Showing papers on "Strain hardening exponent published in 1985"

A Two Surface Model for Transient Nonproportional Cyclic Plasticity, Part 1: Development of Appropriate Equations

Abstract: A two surface stress space model is introduced with internal state variable repositories for fading memory of maximum plastic strain range and non-proportionality of loading Evolution equations for isotropic hardening variables are prescribed as a function of these internal variables and accumulated plastic strain, and reflect dislocation interactions that occur in real materials The hardening modulus is made a function of prior plastic deformation and the distance of the current stress point from the limit surface The kinematic hardening rules of Mroz and Prager are used for the yield and limit surfaces, respectively The structure of the model is capable of representing essential aspects of complex nonproportional deformation behavior, including direction of the plastic strain rate vector, memory of plastic strain range, cross-hardening effects, variation of hardening modulus, cyclic hardening or softening, cyclic racheting, and mean stress relaxation

Time-dependent deformation of metals

Abstract: The basic characteristics of timedependent deformation of metals are described in terms of dislocation properties. At high temperatures, diffusion controlled climb of edge dislocations is the rate limiting process, whereas at low temperatures, other forms of recovery involving cross-slip of screw dislocations operate. A composite model of plastic flow is used to describe the coupling between these recovery processes. The model is patterned after the persistent slip band structures observed in cyclically deformed fcc single crystals. Screw dislocations are allowed to move in the cell interiors and to deposit edge dislocations into the adjoining walls. Cross-slip and climb lead to dislocation rearrangement and annihilation in the two regions. These processes are coupled not only through the dislocation microstructure, but also through the mechanics of the composite structure. The model is used to describe various deformation properties of metals, including stage II, stage III, and stage IV strain hardening and saturation of the flow stress. The coupling of cross-slip and climb controlled recovery processes leads to gradual transitions in strain hardening and gives a natural account of the transition from low temperature deformation to high temperature creep. The model also leads to polarized dislocation structures, internal stresses, and anelastic creep properties.

Kinetics of solution hardening

Abstract: The flow stress of solution hardened single crystals and polycrystals is analyzed with respect to its dependence on temperature and strain rate. An evaluation of literature data, especially at low temperatures and low concentrations in fcc alloys, reveals that the interaction between dislocations and discrete, atomic-sized obstacles (or fixed clusters of them) cannot be responsible for solution hardening. A “trough” model is favored in which the effect of the solutes is postulated to be equivalent to a continuous locking of the dislocations along their entire length, during every waiting period. The macroscopic features of this model are similar to Suzuki’s chemical-hardening model. It can also explain the strong interaction of solution hardening and strain hardening at elevated temperatures, as well as basic features of dynamic strain-aging, in particular its strain dependence.

A unified mechanism of stress corrosion and corrosion fatigue cracking

Abstract: A mechanism of stress corrosion cracking (SCC) is outlined in which anodic dissolution at film rupture sites relieves strain hardening and reduces the fracture stress at the crack tip. Experimental evidence is cited to suggest that relief of strain hardening occurs by interaction of subsurface dislocations with divacancies generated by the anodic dissolution. A transgranular crack propagates by accumulation of divacancies on prismatic planes which then separate by cleavage under plane strain conditions at the crack tip. At appropriate metallurgical and chemical conditions, anodic dissolution and/or divacancy migration may be enhanced at grain boundaries, leading to an intergranular failure mode. Evidence is also available to indicate that cyclic loading relieves strain hardening. Relief of strain hardening by combined cyclic loading and corrosion accounts for the higher incidence of corrosion fatigue cracking (CFC) without the requirement of any critical dissolved species. Data on fatigue of stainless steel at elevated temperature in both vacuum and air provide additional support for the proposed mechanism.

Temperature and strain rate dependence of stress-strain behavior in a nickel-base superalloy

Abstract: The temperature and strain rate dependence of yield and work hardening behavior in elevated temperature stress-strain testing was investigated in the nickel-base superalloy UDIMET 115. This alloy was heat treated to produce a bimodal distribution of hyperfine and coarse γ1 precipitates. Yield behavior is shown to be controlled primarily by dislocation pair cutting of the hyperfine precipitates. Stage II work hardening appears to be governed mainly by the dislocation networks generated on the coarse precipitates as these are bypassed under the Orowan mechanism. Analysis of Stage III work hardening using ϕvs σ plots shows that a steady state exists for the stress-strain deformation of this system. Results are also reported on extremely strong serrated flow at moderately elevated temperatures and a high temperature ductility minimum.

Hardening behavior in fatigue

Abstract: Cyclic hardening behavior has been reviewed (1) in relation to cumulative strain, in which the hardening rate is small compared to that in monotonic deformation but can be related to it under certain conditions, and (2) in relation to the cyclic stress-strain curve, in which it is extremely large because dislocation densities become large in saturation. It is shown that single crystals of both wavy and planar slip character have plateaus in their cyclic stress-strain curves and that the localized strain is similar, although the dislocation structures associated with the regions of persistent slip are different. Strain avalanches are shown to be widely prevalent in cyclic deformation, and their interpretation yields valuable insight about dislocation behavior. Cyclic hardening in polycrystals of both pure metals and alloys is also reviewed. The cyclic stress-strain curves depend strongly on history, microstructure, and test conditions, and the flow stress can be explained by the Schmid factor, Sachs factor, or Taylor factor-depending on those conditions.

Polyaxial Yielding of Granular Rock

Abstract: Results from true triaxial testing on a granular dense marble are analyzed with emphasis on the incremental relations during strain-hardening (initial yield to peak strength) at constant intermediate and minor stresses. The strong dependency of the behavior on the value of intermediate principal stress is confirmed. Consistency of experimental flow rule was revealed for the examined yield states corresponding to initial yield, to a given value of plastic strain invariant, and to peak strength. A stress invariant and the corresponding one of plastic strain increment were almost equal, postulating a simple stress strain relation. The vector of plastic strain increment and the normal vector on the yield surface at the relative point formed an angle ranging from 10 to 23 degrees. On the basis of the preceding observations, a work balance equation, the resulting flow rule, and yield equation were extended to model three-dimensional behavior. Reasonable agreement was obtained between the predicted and experimental stress-strain relations.

Effects of plastic anisotropy and yield surface shape on sheet metal stretchability

Abstract: The influence of plastic anisotropy and the shape of the yield surface on localized necking of thin metal sheets is examined Forming limit curves (FLCs) of strain hardening, rate-sensitive sheets including Ti alloys, Al alloys, and steels are calculated on the basis of the Marciniak-Kuczynski approach using the quadratic Hill or the Drucker yield function in conjunction with either the flow or deformation theory of plasticity The roles of the R-value and the yield surface shape in biaxial stretchability of sheet metals are delineated and discussed in relation to the plasticity theories and yield functions It is concluded that the limit strains decrease with increasing R-value in the e2 > 0 region of an FLC but increase with the R-value in the e2 0 region, and are independent of the R-value at plane strain conditions These mixed, strain-path dependent effects are explained in terms of the shape of the yield surface and a recently proposed critical thickness strain criterion

Thermal cycling of a unidirectional graphite-magnesium composite

Abstract: Thermal cycling induced deformations of a unidirectionally reinforced graphite fibre-magnesium matrix composite are analysed with a micromechanical elastic-plastic model. The model is capable of describing the cyclic thermal behaviour as influenced by the matrix plasticity including strain hardening and Bauschinger effects. The analysis traces the entire thermal history over 18 cycles in the ±100° C range. Predictions correlate well with measured strains, especially in terms of trends in the coefficient of thermal expansion. The results suggest further attention is required for time and temperature dependent stress relaxation rates and the role of defects.

The post-yield behaviour of low-density polyethylenes

Abstract: The post-yield behaviour of linear low-density and high-pressure polymerized low-density polyethylenes have been compared in tension and compression Rubber elasticity theory has been used to describe the strain-hardening region of the stress-strain curves in terms of extension of amorphous regions and entanglement associated with crystalline regions The resulting strain-hardening functions were used to predict the geometry of the neck profiles produced while deforming in tension No relationship between strain hardening and environmental stress-crack resistance was found in that the two types of polyethylenes exhibited very different dependences

Pressure-shear waves in 6061-T6 aluminum and alpha-titanium

Abstract: T he pressure-shear plate impact technique is used to study material behavior at high rates of deformation. In this technique, plastic waves of combined pressure and shear stresses are produced by impact of parallel plates skewed relative to their direction of approach. Commercially pure alpha-titanium and 6061-T6 aluminum are tested under a variety of pressure and shear tractions by using different combinations of impact velocities and angles of inclination. A laser interferometer system is used to monitor simultaneously the normal and transverse components of motion of a point at the rear surface of the target plate. The experimental results are compared with numerical solutions based on an elastic/viscoplastic model of the material. Both isotropic and kinematic strain hardening models are used in the computations. The results indicate that unlike the normal velocity profiles, the transverse velocity profiles are sensitive to the dynamic plastic response and, thus, can be used to study material behavior at high strain rates. For the materials tested the results suggest that the flow stress required for plastic straining increases markedly with increasing strain rate at strain rates above 104s−1. Hydrostatic pressure of the order that exists in the tests (up to 2 GPa) does not affect the plastic flow in 6061-T6 aluminum and appears to have at most a minor effect on the deformation of the titanium.

On the methods of measurement of the flow properties of polyethylenes and their blends

Abstract: Samples of commercial LDPE, HDPE, LLDPE, and their blends were tested in the steady state (rotational and capillary), dynamic, and extensional modes. The steady state data at low rates of deformation followed the dynamic viscosity, η = η′, and at higher rates the complex viscosity η ≃ η*. In elongational tests strain hardening was observed for LDPE and some for HDPE. There was no strain hardening in flow of a standard LLDPE, and the equilibrium extensional viscosity η ≃ 3η′ in full range of deformation rates. In blends with ultrahigh molecular weight PE and with LLDPE strain hardening and an increase of the maximum strain at break, eb, were found. Some newer types of LLDPEs and their homologous blends show the strain hardening behavior. A brief review of the methods of measurement of the flow properties of polyethylene (PE) melt is provided. The text is divided into three parts: (1) types of melt flow; (2) comparative rheology of polyethylenes; and (3) linear low density polyethylene (LLDPE) blends. In the first part, the methods of measurement and correlation between the measured values are discussed. The steady state shearing, dynamic deformation, and uniaxial extensions are considered. In the second part rheological behavior of the three principal types of PEs, low density PE (LDPE), high density PE (HDPE), and LLDPE are presented. In part 3, the flow of four different types of LLDPE blends is reported on.

Stagnation of Strain Hardening During Reversed Straining of Prestrained Aluminium, Copper and Iron

Abstract: L'analyse de la vitesse de durcissement par deformation θ en fonction de la contrainte vraie permet de determiner si la stagnation du durcissement par deformation est un phenomene general dans les metaux a une seule phase ou non, et pour eclaircir l'origine de cette stagnation quand elle a lieu

Strain hardening of high-strength steels

Abstract: Strain hardening and the loss of ductility with increasing strength have been investigated for a series of cold-rolled high-strength steels. The strain hardening exponent n decreases with increasing strength S according to the relationship nSp=C, where p and C are constants for a given strengthening mechanism. The value of p (and hence the ductility) at a fixed strength level depends on the operative strengthening mode. Solid-solution hardening is the most ductile method of strengthening, followed, in order of decreasing ductility, by grain refining, precipitation hardening, partial annealing, and cold working. It is proposed that the influence of a strengthening mechanism is related to the strain at which a steady-state dislocation-cell structure is developed in the material. The lower this critical strain, the lower the ductility, since further strain must then be accommodated by microband formation. The critical strain is considered to be dependent on the rate of accumulation of geometrically n...