Showing papers on "Strain hardening exponent published in 1979"

Annihilation of dislocations during tensile and cyclic deformation and limits of dislocation densities

Abstract: It is proposed that, during dislocation glide at low temperatures, both screw and non-screw dislocations annihilate mutually with dislocations of opposite sign approaching on closely neighbouring glide planes. The experimental evidence is summarized and possible mechanisms are discussed. Phenomenological models of dislocation accumulation during deformation, taking into account the annihilation of dislocations, are formulated. The analysis of selected examples of tensile and cyclic deformation of f.c.c. and b.c.c. metal crystals demonstrates that annihilation of edge and/or screw dislocations occurs during strain hardening and can lead to steady state deformation. It follows that the dislocation densities introduced during deformation cannot exceed well-defined upper limits that are distinctly lower than the hypothetical upper limits estimated for the static case. The observations suggest that the critical spacings of dislocation pairs that annihilate are ∼.50–500 nm for screw and ∼ 1·6 nm for ed...

Mechanical behavior and hardening characteristics of a superplastic Ti-6AI-4V alloy

Abstract: The deformation behavior of a superplastic Ti-6A1-4V alloy at 927°C has been characterized by means of constant strain-rate tensile tests up to large plastic strain. Significant hardening has been recorded in the course of deformation. Microstructural studies on deformed samples indicate the occurrence of simultaneous strain-rate induced grain growth, which explains nearly all of the hardening. A small amount of hardening may also be expected from grain elongation or grain clustering effects. As a result of concurrent grain growth, the strain-rate sensitivity is found to decrease with strain, thus indicating that stress-strain rate behavior determined initially may not be applicable after large amounts of plastic strain. The stressJstrain-rate data obtained from step strain-rate test for a variety of grain sizes, together with the grain growth kinetics plots, provide a means for developing a constitutive description for this material at large strains.

Constitutive Model for Short-Time Loading of Concrete

Abstract: A constitutive model based on nonlinear elasticity is proposed, where the secant values of Young’s modulus and Poisson’s ratio are changed appropriately. This alteration is obtained through the use of a nonlinearity index that relates the actual stress state to the failure surface. The model simulates the strain hardening before failure, the failure itself and the strain softening in the post-failure region. The dilation of the concrete and the influence of all three stress invariants are considered. All stress states including those where there are tensile stresses can be dealt with; however, the model is calibrated using experimental data obtained by a uniaxial compressive and tensile test only. The model predictions are demonstrated to be in good agreement with experimental results involving a wide range of stress states and different types of concrete.

Bifurcation analysis of the triaxial test on sand samples

Abstract: A bifurcation analysis of a strain hardening dilatant sand sample in the triaxial test is carried out. The analysis shows that the triaxial test yields only then the limiting soil properties if 1) the sample is compact enough and 2) if the confining pressure does not exceed a critical value depending on the soil anisotropy and the slenderness of the sample.

Analysis of stress-strain relations by use of an anisotropic hardening plastic potential

Abstract: A method of analyzing plastic behavior by use of an anisotropic hardening plastic potential is proposed. The plastic potential surface in deviatoric stress space is assumed to be the same as the equi-plastic-strain surface. Stress-strain relations in combined loading and in multi-axial cyclic loading are calculated by use of the anisotropic hardening plastic potential and the normality rule of the plastic strain increment vector to the plastic potential surface, which are experimentally determined or confirmed by subjecting thinwalled tubular test specimens of 60 40 brass to combined axial load, internal pressure and torsion. The calculated results agree fairly well with the experimental observations.

Strain and strain-rate hardening effects in punch stretching of 5182-0 aluminum at elevated temperatures

Abstract: The influences of material properties on stretch forming are often studied by testing a wide variety of materials. However, differences in texture, fracture strain, and crystal structure are not taken into account. These material differences are eliminated in the present study by performing tests on a single material (5182-0 aluminum alloy) in which strain hardening, strain-rate hardening, and limit strain vary in a precise manner with temperature and strain-rate. This allows a comparison to be made between experimental results and analytical calculations to separate the contributions of these two types of hardening in distributing strain during elevated temperature forming. Furthermore, the influence of a change in limit strain to overall formability can be assessed since the hardening phenomenon is better understood. The strain distributions developed during forming over a spherical punch are calculated using the finite element method and material properties obtained from tensile tests at 25, 130, and 200°C at varying strain rates. These are compared to experimental strain distributions over the same temperature range. Measurements of limit strains are taken from forming limit diagrams. This research demonstrates that formability is improved at elevated temperatures through increases in both strain-rate hardening and limit strains.

Hardening mechanisms of hard gold

Abstract: Electrodeposited hard gold with 0.6 at.% cobalt has a hardness about four times that of annealed bulk gold and this high hardness cannot be reproduced by standard metallurgical methods. By measuring the hardness for gold and gold alloys subjected to various quenching, annealing, and deformation processes, all common hardening mechanisms such as solution hardening, precipitation hardening, strain hardening, and ’’voids’’ hardening were eliminated as possible major hardening contributors with the exception of the grain size effect. Pure gold with grain sizes ranging from 200 A to 3 μm were prepared using sputtering deposition by varying the substrate temperature during deposition from 55 to 310 °C. Larger grain sizes from 5 to 200 μm were prepared by annealing cold‐drawn gold wire at 300–750 °C. The hardness versus grain diameter followed the Hall‐Petch relation up to a grain size of 0.1 μm. Beyond that, the hardness increased less rapidly. At the grain size of electrodeposited hard gold of 250–300 A, the sputtered pure gold gave the same hardness value also. Therefore, the grain size effect accounts for the observed high hardness of electrodeposited hard gold, with other mechanisms accounting for only small alterations.

Concrete Plasticity Theory for Biaxial Stress Analysis

Abstract: A three-parameter elastic-plastic strain hardening theory for prediction of biaxial stress-strain response of concrete is developed in terms of accumulated equivalent plastic strains in tension and compression. The hardening rule permits individual variation of the current yield value in compression and the current yield values in tension in two principal directions. Hardening functions are determined from tensile and compressive uniaxial tests. The theory is intended for use in the analysis of prestressed thin-shell containment structures. Predictions of stress-strain response are compared with experimental data of material response available in the literature. The technique is then used to predict the response of two large-scale prestressed concrete wall segment biaxial tension tests and the results are compared to the experimental data. The results indicate that the theory can form a basis for practical inelastic analysis of prestressed concrete thin-shell tension structures.

Superposition of alloy hardening, strain hardening, and dynamic recovery

Abstract: The principles and heuristics of flow stress superposition are illustrated for the case that one of the components is due to dislocation/dislocation interactions and is the only one that changes with strain. A simultaneous investigation of the flow stress and its rate sensitivity as a function of strain then allows one to confirm or refute postulated superposition laws and, in addition, to separate the effects of alloying or heat treatment on yield stress and on strain hardening. The slope of the observed stress strain curve depends on the form of the superposition law even if there is no physical influence of alloying on the dislocation storage rate; the frequently observed low initial strain hardening associated with a higher yield stress may in some cases be merely a consequence of a nonlinear superposition. At higher strains, the influence of alloying on dynamic recovery becomes the predominant effect; it also controls the high-temperature creep strength. When dynamic recovery plays an important role, it provides a further straining mechanism which, however, is not additive to the low-temperature strain rate; a form of the superposition law for long-range slip and this dynamic recovery strain is proposed. An application of these principles has demonstrated thatmore » dynamic strain aging is due to an effect of mobile solute atoms on the strain-hardening component of the flow stress, not on the friction stress.« less

Theoretical latent hardening in crystals—I. General equations for tension and compression with application to F.C.C. crystals in tension

Abstract: E quations for latent strengths in single slip, based upon the simple theory of finite distortional crystal hardening introduced by K.S. Havner and A.H. Shalaby (1977), are derived for both tensile and compression tests without restriction as to crystal class. Detailed comparisons between theoretical results and the experiments of P.J. Jackson and Z.S. Basinski (1967) on copper crystals in tension are presented. There is good qualitative agreement between theory and experiment regarding the diversity of anisotropic hardening among slip systems. Moreover, there is satisfactory quantitative agreement between the theory and the extrapolated experimental data in the stage III, large-strain range. It is suggested that further experimental investigation of latent hardening at large prestrains would be desirable. The simple theory predicts anisotropic hardening and the perpetuation of single slip in axial loading of cubic crystals initially oriented for single slip, but predicts symmetric, isotropic hardening of specimens initially oriented in positions of 4, 6 or 8-fold multiple-slip. These predictions are in general accord with experimental observations from tests of f.c.c. and b.c.c. crystals.

The mechanical property of montmorillonite clay at high pressure and implications on fault behavior

Abstract: Preconsolidated montmorillonite clay was deformed up to 30% strain at confining pressures up to 4 kb (400 Mpa) under undrained conditions. The deformation was characterized by plastic yield, strain hardening, a broad peak strength at large strain, and a gradual decline in strength thereafter. In some cases the sample was ruptured, with stress drop of the order of 0.1 kb. At confining pressures greater than 2 kb, the peak strength was about 0.35 kb and did not depend markedly upon confining pressure. These results may have important implications on the stability and the strength of faults.

Comparison and Contrast of Mechanisms, Microstructures, Ductilities in Superplasticity and Dynamic Recovery and Recrystallization

Abstract: The mechanisms of hot deformation with either superplasticity, or dynamic recovery, or dynamic recrystallization are certainly distinct having different ranges of permitted strain rate and temperature, different microstructural preconditions and different strain rate sensitivities. The phenomena are similar in so far as an approximately steady state deformation can be established for each with no strain hardening and with a dynamically stable microstructure being, respectively, fine grains of two phases, recovered subgrains, and recrystallized grains containing a range of substructures. Such deformations proceed at comparatively low flow stresses and with high ductilities particularly comparable in compression or torsion modes of deformation.

The effect of dynamic annealing on dynamic strain aging phenomena in commercial purity titanium

Abstract: A study has been made of the effect of dynamic annealing, associated with climb, on the dynamic strain aging phenomena in commercial purity titanium. In speciemens deformed at a strain-rate of 10−4 s−1 with an average grain diam of about 17 μm, dynamic annealing starts to become important at the temperature of the major work hardening peak maximum. Metallographic evidence supports a conclusion that the shape of the high temperature side of the peak is determined largely by climb controlled processes. Reducing the grain size to 6 μm lowers the temperature, at which dynamic annealing becomes significant, enough so that the work hardening peak, the “blue-brittle” ductility minimum and the yield stress plateau are either nearly eliminated or greatly reduced in importance.

Mechanical‐stress‐induced degradation in homojunction GaAs LED’s

Abstract: The thermal stress in an LED caused by junction heating has been calculated. It is shown theoretically that the change of light output with time is proportional to the third power of thermal stress in the junction. This result is experimentally verified. Mechanical‐stress experiments demonstrate that degradation may occur by means of mechanical stress alone. Using the two‐path model for the quantum efficiency and the time dependence of the stress‐induced lattice‐defect concentration, a degradation formula is derived which can be verified to fit the behavior of many LED’s. The characteristic tapering off seen in most degradation curves can be attributed to strain hardening (dislocation pinning). A dark‐line‐defect progression is observed.

Creep of 2618 Aluminum Under Step Stress Changes Predicted by a Viscous-Viscoelastic Model

Abstract: : Nonlinear constitutive equations are developed and used to predict from constant stress data the creep behavior of 2618 Aluminum at 200 C (392 F) for tension or torsion stresses under varying stress history including step-up, step-down, and reloading stress changes. The strain in the constitutive equation employed includes the following components: linear elastic, time-independent plastic, nonlinear time-dependent recoverable (viscoelastic), nonlinear time-dependent nonrecoverable (viscous) positive, and nonlinear time-dependent nonrecoverable (viscous) negative. The modified superposition principle, derived from the multiple integral representation, and strain hardening theory were used to represent the recoverable and nonrecoverable components, respectively, of the time-dependent strain in the constitutive equations. (Author)

High-Temperature Stress-Strain Behavior of MgO in Compression

Abstract: Compressive stress-strain curves for several types of polycrystalline MgO specimens were correlated with those for single crystals and analyzed as a function of grain size and grain-boundary character at 1200° and 1400°C for several strain rates. The results for fully dense specimens were explained in terms of grain-boundary sliding and intergranular separation in addition to slip. The modification of grain-boundary nature concurrent with heat treatment for grain growth, caused by residual LUF, was associated with enhanced grain-boundary sliding and intergranular separation. For grain sizes <30 μm, it was concluded that the von Miss criteria for ductility could be relaxed by the Occurrence of dislocation climb and, to a limited extent, by intergranular separation. Yield drop corresponding to dislocation multiplication occurred when grain-boundary sliding was initially promoted. Specimens with a liquid phase of adequate viscosity also indicated plasticity accompanied by high strength. Specimens with clean grain boundaries exhibited ductility and normal strain hardening with no intergranular separation.

Deformation and Fracture in Aluminium-Zinc-Magnesium Alloys at Elevated Temperature

Abstract: Deformation and fracture of fine and coarse grain Al-Zn-Mg alloy sheets have been studied near solution-treatment temperature by conducting constant strain-rate tensile tests. Deformation is found to be controlled by a combination of grain deformation and grain boundary processes. Even though fine grain size yields mild superplasticity, strain hardening occurs continuously, and leads to the development of defect structure. Thus, flow stress and rate-sensitivity for large plastic deformation has been found to be dependent on both strain and strain-rate. Metallographic observation of internal cavity formation and growth during deformation is quantified by measurements of density change. Identification of void sites and the void growth kinetics have been considered in conjunction with the flow behavior so that the extent of tensile ductility obtained in these alloys can be understood.

A Model for Fatigue Crack Closure in Ductile Materials

Abstract: Possible contributions to fatigue crack closure from fracture surface undulations and protrusions in ductile materials are evaluated through a simple model. The model is based on the premise that the fatigue crack is open to the full extent of its length and singularity when the crack opening displacement exceeds the height of these protrusions. Our model predicts that crack closure effects will be more pronounced under plane stress as compared to plane strain loading; under spike overloading versus constant amplitude loading; in inert environments as against mildly embrittling environments; and will be generally more pronounced at decreasing values of cyclic and maximum stress intensity levels and stress ratio levels. It is predicted that the extent of crack closure will be dependent on cyclic yield strength and work hardening exponent of the material and in a stronger fashion on the true fracture ductility of the material. These predictions are compared and found to be in good functional and qualitative agreement with currently available data on fatigue crack closure behavior of ductile alloys.

Finite-strain large-deflection elastic-viscoplastic finite-element transient response analysis of structures

Abstract: A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.