Showing papers on "Strain hardening exponent published in 2002"

High tensile ductility in a nanostructured metal.

Abstract: Nanocrystalline metals--with grain sizes of less than 100 nm--have strengths exceeding those of coarse-grained and even alloyed metals, and are thus expected to have many applications. For example, pure nanocrystalline Cu (refs 1-7) has a yield strength in excess of 400 MPa, which is six times higher than that of coarse-grained Cu. But nanocrystalline materials often exhibit low tensile ductility at room temperature, which limits their practical utility. The elongation to failure is typically less than a few per cent; the regime of uniform deformation is even smaller. Here we describe a thermomechanical treatment of Cu that results in a bimodal grain size distribution, with micrometre-sized grains embedded inside a matrix of nanocrystalline and ultrafine (<300 nm) grains. The matrix grains impart high strength, as expected from an extrapolation of the Hall-Petch relationship. Meanwhile, the inhomogeneous microstructure induces strain hardening mechanisms that stabilize the tensile deformation, leading to a high tensile ductility--65% elongation to failure, and 30% uniform elongation. We expect that these results will have implications in the development of tough nanostructured metals for forming operations and high-performance structural applications including microelectromechanical and biomedical systems.

Constitutive analysis in hot working

Abstract: Constitutive equations including an Arrhenius term have been commonly applied to steels with the objective of calculating hot rolling and forging forces. The function relating stress and strain rate is generally the hyperbolic-sine since the power and exponential laws lose linearity at high and low stresses, respectively. In austenitic steels, the equations have been used primarily for the peak stress (strain) associated with dynamic recrystallization (DRX) but also for the critical and steady state stresses (strains) for nucleation and first wave completion of DRX. Since the peak strain is raised by the presence of solutes and fine particles, the stress is raised more than by simple strain hardening increase, thus causing a marked rise in activation energy in alloy steels. In contrast, large carbides, inclusions or segregates, if hard, may lower the peak strain as a result of particle stimulated nucleation. Due to the linear relation between stress and strain at the peak, flow curves can be calculated from the constitutive data with only one additional constant. Maximum pass stresses can also be calculated from a sinh constitutive equation determined in multistage torsion simulations of rolling schedules. Comparison is made between carbon, micro-alloyed, tool and stainless steels and to ferritic steels which usually do not exhibit DRX. Parallels to the effects of impurities and dispersoids on the constitutive equations for Al alloys are briefly discussed.

From dislocation junctions to forest hardening.

Abstract: The mechanisms of dislocation intersection and strain hardening in fcc crystals are examined with emphasis on the process of junction formation and destruction. Large-scale 3D simulations of dislocation dynamics were performed yielding access for the first time to statistically averaged quantities. These simulations provide a parameter-free estimate of the dislocation microstructure strength and of its scaling law. It is shown that forest hardening is dominated by short-range elastic processes and is insensitive to the detail of the dislocation core structure.

A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals

Abstract: A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for: an arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations resulting from a piecewise quadratic Peierls potential; the interaction between the dislocations and an applied resolved shear stress field; and the irreversible interactions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. A chief advantage of the present theory is that it is analytically tractable, in the sense that the complexity of the calculations may be reduced, with the aid of closed form analytical solutions, to the determination of the value of the phase field at point-obstacle sites. In particular, no numerical grid is required in calculations. The phase-field representation enables complex geometrical and topological transitions in the dislocation ensemble, including dislocation loop nucleation, bow-out, pinching, and the formation of Orowan loops. The theory also permits the consideration of obstacles of varying strengths and dislocation line-energy anisotropy. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication in single slip under monotonic loading; the Bauschinger effect under reverse loading; the fading memory effect, whereby reverse yielding gradually eliminates the influence of previous loading; the evolution of the dislocation density under cycling loading, leading to characteristic ‘butterfly’ curves; and others.

Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation

Abstract: A strain gradient dependent crystal plasticity approach is used to model the constitutive behaviour of polycrystal FCC metals under large plastic deformation. Material points are considered as aggregates of grains, subdivided into several fictitious grain fractions: a single crystal volume element stands for the grain interior whereas grain boundaries are represented by bi-crystal volume elements, each having the crystallographic lattice orientations of its adjacent crystals. A relaxed Taylor-like interaction law is used for the transition from the local to the global scale. It is relaxed with respect to the bi-crystals, providing compatibility and stress equilibrium at their internal interface. During loading, the bi-crystal boundaries deform dissimilar to the associated grain interior. Arising from this heterogeneity, a geometrically necessary dislocation (GND) density can be computed, which is required to restore compatibility of the crystallographic lattice. This effect provides a physically based method to account for the additional hardening as introduced by the GNDs, the magnitude of which is related to the grain size. Hence, a scale-dependent response is obtained, for which the numerical simulations predict a mechanical behaviour corresponding to the Hall–Petch effect. Compared to a full-scale finite element model reported in the literature, the present polycrystalline crystal plasticity model is of equal quality yet much more efficient from a computational point of view for simulating uniaxial tension experiments with various grain sizes.

Influence of Matrix Ductility on Tension-Stiffening Behavior of Steel Reinforced Engineered Cementitious Composites (ECC)

Abstract: In this paper, the interaction of structural steel reinforcement and high-performance fiber-reinforced cement composites (HPFRCC) in uniaxial tension is examined. The effects of cementitious composite ductility on the steel reinforced composite deformation behavior are experimentally studied and contrasted to normal reinforced concrete (RC). The substitution of brittle concrete with an engineered cementitious composite (ECC), a particular type of HPFRCC with strain hardening and multiple cracking properties, has shown to provide improved load-deformation characteristics in terms of RC tensile strength, deformation mode, and energy absorption. Analysis of the deformation mechanisms suggests that combining steel reinforcement and ECC results in composite action, where unlike in RC or regular FRC, both constituent materials deform compatibly in the postcracking and postyielding deformation process. This deformation compatibility results in a more uniform strain distribution in reinforcement and composite matrix, reduced interfacial bond stress, and controlled damage at relatively large inelastic composite deformations. Research described here focuses on the influence of composite ductility on the deformation behavior of the RC and its effects on the strain distribution in the reinforcement, composite matrix, and interfacial bond.

Strain Hardening at Large Strains as Predicted by Dislocation Based Polycrystal Plasticity Model

Abstract: A recent strain hardening model for late deformation stages (Estrin, Y., Toth, L.S., Molinari, A., and Brechet, Y., Acta Materialia, 1998, A dislocation-based model for all hardening stages in large strain deformation, Vol. 46, pp. 5509-5522) was generalized for the 3D case and for arbitrary strain paths. The model is based on a cellular dislocation arrangement in which a single- phase material is considered as a composite of a hard skeleton of cell walls and soft cell interiors. An important point in the approach is the evolution of the volume fraction of the cell walls which decreases with the deformation and gives rise to a plateau-like behavior (Stage IV) followed by a drop-off (Stage V) of the strain hardening rate observed at large strains. The hardening model was implemented into the viscoplastic self-consistent polycrystal model to predict hardening curves corresponding to different proportional loading paths. The calculated curves were evaluated to elucidate the path dependence of hardening.

Implementation of cyclic plasticity models based on a general form of kinematic hardening

Abstract: This paper deals with implementation of cyclic plastic constitutive models in which a general form of strain hardening and dynamic recovery is employed to represent the multilinear, as well as non-linear, evolution of back stress. First, in order to incorporate such a general form of kinematic hardening in finite element methods, successive substitution and its convergence are discussed for implicitly integrating stress; moreover, a new expression of consistent tangent modulus is derived by introducing a set of fourth-rank constitutive parameters into discretized kinematic hardening. Then, the constitutive parameters introduced are specified in three cases of the general form of kinematic hardening; the three cases have distinct capabilities of simulating ratcheting and cyclic stress relaxation. Numerical examples are given to verify the convergence in successive substitution and the new expression of consistent tangent stiffness. Error maps for implicitly integrating stress under non-proportional as well as proportional loading are also given to show that the multilinear case of the general form provides high accuracy even if strain increment is very large. Copyright © 2002 John Wiley & Sons, Ltd.

Spatiotemporal analysis of Portevin–Le Châtelier deformation bands: Theory, simulation, and experiment

Abstract: In many solid solutions plastic deformation becomes unstable at sufficiently high temperature due to dynamic strain aging, i.e., repeated breakaway of dislocations from their solute clouds and recapture by mobile solutes, producing stress serrations in constant strain-rate tests or strain bursts in constant stress-rate tests. The instabilities of this well-known Portevin--Le Ch\^atelier (PLC) effect are closely connected with localization of strain in ``PLC deformation bands'' with a width of the order of the specimen thickness and sometimes propagating like a soliton along the specimen. In the present work, the nucleation and propagation of PLC deformation bands is studied by means of a multizone laser scanning extensometer, providing information on local strain along the main part of the specimen, in addition to the conventional measurement of stress serrations. This enables one to differentiate clearly between the bands of types A, B, and C, and to explore their ranges of existence at various temperatures, stresses and strain rates as well as transitions between them along the stress-strain curve. The laser extensometer provides independent data on propagation rate, concentrated strain and width of the bands. These experimental data are compared with a theoretical space-time analysis of propagating PLC bands, which explicitly combines a physical description of the kinetics of dynamic strain aging and plastic deformation. This model provides not only analytical predictions for the above band parameters and their dependences on deformation rate and specimen thickness for Type-A PLC bands, but---by considering types B and C as perturbation modes---is also able to explain the observed transitions between the various types of deformation bands. Moreover, the effect of strain hardening on the appearance of PLC strain localization is elucidated. The analytical predictions are validated by numerical simulations of the model and by comparing them to the experimental findings reported here.

Superplastic behaviour of ultrafine-grained Ti–6A1–4V alloys

Abstract: Superplastic behavior of the ultrafine-grained (UFG) Ti–6A1–4V alloy produced by high pressure torsion (HPT) has been studied. High elongations (more than 500%) have been observed in this alloy during tensile tests at relatively low temperatures and high strain rates. At the same time, the superplastic behavior of this alloy has several specific features such as the relatively low values of strain rate sensitivity of flow stress and significant strain hardening. Moreover, it was shown that the alloy, processed by HPT, demonstrates an outstanding room temperature strength about 1500 MPa after superplastic deformation.

Contact Deformation Regimes Around Sharp Indentations and the Concept of the Characteristic Strain

Abstract: Finite element simulations are performed to analyze the contact deformation regimes induced by a sharp indenter in elastic – power-law plastic solids. As the yield strength (σys) and strain hardening coefficient (n) decrease or, alternatively, as Young’s modulus (E) increases, the contact regime evolves from (i) an elastic–plastic transition, to (ii) a fully plastic contact response, and to (iii) a fully plastic regime where piling-up of material at the contact area prevails. In accordance with preliminary analyses by Johnson, it is found that Tabor’s equation, where hardness (H) = 2.7σr, applies within the fully plastic regime of elastic – power-law plastic materials. The results confirm the concept of the uniqueness of the characteristic strain, ∈r = 0.1, that is associated with the uniaxial stress, σr. A contact deformation map is constructed to provide bounds for the elastic–plastic transition and the fully plastic contact regimes for a wide range of values of σ ys, n, and E. Finally, the development of piling-up and sinking-in at the contact area is correlated with uniaxial mechanical properties. The present correlation holds exclusively within the fully plastic contact regime and provides a tool to estimate σ ys and n from indentation experiments.

Modeling the evolution in microstructure and properties during plastic deformation of f.c.c.-metals and alloys – an approach towards a unified model

Abstract: A new approach to the modeling of work hardening during plastic deformation of f.c.c.-metals and alloys has been recently proposed by the present authors. The model is based on a statistical approach to the problem of athermal storage of dislocations. By combining the solution for the dislocation storage problem with models for dynamic recovery of network dislocations and sub-boundary structures, a general internal state variable description is obtained. The model includes effects due to variations in: (i) stacking fault energy, (ii) grain size, (iii) solid solution content, and (iv) particle size and volume fraction. The result is a work hardening model, which in principle is capable of providing the stress–strain behavior for a given metal or solid solution alloy under condition ranging from deformation in the ambient temperature range to high temperature creep. It will be demonstrated that the model predictions, in terms of microstructure evolution and associated properties, in general, are in good agreement with experimental observations.

Elasto-viscoplastic constitutive equations for polycrystalline fcc materials at low homologous temperatures

Abstract: A kinetic equation for the shearing rates on slip systems based on the thermally activated theory for plastic flow is formulated, and an evolution equation for slip system deformation resistances is developed. These constitutive functions are incorporated in a model for elasto-viscoplasticity of face-centered-cubic (f.c.c.) single crystals. For polycrystalline materials, the classical Taylor assumption is invoked. This constitutive model has been implemented in a finite element program to facilitate simulations of quasi-static as well as dynamic non-homogeneous deformations of polycrystalline f.c.c. materials. The material parameters in the model have been calibrated against existing experimental data for aluminum. The improved physical description for plastic flow and hardening evolution, enables the constitutive model to reproduce the macroscopic stress–strain response in aluminum up to large strains (≈100%), for a wide range of strain-rates (10−3– 10 2 s −1 ), and a wide range of low homologous temperatures (77– 298 K ). Important strain-rate-history and temperature-history effects on the strain-hardening behavior of aluminum are shown to be well represented by the constitutive model.

An age hardening model for Al–7Si–Mg casting alloys

Abstract: Yield strength (YS) ageing curves have been modelled for A356 and A357 aluminium casting alloys below the solvus temperature of the main hardening precipitate. Predictions are based on the Shercliff and Ashby methodology (Acta Metall. Mater. 38 (1990) 1789) for wrought alloys. Differences between strengthening in wrought and cast Al–Si–Mg alloys are considered. A Brinell hardness to YS conversion incorporating strain hardening has been established to enable YS ageing curves to be predicted with reduced experimental effort.