Showing papers on "Strain hardening exponent published in 1980"

Inhomogeneity of rolling texture in fcc metals

Abstract: The cold rolling of metal sheets and strips results in the formation of an inhomogeneous texture. The type and sharpness of texture in layers and the degree of inhomogeneity depend on the friction between rolls and the material and the geometry of the rolling gap. Contrary to the opinion of several authors, it is shown that the inhomogeneity of texture appears not only in the case of small values of thel/h ratio (l/h characterizes the geometry of the rolling gap) but also in the case of large values whenl/h > 5. In the first case shear texture forms in the intermediate layers of the rolled sheet while in the second, in its outer layers. The results of experiments carried out on aluminum, silver and 70/30 brass clearly show that the sensitivity of metals and alloys to the formation of an inhomogeneous texture is caused by their flow characteristics: yield strength (Y) and the work hardening exponent (m). High values ofY andm will tend to hinder the shear deformation, and consequently they will hinder the occurrence of inhomogeneity.

Quasi-Static Steady Crack Growth in Small-Scale Yielding

Abstract: A numerical analysis of quasi-static, steady-state crack growth under small-scale yielding conditions has been carried out for antiplane shear (Mode III) and plane strain, Mode I. In addition to results for an elastic-perfectly plastic solid, the study includes results relating to the influence of strain hardening on stable crack growth. Limited results based on a corner theory of plasticity give some indication of the extent to which stable crack growth predictions are sensitive to the type of plasticity theory used.

Large Strain, High Strain Rate Testing of Copper

Abstract: This paper describes the development of a high-speed torsional testing machine and results obtained on the strain-rate dependent strength of copper at large shear strains. Test techniques and data obtained are intended to be useful in applications such as ballistics and machining. For copper, the results indicate positive strain hardening behavior to very large strains under low rate, isothermal conditions and the transition to adiabatic thermal softening, shear instability and localization (shear banding) at high rates.

Measurement and Analysis of Plane-Strain Work Hardening

Abstract: A new technique for measurement of plane-strain work hardening has been developed which uses tensile loading and computer analysis for interpretation, and which eliminates the experimental uncertainties of large strain gradients, friction, and out-of-plane bending inherent in the usual plane-strain deformation modes. Plane-strain and tensile work-hardening curves have been measured for 2036-T4 aluminum alloy using several types of sheet specimens. The work-hardening rate in plane strain is lower than that in uniaxial tension. In each case a Voce-type empirical work hardening law represents the data well. Hill’s theories cannot account for these data because the isotropic hardening assumption is violated. A method of analysis was introduced to determine Hill’s newm parameter as a function of strain andm was found to vary from 1.6 to 2.0 in the strain range 0.02 ≤ e ≤ 0.18.

Network disentanglement and time‐dependent flow behaviour of polymer melts

Abstract: For small strains Lodge's rubberlike-liquid theory is a valid description of the rheological behaviour of polymer melts, but at higher strains the theory fails: The phenomenon of shear thinning which is characteristic for the shear flow of nearly all polymer liquids is not explained, and in elongation the deviation of the experimental data from the predictions of Lodge's theory reflect also a flow thinning, and not a strain hardening in spite of the pronounced S-shape of the stress-strain diagrams. Comparing the measured stress growth and stress relaxation data with the predictions of the theory, it must be concluded that the temporary physical network structure of the polymer melt is destroyed increasingly with the magnitude of the deformation. Hence, the number of entanglements decreases with increasing strain. For simple shear and uniaxial extension of a well-defined polyethylene melt the strain dependence of the relative entanglement density is discussed. The irreversibility of the disentanglement process of the network is considered.

Neck profiles in drawn linear polyethylene

Abstract: Neck profiles, neck propagation velocities and draw loads were measured for a series of linear polyethylene samples drawn in a tensile testing machine at 21, 75 and 100° C. The results were used to determine the profiles of strain, strain rate and draw stress in the neck. Elementary considerations show that the strain rate field in the neck relates to the strain hardening and to the strain rate sensitivity. A point of particular interest is that strain hardening appears to relate primarily to the polymer molecular weight whereas the strain rate sensitivity is more sensitive to the initial thermal treatment. The relationship of the present work to studies of true stress-true strain-true strain rate surfaces is discussed.

The effect of chain structure on the annealing and deformation behaviour of polymers

Abstract: In a tensile test ductile thermoplastics may give either uniform deformation or necking. Recently it has been found that those giving uniform deformation either, are known to have extended chain configurations in solution, or have chemical formulae with linear structures and relatively few flexible bonds. The observed differences in behaviour can be predicted from a viscosity retarded rubber elasticity model in which a constant related to chain flexibility is introduced, which quantifies the strain hardening of the material. It is argued that the early development of strain hardening generally interferes with the localization of plastic strain in shear bands or crazes (as well as in a neck) and correlates with the stress cracking performance of high density polythenes.

Dislocation theories of work hardening and yield surfaces of single crystals

Abstract: The nature of existing dislocation hardening mechanisms are analyzed. This analysis shows that the hardening mechanisms can be classified into two categories: isotropic and kinematic; consequently a general physical hardening law, which incorporates the concept of the degree of isotropy in work hardening, is proposed. The corresponding motions of yield surface in both stress and strain space are examined on the basis of this general hardening law and its two extreme cases: isotropic and kinematic hardening.

A viscoplastic material model and its application to cyclic loading

Abstract: A kinematic hardening model is generalized by introducing plastic and viscous residual “back” stresses α, β that govern the translation of the yield surface. The evolution equations for α and β are proposed and the material functions are identified for a construction steel by carrying out tension-compression tests at different strain rates. The cyclic tests with changing strain amplitudes and frequencies are next carried out and model predictions are compared with experimental results.

Cyclic creep of type 304 stainless steel during unbalanced tension-compression loading at elevated temperature

Abstract: Samples of Type 304 stainless steel were subjected to cyclic stresses with a positive mean stress at 300 and 560°C. Very rapid net elongation was observed whenever the stress limits were such as to produce a plastic strain amplitude of the same order of magnitude as the elastic strain at the peak stress. The maximum mean strain-rate, or cyclic creep rate, for a given peak tensile stress was achieved when the mean stress was just slightly above zero. Increasing the mean stress caused the mean strain rate to de-crease. The sensitive dependence of the mean strain-rate on the plastic strain ampli-tude and inverse dependence on the mean stress indicates that remobilization of disloca-tions by the reverse strain is an important mechanism for cyclic-creep acceleration. Although rapid cyclic creep was observed at both temperatures, a measurable mean strain rate was found for a much narrower range of stress conditions at 560 than at 300°C. The strain accumulated during cyclic creep did not produce any strain hardening, but did influence the shape of the stress-strain curve in a subsequent tensile test.

Prediction of ductile tearing using a proposed strain hardening failure assessment diagram

Abstract: The author has recently completed an evaluation of an engineering failure assessment approach developed at the Central Electricity Generating Board (CEGB) of the United Kingdom and became aware of certain limitations of this approach. The CEGB failure assessment approach, referred to in the United Kingdom as R-6, is an engineering approach to the elastic-plastic fracture mechanics assessment of structural components.

Strength of Composite Beams with Web Openings

Abstract: An ultimate strength analysis of composite beams with unreinforced, rectangular web openings is presented. The analysis is developed for general beam geometry and material properties, and for a single web opening of any practical depth, width and location. The beneficial effects of strain hardening and the shear contribution of the slab are neglected, and a four hinge failure mechanism at the opening is assumed. Analytical results indicate that a composite section with a web opening has a significantly higher bending strength than the corresponding noncomposite section, and that variations in opening length, height and eccentricity can have a significant effect on the ultimate strength. Comparison of the analytical results with the limited experimental data available indicates that the theory provides a very conservative estimate of the ultimate strength. The discrepancy between theory and test results is attributed primarily to strain hardening and the shear contribution of the slab.

A finite element solution for plasticity with strain-hardening

Abstract: Three basic boundary value problems areformulated in terms of stresses and hardening parameters Piecewise hnear simphcial éléments are employed and some error estimâtes derived, provided certain regulanty of the exact solution holds Ifthe solution is not regular, the convergence is proven Resumé — Trois problèmes aux limites fondamentaux sont exprime s en font tion des contraintes et de patamettes deaouissage On utilise des éléments finis simplutain (ineaues paf moueaux et on établit des majorations d'erreur, moyennant une certaine régulante de la solution exacte Si la solution n'est pas reguliere, on démontre la convergence The flow theory of plasticity with stram-hardenmg matenal (cf. [5]) has been studiedrecentlybyC. Johnson [8],Groger [3]andNeöas [6] from a new point of view, pioneered by Nguyen Quoc Son [14] and Halphen-Nguyen Quoc Son [4] The common idea of their existence proofs is to formulate the problem by means of vanational mequahty of évolution and to use a penalty method. Vanous incrémental fmite element solutions have been published in the engineering literature. To the author's knowledge, ho wever, the only theoretical convergence analysis have been presented by C. Johnson [9] In the present paper, we propose another variant of the incrémental fini te element method, startmg from the formulation of the quasi-staticj^roblem in terms of stresses and^ ïïârdenmg parameters only. Whereas m the mixed method of [9] the stresses and hardemng parameters are approximated by piecewise constant functions and the displacements by piecewise hnear functions, we employ piecewise hnear functions for both the stresses and the hardemng parameters. The stress approximations consist of equihbnated tnangular or tetrahedral blockelements respectively (cf [15, 7, 11, 12]) (*) Reçu novembre 1979 (*) Mathematical Institute of the Czechoslovak Academy of Sciences, Zitna 25, Praha 1, Tchécoslovaquie R A I R O Analyse numenque/Numencal Analysis, 0399-0516/1980/347/$ 5 00 © Bordas-Dunod

Site Factors Controlling Liquefaction

Abstract: A finite element procedure for determining the dynamic response and liquefaction susceptibility of a deposit of saturated sand subjected to an arbitrary bedrock acceleration is developed. The method is structured in accordance with the generalized Biot constitutive equations for an inelastic two-phase medium, and it includes a law of the endochronic type to model the deviatoric constitutive behavior of the sand. The approach has the capability of accounting for: (1) Strain hardening and softening; (2) densification; (3) hysteretic and viscous damping; (4) the development of pore pressure due to volume change; and (5) consolidation due to internal pressure generation. The results reported in this investigation demonstrate that "site" factors, such as the shear resistance of the overburden, seepage conditions, nature of the loading history, layer thickness, bulk compressibility, and phase coupling, greatly affect the pore pressure increase in saturated sand layers subjected to a seismic excitatin. (Authors)

Improving the formability of low carbon sheet steel by control of interstitial carbon content and temperature

Abstract: Several authors have shown a relationship between strain rate sensitivity and the formability of sheet metals In this study it is shown that by cooling to subzero temperatures the strain rate sensitivity of low carbon sheet steel can be improved dramatically and that this increased strain rate sensitivity leads to improved formability At laboratory strain rates the optimum conditions for improved formability, a temperature of ∼70 °C and an interstitial carbon content of ∼20 ppm, were determined experimentally Optimization involves a tradeoff between strain rate sensitivity, strain hardening and fracture strain Testing under these conditions leads to an improvement in formability of ∼13 pct

Simultaneous Stress Relaxation in Tension and Creep in Torsion of 2618 Aluminum at Elevated Temperature.

Abstract: : Experiments are reported for stress relaxation and simultaneous stress relaxation and creep with proportional and non proportional loading and unloading. Results were compared with predictions of a viscous-viscoelastic theory, and modifications, and strain hardening. Predictions were calculated from results of combined constant-stress tension and torsion creep and recovery tests only, which were reported previously. Results showed that a modified viscous-viscoelastic theory predicted all the observed features and predicted the creep and relaxation rates reasonably well. (Author)

Comparison of a Dual Phase Steel with Other Formable Grades

Abstract: The forming properties of an as-rolled dual phase steel were measured and compared with those of three other formable grades of steel sheet. In addition to standard tensile tests, hydraulic bulge, stretch bend, hole expansion and dome stretching tests were performed and forming limit curves and fracture maps obtained. The results show that the strain hardening rate in the dual phase steel is initially higher than in a 50 ksi (350 MPa) HSLA steel but at about 15 pct strain it becomes lower. Fracture strains are similar to those in an 80 ksi (560 MPa) HSLA steel. It is shown that significant strain occurs in the flanks of the stretch bend test piece particularly with the dual phase steel and that the results must be interpreted with care. The hole expansion test indicated that the sheared edged ductility of the dual phase steel was superior to that of an 80 ksi HSLA steel. The discussion includes a correlation of the different mechanical tests and observations on the selection of steels for various types of formed parts.

Generalized Plane-Strain Problems in an Elastic-Plastic Thick-Walled Cylinder

Abstract: : A new finite-difference approach has been developed for solving the generalized plane-strain problems of partially-plastic thick-walled cylinders made of strain-hardening or ideally-plastic materials. The tube is assumed to obey the Von Mises' criterion, the Prandtl-Reuss flow theory and the isotropic- hardening rule. The forces include internal pressure, external pressure, and end force. An incremental approach is used and no iteration is needed for each increment. The approach is simpler than others yet quite general and accurate. The desired accuracy can be achieved by reducing the grid sizes and load increments. Some numerical results for the stresses and displacements in partially-plastic thick-walled cylinders with either open-end or closed-end conditions are presented.