Showing papers on "Strain hardening exponent published in 1994"

Strain gradient plasticity: Theory and experiment

Abstract: Dislocation theory is used to invoke a strain gradient theory of rate independent plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocation. The density of the geometrically necessary dislocations scales with the gradient of plastic strain. A deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening. The theory is a non-linear generalization of Cosserat couple stress theory. Tension and torsion experiments on thin copper wires confirm the presence of strain gradient hardening. The experiments are interpreted in the light of the new theory.

Deformation behaviour of ultra-fine-grained copper

Abstract: Mechanical behaviour and structural changes, such as the evolution of grain and dislocation structures and the formation of slip lines and grain-boundary-sliding traces, of a submicron-grained (SMG) copper during room-temperature compression have been studied. It is suggested that the absorption of dislocations into grain boundaries (GBs) is due to the migration and sliding of some highly non-equilibrium GBs during the deformation process and is influenced by high level internal stresses. From this point of view, the unusual behaviour of SMG copper, in particular, the high yielding and flow stresses, the absence of strain hardening, high plasticity and low strain rate sensitivity, are explained. Analogies of the mechanical behaviour of SMG copper with mechanical properties of metallic materials at large plastic strains in stage IV are discussed.

High melt strength, propylene polymer, process for making it, and use thereof

Abstract: Disclosed is a normally solid, high molecular weight, gel-free, amorphous to predominantly crystalline, propylene polymer characterized by high melt strength due to strain hardening which is believed to be caused by free-end long chain branches of the molecular chains forming the polymer. Also disclosed is a process for making the polymer by high energy radiation of a normally solid, high molecular weight, linear, propylene polymer in a reduced active oxygen environment, maintaining the irradiated material in such environment for a specific period of time, and then deactivating free radicals in the material. Further disclosed is the use of the strain hardening polymer in extensional flow operations such as, for example, extrusion coating, film production, and thermoforming.

Fabricated articles made from ethylene polymer blends

Abstract: The disclosed ethylene polymer compositions have et least one homogeneously branched substantially linear ethylene/α-olefin interpolymer and at least one heterogeneously branched ethylene polymer. The homogeneously branched linear or substantially linear ethylene/α-olefin interpolymer has a density from about 0.88 to about 0.935 g/cm3 and a slope of strain hardening coefficient greater than or equal to about 1.3. Films made from such formulated compositions have surprisingly good impact and tensile properties, and have an especially good combination of modulus and toughness.

On the Anelastic Flow with Damage

Abstract: Within the thermodynamics of irreversible processes and the concept of in ternal state variables, a general phenomenological theory of coupled damage-elasto- (visco)plasticity at small strains is g...

A nonproportionality parameter and a cyclic viscoplastic constitutive model taking into account amplitude dependences and memory effects of isotropic hardening.

Abstract: The present paper is concerned with the formultion of a viscoplastic constitutive model describing both cyclic hardening and cyclic softening under proportional and nonproportional loading conditions. First a nonproportionality parameter and the relevant internal structural tensor to describe the nonproportional hardening is discussed in detail. Internal variables and the related evolution equations to describe the amplitude dependence of cyclic hardening/softening are also examined. Then the history effects of cyclic hardening and softening are considered in the evolution equations of isotropic hardening variable. The proposed model is established by incorporating these equations into Chaboche model

The influence of particle distribution on the mechanical response of a particulate metal matrix composite

Abstract: A self-consistent model, based on Eshelby's equivalent inclusion method, has been developed to predict to flow of a particulate-reinforced alloy. The model gives excellent agreement with the measured elastic moduli for Al/SiC composites. Beyond the elastic limit, the model predicts an increase in the initial work hardening rate with increasing particle content. At large strains (above about 1%) the stress-strain behaviour of the composite is parallel to that of the unreinforced alloy. The results agree well with those obtained by Bao et al. [G. Bao, J. W. Hutchinson and R. M. McMeeking, Acta metall. mater.39, 1871 (1991)] using finite element methods, indicating that solutions based on average stress fields around particles do capture the essential features of composite strengthening. However, the current treatment can be readily extended to treat the effect of an inhomogeneous particle distribution on strength. As the degree of particle clustering increases, an increase in the rate of initial work hardening is predicted. Moreover, the strengthening ratio is increased substantially by clustering.

Kinematic hardening rules for simulation of ratchetting behavior

Abstract: The present authors formulated kinematic hardining rules on the assumption that each component of back stress, αi, has a critical state for its dynamic recovery to be fully activated. These rules have a feature that only the projection of plastic strain rate to the direction of αi contributes to the dynamic recovery. They are thus in contrast with the previous rules in which the accumulated plastic strain rate enters into the dynamic recovery term. We compare the present and such previous rules by applying them to multiaxial and uniaxial ratchetting experiments of modified 9Cr-1Mo steel at 550°C

Synthesis, processing, and deformation of bulk nanophase Fe-28Al-2Cr intermetallic

Abstract: Nanophase Fe-28Al-2Cr powder was obtained by ball milling and consolidated by shock wave compaction Fully-dense well-bonded compacts were produced with a diameter of 32 mm and a thickness of [approx]6 mm The grain size in the compacts was [approx]80 nm In tension, the nanophase intermetallic is brittle with a failure strength ([sigma][sub f] = 065 GPa) comparable to a coarse-grained intermetallic with similar composition In compression, the nanophase material exhibits superplastic-like flow during room temperature quasistatic deformation to true strains greater than 14 The compressive flow strength is 21 GPa and no macroscopic strain hardening is observed This behavior is compared to the coarse-grained material that has a yield strength of 025 GPa, displays significant work hardening and little tension-compression anisotropy TEM examination of the nanophase material before and after deformation shows a refinement of the microstructure during deformation The microstructure refines to [approx]10 nm grains surrounded by amorphous material

Shear and elongational flow properties of polypropylene meltsa)

Abstract: The rheological properties of polypropylene melts were investigated in oscillatory shear flow, capillary rheometry, and uniaxial elongation at constant tensile stress as well as constant strain rate. At small stresses the steady‐state elongational viscosity of linear conventional polypropylene has the threefold value of the shear viscosity. With increasing stress both the shear and elongational viscosity decrease. The transient elongational viscosity at constant strain rate is equal to the threefold value of the linear viscoelastic stressing viscosity as calculated from the relaxation time spectrum. In contrast, long chain branched polypropylene shows a maximum in the steady‐state elongational viscosity and pronounced strain hardening in experiments at constant strain rate above an elongation of e=1. These phenomena are obtained by less than three branches per molecule. The description of the strain hardening by means of the Lodge model underestimates the measured data at deformation rates less than e=0.2 s−1. An improvement is obtained by adding a rubber‐like stress component to the tensile stress.

Finite element simulations of shear localization in plate impact

Abstract: S hear band development in a tungsten heavy alloy (WHA) during pressure-shear plate impact is analysed numerically. The alloy has a microstructure of hard tungsten grains embedded in a soft alloy matrix. A two-dimensional, plane strain model of the alloy microstructure is used in the computations. For this model microstructure a fully coupled thermo-mechanical initial boundary value problem is formulated and solved, accounting for finite deformations, inertia, heat conduction, thermal softening, strain hardening and strain-rate hardening. Calculations are carried out for distributions of uniform grains and for micro-structures obtained from digitized micrographs of the actual alloy. The effects of variations in grain volume fraction and grain size are considered. Experiments and the numerical calculations show that the two phase alloy is more susceptible to shear banding than either of the constituent phases. While the onset of shear localization depends on the grain distribution and volume fraction, the shear band width is found to be set by heat conduction and is insensitive to the grain volume fraction and the grain morphology, The shear band width obtained from the calculations is in good agreement with what is observed in the experiments. Furthermore, the computed shapes of the deformed tungsten grains inside the band resemble closely the observed shapes of the deformed grains in the experiments.

Simulations of forest interactions and strain hardening in FCC crystals

Abstract: The strain hardening properties of FCC single crystals are examined with the help of a three-dimensional simulation of dislocation dynamics and interactions at mesoscale. The basic properties discussed are the line tension of the dislocations, the conditions at which sessile junctions are formed at the intersection of two slip systems and the stability of these locks. The relation between the flow stress and the square root of the intersecting dislocation density is examined in areal glide and in multislip conditions. A validation of the model is performed by comparison with experimental results on copper single crystals. At the small strains reached by the simulation and in multislip conditions, strain hardening is found to originate from the continuous increase of forest density rather than from the formation of immobile loops around clusters of forest obstacles. It is suggested that at larger strains a stabilizing mechanism, possibly cross-slip, should enhance the dislocation storage processes and initiate the formation of dislocation cells.

Influences of cell walls and grain boundaries on transient responses of an if steel to changes in strain path

Abstract: The effects of changes in strain path on plastic behaviour in sheets of an interstitial-free steel with two widely different grain sizes were investigated. The sheets were prestrained in rolling and, apart from supplementary tests, they were tested in uniaxial tension at 90° to the rolling direction. The results support the following conclusions. The magnitude of the increase in reloading yield stress and amplitude of the subsequent reduction in work hardening depend on the strength of dislocation walls generated in the prestrain rather than the grain size. The walls are more effective barriers to dislocation glide in freshly activated slip systems than to glide in the original slip systems operating in the prestrain. The primary cause of the subsequent reduction in hardening rate is disruption and partial dissolution of the original dislocation substructure. The final recovery in hardening rate is caused by generation of a new substructure compatible with the new deformation mode.

Development of microbands in mild steel during cross loading

Abstract: Mild steel specimens are submitted to a complex strain path (tension-shear sequence). The stress decrease recorded at the beginning of the second path is associated at the grain scale with a localization of the deformation in microbands. These microbands are associated with a single crystallographic slip system and carry the main part of the imposed strain. The prediction of the active slip systems during both the prestrain and the second path with the Taylor and static models leads to a necessary condition for the development of microbands: the slip system having the maximum Schmid factor must have been latent during the prestrain. At high strain level, the material resumes strain hardening and the dislocation structure is then composed of sheets parallel and/or perpendicular to the shear direction. The origin of the flow localization and the transition between the two types of structures, i.e. microbands and dislocation sheets, are then discussed.

Compressional behaviour of carbon fibres: Part IIModulus softening

Abstract: Spectroscopic-mechanical studies have been conducted on a range of carbon fibres by bonding single filaments on the top surface of a cantilever beam. Such a loading configuration allows the acquisition of the Raman spectrum of carbon fibres and the derivation of the Raman frequency strain dependence in tension and compression. Strain hardening phenomena in tension and strain softening phenomena in compression were closely observed. The differences in the slopes of the Raman frequency versus applied strain curves in tension and compression respectively, have been used to obtain good estimates of the compression moduli (...)

Numerical analysis of plasticity effects in the hole-drilling residual stress measurement

Abstract: The aim of this work was to analyze the effect of plasticity on residual stress measurement when the through thickness center-hole technique is used. The study investigated the effect of the most important loading, measuring, and material parameters, i.e., the residual stress intensity, the ratio between the principal residual stresses, the orientation of the strain-gage rusette with reference to the residual stress principal directions, the yield strength, and the strain hardening characteristics of the material. By means of a finite element simulation of the measurements, the errors that are usually produced by the direct use of ASTM E 837 (Test Method for Determining Residual Stresses by the Hole-Drilling Strain Gage Method) for the elaboration of the rosette strain gage readings was firstly determined by considering large enough ranges of the above-mentioned parameters to represent many conditions of practical concern. Afterwards it was shown that, at least within the limit of validity of the model, a considerable reduction of those errors can be obtained by using the proposed analytical procedure for elaborating the readings of a classical these elements strain-gage rosette. Moreover, the use of a new type of rosette with four radially oriented strain gages was proposed which could lead to further improvement of the measurement accuracy in any considered condition.

High melt strength, ethylene polymer, process for making it, and use thereof

Abstract: A normally solid, high molecular weight, gel-free, irradiated ethylene polymer is characterized by high melt strength due to strain hardening elongational viscosity, which is believed to be caused by free-end long chain branching of the molecular chains forming the polymer. The polymer is prepared by (1) irradiating a normally solid, high molecular weight ethylene polymer without strain hardening elongational viscosity while in the solid state in an environment in which the active oxygen concentration is less than 15% by volume, maintaining the irradiated material in this environment while in the solid state for a specific period of time, and then deactivating free radicals present in the material.

Low strain plasticity in a particulate metal matrix composite

Abstract: The strengthening that arises when reinforcing an aluminum alloy with approximately equiaxed shaped SiC particles has been measured, with careful attention paid to the elastic-plastic transition The results indicate that the majority of strengthening develops at low strains, due to the high initial strain hardening rate exhibited by these composite materials This can be interpreted in terms of stress partitioning to the second phase particles during the elastic/plastic transition and beyond The experimental results are compared with a self-consistent model based on Eshelby's equivalent inclusion method The model predictions are in good agreement with experimental data, once effects due to the inhomogeneous distribution of particles are incorporated

Strain-hardening and recovery during the creep of pure polycrystalline magnesium

Abstract: We report on creep and stress relaxation test results for pure polycrystalline magnesium. The experiments consisted of constant load creep tests conducted until steady-state was obtained followed by stress relaxation tests to study the strain-hardening and recovery behaviour of the materials. The tests were carried out over a range of applied stresses, 20–50 MPa, and test temperatures, 150–250°C, in order to determined stress and temperature dependencies of the high temperature plastic deformation behaviour. The strain-hardening coefficient, H , is derived from the experimentally generated steady-state creep rate, e s , and the dynamic recovery rate, R , data by using the well-known Bailey-Orowan relationship. It is found that the strain-hardening coefficient, H , during steady-state creep remains essentially constant with a magnitude of 0.27 E ( E is the elastic modulus) at 200°C and is independent of the applied stress. The creep strain rate is primarily determined by the recovery rate which is the rate determining mechanism during recovery creep. This set of experimental results is then examined in terms of creep equations and the dislocation network models for recovery creep deformation. It is shown that the present experimental data measured for pure polycrystalline magnesium lend support to the theoretical models based on dislocation link length distribution (dislocation network models) for recovery creep.

Anisotropic plasticity model for foams and honeycombs

Abstract: A three‐dimensional plasticity model is developed for foams and honeycombs. The model accounts for the transverse isotropy of foams and the orthotropy of honeycombs by incorporating a shift on stress that provides a yield surface in the form of a sphere with the centroid shifted from the origin in the principal stress space. To model the extensive strains that occur at constant stress, an elastic‐perfectly plastic formulation is used until a critical plastic volumetric strain is reached. Then the initiation of lockup is represented as an isotropic hardening function of plastic volumetric strain. Both elastic and plastic constants are given as functions of the initial density of the cellular material. With lockup, the elasticity tensor transforms to that of the parent solid. To account for strain‐rate effects, the plateau stresses and the hardening parameter are taken as functions of volumetric strain rate. For each material, experimental data are given for various densities and illustrative plots are give...

The double effect of grain size on the work hardening behaviour of polycrystalline copper

Abstract: Following the approach by Ashby, one can consider that strain compatibility between adjacent grains of a polycrystal generates geometrical dislocations. These dislocations participated in the strengthening mechanism in conjunction with statistically stored dislocations which are related to the single-crystal behavior. The dislocations of either species are indistinguishable and, as a whole, they may contribute to cell formation. The dislocation structure formed in a polycrystal is then a function of the major or minor intergranular accommodation complexity. At intermediate strain values the accommodation is distributed over the cells leading to a linear relationship between the tensile stress and the inverse of the cell size, whatever the grain size of the tested samples. The aim of the present work is to check that the presence of statistical and geometrical dislocations in the grains, as well as the fact that at the very early stage of plastic deformation the mean free path of dislocations is of the order of the grain size, leads to a double effect of the grain size on the work hardening behavior of polycrystalline copper. Moreover, careful analysis of the mechanical behavior of polycrystalline copper, including the microstructural aspects of plastic deformation, is performed, allowing the understanding of themore » relationship between the work hardening ratio and the grain size.« less

Constitutive description of work- and shock-hardened copper

Abstract: Constitutive models are an essential part of large-scale computational codes which describe material behavior, since they provide the relationship between stress ([sigma]), strain ([epsilon]), strain rate ([epsilon]), and temperature (T). However, plastic deformation is an irreversible and path-dependent process, and a number of parameters affect the development of the deformation structure and, as a consequence, the mechanical response. The stress state, strain rate, and temperature affect the evolution of the microstructure, and the strain, current temperature and strain rate alone are frequently not sufficient to describe it. The constitutive equations that have been developed fall broadly into two groups: (a) empirical constitutive equations; (b) microstructural-based constitutive equations. Work-hardened metals may undergo dynamic recrystallization if the deformation temperature is in the range of 0.4 to 0.5 T[sub m], where T[sub m] is the absolute melting temperature. This dynamic recrystallization is accompanied by marked changes in the thermomechanical response of the material, which are not addressed by the constitutive equations discussed. The objective of this note is to develop a procedure for incorporating these important microstructural evolution elements into the constitutive equations that describe plastic deformation.