Showing papers on "Strain hardening exponent published in 1995"

Determining the mechanical properties of small volumes of material from submicrometer spherical indentations

Abstract: The stress/strain behavior of bulk material is usually investigated in uniaxial tension or compression; however, these methods are not generally available for very small volumes of material. Submicrometer indentation using a spherical indenter has the potential for filling this gap with, possibly, access to hardness and elastic modulus profiles, representative stress/strain curves, and the strain hardening index. The proposed techniques are based on principles well established in hardness testing using spherical indenters, but not previously applied to depth-sensing instruments capable of measurements on a submicrometer scale. These approaches are now adapted to the analysis of data obtained by stepwise indentation with partial unloading, a technique that facilitates separation of the elastic and plastic components of indentation at each step and is able to take account of the usually ignored phenomena of “piling up” and “sinking in”.

A computational approach to ductile crack growth under large scale yielding conditions

Abstract: Mode I crack initiation and growth under plane strain conditions in tough metals is computed using an elastic-plastic continuum model which accounts for void growth and coalescence ahead of the crack tip. The material parameters are the Young’s modulus, yield stress and strain hardening exponent of the metal, along with the parameters characterizing the spacing and volume fraction of voids in material elements lying in the plane of the crack. For a given set of these parameters and a specific specimen, or component, subject to a specific loading, relationships among load, load-line displacement and crack advance can be computed with no restrictions on the extent of plastic deformation. Similarly, there is no limit on crack advance, except that it must take place on the symmetry plane ahead of the initial crack. Suitably defined measures of crack tip loading intensity, such as those based on the J-integral, can also be computed, thereby directly generating crack growth resistance curves. In this paper, the model is applied to five specimen geometries which are known to give rise to significantly different crack tip constraints and crack growth resistance behaviors. Computed results are compared with sets of experimental data for two tough steels for four of the specimen types. Details of the load, displacement and crack growth histories are accurately reproduced, even when extensive crack growth takes place under conditions of fully plastic yielding.

An analysis of fully plastic Brinell indentation

Abstract: Indentation of a hard sphere into inelastic solids, Brinell indentation, is examined theoretically and numerically by aid of classical plastic flow theory. With the main interest focused on fully plastic behaviour at indentation the mechanical analysis is carried out for power-law hardening rigid-plastic materials where self-similarity features play a dominant role. It is explained in detail how the problem of a moving contact boundary may be reduced to a stationary one by an appropriate transformation of field variables. Within this setting classical empirical findings by Meyer (1908) and O'Neill (1944) are established on a rigorous theoretical ground. In particular, it is shown to advantage also for nonlinear materials how intermediate solutions for a flat die may by cumulative superposition generate solutions for a class of curved indenters. In the case of perfect plasticity it turns out in the present context that indentation hardness is independent of die profiles. For hardening solids when the material behaviour is history dependent, reduction to a stationary geometry is achieved also by expressing the accumulated strain by cumulative superposition. The intermediate flat die problem is then solved for a variety of hardening exponents by a finite element procedure designed to account for material incompressibility. With finite element computations as a basis desired solutions are obtained by straightforward numerical superposition procedures. Detailed results are then given for bulk quantities such as the mean contact pressure as well as relevant field variables. The influence of hardening characteristics on sinking-in and piling-up of indented surfaces and contact pressure distributions are discussed in the light of earlier findings based on deformation theory of plasticity and available discriminating experiments. Correlation is particularly sought with the celebrated universal hardness parameters proposed by Tabor (1951) and the existence of representative strain measures. Attention is also given to the elastic-plastic transition region of Brinell indentation in search for loading levels sufficiently high that the results tend to an asymptotic fully plastic state. A standard finite element technique employing contact elements for a moving boundary is used to analyse with tolerable accuracy the influence of elasticity and more elaborate hardening behaviour. Some relevant features are shown for a sequence of solutions from elastic Hertzian to fully plastic behaviour.

Superplasticity in powder metallurgy aluminum alloys and composites

Abstract: Superplasticity in powder metallurgy aluminum alloys and composites has been reviewed through a detailed analysis. The stress-strain curves can be put into four categories: a classical well-behaved type, continuous strain hardening type, continuous strain softening type and a complex type. The origin of these different types of stress-strain curves is discussed. The microstructural features of the processed material and the role of strain have been reviewed. The role of increasing misorientation of low angle boundaries to high angle boundaries by lattice dislocation absorption is examined. Threshold stresses have been determined and analyzed. The parametric dependencies for superplastic flow in modified conventional aluminum alloys, mechanically alloyed alloys and aluminum alloy matrix composites is determined to elucidate the superplastic mechanism at high strain rates. The role of incipient melting has been analyzed. A stress exponent of 2, an activation energy equal to that for grain boundary diffusion and a grain size dependence of 2 generally describes superplastic flow in modified conventional aluminum alloys and mechanically alloyed alloys. The present results agree well with the predictions of grain boundary sliding models. This suggests that the mechanism of high strain rate superplasticity in the above-mentioned alloys is similar to conventional superplasticity. The shift of optimum superplastic strain rates to higher values is a consequence of microstructural refinement. The parametric dependencies for superplasticity in aluminum alloy matrix composites, however, is different. A true activation energy of 313 kJ mol−1 best describes the composites having SiC reinforcements. The role of shape of the reinforcement (particle or whisker) and processing history is addressed. The analysis suggests that the mechanism for superplasticity in composites is interface diffusion controlled grain boundary sliding.

An improved Gurson-type model for hardenable ductile metals

Abstract: The aim of this paper is to improve the modelling of strain hardening within the framework of the famous Gurson model for porous ductile metals. Indeed, although the original derivation of this model, for an ideal-plastic matrix, was based on a micromechanical analysis of some representative volume element, namely a hollow rigid-plastic sphere loaded axisymmetrically, the extension to the case of a hardenable matrix was of purely phenomenological and macroscopic nature, and this entailed a number of drawbacks. The phenomenological model was incompatible with the classical, exact solution to the problem of a hollow rigid-hardenable sphere loaded hydrostatically; also, the prediction that for any loading path corresponding to a fixed triaxiality, the curve representing porosity as a function of equivalent strain depended only on the initial porosity and the triaxiality but not on the hardening exponent, was incorrect. A new model solving these difficulties, based on an approximate analysis of a hollow rigid-hardenable sphere subjected to some axisymmetric loading, is proposed. Two types of hardening are considered: isotropic, as in Gurson's original model, and kinematic, as in Mear and Hutchinson's variant of Gurson's model. Comparisons with some finite element simulations evidence the improvements brought.

On the Hall-Petch relationship and substructural evolution in type 316L stainless steel

Abstract: Tensile specimens of Type 316L stainless steel having grain sizes in the range 3.1–86.7 μm were deformed to 34% strain at temperatures 24, 400 and 700°C and strain rate 1 × 10−4s−1 to investigate the Hall-Petch (H-P) relationship, the nature of stress-strain curves and the substructure development. Upto ∼5% strain the H-P relationship exhibits bi-linearity whereas the single Hall-Petch relation is exhibited at larger strains. The presence of bi-linearity is explained by the back stress associated with the difference in the dislocation densities in the vicinity of grain boundary and in the grain interior. The log stress (σ)-log strain (e) plots depict three regimes and follow the relationship σ = Ken in each regime, but with varying magnitudes of the strength coefficient (K) and strain-hardening exponent (n).

Strain-Hardening Behavior of Shear Panels Made of Low-Yield Steel. I: Test

Abstract: This paper proposes simple models that can simulate the hysteretic behavior of shear panels made of low-yield steel, which exhibits significant strain-hardening under load reversals. The models are based on either the bilinear or the Ramberg-Osgood model, and combine kinematic and isotropic hardening in a linear manner by the introduction of a weighting coefficient. The accuracy of these models is demonstrated by comparing hysteresis curves obtained from these models with experimental hysteresis curves, which have been supplied by a quasi-static loading test with a prescribed deformation history and by a pseudodynamic test. Programming of these models is found to be very easy, involving only slight modification of the programs developed for the bilinear and the Ramberg-Osgood models. Thus, these models can readily be incorporated into inelastic dynamic response analysis of structures having shear panels made of low-yield steel as hysteretic dampers.

Effects of microstructural variables on the deformation behaviour of dual-phase steel

Abstract: An expression for the stress of martensite in dual-phase steel was developed, which shows the interdependence of the stress of martensite and strain hardening in the ferrite matrix and the contribution of microstructural variables (the volume fraction of martensite fm, ferrite grain size df, and martensite particle size dm). The onset of plastic deformation of martensite in dual-phase steel was predicted to depend on its yield strength and the microstructural variables, and this was verified by the modified Crussard-Jaoul analysis. It was found that for this dual-phase steel, refining the grain size and increasing fm increase the flow stress and raise the strain hardening rate at low strains, but little affect the strain hardening rate at high strains. The effect of the ferrite grain size on the flow stress of this dual-phase steel was found to obey the Hall-Petch relation, i.e. σ = σ 0 e + K e d f − 1 2 , where the Hall-Petch intersection σ0e and slope Ke are functions of strain, fm and dm. The effects of the plastic deformation of martensite and the microstructural variables on the strain hardening rate and the Hall-Petch behaviour were analysed in terms of the densities of statistically stored dislocations and geometrically necessary dislocations using the previously developed theoretical model.

The mechanical response of a 6061-T6 A1/A12O3 metal matrix composite at high rates of deformation

Abstract: The mechanical properties of a 6061-T6 aluminum alloy reinforced with a 20 vol.% fraction of alumina particles and of an unreinforced 6061-T6 alloy are studied over a range of strain rates (10-4to 6 x 105s-1) using quasistatic compression, compression and torsion Kolsky Bars, and high strain rate pressure-shear plate impact. At a given strain rate the composite displays increased strength but essentially the same strain hardening as the matrix. However, the composite displays a stronger rate-sensitivity than does the unreinforced alloy at high rates of deformation (>103s-1). The rate-sensitivity of the unreinforced alloy is shown to be largely the result of the imposed strain rate rather than of the rate history. For quasistatic deformations, a model proposed by Bao et al. (1991) describes the behavior of the composite fairly accurately given the behavior of the unreinforced alloy. This paper presents an extension of the model that is able to predict the dynamic behavior of the composite given the dynamic response of the monolithic alloy.

Effect of Fiber Volume Fraction on the Off‐Crack‐Plane Fracture Energy in Strain ‐Hardening Engineered Cementitious Composites

Abstract: In this paper, the results of an experimental study on the effect of fiber volume fraction on the off-crack-plane fracture energy in a strain-hardening engineered cementitious composite (ECC) are presented. Unlike the well-known quasi-brittle behavior of fiber-reinforced concrete, ECC exhibits quasi-ductile response by developing a large damage zone prior to fracture localization. In the damage zone, the material is microcracked but continues to strain-harden locally. The areal dimension of the damage zone has been observed to be on the order of 1,000 cm{sup 2} in double cantilever beam specimens. The energy absorption of the off-crack-plane inelastic deformation process has been measured to be more than 50% of the total fracture energy of up to 34 kJ/m{sup 2}. This magnitude of fracture energy is the highest ever reported for a fiber cementitious composite.

Further analysis of the size effect in indentation hardness tests of some metals

Abstract: The variation of apparent hardness observed in previously reported Vickers indentation tests of metals is reexamined. Common deseriptions of the effect are shown to be inaccurate: the variation of apparent hardness is monotonic but not simple. The effect is consistent with varying size of a previously postulated “plastic hinge” at the perimeter of the indent. This complexity confers uncertainty on the estimation of characteristic macrohardness from small scale tests. Association of the indentation size effect with friction and with strain hardening is confirmed.

On the effect of macroporosity on the tensile properties of the Al-7%Si-0.4%Mg casting alloy

Abstract: The purpose of the present note is to put forward a simple model which predicts the effect of porosity on the tensile behavior of the Al-7%Si-0.4%Mg alloy in the T-6 condition. In order to validate the calculations, the predictions of the model are contrasted against the experimental results of Surappa et al. for the same material. On the assumption that localized porosity in a tensile sample concentrates the strain due to the reduce load bearing area, the rate of strain concentration can be described using existing models for the growth of plastic instabilities. By assuming that fracture occurs in the region of maximum strain at a given value of the local strain, the overall strain to fracture can be calculated for different levels of porosity. The procedure can be applied to calculate the effect of porosity on the fracture stress. The calculations indicate that even low levels of localized porosity may have a significant effect on both the tensile ductility and the tensile strength of the material. These predictions are in good agreement with published results for the casting alloy Al-7Si-0.4Mg T-6.

Influence of peak pressure and temperature on the structure/property response of shock- loaded Ta and Ta-10W

Abstract: The deformation behavior and substructure evolution of unalloyed-Ta and Ta-10W under quasistatic conditions have been compared to their respective responses when shock prestrained to 20 GPa at 25 °C as well as to unalloyed-Ta shocked to 7 GPa at 25 °C, 200 °C, and 400 °C. The reload yield behavior of shock-prestrained Ta and Ta-10W did not exhibit enhanced shock hardening when compared to their respective quasistatic stress-strain response at an equivalent strain level. In addition, the reload yield behavior of Ta shock prestrained to 7 GPa at 200 °C or 400 °C was found to exhibit increased hardening compared to the shock prestraining at 25 °C. The quasistatic substructure evolution and shock-hardening responses of Ta and Ta-10W were investigatedvia transmission electron microscopy (TEM). The dislocation substructures in both materials and at each strain rate condition and temperature were similar and consisted primarily of long, straight, ( α/2) 〈111〉 type screw dislocations. The propensity for long, straight screw dislocations, irrespective of the loading condition, supports the theory of strong Peierls stress control on defect generation and defect storage. The substructure evolution and mechanical behavior of Ta and Ta-10W are discussed in terms of defect storage mechanisms and compared to the mechanisms operative in face-centered cubic (fcc) metals.

Grain refinement and superplasticity in 5083 Al

Abstract: A preliminary investigation of thermomechanical processing of 5083 aluminum plate (Al-4.7%Mg-0.7%Mn) was undertaken to develop a fine-grain sheet for superplastic forming applications. Significant differences in grain size and the extent of superplasticity are seen in hot-rolled vs. cold-rolled sheets, with tensile elongations exceeding 600% for the cold-rolled alloy. Additionally, a separate fine-grain sheet of the same alloy, produced by Alusuisse Co., was studied in greater detail. Superplastic deformation behavior of this sheet was investigated under uniaxial tension over the temperature range of 500–565 °C. Strain rate sensitivity values greater than 0.3 were observed over a strain rate range of (3 × 10−5)–(1 × 10−2) s−1 with a maximum value of 0.65 obtained for strain rate of 5 × 10−4 s−1 at 565 °C. Constant-velocity tension tests consistently show larger strains to failure and lower strain hardening rate than the corresponding “constant-strain-rate” tests for the range investigated. A short but rapid prestraining step, prior to the normal superplastic straining, produced enhanced tensile elongation at all temperatures. Under the two-step schedule, a maximum tensile elongation of 600% was obtained at 550 °C, which was regarded as the optimum superplastic temperature under this condition. This paper and a companion paper are used to provide the details of results obtained to date from this study.

Heat treated martensitic steels: microstructural systems for advanced manufacture

Abstract: This paper describes the microstructure, deformation, and fracture of low-temperature-tempered (LTT) martensitic steels. The microstructural reasons for the ability of these steels to achieve ultrahigh strengths and the factors controlling ductility and toughness are described for low-carbon, medium-carbon, and high-carbon LTT martensitic steels. The key strengthening mechanism of LTT martensitic steels is the strain hardening provided by the transition carbide/dislocation substructure of the martensite crystals. In low- and medium-carbon steels, LTT microstructures fail by ductile fracture mechanisms, and ductility decreases as strain hardening rates increase with increasing carbon content. In high-carbon LTT steels, quench embrittlement associated with phosphorus segragation and cementite formation at austenite grain boundaries limits toughness and fatigue resistance. Approaches which permit the application of the high strengths of high-carbon LTT steels and minimize the effects of quench embrittlement are discussed.

Mechanical properties and microstructure of cast oxide-dispersion-strengthened aluminum

Abstract: Oxide-dispersion-strengthened aluminum containing 25 vol.%, 0.28 μm, alumina dispersoids was fabricated by pressure infiltration. The mechanical properties at room and elevated temperature are presented for both as-cast, coarse-grained materials and extruded, fine-grained materials. Although the room temperature yield strength is low (about 60 MPa), the 0.2% proof stress and ultimate tensile stress are much higher (about 200 MPa and 330 MPa respectively) as a result of the very high strain hardening rate. However, the initially high strain hardening rate decreases with strain. This behavior is explained by extending a model by Ashby for dilute dispersion-strengthened metals to the case of a matrix containing a large volume fraction of large particles, whereby the interaction of primary glide dislocations with secondary loops punched by dispersoids is considered.

The experimental observation and numerical prediction of planar entry flow and die swell for molten polyethylenes

Abstract: We report experimental observations and matching numerical simulations for the planar entry flow and die swell of two high-density polyethylenes (HDPEs) and one low-density polyethylene (LDPE) Experimental data for stress fields, centreline velocities and die swell are reported for each polymer These results are compared with numerical simulation The materials are characterized in simple shear using a Wagner integral constitutive equation with a discrete spectrum of relaxation times and a single parameter damping function The numerical simulation has been carried out using a finite element software package, Polyflow Self consistency in the stress and die swell data are found for one HDPE, but the other HDPE and the LDPE show an extensional strain hardening response which is not predicted using the simple shear rheology data In the latter cases, the numerical predictions consistent with entry flow experimental observations can be achieved if extensional flow damping parameters, rather than simple shear damping parameters, are chosen For the LDPE, an increase in the strain hardening parameter results in the numerical prediction of upstream recirculation vortices in the entry region, which qualitatively agrees with the experimental observations Apparent inconsistencies in the absolute values of measured and simulated velocity profiles are explained in terms of the 2D nature of the simulation and a 3D component to the experimental flow

Computational plasticity : the variational basis and numerical analysis

Abstract: The quasistatic problem of elastoplasticity with combined kinematic and isotropic hardening is considered, with particular emphasis on variational aspects and numerical approximations of this problem. It is shown that the problem may be formulated variationally in two alternative, dual, forms; both formulations are variational inequalities, but they diier from each other in the form they take, and in the set of variables they use. These problems are referred to as primal and dual formulations, and for each formulation the issue of existence and uniqueness of solutions is discussed in detail. Error analysis of temporally semi-discrete, spatially semi-discrete and fully-discrete approximations of the quasistatic problem is given in the context of both variational formulations. Finally, some popular solution algorithms are reviewed, and their properties are investigated. Of particular interest are conditions under which such algorithms converge, and the role played by the choice of algorithmic moduli, in the behaviour of these algorithms.

Analytical and finite element predictions of residual stresses in cold worked fastener holes

Abstract: Two-dimensional finite element (FE) studies, for plane stress, plane strain and axisymmetric conditions, were conducted to simulate 4 per cent cold working of a 6.35 mm diameter hole in a 6 mm thick plate of 2024 T 351 aluminium alloy. The simulations were used to assess the influence of strain hardening, the role of reversed yielding and through-thickness residual stress distributions. Experiments were also conducted to determine the tensile and compressive stress-strain response of the aluminium alloy, revealing a pronounced Bauschinger effect and non-linear strain hardening in compression. The FE simulations and results from several earlier analytical models were compared and substantial differnces found in the region of reversed yielding. Approximations used to model the compressive deformation behaviour of the material overestimate the compressive residual stresses at the hole edge. From the axisymmetric FE model a residual stress gradient through the plate thickness was found. The plane stre...

On the role of particle cracking in flow and fracture of metal matrix composites

Abstract: The flow response of particle-reinforced metal matrix composites is studied using finite element methods. Unit cells containing either intact or cracked particles in a power law hardening matrix are used to determine the corresponding asymptotic flow strengths. The effects of the hardening exponent and the elastic mismatch between the particles and the matrix on the flow response are examined. For comparison, the flow response of power law hardening solids containing penny-shaped cracks is also evaluated. The latter results are found to be in reasonable agreement with those corresponding to composites that contain low volume fractions of cracked particles. The asymptotic results are used to develop a one-dimensional constitutive law for composites which undergo progressive damage during tensile straining. This law is used to evaluate the strain at the onset of plastic instability. It is proposed that the instability strain be used as a measure of tensile ductility when the particle content is low and the particles are uniformly distributed through the matrix.

Inertial Effects on Void Growth in Porous Viscoplastic Materials

Abstract: The present work examines the inertial effects on void growth in viscoplastic materials which have been largely neglected in analyses ofdynamic crack growth and spallation phenomena using existing continuum porous material models. The dynamic void growth in porous materials is investigated by analyzing the finite deformation of an elastic/viscoplastic spherical shell under intense hydrostatic tensile loading. Under typical dynamic loading conditions, inertia is found to have a strong stabilizing effect on void growth process and consequently to delay coalescence even when the high rate-sensitivity of materials at very high strain rates is taken into account. Effects of strain hardening and thermal softening are found to be relatively small. Approximate relations are suggested to incorporate inertial effects and rate sensitivity of matrix materials into the porous viscoplastic material constitutive models for dynamic ductile fracture analyses for certain loading conditions.

The mechanical behavior of an aisi type 310 stainless steel

Abstract: An AISI type 310 austenitic stainless steel was tensile tested over a range of strain rates, ∈ =5×10 −1 s −1 , and test temperatures, T = 298 to 1073 K, in order to determine the strain rate and temperature dependencies of the plastic deformation behavior. It is found that both the yield stress, σ Y , and the ultimate tensile stress, σ UTS , are linearly related to the natural logarithm of strain rate, In ∈ , at all test temperatures. Serrated yielding (dynamic strain aging) was observed within a certain range of temperatures and strain rates. The dynamic strain hardening stress, Δ σ H = σ UTS − σ Y , is larger for lower strain rates, and the peak of the Δ σ H vs T plot moves from about 700 to 1000 K when the strain rate is increased from 5 × 10 −5 to 5 × 10 −1 s −1 . Both the yield stress and the ultimate tensile stress decrease with temperature in a similar manner. The ductility of the steel is also dependent on both temperature and strain rate. For lower strain rates ( ∈ =5×10 −2 to 5×10 −3 s −1 ), the elongation to fracture, δ %, increases with temperature from about 38% ( T = 298 to 873 K) up to 75% ( T > 900 K); for higher strain rates ( ∈ =5×10 −2 to 5×10 −1 s −1 ), δ % is smaller lying within the range of 29–39%. The experimental results are analyzed in terms of thermal activation processes for plastic deformation of crystalline materials. It is shown that the activation volume and activation energy are smaller at lower temperatures (298–573 K) and larger at higher temperatures (673–1073 K) indicating two distinctive flow processes for the low and high temperature regions.

Influence of nitride (Cr2N) precipitation on the plastic flow behavior of high-nitrogen austenitic stainless steel

Abstract: Aging at 700 °C results in grain boundary nitride precipitation only, while aging at 900 °C results in grain boundary and cellular precipitation (40 vol%). These thermal treatments have a small but positive effect on YS, no effect on the UTS, but dramatically reduce the ability of the material to deform under localized plastic deformation (necking), leading to reduced tensile ductility. The plastic flow behavior of all annealed and aged high-nitrogen samples were modeled using the modified Ludwik relation (equation 2). Below the UTS, grain boundary nitride precipitation at 700 °C has no measurable effect on the plastic flow behavior of the material, and the modeling parameters n1, K1, n2, and K2 have values which do not deviate significantly from the behavior of the un-aged material. Cellular precipitation, caused by aging at 900 °C, does significantly affect the plastic flow behavior of the material at both low and high strains. Cellular precipitation causes both increased strengthening of the matrix in the low strain regime (0.001 < e < 0.03) and systematic decreases in the strain hardening exponent (n1) and strength coefficient (K1) with increased aging. The rate of strain hardening (dσde) measured from the σ-e plots is unaffected by isothermal aging and nitride formation.