Showing papers on "Strain hardening exponent published in 1972"

Elasto‐plastic stress analysis. A generalization for various contitutive relations including strain softening

Abstract: SEVERAL SIMILAR PROCESSES FOR SOLVING ELASTO-PLASTIC PROBLEMS ARE DISCUSSED IN THE CONTEXT OF A GENERAL FORMULATION WHICH INCLUDES ASSOCIATED AND NON- ASSOCIATED PLASTICITY RELATIONS AND STRAIN HARDENING AS WELL AS STRAIN SOFTENING BEHAVIOR. ADVANTAGES OF THE "INITIAL STRESS" PROCESS ARE EMPHASIZED FOR A WIDE CATEGORY OF PROBLEMS; THE ISOPARAMETRIC FORMULATION IS USED THROUGHOUT. THIS PROCESS, RENAMED THE "RESIDUAL FORCE METHOD", FORMS THE BASIS OF THIS PAPER; IT IS DEMONSTRATED THAT FURTHER IMPROVEMENTS CAN BE OBTAINED BY SUITABLE MODIFICATIONS. /DOT/

Stress Distribution at the Interface Between Tool and Chip in Machining

Abstract: Stress distribution along a tool rake face were measured directly in the orthogonal machining of various metals. The method of measurement was based on the use of a composite tool which was divided into two parts parallel to a cutting edge in order to measure separately the force acting on one section of the tool. The stress distributions under actual cutting conditions were revealed, and the relationship between the nature of stress distribution and the mechanical properties of work material was clarified. It was ascertained that the nature of stress distribution was closely connected with the strain hardening index of work material and the frictional coefficient between tool and material.

The application of a dislocation model to the strain and temperature dependence of the strain hardening exponent n in the Ludwik-Hollomon relation between stress and strain in mild steels

Abstract: With the aid of a dislocation model for the stress-strain relationship of α-Fe, analytical expressions for the strain and temperature dependence of the exponentn in the relation, σ= K · e n, are derived. These account quite accurately for experimental results obtained with several low alloy steels. It is shown thatn varies continuously with strain but that the theoretical and experimental log σ-log e curve in most cases can be approximated by two straight lines in accordance with the well-known “double-n” behavior. The strain, e1 at which the two lines intersect is equal to the strain at which the theoretical n(e) curve has an inflection point. With the model presented it is also possible to account for the temperature dependence ofn(e) and of e1 within the temperature range −78° to 500°C.

Finite element analysis of strain-softening clay

Abstract: Strain-softening stress-strain behavior and the resulting progressive type failure are of importance in many geotechnical problems. Available analyses are limited in scope or are empirical in nature as mathematical formulations become difficult. Stress-strain-strength models presented in the literature are reviewed, and it is noted whether the models can accommodate strain-softening behavior. An approach based on the theory of plasticity is suggested and applied by means of the finite element method, to determine the undrained load-deformation curve and bearing capacity for a circular foundation on saturated clay. The accuracy of the analysis in the plastic range is evaluated, and the results from computations with and without plastic strain-softening are compared. A dramatic increase in deformations and reduction in bearing capacity was found for only relatively modest amounts of strain-softening. The numerical analysis is used to evaluate deformation and bearing capacity data obtained from a circular test fill in the field.

Plastic flow in binary substitutional alloys of BCC iron-effects of wire drawing and alloy content on work hardening and ductility

Abstract: The strength of cold-drawn, titanium-gettered iron wires can be substantially increased by substitutional solutes. For the elements studied, strengthening is progressively less in the order Si, Pt, Mn, Ni, Cr, and Co. The strengthening effect of the solute increases with strain, but at a greatly diminishing rate for true strains greater than unity. Six at. pct Si reduces the strain necessary to achieve a tensile strength of 200,000 psi (1380 MN/m2) from 7.3 for iron to 3.7. This effect of alloying on strain hardening appears to be related to the strength of the annealed alloy rather than to the specific alloying element used to achieve that strength. Also, the reduction-of-area ductility of the drawn wires is more closely related to the tensile strength of the wire than to its alloy content or degree of cold work. A fibrous cellular substructure is formed in all the alloys, but the formation of these cells is displaced to higher strains, the greater the strengthening effect of the solute. The transition from homogeneously distributed, tangled dislocations to a cellular substructure has no effect on the rate of strain hardening of the alloy-alloying can be used effectively as a substitute for cold work without adversely affecting the resistance of the alloy to ductile failure.

Plastic deformation and strain hardening in pure Nacl at low temperatures

Abstract: The plastic deformation and strain hardening of NaCl crystals and f.c.c. crystals have much in common. The easy glide hardening rate for NaCl can be as low as that observed in copper. Random slip on the conjugate system can increase the hardening rate and cut short the easy glide extension. In Stage II of deformation, such secondary slip produces impenetrable obstacles to dislocations on the primary system in the form of long, narrow, and thin dislocation bands. With increasing strain, the primary dislocations, obstructed by the secondary dislocation bands, stress the latter, first in compression then in tension, as can be followed by the photoeleastic effect. The internal stresses of such birefringent secondary slip bands do not directly affect the now stress. The impenetrable bands, acting similarly to non-deformable fibres in a ductile matrix, govern the flow stress through the dimensions of the inter-band regions. Hardening occurs when the long-range stresses due to deformation incompatibilit...

An approximate theoretical study of the dynamic plastic behavior of shells

Abstract: An approximate theoretical procedure is presented which may be used to estimate the dynamic plastic response of arbitrarily shaped shells. The influence of finite-deflections is retained in the analysis, but material elasticity, strain hardening and strain rate sensitivity are disregarded. The two particular cases of a complete spherical shell which is subjected to a spherically symmetric pressure pulse and a fully clamped cylindrical shell loaded impulsively are considered in some detail. It is observed that the predictions for these two cases agree favourably with the results of more exact rigid-plastic theories.

Determination of Dislocation Velocities and Densities from the Deformation Waves of Discontinuous Yielding

Abstract: The deformation waves that accompany the repeated discontinuous yielding of metals are analyzed with respect to utilizing their characteristics to determine dislocation velocities and densities as functions of stress and strain. Repeated yielding experiments were performed on an annealed 2024 aluminum alloy and an α‐brass using a ``dead‐weight'' loading apparatus. Measurements were taken of deformation wave velocities and widths and the associated plastic strain increments and strain rates. The calculated dislocation velocities and densities appear to be reasonable and consistent.

Interaction between Dislocation Pile Ups

Abstract: The interaction between two pile ups containing equal number of dislocations in four different configurations is calculated by an approximate analytical method. The calculated lengths of the interacting pile ups are compared with those obtained numerically, and shown to be in good agreement. Both analytical and numerical results show that the interaction between the pile ups is appreciable when the interplanar spacing of the pile up is less than the length of an isolated pile up. The analytical method presented here could prove useful in the study of strain hardening of solids.

Relationships for tensile creep under transient stresses

Abstract: The tensile creep occurring during and immediately after loading has been studied for an 11 per cent chromium steel and a nickel-base alloy at elevated temperatures It was found that the strains incurred during loading are dependent upon loading rate and can be estimated from consideration of the equations for static creep by using the assumption of strain hardening The strain incurred during slow loading causes the processes of creep to be at a more advanced stage when the static phase commences so that the resulting strain rates are also dependent upon the rate of loading Rapid loading tends to produce almost wholly elastic strains so that the subsequent static phase involves a more fundamental shape of creep curveThe approach was extended to consider minimum creep rate and fracture, and it was shown that they could be related to applied stress by use of the creep equation The shapes of the stress-strain hysteresis loops were also derived from the creep equation and estimates based on stati

Interactions between creep, fatigue, and strain-aging in two refractory metal alloys

Abstract: The application of low-amplitude, high-frequency fatigue vibrations during creep testing of two strain-aging refractory alloys (molybdenum-base TZC and tantalum-base T-111) significantly reduced the creep strength of these materials This strength reduction caused dramatic increases in both the first stage creep strain and the second stage creep rate The magnitude of the creep rate acceleration varied directly with both frequency and A ratio (ratio of alternating to mean stress), and also varied with temperature, being greatest in the range where the strain-aging phenomenon was most prominent It was concluded that the creep rate acceleration resulted from a negative strain rate sensitivity which is associated with the strain aging phenomenon in these materials (A negative rate sensitivity causes flow stress to decrease with increasing strain rate, instead of increasing as in normal materials) By combining two analytical expressions which are normally used to describe creep and strain aging behavior, an expression was developed which correctly described the influence of temperature, frequency, and A ratio on the TZC creep rate acceleration

Experimental study of the origin of strain-rate sensitivity in a common Pb-Sn alloy

Abstract: The origin of strain-rate sensitivity existing in the room-temperature plastic distortion of a 60 pet Pb-40 pet Sn alloy is examined experimentally using simple tension loadings. It is found that the response of this material to both constant stress and constant strain-rate loadings is accurately described by a single uniaxial constitutive relation which is independent of the instantaneous level of straining rate and dependent explicitly only on stress, strain and lapse-time variables. The rate sensitivity exhibited by this alloy during room-temperature quasistatic tensile deformations is thus concluded to be explainable directly in terms of a combination of the competing effects of strain hardening and time-dependent thermal softening without the necessity of introducing explicit strain-rate mechanisms of any kind.

The Influence of Cyclic Hardening and Microstructure on the Fatigue of an Al–Si Alloy

Abstract: An investigation has been made into the influence of cyclic hardening and microstructure on the fatigue of an Al–l % Si alloy in reversed bending over a life range of 104–107 cycles. It is found that in fatigue the solution-treated structure is stronger than the aged structures, contrary to the behaviour in tensile testing. At high stress amplitudes, the solid solution hardens very considerably because the density of dislocation loops becomes high as a result of strain-ageing. In particular, this greatly extends the crack-growth stage. At low stress amplitudes, the crack-initiation stage is very long in the solution-treated alloy but in the aged alloy microcracks nucleate rapidly at grain-boundary areas. The empirical Manson relation is valid approximately for plastic strain amplitudes and the observed variation in the exponent is shown to be a result of differences in hardening and in crack initiation and propagation rates among the structures tested.

Spherical wave propagation in a viscoplastic medium

Abstract: A study is presented of the problem of spherical wave propagation in an infinite viscoplastic medium. The surface of a spherical cavity is subjected to a uniform impact load which is continuously maintained. The material is elastic/viscoplastic, satisfying Mises condition, isotropic hardening, and viscoplastic incompressibility. A generalized form of Malvern's constitutive relation is used with a bilinear static shear stressshear strain curve, the method of characteristics, and an IBM 7040–7094 digital computer. Particular emphasis is placed on the influence of strain hardening and of the viscosity coefficient. It is shown that changes in the strain hardening coefficient and in the viscosity coefficient have considerable influence on the results, which is to some extent unexpected in view of previous work on this subject.

Dynamic Properties of S-200-E Beryllium

Abstract: : Results of an experimental study of the dynamic properties of S-200- E beryllium are presented Areas studied included uniaxial stress behavior, elastic constants, equation of state, elastic precursor decay, and shock wave profiles The material showed a yield 'plateau' and then significant strain hardening, and exhibited strain rate sensitivity Longitudinal and shear wave velocities at 20C were 1284 and 886 mm/microsec The shock wave equation of state up to 30 kb was determined to be linear: sigma sub H = 07 + 1527 u sub p Compressive wave tests showed a ramped, non-steady-state elastic precursor, and shock wave profiles showing both release behavior and attenuation were obtained Scanning microfractographs were taken of spall fracture surfaces

A Rate-Dependent Constitutive Model of Shock-Loaded S-200 Beryllium.

Abstract: : A rate-dependent constitutive model is developed for the one-dimensional deformation of S-200 beryllium at room temperature. The current knowledge of dislocation dynamics is used in formulating the constitutive model from consideration of the basic physical mechanisms that are involved in plastic flow processes. The constants which arise in the model are evaluated from macroscopic data, including quasi-static strain hardening data, low-to-medium strain rate data, and stress wave profiles. A numerical scheme for incorporating this constitutive model into one-dimensional, finite-difference computer codes has been developed and implemented into the RIP code. Calculations of the attenuation of thin stress pulses show excellent agreement with experimental observations. (Author)

Shakedown of Strain-Hardening Structures

Abstract: Elastic perfectly plastic theory predicts progressive permanent deformations of statically indeterminate structure with each cycle of variable repeated loading above the so-called shakedown load. Experimental evidence of this behavior, however, is contradictory. In an effort to explain some of the observed discrepancies, a theory of incremental deformations is developed which includes the effects of strain hardening of the material. On the basis of calculations, the importance of strain-hardening is assessed, and results of two earlier test programs are used to verify the validity of the approach. On the basis of comparison of analytical and experimental results, it is concluded that strain-hardening must be included for realistic prediction of the incremental deformations of steel structures.

Estimation of creep and fatigue behaviour under cyclic loading

Abstract: Equations to estimate creep behaviour under cyclic stressing have been developed from the assumption of strain hardening. Reasonable correlations were obtained with experimental data for tensile-stress cycling of a nickel alloy and an 11 per cent chromium steel at elevated temperatures. A cyclic hardening effect was identified which lowers rates of strain accumulation and leads to unexpectedly long endurances, particularly at the higher loading rates and temperatures. However, this causes estimated lives to err on the safe side. Behaviour is predominantly fatigue-dependent at the lower temperatures but either creep or fatigue may predominate at intermediate temperatures. Assumption of linear damage enabled reasonable estimates of lives to be made for different loading rates and stresses by use of readily available creep and plain fatigue data. There was no evidence of any creep-fatigue interaction that could cause reduced endurances.