Showing papers on "Strain hardening exponent published in 2003"

Model of plastic deformation for extreme loading conditions

Abstract: We present a model of metallic plastic flow suitable for numerical simulations of explosive loading and high velocity impacts. The dependence of the plastic strain rate on applied stress at low strain rates is of the Arrhenius form but with an activation energy that is singular at zero stress so that the deformation rate vanishes in that limit. Work hardening is modeled as a generalized Voce law. At strain rates exceeding 109 s−1, work hardening is neglected, and the rate dependence of the flow stress is calculated using Wallace’s theory of overdriven shocks in metals [D.C. Wallace, Phys. Rev. B 24, 5597 (1981); 24, 5607 (1981)]. The thermal-activation regime is continuously merged into the strong shock limit, yielding a model applicable over the 15 decades in strain rate from 10−3 to 1012 s−1. The model represents all aspects of constitutive behavior seen in Hopkinson bar and low-rate data, including a rapid increase in the constant-strain rate sensitivity, with 10% accuracy. High-pressure behavior is co...

Initiation of Dynamic Recrystallization in Constant Strain Rate Hot Deformation

Abstract: In constant strain rate tests, the occurrence of dynamic recrystallization (DRX) is traditionally identified from the presence of stress peaks in flow curves. However, not all materials display well-defined peaks when tested under these conditions. Using plain carbon, Nb-bearing and 321 austenitic stainless steels, it is shown that the onset of DRX can also be detected from inflections in plots of the strain hardening rate θ against stress a or, equivalently, from inflections in In θ-In a and In θ-e plots regardless the presence of stress peaks in the flow curves. These observations are verified by means of metallography. A unified description of the flow curve is introduced based on normalization of the stress and strain by the respective peak or steady state values. This approach reveals that, in a given material, the ratio of DRX critical stress to the peak or steady state stress is constant, as is that of the critical strain to the corresponding strain values. Furthermore, it is shown that the present technique can be used to establish the occurrence of DRX when this cannot be determined unambiguously from the shape of the flow curve.

The Role of Collinear Interaction in Dislocation-Induced Hardening

Abstract: We connected dislocation-based atomic-scale and continuum models of plasticity in crystalline solids through numerical simulations of dislocation intersections in face-centered cubic crystals. The results contradict the traditional assumption that strain hardening is governed by the formation of sessile junctions between dislocations. The interaction between two dislocations with collinear Burgers vectors gliding in intersecting slip planes was found to be by far the strongest of all reactions. Its properties were investigated and discussed using a multiscale approach.

On the relationship between microstructure, strength and toughness in AA7050 aluminum alloy

Abstract: The effect of process parameters such as quench rate and precipitation heat treatment on the compromise between the toughness and the yield strength of AA7050 aluminum alloy (AlZnMgCu) are investigated, as well as the anisotropy of this compromise in the rolling plane. Fracture toughness is experimentally approached by the Kahn tear test. The microstructure is studied quantitatively in detail by a combination of scanning electron microscopy, transmission electron microscopy and small-angle X-ray scattering, and the relative fractions of the various fracture modes as a function of microstructural state are quantitatively determined on scanning electron microscopy images. Toughness is confirmed to be minimum at peak strength, and lower for an overaged material than for an underaged material of the same yield strength. A lower quench rate is shown to result in an overall reduction of toughness, and in a reduced evolution of this toughness during the aging heat treatment. The overall toughness is also lowered when the main crack propagation direction is parallel to the preferential elongation direction of the coarse constituent particles (rolling direction). The competition between intergranular and transgranular fracture is explained in terms of the modifications of the work hardening rate, and of grain boundary precipitation. The evolution of fracture toughness is qualitatively explained in terms of evolution of yield stress, strain hardening rate, grain boundary precipitation and intragranular quench-induced precipitates.

Elongational viscosity of narrow molar mass distribution polystyrene

Abstract: Transient and steady elongational viscosity has been measured for two narrow molar mass distribution polystyrene melts of molar masses 200 000 and 390 000 by means of a filament stretching rheometer. Total Hencky strains of about five have been obtained. The transient elongational viscosity rises above the linear viscoelastic prediction at intermediate strains, indicating strain hardening. The steady elongational viscosities are monotone decreasing functions of elongation rate. At elongation rates larger than the inverse reptation time, the steady elongational viscosity scales linearly with molar mass at fixed elongation rate.

Tensile deformation behavior of aluminum alloys at warm forming temperatures

Abstract: Uniaxial tensile deformation behavior of three aluminum sheet alloys, Al 5182+1% Mn, Al 5754 and Al 6111-T4, are studied in the warm forming temperature range of 200–350 °C and in the strain rate range of 0.015–1.5 s −1 . Approaches have been made to process the selected aluminum sheet alloys so that the microstructural change during warm forming provides adequate recovery favorable to formability but does not deteriorate the post-forming properties. The total elongation in uniaxial tension is found to increase with increasing temperature and to decrease with increasing strain rate. The enhanced ductility at elevated temperatures is contributed primarily from the post-uniform elongation which becomes dominant at elevated temperatures and/or at slow strain rates. The enhancement of strain rate sensitivity ( m value) with increasing temperature accounts for the ductility improvement at elevated temperatures. The uniaxial tensile test is identified to serve as a screening test for ranking relative formability among different sheet alloys. Based on this criterion, the strain hardened 5xxx alloys (Al 5182+Mn and Al 5754) have shown better formabilities than the precipitation hardened alloy (Al 6111-T4).

Micromechanical modeling of the elasto-viscoplastic behavior of semi-crystalline polymers

Abstract: A micromechanically based constitutive model for the elasto-viscoplastic deformation and texture evolution of semi-crystalline polymers is developed. The model idealizes the microstructure to consist of an aggregate of two-phase layered composite inclusions. A new framework for the composite inclusion model is formulated to facilitate the use of finite deformation elasto-viscoplastic constitutive models for each constituent phase. The crystalline lamellae are modeled as anisotropic elastic with plastic flow occurring via crystallographic slip. The amorphous phase is modeled as isotropic elastic with plastic flow being a rate-dependent process with strain hardening resulting from molecular orientation. The volume-averaged deformation and stress within the inclusions are related to the macroscopic fields by a hybrid interaction model. The uniaxial compression of initially isotropic high density polyethylene (HDPE) is taken as a case study. The ability of the model to capture the elasto-plastic stress–strain behavior of HDPE during monotonic and cyclic loading, the evolution of anisotropy, and the effect of crystallinity on initial modulus, yield stress, post-yield behavior and unloading–reloading cycles are presented.

Dislocation density-based modeling of deformation behavior of aluminium under equal channel angular pressing

Abstract: In this study, the deformation behavior of aluminium during equal channel angular pressing (ECAP) was calculated on the basis of a dislocation density-based model. The behavior of the material under ECAP, including the dislocation density and cell size evolution as well as texture development, was simulated using the finite element method (FEM). The simulated stress, strain and cell size were compared with the experimental data, which were obtained by ECAP for several passes in a modified Route C regime. Good agreement between simulation results and experimental data, including strain distribution, dislocation density and cell size evolution, strain hardening and texture development was obtained. As concerns the general trends, the stress was found to increase rapidly in the first ECAP pass, the strain-hardening rate then dropping from the second pass on. Calculations showed a non-uniform strain distribution evolving in the course of ECAP. The simulated cell size is also in good agreement with the experiment, particularly with the observed rapid decrease of the cell size during the first pass slowing down from the second pass onwards. Larger cells were found to form in the upper and the lower parts of the workpiece where the strain is smaller than in the middle part. Due to the accumulation of strain throughout the workpiece and an overall trend to saturation of the cell size, a decrease of the difference in cell size with the number of passes was predicted.

Temperature and strain rate effects on the strength and ductility of nanostructured copper

Abstract: We show that the yield strength for Cu with ultrafine grain sizes becomes obviously temperature and strain-rate dependent, in contrast to the temperature/rate insensitive behavior of conventional face-centered-cubic metals. A thermally activated deformation mechanism is operative at room temperature and especially at slow strain rates, but not at 77 K. In addition to the gain in strength, the tensile ductility and particularly uniform strains also increase at cryogenic temperatures and with increasing strain rate, as a result of improved strain hardening due to suppressed dynamic recovery.

Deformation mechanism crossover and mechanical behaviour in nanocrystalline materials.

Abstract: We use molecular dynamics simulations to elucidate the transition with decreasing grain size from a dislocation- to a grain-boundary-based deformation mechanism in nanocrystalline fcc metals. Our simulations reveal that this crossover is accompanied by a pronounced transition in the mechanical behaviour of the material; namely, at the grain size where the crossover occurs (the 'strongest size'), the strain rate under tensile elongation goes through a minimum. This simultaneous transition in both the deformation mechanism and the corresponding mechanical behaviour offers an explanation for the experimentally observed crossover in the yield strength of nanocrystalline materials, from Hall-Petch hardening to 'inverse Hall-Petch' softening.

Strain hardening of various polyolefins in uniaxial elongational flow

Abstract: In this contribution correlations between the type of strain hardening of long-chain branched polyethylenes and the level of their zero shear-rate viscosities in comparison to linear polyethylenes are described. For polyethylenes of various branching structures four different types of strain hardening can be observed. Type I: strain hardening is approximately independent of elongational rate. Type II: strain hardening decreases with increasing elongational rate. Type III: strain hardening increases with increasing elongational rate. In addition to that, materials are found which do not show strain hardening within the experimental window (type IV). Qualitative correlations with the dependence of the zero shear-rate viscosity on the weight average molecular mass can heuristically be deduced. Polyethylenes of type IV fulfill the well-established relationship η0∼Mw3.4, samples of types I and II give higher zero shear-rate viscosities than the linear products. Type III samples generally exhibit zero shear-rat...

Grain boundary versus transgranular ductile failure

Abstract: The competition between intergranular and intragranular fracture is investigated using a bilayer damage model, which incorporates the relevant microstructural features of aluminium alloys with precipitate free zones (PFZ) nearby the grain boundary. One layer represents the grain behaviour: due to precipitation, it presents a high yield stress and low hardening exponent. The other layer represents the PFZ which has the behaviour of a solid solution: it is much softer but with a much higher strain hardening capacity. In both layers, void growth and coalescence is modelled using an enhanced Gurson-type model incorporating the effects of the void aspect ratio and of the relative void spacing. The effects on the ductility (i) of the flow properties of each zone, (ii) of the relative thickness of the PFZ, and (iii) of the particles spacing and volume fraction in the PFZ are elucidated. Comparisons are made with experimental data. Based on the previous analysis, qualitative understanding of trends in the fracture toughness of aluminium alloys can be gained in order to provide a link with the thermal treatment process. (C) 2003 Elsevier Science Ltd. All rights reserved.

A physically based model for TRIP-aided carbon steels behaviour

Abstract: A physically based model for TRIP carbon steels is developed suitable to predict the macroscopic behaviour of multi-constituent aggregates. It includes the effects of phase composition and morphology on flow stress and strain hardening. In a first part, a detailed description of the stress-assisted and strain-induced martensitic transformation kinetics is given based on a generalised form of the Olson–Cohen model. The appearance of the much harder martensitic phase during plastic straining gives rise to a strong hardening of the retained austenite islands. The matrix behaviour is described using a model previously developed for ferritic–martensitic steels. A quite simple but accurate homogenisation approach is used to determine the TRIP steel behaviour. The predicted evolution of strain-induced martensite volume fraction, flow stress and incremental work hardening is in good agreement with experimental data and illustrates the critical importance of the retained austenite stability on the formability of TRIP steels.

Hardness trends in micron scale indentation

Abstract: A continuum theory for elastic-plastic solids that accounts for the size-dependence of strain hardening is employed to analyze trends in the indentation hardness test. Strain gradient plasticity theory incorporates an elevation of flow stress when non-uniform plastic deformations occur at the micron scale. Extensive experimental data exists for size-dependence of indentation hardness in the micron range for conical (pyramidal) indenters, and recent data delineates trends for spherical indenters. Deformation induced by rigid conical and spherical indenters is analyzed in two ways: by exploiting an approximation based on spherically symmetric void expansion and by finite element computations. Trends are presented for hardness as a function of the most important variables in the indentation test, including the size of the indent relative to the material length parameters, the strain hardening exponent, the ratio of initial yield stress to Young's modulus, and the geometry of the indenter. The theory rationalizes seemingly different trends for conical and spherical indenters and accurately simulates hardness data presented recently for iridium, a low yield strain/high hardening material. The dominant role of one of the material length parameters is revealed, and it is suggested that the indentation test may the best means of measuring this parameter.