low-density polyethylenes by the essential work of fracture: Changes induced by thermal treatments and testing temperature

Abstract: The tensile deformation and fracture behavior of commercially available low-density polyethylene (LDPE) films, having different molecular characteristics, was studied. Submitting samples to specific thermal histories controlled the morphological structure of these semicrystalline polymers. Phase-structure analysis of the resulting materials was performed by DMA and DSC analyses. The plane-stress essential work of fracture methodology was chosen because the materials used had failed after complete necking of the remaining ligament. Significant differences in behavior, induced by thermal treatments, were found for the tensile yield stress and the specific nonessential work of fracture, but not in the specific essential work of fracture. The results show that the mechanical properties and fracture behavior depend not only on the crystallinity levels and molecular weight characteristics of the samples, but also upon the degree of structural continuity. The β-relaxation process, associated with the crystal-amorphous interphase, strongly influences the fracture behavior at testing temperatures chosen below the β-relaxation temperature. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 781–796, 1999

Studies of Elastic-Plastic Instabilities

Abstract: Analyses of plastic instabilities are reviewed, with focus on results in structural mechanics as well as continuum mechanics. First the basic theories for bifurcation and post-bifurcation behavior are briefly presented. Then, localization of plastic flow is discussed, including shear band formation in solids, localized necking in biaxially stretched metal sheets, and the analogous phenomenon of buckling localization in structures. Also some recent results for cavitation instabilities in elastic-plastic solids are reviewed.

A nonlocal two-dimensional analysis of instabilities in tubes under internal pressure

Abstract: Studies of the post-bifurcation behaviour and imperfection-sensitivity of elastic–plastic tubes under internal pressure are carried out. When increasing enclosed volume is prescribed, the first critical bifurcation mode for cylindrical tubes is an axisymmetric non-cylindrical mode occurring shortly after the maximum pressure point. Thereafter, bifurcation into a non-axisymmetric mode occurs, leading to localized necking of the tube wall in the hoop direction. A 2-D membrane analysis based on a conventional (local) plasticity theory shows the bifurcations into the axisymmetric and non-axisymmetric modes. However, a full 3-D analysis is required to give an accurate description of the neck development on one side of the tube wall. If the axial variation in the deformation pattern is neglected, the analysis of neck development is reduced to a 2-D plane strain problem. In the present work, the 3-D post-bifurcation behaviour is approximated by a 2-D nonlocal membrane finite element analysis. The third dimension (the thickness direction) is taken into account in the continuum description by an incorporated length scale based on the current thickness of the tube wall. In the case of post-necking behaviour of stretched thin sheets, this has been found to give a good approximation of the real 3-D post-necking behaviour. Results for the post-bifurcation behaviour of the tube under internal pressure are presented.

Continuum mechanics characterization of plastic deformation-induced oxide film rupture

Abstract: The film rupture behaviour of dynamically strained metastable Ti-15wt% Mo-3wt% Nb-3wt% Al in the solution-treated and aged (STA) (β + α) condition that is prone to coplanar slip was examined. Film rupture was detected by rapid data acquisition (10 000 Hz, 40 nA resolution) of repassivation current transients on fatigue precracked, circumferentially notched, and smooth tensile specimens. Finite element modelling of notch stress and strain fields was conducted to correlate the onset of film rupture with continuum mechanics analysis of notch stress and strain fields. Discrete film rupture repassivation transients were only observed in notched and smooth specimens when local notch stresses exceeded the uniaxial tensile yield strength of the STA alloy over a depth of about four grain diameters, and upon necking, respectively. Such extensive plastic deformation was a necessary but not sufficient criterion for observation of discrete current transients. Local plastic strain rates exceeding 1.4 × 10−5s−1...

Cavitation behaviour in fine grain 3Y-TZP during tensile and compressive superplastic flow

Abstract: Studies of cavitation in Y-TZP during superplastic flow have been made for both tensile and compressive deformation conditions. It was observed that the morphologies of cavities near the fracture faces of tensile specimens varied markedly with testing conditions and in most cases differed from those near the gauge heads. Two quite different forms of cavitation behaviour were observed leading to high and low strains to failure, respectively. For optimum conditions of superplastic flow, of high temperature/low strain rate (low stress), when large elongations were observed, cavities were either spherical or elongated parallel to the tensile axis. Those near the fracture face interlinked in a plastic (necking) mode to give transverse cavities and subsequent failure. At high strain rate/low temperature (high stress), transverse intergranular cracking played a dominant role in failure at low elongations. For intermediate conditions of temperature/strain rate, elongated cavities developed parallel to the tensile axis, but near the fracture face these usually interlinked by transverse cracking. These conditions were associated with intermediate elongations to failure. For the assessment of cavity growth mechanisms, artificial pores were introduced into fine grain Y-TZP specimens and changes in their shape and size during tensile or compressive deformation were investigated. Results show that the change of pore volume, in the superplastic regime, is controlled by plastic deformation of the matrix and can be described by the relationship of dR/dɛ = ;ηR, where ɛ is the true strain, η the cavity growth rate parameter and R is the radius of the pore.

Application of a necking criterion to PET fibers in tension

Abstract: A criterion to predict instability in rate-dependent materials is developed. It is implemented for PET fibers in tension at three temperatures: 60, 75, and 80°C. At 60°C, necking is always observed, whereas at 80°C, the deformation is uniform, and 75°C marks a transition region, where necking is observed only at higher speeds and the deformation is otherwise uniform. As a necessary tool in the implementation of this criterion, the stress-strain behavior of PET is modeled using a combination of an Eyring process, a Gaussian network, and a linear elastic element. The resulting instability model gives predictions that are generally consistent with the experimental observations at all temperatures.