Showing papers on "Hardening (metallurgy) published in 1987"

Measurement of the temperature profile during shear band formation in steels deforming at high strain rates.

Abstract: A torsional Kolsky bar (split-Hopkinson bar) was used to deform tubular specimens of AISI 1018 cold rolled steel and AISI 1020 hot rolled steel at a nominal strain rate of 103s−1. Shear bands were observed to form in both steels, and the temperature of the material in the bands was measured by determining the infrared radiation emitted at the metal surface. For this purpose, a linear array of ten indium-antimonide detectors was used to determine temperature history at ten neighboring points lying across the projected path of the shear band. Results showed that shear bands in these steels are relatively wide, that the maximum temperature rise in the band is about 450°C and that the temperature distribution across the band is consistent with results of stability analyses. The two steels have very different work hardening rates and the strain at which localization is first observed is very different for the two steels : in the cold-rolled steel it occurs at about 15% strain, while in the hot-rolled the strain is near 100%. This result also is consistent with predictions of the analyses.

An Evaluation of Recent Developments in Hardening and Flow Rules for Rate-Independent, Nonproportional Cyclic Plasticity

Abstract: The Mroz kinematic hardening rule has previously demonstrated superior capability to correlate cyclically stable nonproportional stress-strain response. In this paper, recently proposed kinematic hardening rules for single and multiple surface cyclic plasticity models are evaluated. Significant improvement over the Mroz rule, without loss of generality, is achieved with a deviatoric stress rate-dominated rule proposed by Tseng and Lee for two surface theory. Recent approaches for correlation of the modulus function and isotropic hardening are discussed. The norm of the Mroz distance vector is found to uniquely correlate the variation of plastic hardening modulus through a cycle; it is necessary to include a measure of instantaneous nonproportionality, however, to properly normalize the modulus function. A new evolution equation is offered to correlate the additional isotropic hardening observed during nonproportional loading, and several contemporary approaches are also considered.

Models of viscoplasticity some comments on equilibrium (back) stress and drag stress

Abstract: Phenomenological and microstructural motivations for the terms appearing in the title are found in a literature survey. Although the interpretations differ with various investigators a strong tendency is observed to consider plastic flow as rate dependent. It is stated that plastic strain takes time to develop and the existnce of an equilibrium stress is postulated at which plastic strain is fully developed. It is similar to the back stress used in materials science. The drag stress introduced from microdynamical studies performs the same function as the isotropic variable in plasticity. Most of the theories that describe the transient and steady-state behavior of metallic alloys make the inelastic strain rate a function of the over (effective) stress. It is shown that this concept has considerable advantages in the modeling of changes of viscous (time- or rate-dependent) and plastic (time- or rate-independent) contributions to hardening that are observed in cyclic loading and dynamic plasticity.

Lime treatment of asphalt to reduce age hardening and improve flow properties

Abstract: This paper examines the effects of lime on asphalt age-hardening. The study takes into account the effects of both lime type and concentration and asphalt composition (source). The effects of lime on asphalt stiffness at higher temperatures and on asphalt low-temperature flow properties are also evaluated. High-temperature stiffness and low-temperature flow properties are important in controlling permanent pavement deformation and thermally-induced cracking.

Asymptotic Fields in Steady Crack Growth with Linear Strain-Hardening,

Abstract: The asymptotic stress and velocity fields of a crack propagating steadily and quasi-statically into an elastic-plastic material are presented. The material is characterized by J 2 -flow theory with linear strain- hardening. The possibility of reloading on the crack flanks is taken into account. The cases of anti-plane strain (mode III), plane strain (modes I and II), and plane stress (modes I and II) are considered. Numerical results are given for the strength of the singularity and for the distribution of the stress and velocity fields in the plastic loading, elastic unloading and plastic reloading regions, as functions of the strain-hardening parameter. An attempt is made to make a connection with the perfectly-plastic solutions in the limit of vanishing strain-hardening.

Ductile two-phase alloys: Prediction of strengthening at high strains

Abstract: When alloys containing two ductile phases are heavily deformed, composite-like microstructures develop and strengths well in excess of either of the phases in single phase form may be exhibited as a result of microstructure/dislocation density effects. In this paper a previously-published model for such strengthening is reviewed, and its application in a predictive capacity discussed. Flow stressvs fabrication strain data for the two components in single phase form and for one two-phase alloy are necessary for this purpose. The model may then be applied to predict strength for any other two-phase alloy as a function of composition, fabrication strain, and interphase spacing. The approach is illustrated using existing data for several alloy systems. For Ag-Fe and Cu-Nb alloys (with very limited mutual solubility) strengths can be predicted within 15 to 20 pct of the experimental values over the entire range of strains and volume fractions for which data are available. In systems where the potential for precipitation hardening exists (e.g., Cu-Fe) thermal history is important. When such hardening becomes a significant factor, the model cannot be used in its present form due to uncertainty over how to “add” the strengthening from this effect. Such hardening may, however, be useful in further improving the properties of these materials.

A Physically Based Internal Variable Model for Rate Dependent Plasticity

Abstract: In 1978 Krieg et al. published a ‘unified creep-plasticity’ model for rate-dependent deformation of metals, incorporating a power-law relationship between inelastic strain rate, applied stress, and instantaneous value of two internal variables.1 The internal variables were permitted to evolve by a Bailey—Orowan process, including strain hardening and recovery. Hardening was taken to be linear and to increase the internal variables rather than the flow stress directly; recovery was treated as thermal (as opposed to dynamic strain-activated) only, where the kinetics were derived from dislocation mechanics for the process in question. The physical basis was established because (a) the power-law flow rule was taken to be a mathematically convenient approximation to rate-process theory at fixed microstructural state, (b) linear strain hardening in polycrystals is usually viewed as an aggregate manifestation of the linear (stage II) hardening behavior of fcc single crystals oriented initially for single slip and in the absence of dynamic recovery,2,3 and (c) the recovery kinetics were derived from dislocation models. The value of physical bases follows, of course, from the confidence (indeed the meaning) that is given to extrapolation of the relationship beyond the range of measured data.

Deformation Hardening and Thinning in Both Elongation and Shear of a Low Density Polyethylene Melt

Abstract: Polymer melts show “thinning” in shear deformation and “hardening” in simple elongation; the latter phenomenon is especially pronounced for melts of branched polyethylene (LDPE). Elongation hardening and shear thinning are closely connected with the deformation histories in simple elongational and simple shear flows. These flows are used for material characterization, and they are adequate for purely viscous and purely linear viscoelastic liquids. For elastic liquids with slowly fading memory, however, the first principal stretch rate λ1(t) turns out to be a better reference than the components of the strain rate tensor, and λ1(t) is very different for the two conventional test modes, viz. simple elongation and simple shear. For a more relevant comparison of the rheological behavior in elongation and shear, we therefore deformed a LDPE melt at 150°C such that λ1(t) was the same in both test modes. The LDPE melt investigated showed hardening in elongation as well as in shear when λ1 increased exponenti...

Cyclic hardening mechanisms in NIMONIC 80A

Abstract: A nickel base superalloy was fatigued under constant plastic strain range (Δep) control. The hardening response was investigated as a function of Δep and particle size of the γ ′ phase. Hardening was found to be a function of the slip band spacing,i. Numerous measurements ofi and other statistical data on the slip band structures were obtained. Interactions between intersecting slip systems were shown to influence hardening. A Petch-Hall model was found to describe best this relationship between the response stress and the slip band spacing.

A simplified model of heat generation during the uniaxial tensile test

Abstract: The temperature rise in a sheet tensile specimen has been calculated by the finite difference method for a plain-carbon steel at various strain rates and in several environments. Prior to necking, a uniform heat generation function is used with the governing flow equation while during the post-uniform strain, an empirical heat generation function is used. The empirical function is based on a strain distribution equation generated by curve fitting of experimental data. The effect of heat transfer conditions on the temperature increase has been discussed. The maximum temperature rise in air may reach 42 K at the center of an I.F. steel specimen at a strain rate of 10-2/s. The instability strain during tensile testing has been predicted by taking into account strain hardening, strain-rate hardening, and deformationinduced heating. The results show that significant deformation heating can occur during tensile testing in air at “normal” strain rates near 10-2/s, and that the uniform elongation can be affected markedly. Predictions for other alloys based on tabulated data are also presented.

Stress and strain fields at the tip of a sharp V-notch in a power-hardening material

Abstract: The stress and strain fields at the tip of a sharp V-notch in a power hardening material are researched in this paper. It is found that the singularity of strain energy density at the tip is first slightly decreased and then increased when the hardening exponent n increases if the notch angle is not too large. It is also found that the singularity of strain energy density at the tip is nearly the same when n ≤ 40 and β ≤ 45° for fixed β. The analytical formula of the strain field at the tip for an ideal plastic material is found. The difference in the distribution of circumferential stresses σϑ for various n isn't large when the notch angle 2β is fixed; but the distribution of the radial stresses σr for different n is significantly different.

Some experimental results on yield condition in plane stress state

Abstract: In the present paper, the determination of yield locus curves for deep drawing sheet metal is described. The experiments are based on the combination of biaxial tension tests on plane cross-shaped specimens with uniaxial tension and compression tests performed on conventional specimens. The influence of preloading (prestrain) on the hardening behaviour is discussed. The material coefficients are computed through the equalization of the test results by means of a quadratic formulation of the yield condition. Finally, the material coefficients are given as functions of the prestrain of specimens in the rolling direction.

Effects of thermomechanical history on hardness of aluminium

Abstract: A viscoplastic constitutive model with an evolving internal state variable, called hardness, has been developed for commercially pure aluminium. One application of such a constitutive model is in process modelling where hardness distributions may be predicted throughout the workpiece. This paper assesses the accuracy with which microhardness measurements of quenched specimens correlate with the hardness predicted by the constitutive model for various imposed thermomechanical histories. Using axisymmetric compression, different hardness values are achieved by various tests, both underdeveloped (increasing hardness) and overdeveloped (decreasing hardness) structures being produced during deformation. The steady state flow stress and hardness for a particular strain rate and temperature may be achieved with less strain by first deforming at a high strain rate and then decreasing the strain rate. The constitutive model accurately predicts the amount of prestrain required at the higher strain rate. Dif...