Showing papers on "Necking published in 1992"

A constitutive model for transformation plasticity accompanying strain-induced martensitic transformations in metastable austenitic steels

Abstract: We propose a constitutive model which describes the transformation plasticity accompanying strain-induced martensitic transformation in nonthermoelastic alloys. The model consists of two parts: a transformation kinetics law describing the evolution of the volume fraction of martensite and a constitutive law defining the flow strength of the evolving two-phase composite. The Olson-Cohen model for martensite volume fraction evolution is recast in a generalized rate form so that the extent of martensite nucleation is not only a function of plastic strain and temperature, but also of the stress state. A selfconsistent method is then used for predicting the resultant stress-strain behavior. The model describes both the hardening influence of the transformation product, and the softening influence of the transformation itself, as represented by a spontaneous transformation strain. The model is then implemented in a finite element program suitable for analysis of boundary value problems. Model predictions are compared with existing experimental data for austenitic steels. We present results from a few simple analyses, including tensile necking, illustrating the critical importance of stress state sensitivity in the evolution model.

Video-controlled tensile testing of polymers and metals beyond the necking point

Abstract: A novel technique has been developed to record the intrinsic plastic behaviour of ductile materials by monitoring the effective strain and the effective stress in the mid-plane of hour-glass-shaped tensile specimens. The method utilizes a computer-aided video extensometer which analyses the sample profile in real time. The effective strain is computed automatically from the minimum diameter, and the effective stress is deduced from the applied load by taking into account the stress triaxiality corresponding to the local radius of curvature of the sample profile. Furthermore, a digital closed-loop system controls the ram speed of the hydraulic tensile testing machine in such a way that the local effective strain rate is maintained at a constant value. It is shown that most polymeric and metallic materials are entitled to be investigated by this method, which gives access in real time to the constitutive plastic equation, up to strains far beyond the necking point. The capabilities of the technique are illustrated and discussed critically, with more details for two polymers of different structures: polyethylene and polycarbonate.

Lithospheric necking and regional isostasy at extensional basins 1. Subsidence and gravity modeling with an application to the Gulf of Lions Margin (SE France)

Abstract: We present a numerical pure-shear stretching model to study the effect of the “depth of lithospheric necking” on the state of flexure at extensional basins. This model avoids the need for low flexural rigidities during synrift basin subsidence. The model also accounts for long-standing rift flank uplifts in the absence of significant thermal anomalies or underplating beneath rift shoulders, and it predicts low β factors beneath basin centers. Numerical modeling of synthetic continental rift zones and rifted continental margins together with their gravity characteristics demonstrates that isostatic residual anomalies are sensitive indicators of the state of flexure at extensional basins, particularly at basin margins. Isostatic residual anomalies are particularly useful to study the state of lithospheric flexure because the results are not biased by assumptions on the loads that have to be made in a forward modeling approach. Previous studies of lithospheric flexure and gravity modeling might have underestimated flexural rigidities at extensional basins. Comparison of predicted gravity anomaly signatures with gravity data suggests that at narrow rift basins and young rifted continental margins, upward flexure occurs more commonly than does downward flexure. This can be explained by intermediate or deep levels of necking (>15 km). For rifted continental margins, the apparent transition in the state of flexure during basin evolution from upward to downward flexure points to intermediate levels of necking (15–20 km). The occurrence of intermediate to deep levels of necking at narrow rift basins and intermediate levels of necking at rifted margins is in accordance with brittle-ductile rheological models of the lithosphere. An intermediate depth range for the level of lithospheric necking at rifted continental margins is consistent with a scenario in which rifting preferentially occurs in an area where the lithosphere is weakened by a thickened crust Rifting in areas of stronger lithosphere, as for example cratons, is probably more often associated with a deep level of necking, explaining the widespread occurrence of rift shoulders at failed rift basins. We have tested several depths of necking and a model of local isostasy for the Gulf of Lions margin in the northwestern Mediterranean. At positions of deep synrift grabens, models with depths of necking of 25–35 km predict crustal thicknesses that are more in accordance with observations than are models with a shallower level of necking. It appears that local isostasy cannot account for the present-day basin configuration and at the same time reproduce the observed strongly laterally varying bathymetry at the end of rifting, supporting a significant postrift flexural rigidity.

On the coupled thermomechanical treatment of necking problems via finite element methods

Abstract: SUMMARY The necking process of a bar in an uniaxial tension test is influenced by the heat production due to inelastic deformations. Thus, for an analysis of this problem the thermomechanical coupling has to be considered. A finite element model and an associated algorithm are developed for this purpose. This computational tool allows the study of adiabatic processes as well as processes with heat flux. The analysis of the necking process of a perfectly cylindrical specimen shows that, in contrast to isothermal and adiabatic cases, no bifurcation occurs in the case where heat flux is considered. 1. INTRODUCTION A variety of experimental, analytical and numerical investigations have lead to a basic under- standing of the mechanisms pertaining to the diffuse necking process in a circular ductile bar tensile test. A number of papers have been published in which numerical simulations of this phenomenon within the framework of classical elastoplasticity can be found, see e.g. Chen6 or Needleman. Any advanced simulation of the necking problem should consider the fact that heat production due to dissipated mechanical work in plastic deformations will lead to temperature changes in the specimen when the test is performed at finite rates. In the context of a pure adiabatic process the associated bifurcation loads of cylindrical specimen has been investigated by Bruhns and Mielniczuk. Several numerical concepts for coupled thermomechanical processes have been developed in Argyris and Doltsinis2 and Argyris

Lithospheric necking and regional isostasy at extensional basins 2. Stress‐induced vertical motions and relative sea level changes

Abstract: We investigate long-wavelength differential vertical motions at extensional basins which are the result of temporal changes in the intraplate stress field in the lithosphere. These stress-induced vertical motions are intimately coupled to the state of flexure (flexural curvature) of the lithosphere. We compare a previous model of flexure under the sediment load only (FSL model) and a recent more consistent model, which incorporates regional compensation of other vertical loads induced by lithospheric extension as well. These additional loads are controlled by the depth at which the necking of the lithosphere occurs (DON model). Tlie FSL model and models assuming a shallow level of necking (≤15 km) are very similar, they predict tilting of the basin with the hinge point landward of the shelf edge. Compression results in uplift of the landward pan of the basin, which generally corresponds to the coastal plain or inner to middle shelf, and downwarping of the outer shelf and slope. The differential vertical motions correspond to relative sea level cycles which are out of phase in different parts of the basin. Internal architecture of systems tracts can be different from predictions by eustasy. By contrast, deeper levels of necking (>20 km) predict a uniform sense of motion landward of the shelf edge. Type I sequence boundaries can be very easily induced for these conditions, and sequence stratigraphie features are probably hard to distinguish from predictions by eustasy. These results are for a pure elastic plate rheology. Stress-induced vertical motions for a more realistic depth-dependent rheology are more complicated because of the additional effect of stress-induced reduction of flexural rigidity. For these conditions, gradual buildup of tension causes a complete relative sea level cycle. For high tensional stress levels, total vertical motions become rather similar to vertical motions for compression. This may be of importance for the issue of global synchroneity of relative sea level changes.

Extended Charles–Hillig Theory for Stress Corrosion Cracking of Glass

Abstract: The work originally performed by Charles and Hillig (C&H) on the chemical stress corrosion cracking of glass is based on the chemical reaction rate theory and restricts the analysis to only the kinetic change at the exact location of the crack tip. As a result, crack sharpening/blunting is predicted when the applied stress lies above/below the static fatigue limit. The present paper extends the investigation within the same physical framework to the geometric change of the entire cavity surface, particularly in the vicinity of the cavity apex region. It has been found that a physical-property-dependent parameter (m) exists which exerts a strong influence on the crack-tip morphology. In the case of m=mth, where mth is a threshold m which assumes a value of ∼ 45 for an elliptical cavity having a minor to major axes ratio of 0.01, the current predictions reduce to the C&H results. In general, however, m≠mth, and the single-valued fatigue limit degenerates into a range of applied stresses under which either enhanced blunting (m > mth) or necking (m 45, suggesting that enhanced blunting takes place at the crack tip when external loads are applied at a moderate level for a typical crack having an initial major to minor axes ratio > 100 in a soda–lime glass specimen.

Evolution of dislocation structures and deformation behavior of iron at different temperatures: Part I. strain hardening curves and cellular structure

Abstract: The deformation behavior of iron has been investigated at different temperatures by means of tension tests. There exist two temperature ranges for deformation. In the low-temperature range(T < 293 K), the flow stress σ, the work-hardening rate θ at e = 0.06, and the yield stress σy decrease with increasing temperature, but in the higher temperature range(T ≥: 293 K), σ and θ at the same strain increase while σy decreases more slowly. The change of dislocation density, with temperature, ate = 0.06 exhibits the same tendency as that of the flow stress. The strainhardening rates decrease almost linearly with increasing stress up to necking in the low-temperature range, except the initial strain range. At the higher temperature range, the hardening rates decrease linearly with stress only at the early stage of deformation, but above certain strains, the decreases become more gradual; that is, the G-cr curves deviate from the linear region. The evolution of dislocation structure has also been observed by transmission electron microscopy (TEM). The results show that a substructural transition takes place in the nonlinear range of G-cr curves. In the linear decreasing region of strain-hardening curves, the deformation is controlled by the uniformly distributed dislocations or cell multiplication prevails. However, in the nonlinear region of G-cr curves, cell multiplication seems to be balanced by cell annihilation.

Electron-beam-enhanced flow and instability in amorphous silica fibres and tips

Abstract: Amorphous silica structures which are a few nanometres in width and tens of nanometres in length are seen to become unstable under intense electron irradiation against plastic deformation, necking and failure. Similarly irradiated atomistically sharp tips, which are observed to be stable in crystalline materials, undergo rapid blunting in amorphous structures, caused by evaporation and enhanced viscous flow. The tip extremities separate into spherical bulbs by necking, and local clustering is seen during fluctuations in the microscopic structure. The observations provide information on the nature of microscopic diffusion and flow, during kinetic phenomena such as failure of amorphous structures.

Can necking apparatus with spindle containing pressurizing gas reservoir

Abstract: A method and machine for forming can necks in metal container bodies is disclosed. The machine comprises a pilot assembly coaxially situated and longitudinally movable with respect to and within a necking die member having an annular static die forming surface longitudinally advanced into contact with the can side wall defining the open end. Prior to necking, the pilot assembly is inserted into the open end and then stopped. Continued forward movement of the necking die member opens a valve between the pilot assembly and die member to flow pressurized fluid from a reservoir in the pilot to pressurize the can. This prevents crushing of the can under necking loads. The reservoir is located entirely within the pilot shaft and has a dimensional volume greater than the can body interior volume. This results in rapid delivery of pressurized fluid into the can before the greatest necking loads are applied to the side wall.

Tensile behavior of the L12 compound Al67Ti25Cr8

Abstract: Temperature-related variations in tensile yield strength and ductility were studied on cast, homogenized and isothermally forged Al67Ti25Cr8. Yield strength dropped discontinuously between 623 K and 773 K and then decreased gradually with increasing temperature. Below 623 K, fracture occurred prior to macroscopic yielding. Ductility decreased from 0.2 percent at 623 K to zero at 773 K, but increased again at higher temperatures. At 1073 K, an elongation of 19 percent was obtainable, and ultimate tensile strength and localized necking were observed. Fracture surfaces and deformed microstructures were examined. The 1073 K tensile specimen that exhibited 19 percent elongation showed grain boundary serrations and some evidence of recrystallization (likely dynamic) although fracture occurred predominantly via an intergranular mode.

The temperature and orientation dependence of tensile deformation and fracture in NiAl single crystals

Abstract: The tensile deformation and fracture behaviours of stoichiometric NiAl single crystals were investigated as functions of temperature and crystal orientation. Nominal stress-strain curves largely depended on temperature and crystal orientation. The flow strength was generally high for single crystals with orientation [001] and low for single crystals with orientations [ 1 11] and [ 1 22]. The tensile elongations remained low at low temperatures increased rapidly with increasing temperature, gave sharp and very high peaks at intermediate temperatures and then decreased rapidly with increasing temperature. The ductile-brittle transition temperature (DBTT) defined by the reduction in area (RA) occurred at a slightly higher temperature than the DBTT defined by the elongation and then the values of RA reached 100% at sufficiently high temperatures. At low temperatures, cleavage fracture with river patterns was observed and their preferential fracture planes were determined to be (011). At a temperature where the elongation peak was observed, the sample surfaces became corrugated and macroscopic fracture with river patterns proceeded along a plane perpendicular to stress axis without showing apparent necking. At high temperatures where the elongation decreased with increasing temperature, fracture was established by marked necking and exhibited knife-edge or chisel point fracturing, depending on the crystal orientation. On the basis of these results, a discussion of the plastic deformation and fracture mechanisms was attempted.

Strain-rate and temperature-dependent stress-strain curves of Sn-Pb eutectic alloy

Abstract: Tensile tests on cast Sn-Pb eutectic alloy have been carried out at 25, 100, 140, 170°C and several strain rates ranging from 7×10−3−7×10−5s−1. The stress-strain curves obtained were strongly dependent on strain rate and temperature. Under the conditions tested, higher strainrates gave a higher stress-strain curve and a larger strain at fracture. The tensile strength may be expressed by a power function of strain rate whose exponent and coefficient are governed by a kind of Arrhenius' equation. The nominal stress-strain curves showed significant work softening due to diffuse necking; however, the true stress-strain curve exhibited slight work softening. Thus the elastic perfectly viscoplastic model can be applied to the solder.

Forming limit diagrams calculated using Hill’s nonquadratic yield criterion

Abstract: Forming limit diagrams (FLD) are calculated based on an extension of previous analyses by Jones and Gillis[4,5,6] and Choiet al. [8,9] They idealized the sheet metal deformation into three phases: (I) homogeneous deformation up to maximum load, (II) deformation localization under constant load, and (III) local necking with a precipitous drop in load. They described the plastic behavior of sheet metals using a generalized quadratic flow law proposed by Jones and Gillis (JG). In the current analysis, Hill’s nonquadratic flow law for sheets having in-plane isotropy{su[101]} is used in conjunction with the three-stage deformation approximation. Calculated FLDs com- pare very favorably to experimentally determined results for aluminum-killed (AK) steel and aluminum alloys 2036-T4, 1100-H19, 5052-H32, 3003-0, and 3004-0. The comparison is fair for the titanium alloy Ti-6A1-4V. The agreement is poor for the strain rate-insensitive aluminum alloys 5052-0, 5052-H241, 5154-H111, and 6061-T4.

Relaxation in permanent networks

Abstract: Large-strain relaxation in permanent networks (natural rubber, PMMA) is explained by applying thermodynamics of irreversible processes and using the van der Waals network model. The memory function is shown to be strain-invariant. Independent Onsager processes characterized by the relaxation-time distribution are altogether coupled in the same manner to the global level. The macroscopically nonlinear response, including necking in the glass-transition regime is discussed.

Flow-induced on-line crystallization of rodlike molecules in fiber spinning

Abstract: The micromechanical description of nonisothermal flow-induced crystallization of a polymeric liquid with rodlike molecules is the main part of the fiber spinning model described here. Solutions of the governing equations show that an increase in winding velocity leads to the appearance of an on-line flow-induced crystallization zone in a fiber. This zone manifests itself in accelerated formation (necking) due to the release of heat of crystallization which results in the decrease of viscosity. Liquid crystallinity grows very rapidly in the necking region, which, in turn, leads to the growth of viscosity after some minimal value, which finally arrests fiber deformation.

Hard elastic polypropylene-nature, internal friction, and surface energy

Abstract: Tensile tests were performed at low temperatures, both in liquid and gaseous nitrogen and also at room temperature, using a series of polypropylene (PP) samples with various technological parameters. Crystalline morphology was also measured for film samples. The results show that liquid nitrogen or solvents can induce materials to create hard elasticity, which strongly supports the ‘bulk-microfibril composite structure” proposed by Baer et al., and suggests that the nature of hard elasticity is essentially a craze phenomenon. Three conditions of forming hard elastic structure are discussed. The results from long-time relaxation of hard elastic polypropylene (HEPP) and the improvement of necking of the PP samples in ethanol and water suggest that elastic recovery is reduced by internal friction. The relation between morphology and elasticity is also discussed. The methods of estimating the contribution of surface energy in the recovery process and the increase of surface energy of HEPP during the stretching process are provided. The contribution of surface energy to recovery is about 43% to 66% in the first cycle and after relaxation for 1 h at a maximum of 50% strain. The increased surface energy during stretching is about twice the recovery work done by surface energy.

On the rheology of cold drawing. II: Viscoelastic materials

Abstract: In this second paper in a series on cold drawing of polymeric fibers and films, asymptotic formulae are derived for the tension in thin bodies of nonlinearly viscoelastic materials subject to inhomogeneous stretching. The formulae, which are valid to within an error of fourth order in sample thickness, give the tension in fibers and films as functionals of the histories of the local stretch and its first two spatial gradients. It is shown that the theory obtained by taking the formulae to be exact is consistent with thermodynamical principles. Material response for various types of histories is discussed, and the theory is employed to calculate the creep response of fibers under static loads. Numerical solutions of the evolution equation for the stretch field in creep show that for an appropriate class of materials with slowly fading memory there is a range of applied loads for which an initially homogeneous deformation evolves into a well defined neck whose edges advance at high speed along the fiber and in so doing transform moderately stretched material into highly stretched (i.e., drawn) material. The calculated fiber profiles and the predicted dynamics of neck formation and growth are in good accord with familiar observations. A description is given of the circumstances under which one can use instantaneous (i.e., high speed) response functions to calculate fiber profiles in rapidly growing necks.

Mechanical Alloying of Immiscible Elements

Abstract: We propose for the first time, a quantitative thermodynamic explanation for the formation of solid-solutions of immiscible elements by mechanical alloying. It is shown how codeformation of a hard and a soft phase results in the formation of disc or needle shape particles possessing large aspect ratios. As the particle size drops to about 10nm with continued deformation, the particle tips and edges generate nanometer size fragments upon subsequent necking. Using simple thermodynamic arguments we show how otherwise immiscible atoms of these fragments will enter in solution and that this process can lead to their full dissolution.

The effects of rate sensitivity and plastic potential surface curvature on plastic flow localization in porous solids

Abstract: Plastic flow localization in porous elastic-viscoplastic solids is analyzed with an emphasis on the effects of material rate sensitivity and plastic potential surface curvature. The effect of rate sensitivity is included in a material model that accounts for a change of yield surface curvature in a rate-insensitive porous ductile solid. Shear band formation under plane strain and axisymmetric tension, and localized necking in biaxially stretched sheets are analyzed by using the present material model. The results illustrate the interactions of the effects of void nucleation and growth, material rate sensitivity and plastic potential surface curvature on plastic flow localization. The effects of nonproportional straining paths on localized necking in thin sheets are also demonstrated.

Bifurcations in elastic-damaging materials

Abstract: Continuum damage theories describe the progressive reduction in stiffness and strength of brittle materials resulting from the initiation and growth of microcracks and microvoids. When brittle materials are loaded into the nonlinear regime, they often exhibit localized zones of intense deformation and the eventual formation of macrocracks. Criteria for diffuse and discontinuous bifurcations have previously been developed and used to study the initiation of necking and localization in elastic-plastic materials. In this investigation, the same bifurcation criteria are applied to continuum damage theories. Since the bifurcation criteria depend on the fourth-order tangent modulus tensor, the first step in this investigation is the derivation of the tangent modulus tensor for a general continuum damage theory. An eigenanalysis of the symmetric part of the tangent modulus tensor is then shown to fully characterize the potential diffuse and discontinuous bifurcations associated with a given continuum damage theory.