Showing papers on "Strain hardening exponent published in 1981"

The Penny-Shaped Crack and the Plane Strain Crack in an Infinite Body of Power-Law Material

Abstract: A study is carried out of the problem of a penny-shaped crack in an infinite body of power-law material subject to general remote axisymmetric stressing conditions. The plane strain version of the problem is also examined. The material is incompressible and is characterized by small strain deformation theory with a pure power relation between stress and strain. The solutions presented also apply to power-law creeping materials and to a class of strain-rate sensitive hardening materials. Both numerical and analytical procedures are employed to obtain the main results. A perturbation solution obtained by expanding about the trivial state in which the stress is everywhere parallel to the crack leads to simple formulas which are highly accurate even when the remote stress is perpendicular to the crack.

On the Characterization of Strain-Hardening in Plasticity.

Abstract: : In the context of a purely mechanical, rate-type theory of elastic-plastic materials and utilizing a strain space formulation, this paper is concerned mainly with developments pertaining to strain-hardening behavior consisting of three distinct types of material response, namely hardening, softening and perfectly plastic behavior. It is shown that such strain-hardening behavior may be characterized by a rate-independent quotient of quantities occurring in the loading criteria of strain space and the corresponding loading conditions of stress space. With the use of special constitutive equations, the predictive capability of the results obtained are illustrated for strain-hardening response and saturation hardening in a uniaxial tension test.

Endochronic Description of Cyclic Hardening Behavior for Metallic Materials

Abstract: The cyclic hardening behavior of metallic materials at a prescribed constant plastic strain rate is investigated. The development is within the framework of the endochronic theory of viscoplasticity. It has been shown that a cyclic steady state can be attained theoretically, in agreement with the experimental finding. A general expression for describing the stress-strain relation for all cycles of a fatigue test with fixed total strain amplitude is presented and the peak stress of each cycle at different specified total strain level is also investigated.

Comparison of plane-strain and tensile work hardening in two sheet steel alloys

Abstract: Extended tensile tests and newly-devised plane-strain tests have been performed on two commercial sheet steels: an aluminum-killed (A-K) steel and a cold-rolled, dual-phase (D-P) steel. Up to uniform strain in uniaxial tension, the average work-hardening rate of both steels was found to be independent of strain state (isotropic hardening). The planestrain behavior of both steels was in good agreement with predictions of Hill’s old theory of normal anisotropic plasticity. At larger strains, the work-hardening rate in tension is greater than in plane strain. All of the tests were adjusted to reflect constant strain rates and all results were well represented by work hardening of the Hollomon type.

Macrostructure and mechanical behavior of fibers of poly‐p‐phenylene benzobisthiazole

Abstract: Morphology and tensile behavior of wet-spun fibers of poly-p-phenylene benzobisthiazole have been investigated. The as-spun fibers contain a large number of voids, which result in void-localized tensile failure. The stress–strain behavior is elastic–plastic with strain hardening. This behavior is shown to be the result of residual stresses which arise during the wet-spinning process.

Nonlinear Finite Element Analysis of Pull-Out Test

Abstract: A specific pull-out test used to determine in-situ concrete compressive strength is analyzed. This test consists of a steel disc that is extracted from the structure. The finite element analysis considers cracking as well as strain hardening and softening in the pre- and post-failure region, respectively. The aim is to attain a clear insight into structural behavior. Special attention is given to the failure mode. Severe cracking occurs and the stress distribution is very inhomogeneous. However, large compressive forces run from the disc in a rather narrow band towards the support and this constitutes the load-carrying mechanism. The failure is caused by the crushing of the concrete in this region, and not by cracking.

Plastic relaxation of the transformation strain energy of a misfitting spherical precipitate: linear and power-law strain hardening

Abstract: Complete solutions to the displacement, stress and strain fields, plastic zone size and misfit energy are calculated for an isotropic misfitting spherical precipitate under the assumptions of von Mises’ yield criterion and incremental plasticity. Analytical solutions are obtained for the case of linear strain hardening while a numerical technique is necessary for the case of power-law hardening. Large changes in the stress field in the regions surrounding the precipitate are observed when contrasted with the elastic state. The energy of the relaxed state is found to be a strong function of the strain-hardening parameter as is the plastic work done during the relaxation process. The plastic zone size, however, is not strongly dependent upon the strain-hardening parameter and for a homogeneous precipitate is independent of it.

Strain hardening at high strain in aluminum alloys and its effect on strain localization

Abstract: The modes of strain localization in the tensile testing of a sheet sample are diffuse necking, localized necking and, in some materials, localization in an unstable shear band. In a tensile test of a rate insensitive material, the normalized strain hardening parameter,H = (1/σ)(dσ/de) has the values ofH = 1 for diffuse necking andH = 0.5 for localized necking. Curves ofH vs strain were obtained up to large values of plastic strain using the hydraulic bulge test. The materials selected were commercially important sheet alloys in the condition normally used for forming. It is shown that the materials have similarH vs strain curves in the range of uniform tensile straining, but the curves diverge widely at higher strains whereH falls below 1. This has important consequences on strain localization behavior. The limit strains of the alloys in simple tension and punch stretching show reasonable correlation with their values ofH and those alloys which are susceptible to catastrophic shear failure have low values ofH at high strains. Strain rate sensitivity adds to or subtracts from theH values obtained in this study and has an additional influence on strain localization.

Strain hardening and dynamic recovery

Abstract: Work hardening and creep of pure metals are surveyed on the basis of the correlation between the main features of structure evolution and macroscopic behavior. At low strains dislocation storage follows geometrical rules resulting in a stage of athermal hardening. In the subsequent stage the hardening coefficient becomes temperature dependent. This can be described consistently by the increasing influence of a thermally activated dynamic-recovery component which superimposes upon the athermal hardening component. In this regime dislocations arrange in a cellular pattern, i.e., cell walls at low temperatures and subboundaries at high temperatures. As strain continues the development of the cellular structure appears to be disturbed by structural instabilities and inhomogeneities of deformation, such as dynamic recrystallization, micro-bands and shear bands. The influence of these processes on work hardening makes it necessary to distinguish four different stages of work hardening and has important consequences for the interpretation and evaluation of steady state flow.

Cyclic deformation of Nb single crystals I. Influence of temperature and strain rate on cyclic hardening, shape changes and stress asymmetry

Abstract: Niobium single crystals with single glide orientation have been cyclically deformed in tension-compression, at total axial strain amplitudes between 0.3 × 10−3 and 6.0 × 10−3. The cyclic hardening, the changes in shape of the crystals and the asymmetry of the hysteresis loop, have been studied at different temperatures (between 250 K and 354 K) and different strain rates (between 3.0 × 10−5 ' s−1 and 1.2 × 10−2 s−1). The cyclic stress-strain curves exhibit four different hardening regions, the main characteristic being the existence of a “plateau” region at low strain amplitudes where a limited amount of hardening or softening is observed. The length of this plateau increases as the temperature is decreased or the strain rate increased, and an interpretation is given in terms of the relative absence of dislocation-dislocation interactions. The shape of the cyclic stress-strain curves is found to depend on the cyclic strain history of the crystals, especially at the small strain amplitudes. The ch...

Strain-rate history and temperature effects on the torsional-shear behavior of a mild steel: Strain-rate history effects on the mechanical behavior of a mild steel are studied experimentally. The influence of a jump in strain rate from 10−3 to 103 s−1 at temperatures from −150 to 400°C and different large prestrains on the flow and fracture characteristics is presented and discussed

Abstract: Previous investigations on the effects of strain-rate and temperature histories on the mechanical behavior of steel are briefly reviewed. A study is presented on the influence of strain rate and strain-rate history on the shear behavior of a mild steel, over a wide range of temperature Experiments were performed on thin-walled tubular specimens of short gage length, using a torsional split-Hopkinson-bar apparatus adapted to permit quasi-static as well as dynamic straining at different temperatures. The constant-rate behavior was first measured at nominal strain rates of 10−3 and 103 s−1 for −150, −100, −50, 20, 200 and 400°C. Tests were then carried out, at the same temperatures, in which the strain rate was suddenly increased during deformation from the lower to the higher rate at various large values of plastic strain. The increase in rate occurred in a time of the order of 20 μs so that relatively little change of strain took place during the jump.The low strain-rate results show a well-defined elastic limit but no yield drop, a small yield plateau is found at room temperature. The subsequent strain hardening shows a maximum at 200°C, when serrated flow occurs and the ductility is reduced.The high strain-rate results show a considerable drop of stress at yield. The post-yield flow stress decreases steadily with increasing temperature, throughout the temperature range investigated. At room temperature and below, the strain-hardening rate becomes negative at large strains. The adiabatic temperature rise in the dynamic tests was computed on the assumption that the plastic work is entirely converted to heat. This enabled the isothermal dynamic stress-strain curves to be calculated, and showed that considerable thermal softening took place.The initial response to a strain-rate jump is approximately elastic, and has a magnitude which increases with decrease of testing temperature; it is little affected by the amount of prestrain. At 200 and 400° C, a yield drop occurs after the initial stress increment. The post-jump flow stress is always greater than that for the same strain in a constant-rate dynamic test, the strain-hardening rate becoming negative at large strains or low testing temperature. This observed effect of strain-rate history cannot be explained by the thermal softening accompanying dynamic deformation.These and other results concerning total ductility under various strain-rate and temperature conditions show that strain-rate history strongly affects the mechanical behavior of the mild steel tested and, hence, should be taken into account in the formulation of constitutive equations for that material.

Work-softening and hardening behaviour of granular rocks

Abstract: Work-Softening and Hardening Behaviour of Granular Rocks Experimental results from granular and dense rocks indicated that the plastic strain increment vector was inclined at a constant angle (approximately 70°) to the tangent of a curve fitted either to peak strength data or to strength data associated with a given value of axial or volumetric strain. The angle of inclination was independent of the direction of stress increment. When a small axial strain was exceeded changes of volumetric strain were found to be non-zero and had a linear relationship with the corresponding changes of axial strain. This applied for both work-softening and work-hardening behaviour. Close links between volumetric strain and microfacturing and between the ratios of stress and of strain increments were revealed. The role of confining pressure was predominant and the mode of deformation was cataclastic for granulated and intact marbles.

Stress Analysis for Kinematic Hardening in Finite-Deformation Plasticity.

Abstract: : Kinematic hardening represents the anisotropic component of strain hardening by a shift, alpha, of the center of the yield surface in stress space. The currently adopted approach in stress analysis at finite deformation accounts for the effect of rotation by using Jaumann derivatives of alpha and the stress. This analysis generates the unexpected result that oscillatory shear stress is predicted for monotonically increasing simple shear strain. Simple shear strain growing at constant rate gamma-dot = k yields a spin in the plane of shearing having the constant magnitude k/2. The effect of this on the evolution equation for the shift tensor alpha causes the latter to rotate continuously. In contrast, the kinematics of simple shear prescribe that no material directions rotate by more than pi radians. These two features seem inconsistant since the shift tensor has its origin embedded in the material, for example as rows of dislocations piled up against grain boundaries. By defining a modified Jaumann derivative based on the angular velocity of directions embedded in the body which characterize the effective resultant orientation of the micro-mechanisms responsible for the anisotropic hardening, a method of stress analysis is implemented which eliminates the inconsistency and yields a monotonically increasing shear stress. (Author)

Method for determining the hardness of strain hardening articles of tungsten-nickel-iron alloy

Abstract: The present invention is directed to a rapid nondestructive method for determining the extent of strain hardening in an article of tungsten-nickel-iron alloy. The method comprises saturating the article with a magnetic field from a permanent magnet, measuring the magnetic flux emanating from the article, comparing the measurements of the magnetic flux emanating from the article with measured magnetic fluxes from similarly shaped standards of the alloy with known amounts of strain hardening to determine the hardness.

Cyclic strain hardening of 316 stainless steel at elevated temperatures

Abstract: The cyclic strain hardening occurring during fatigue testing at 550°C was studied in terms of the dislocation structures developed. The dislocations are collected in dense tangles which form the boundaries of a cell structure. The stress required to push through, or eject, a dislocation from the cell boundary predicts the flow stress. These values showed good correlation with the cyclic shear stresses obtained by applying the Tresca criterion, which underlies its usefulness in design under cyclic loads. Carbide particles are shown to precipitate on grain and cell boundaries.

Some Observations on Time-Hardening and Strain-Hardening Rules for Creep in Zircaloy-2

Abstract: A study was made of the applicability of time-hardening and strain-hardening rules to describe creep deformation in Zircaloy-2 under variable stress and temperature conditions. Variable stress and ...

Creep of 2618 Aluminum under Side Steps of Tension and Torsion and Stress Reversal Predicted by a Viscous-Viscoelastic Model.

Abstract: : Nonlinear constitutive equations were developed and used to predict the creep behavior of 2618-T61 Aluminum at 200 C (392 F) for combined tension and torsion stresses and under varying stress histories including side step stress changes and stress reversals. The constitutive equations consist of 5 components: linear elastic; time-independent plastic; nonlinear time-dependent plastic recoverable; nonlinear time-dependent nonrecoverable under positive stress; and nonlinear time-dependent nonrecoverable under negative stress. For time-dependent stress inputs, the modified superposition principle and strain hardening are used to describe the behavior of nonlinear time-dependent recoverable and nonlinear time-dependent nonrecoverable respectively. The theory which combines all these features, the viscous-viscoelastic theory, and other modified theories were used to predict from information from constant stress creep the creep behavior of 2618 aluminum under the above stress histories with very satisfactory agreement with the experimental results. (Author)

Experiments on plastic deformation at finite strains

Abstract: The strain hardening behavior of metals at large plastic strains is difficult to assess experimentally. Consequently, many different techniques have been used to study such behavior and no clear experimental picture has evolved. In this paper experiments are reviewed on finite plastic deformation with emphasis on work reported since the comprehensive review of Gil Sevillano, van Houtte, and Aernoudt. The macroscopic strain hardening behavior is the primary concern, but its dependence on crystal structure, purity, alloying, microstructure, stacking fault energy, grain size, and deformation mode, is also discussed.