Showing papers on "Necking published in 1997"

On crystal plasticity FLD analysis

Abstract: This paper is concerned with the computation of forming limit diagrams (FLDs) using a rate-sensitive polycrystal plasticity model together with the Marciniak–Kuczynski approach. Sheet necking is initiated from an initial imperfection in terms of a narrow band. The deformations inside and outside the band are assumed to be homogeneous and conditions of compatibility and equilibrium are enforced across the band interfaces. Thus, the polycrystal model needs only to be applied to two polycrystalline aggregates, one inside and one outside the band. Each grain is modelled as an FCC crystal with 12 distinct slip systems. The response of an aggregate comprised of many grains is based on an elastic–viscoplastic Taylor‐type polycrystal model developed by Asaro and Needleman (1985). The effects of initial imperfection intensity and orientation, initial distribution of grain orientations, crystal elasticity, strain rate sensitivity, single slip hardening and latent hardening on the FLD are discussed in detail. The predicted FLD is compared with experimental data for an aluminium alloy sheet.

Deformation, fracture, and mechanical properties of low-temperature-tempered martensite in SAE 43xx steels

Abstract: Uniaxial tensile tests were performed on 4330, 4340, and 4350 steels in the as-quenched (AQ) condition and after quenching and tempering at 150 °C, 175 °C, and 200 °C for times of 10 minutes, 1 hour, and 10 hours, respectively. Strength parameters decreased and ductility parameters increased continuously with increasing tempering. Mechanical properties are presented as a function of tempering conditions and steel carbon content, and hardness and ultimate strength changes are given as a function of Hollomon—Jaffe tempering parameters. All tempered specimens, except for some lightly tempered 4350 specimens, deformed plastically through necking instability and failed by ductile fracture. The stresses required for the ductile fracture, estimated from an analysis of the interfacial stresses at particles in the neck at fracture, showed no systematic variation with carbon content or tempering conditions despite significant variations in deformation and strain hardening. The AQ specimens of the 4340 and 4350 steels, and some of the lightly tempered 4350 steels, failed by brittle mechanisms. The deformation and fracture of the low-temperature-tempered 43xx steels are discussed in terms of the changes in fine structure, namely, the formation of transition carbides and a rearranged dislocation substructure that evolve from an AQ martensitic substructure consisting of dislocations with and without carbon atom segregation.

Crystallinity improvement of Bi2Sr2CaCu2O8+δ single crystal by TSFZ method

Abstract: High-quality Bi2Sr2CaCu2O8+δ single crystals have been grown successfully by the traveling solvent floationg zone (TSFZ) method with the necking technique. The crystallinity was characterized by a double-crystal X-ray diffractometry. The full-width at half maximum (FWHM) of the rocking curve was improved from 120 arcsec to 75 arcsec by the necking technique using a single crystal seed.

Resistance Spot Weld Failure Loads and Modes in Overload Conditions

Abstract: The failure modes of two single-weld specimens, the coach-peel and the tensile-shear specimens, were studied in detail. Weld overload experiments, along with optical and scanning electron microscopy, revealed that the coach-peel specimen failed by microvoid coalescence (ductile fracture) near the weld nugget/heat affected zone (HAZ) boundary and that the tensile-shear specimen failed predominately by localized necking (shear localization) near the HAZ/base metal boundary. Empirical data extracted from measurements performed on metallurgical cross sections of interrupted coach-peel and tensile-shear specimens established the deformed characteristic material distance (coach-peel) and the existence of a critical thickness strain for localized necking (tensile-shear). These quantities were used to predict weld failure via finite element analysis as described in Ref I. The work presented here is the first step in a larger project that is focused on developing a methodology for predicting spot weld overload failure in detailed finite element simulations of spot-welded joints. This methodology is based upon the failure phenomena (as reported here) and detailed characterization of the HAZ (as reported in Ref I). The main requirement of this predictive methodology is that it be adaptable to any combination of joint configuration and loading direction. This predictive methodology will serve as the basis for the final step of developing a model of resistance spot weld failure based upon a simpler representation of the spot weld that can be used in car crash simulation models.

A Unified Damage Approach for Predicting Forming Limit Diagrams

Abstract: Plastic deformation in sheet metal consists of four distinct phases, namely, uniform deformation, diffuse necking, localized necking, and final rupture. The last three phases are commonly known as nonuniform deformation. A proper forming limit diagram (FLD) should include all three phases of the nonuniform deformation. This paper presents the development of a unified approach to the prediction of FLD to include all three phases of nonuniform deformation. The conventional method for predicting FLD is based on localized necking and adopts two fundamentally different approaches. Under biaxial loading, the Hill's plasticity method is often chosen when α (= ∈ 2 /∈ 1 ) 0 or when the biaxial stretching of sheet metal is significant. The M-K method, however, suffers from the arbitrary selection of the imperfection size, thus resulting in inconsistent predictions. The unified approach takes into account the effects of micro-cracks/voids on the FLD. All real-life materials contain varying sizes and degrees of micro-cracks/voids which can be characterized by the theory of damage mechanics. The theory is extended to include orthotropic damage, which is often observed in extensive plastic deformation during sheet metal forming. The orthotropic FLD model is based on an anisotropic damage model proposed recently by Chow and Wang (1993). Coupling the incremental theory of plasticity with damage, the new model can be used to predict not only the forming limit diagram but also the fracture limit diagram under proportional or nonpropor-tional loading. In view of the two distinct physical phenomena governing the cases when α (=∈ 2 /∈ 1 ) 0, a set of instability criteria is proposed to characterize all three phases of nonuniform deformation. The orthotropic damage model has been employed to predict the FLD of VDIF steel (Chow et at., 1996) and excellent agreement between the predicted and measured results has been achieved as shown in Fig. 1. The damage model is extended in this paper to examine its applicability and validity for another important engineering material, namely aluminum alloy 6111-T4.

Extensional styles and gravity anomalies at rifted continental margins: Some North Atlantic examples

Abstract: Regional isostatic adjustment of the buoyancy forces created by lithospheric stretching during rifting is used to predict the crustal structure and gravity anomalies across rifted continental margins. Following earlier studies, we assume that stretching and necking of the lithosphere occurs around a “depth of necking,” which is the level of no vertical motion in the absence of gravitational forces. Differences in the depth of necking, coupled with lateral variation in flexural rigidity, can account for many of the variations in tectonic style observed across rifted continental margins and associated rifted basins. We investigate here seven transects crossing the rifted margin around the North Atlantic which display considerable variations in subsidence, crustal thickness variations, and gravity signatures. These are located where high-quality seismic data are available as a constraint. Two conjugate margin segments are included to test for asymmetry in depth of necking which might be evidence of a simple shear mode of extension. Results suggest that both shallow (3 to 10 km) and deep (20 to 25 km) depths of necking occur. The depth of necking appears to be related to the intrinsic strength maximum within the lithosphere, rather than to the depth of preexisting structure. Shallower depths of necking may result from heating of the lithosphere during extension which decreases the depth of maximum strength. Deeper depths of necking may occur when the rates of extension are low and significant heating of the lithosphere does not occur. The depth of necking on at least one margin transect gives results very similar to a locally (Airy) compensated model, even though the lithosphere exhibits finite strength. Both conjugate margin segments display shallow depths of necking and favor a pure shear rather than a simple shear mode of extension.

Relationships between molecular and plane-stress essential work of fracture parameters in amorphous copolyesters

Abstract: The plane-stress fracture toughness of amorphous copolyester (aCOP) sheets of different intrinsic viscosity (IV) was determined by the essential work of fracture (EWF) concept using tensile-loaded deeply double-edge notched (DDEN-T) specimens. It was found that the specific essential work of fracture (we) is a composite parameter: its constituents are relied on yielding (we,y) and necking (we)/ respectively. The we values, and especially we,y did not change as a function of IV. This finding along with the fact that the mean entanglement length of the aCOP series was constant, suggest that we,y (which is related to the critical plane-strain toughness value) is likely dependent on the entanglement network. This assumption was reasoned by the observation that the plastic zone was completely recovered after annealing the specimen beyond the glass transition temperature (Tg). Recall that the shape recovery in case of cold-drawing (i.e. deformation below Tg) is controlled by the initial entanglement network structure in amorphous polymers.

Advanced methods in materials processing defects

Abstract: Damage Modeling . On the dynamic cavitation in solids (L. Badea, M. Predeleanu). A ductile damage model including shear stress effect (J.C. Boyer, C. Staub). A mesoscopic approach of ductile damage during cold forming processes (G. Brethenoux et al). A fully coupled elasto-plastic damage theory for anisotropic materials (J.F. Charles et al. Mathematical modelling of dynamical deforming and combined microfracture of damageable thermoelastoviscoplastic medium (A.B. Kiselev). A mathematical model for the formation and development of defects in metals (V.L. Kolmogorov, V.P. Fedotov, L.F. Spevak). Healing of metal microdefects after cold deformation (V.L. Kolmogorov, S.V. Smirnov). Damage Evaluation and Rupture . The influence of critical defect size in a ceramic of alumina elaborated by process sol-gel route (N.A. Almeida Camargo, M. Murat, E. Bittencourt). Defect evolution during machining of brittle materials (A. Chandra et al). Modeling the influence of gradients in strength on the evolution of damage in metals (P.R. Dawson, D.J. Bammann, D.A. Mosher). On the fracturing of brittle solids with microstructure (I.St. Doltsinis). Fracture prediction of sheet-metal blanking process (R. Hambli et al). Elastic-plastic finite-element modelling of metal forming with damage evolution (P. Hartley et al). Processing of zinc oxide varistors: sources of defects and possible measures for their elimination (A.N.M. Karim, S. Begum, M.S.J. Hashmi). Analysis of metallic solid fractures by quasimolecular dynamics (Y.S. Kim, J.Y. Park). Damage framework for the prediction of material defects: identification of the damage material parameters by inverse technique (F. Lauro et al). Damage influence in the finite element computations for large strains elastoplastic mechanical structures (P. Picart, G. Piechel, J. Oudin). Microplasticity and tensile damage in Ti-15V-3Cr-3A1-3Sn alloy and Ti-15V-3Cr-3A1-3Sn/SiC composite (W.O. Soboyejo et al). Strain Localization and Instability Analysis . Defects in hydraulic bulge forming of tubular components and their implication for design and control of the process (M. Ahmed, M.S.J. Hashmi). Numerical and experimental analysis of necking in 3D sheet forming processes using damage variable (M. Brunet, S. Mguil-Touchal, F. Morestin). Localization of deformation in thin shells with application to the analysis of necking in sheet metal forming (J.C. Gelin, N. Boudeau). Microcrack induced bifurcation of stress-strain relations for sintered materials (D.G. Karr, S.A. Wimmer). Instability analysis for ellipsoidal bulging of sheet metal (D.W.A. Rees). Formability Characterization . Compression of a block between cylindrical dies and its application to the workability diagram (S. Alexandrov, N. Chikanova, D. Vilotic). Sheet metal formability predicted by using the new (1993) Hill's yield criterion (D. Banabic). Characterization of the formability for aluminum alloy and steel sheets (F. Barlat et al.

Necking mechanism and its elimination in uniaxially drawn films of poly(ethylene naphthalate) (PEN)/polyetherimide (PEI) blends

Abstract: The influence of blend composition on the deformation behavior of cast amorphous PEN/PEI blends were investigated above their respected glass transition temperatures. PEN inherently shows a sharp necking phenomenon when stretched at temperatures as high as 20°C above its glass transition temperature. This was attributed to highly localized rapid alignment of naphthalene planes parallel to the surface of the films. The addition of PEI was observed to reduce this necking behavior. The neck formation completely disappears when the PEI fraction exceeds 10% in the blend. X-ray studies indicate that the increase of PEI hinders the rapid alignment of naphthalene planes parallel to the surface of the films. The presence of PEI chains in the blend was found to increase the overall friction between the polymer chains in the system and this was found to prevent the formation of highly localized necks. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 2059–2074, 1997

Plastic-flow and microstructure evolution during hot deformation of a gamma titanium aluminide alloy

Abstract: The hot workability of a near gamma titanium aluminide alloy, Ti-49.5Al-2.5Nb-1.1Mn, was assessed in both the cast and the wrought conditions through a series of tension tests conducted over a wide range of strain rates (10−4 to 100 s−1) and temperatures (850 °C to 1377 °C). Tensile flow curves for both materials exhibited sharp peaks at low strain levels followed by pronounced necking and flow localization at high strain levels. A phenomenological analysis of the strain rate and temperature dependence of the peak stress data yielded an average value of the strain rate sensitivity equal to 0.21 and an apparent activation energy of ∼411 kJ/mol. At low strain rates, the tensile ductility displayed a maximum at ∼ 1050 °C to 1150 °C, whereas at high strain rates, a sharp transition from a brittle behavior at low temperatures to a ductile behavior at high temperatures was noticed. Dynamic recrystallization of the gamma phase was the major softening mechanism controlling the growth and coalescence of cavities and wedge cracks in specimens deformed at strain rates of 10−4 to 10−2 s−1 and temperatures varying from 950 °C to 1250 °C. The dynamically recrystallized grain size followed a power-law relationship with the Zener-Hollomon parameter. Deformation at temperatures higher than 1270 °C led to the formation of randomly oriented alpha laths within the gamma grains at low strain levels followed by their reorientation and evolution into fibrous structures containing γ + α phases, resulting in excellent ductility even at high strain rates.

Staggered die method and apparatus for necking containers

Abstract: A necking appatus for producing a smooth, inwardly tapered necked-in portion on a cylindrical container (16) includes a plurality of necking modules and a turret (70) which is rotatably mounted in each module about an axis of rotation. Each turret includes an upper turret frame (76) which is mounted on the axis of rotation and which can be moved axially relative to the turret and a lower turret frame (74). A plurality of necking dies are mounted on the upper turret frame, and a plurality of container supports (120) are axially aligned with the necking dies and are mounted on the lower turret frame for axial movement. Each necking die includes a necking portion (204) for engaging and necking a side wall of a container as the aligned container support moves a container toward the necking die. The positions of the necking dies are adjusted by spacers (310) so that the necking portion of each die does not engage the tapered necked-in portion (211) of the container as the container support is moved toward the die.

The effect of Al on mechanical properties and microstructures of Fe-32Mn-12Cr-xAl-0.4C cryogenic alloys

Abstract: The effect of Al addition (0–3 wt%) on tensile properties and microstructures of Fe-32Mn-12Cr- x Al-0.4C cryogenic alloys were investigated at temperatures ranging from −196 to 250 °C. The Al is an austenite stabilizer suppressing the formation of the strain induced ɛ -martensite, while it behaved as a δ -ferrite stabilizer when added to 3 wt%. The Fe-32Mn-12Cr-0Al-0.4C alloy showed the strain induced ɛ -martensite after tensile deformation at −196 °C. Deformation twins were observed in deformed cryogenic alloys except Fe-32Mn-12Cr-2Al-0.4C alloys at temperatures ranging from −196 to 25 °C. The formation of both the deformation twins and the strain induced ɛ -martensite enhanced the tensile elongation by retarding local necking. The Fe-32Mn-12Cr-(0,1,3)Al-0.4C alloys exhibited elongation peaks within a temperature range forming the deformation twins. As the stacking fault energy increases with increasing Al content, the elongation peak shifted to lower temperature with increasing Al content in Fe-32Mn-12Cr- x Al-0.4C alloy. The continuous formation of strain induced phases, deformation twins and ɛ -martensite, up to a large strain was important to increase the tensile elongation of Fe-32Mn-12Cr- x Al-0.4C cryogenic alloys.

Stable web having enhanced extensibility and method for making the same

Abstract: The present invention provides a stable material having enhanced extensibility and a method for making the same. A tensioning force is applied to a neckable material to neck the material. The necked material is then subjected to mechanical stabilization to provide a stabilized extensible necked material. The stabilized extensible necked material is easily extended in a direction parallel to the direction necking.

Time and temperature dependent deformation of poly(ether ether ketone) (PEEK)

Abstract: The stress-strain behavior in tension and the effect of temperature on the creep of poly(ether ether ketone) (PEEK) have been studied. At room temperature, ∼130° below the glass-transition temperature, the material does not become brittle, and the specimens show necking in tension over a wide range of elongation rates. The stress and strain at yield and the strain at break are almost linear functions of the logarithmic elongation rate. The values of stress and strain at yield increase slightly with increasing elongation rate, while the strain at break decreases markedly. The short-term creep tests were conducted at temperatures extending from 20 to 200°C. The glass-transition temperature was found to be about 155°C. The creep of PEEK is greatest at temperatures above 130°C. In the glass region the time dependence of the deformation is much weaker. It has been found that the time-temperature relation for PEEK corresponds well with its thermorheological simplicity in the temperature range investigated. The data on the temperature shift factor below and above the glass-transition temperature may be fitted separately to the Arrhenius and Williams-Landel-Ferry (WLF) equations, respectively. The long-term creep tests show that PEEK has excellent creep resistance at room temperature. After 14-month tests at a stress level of 30 MPa the total strain exceeds the instantaneous elastic strain only by a factor of 1.15.

On the Stability of Biaxial Stretching With Application to the Optimization of Superplastic Blow-Forming

Abstract: The instability of biaxial stretching of thin sheets of viscoplastic metals under plane stress conditions is investigated using a linear stability analysis. An instability criterion for biaxial stretching is developed based on the assumption that localized necking initiates along the direction perpendicular to the major principal stress direction. Various optimum variable strain rate paths, which ensure a stable deformation of the sheet without neck formation, are computed for different strain ratios based on the instability analysis. The variable strain rate paths are applied in the finite element modeling of the superplastic uniaxial extension of a tabular specimen and superplastic blow-forming of a hemisphere. A reduction of forming time is achieved compared with the established constant strain rate forming method, while uniformity in the thickness distribution of the formed parts are maintained.

Temperature and strain rate dependence of yield strain and deformation behavior in polyethylene

Abstract: The deformation behavior of a range of polyethylene materials which differ with respect to both their short-chain branch content and molecular weight has been studied. Mechanical measurements carried out over a wide range of temperatures have shown that there is a sudden transition in the measured tensile yield strain at a temperature which is dependent on both the grade of material and the applied strain rate. Above the transition temperature all of the materials behave in a nonlinear viscoelastic manner and the wide-angle X-ray scattering patterns obtained have shown that at low applied strains reorientation of the lamellae is observed before necking. Below the transition temperature the materials all behave in an elastic-plastic manner and there is no evidence of lamellar reorientation before necking. This transition in yield mechanism is not apparent when considering the yield stress data alone. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 545–552, 1997

An atomistic study on the stretching of nanowires

Abstract: In this work we present an atomic-scale investigation of elastic and plastic deformation, and force variations in metal nanowires that are pulled from their ends. The atomic simulations are performed by using a molecular dynamics method with an empirical two-body potential; the effect of the initial size, shape, temperature and rate of stretching on the necking and fracture are investigated. We find that the necking occurs mainly due to the formation of a new layer with a smaller cross-section after every structural yield, and concurrently the tensile force falls abruptly. The relationship between the atomic structure and the conductance of the wire is analysed by constructing a realistic potential for the neck in terms of a linear combination of atomic pseudopotentials and by calculating the conductance using the transfer matrix method. Our results show that the variation of the conductance is strongly correlated with the sudden structural changes in the neck, and reflects the quantization of electronic states in the neck, but not the quantization of the conductance.

Modular can necking apparatus

Abstract: An apparatus (10) for progressively reducing a neck diameter of an open can is disclosed which comprises a plurality of identical modules (12) arranged side by side on a generally horizontal floor surface. Adjacent modules (12) are mated together with preferably four spaced datum plates (104) residing in a common vertical plane so as to triangulate and accurately align the modules (12).

Strain distribution in copper tensile specimens prestrained in rolling

Abstract: Sequences of orthogonal rolling-tension experiments were performed on polycrystalline copper sheets The effect of strain path change on subsequent yield and flow behavior has been investigated Optical microscopy and transmission electron microscopy (TEM) were used to clarify the physical mechanisms occurring during the second deformation The observed increase in yield stress in reloading was related to the change of slip systems corresponding to the glide of dislocations with a Burgers vector, which had not been active during prestrain The transient observed in the workhardening behavior after the path change corresponds to the appearance of disorganization in the dislocation microstructure It was shown that no special feature of slip behavior inside the grains can be related to the nonhomogeneous surface deformation observed at the beginning of reloading Also, the plastic instability of prestrained samples corresponding to the maximum load in tension does not seem to be directly controlled by the developed local substructure The nonuniform deformation observed in reloading was studied using a simplified macroscopic two-zone model It takes into account the presence of geometrical defects in the samples and considers the importance of the mechanical behavior The macroscopic results, concerning the delay of starting deformation in some regions, are explained by the model, which allows formulation of an analytical condition necessary for deformation to spread through the length of the sample before necking takes place

On the plastic deformation of bulk syndiotactic polypropylene

Abstract: The plastic deformation of syndiotactic polypropylene (sPP) bulk samples has been investigated. A structural comparison of the initial states before and after plastic deformation by necking is carried out by X-ray diffraction observations. Independent of the initial states (amorphous, semi-crystalline with different crystal phases), only the planar all-trans crystal form of sPP is present in the deformed samples after necking. Form these results, molecular mechanisms of the plastic deformation in the neck zone of semi-crystalline polymers will be discussed.

On the plastic behavior of homogeneous ethylene copolymers compared with heterogeneous copolymers

Abstract: The plastic behavior of homogeneous ethylene-octene copolymers and heterogeneous ethylene-butene copolymers has been compared on uniaxial tensile draw. True-stress-strain curves have been determined for various draw temperatures and strain-rates. Significant differences in yield behavior and strain-hardening have been revealed between the two types of materials, at equivalent crystallinity. In parallel, thermal analysis gave an indication that homogeneous copolymers have much narrow distributions of lamellae thicknesses together with lower values of the most probable thickness. Quantitative data from small-angle X-ray scattering support the latter point. An estimation of the surface free energy has revealed a more disordered chain-folding topology for the homogeneous copolymers. Interpretation of the mechanical behavior is based on the framework of a previous model for the plastic deformation of polyethylene involving competition of homogeneous and heterogeneous crystal slip processes. The former process governs the ability of the material to develop macroscopically homogeneous plastic deformation; the second process is a precursor to necking. It is proposed that the nucleation of dislocations, which is the basic mechanism of the homogeneous crystal slip, is favored for homogeneous copolymers, owing to the lower value of the most probable lamellae thickness. More tie molecules and chain entanglements in the disordered amorphous phase may also favor stable homogeneous plastic deformation in the case of homogeneous copolymers.