Showing papers on "Strain hardening exponent published in 1976"
TL;DR: The authors showed that the difference between the tensile and compressive strengths of tempered martensites is primarily a manifestation of the general pressure dependence of flow stress in these materials and that the volume expansion after deformation was much smaller than that predicted by the normality flow rule of plasticity theory for materials with such pressure dependence.
Abstract: Earlier results showed that the difference between the tensile and compressive strengths of tempered martensites is primarily a manifestation of the general pressure dependence of flow stress in these materials. However, the same results also showed that the volume expansion after deformation was much smaller than that predicted by the normality flow rule of plasticity theory for materials with such pressure dependence. Additional results now obtained on maraging and HY-80 steels support these conclusions. The results for all these materials exhibit a strong, but not perfect, correlation between pressure dependence, yield stress, and volume expansion. The volume expansion, however, which is believed to result primarily from the generation of new dislocations, is very small and does not appear to be essential to the pressure dependence. Most of the pressure dependence, the portion responsible for the discrepancy with the normality flow rule, may be an effect on dislocation motion. The results suggest that an appropriate plasticity model would be one in which the octahedral shear yield stress is linearly dependent on the mean pressure, but the volume change is negligible in violation of the normality flow rule. Such a model has been proposed previously for the plastic deformation of soils. However, unlike that model, the present theory includes strain hardening.
230 citations
82 citations
TL;DR: In this paper, the translational rule in a nonlinear, kinematic hardening model was modified to simulate cyclic loading and axial strain accumulation for asymetric stress cycle.
Abstract: By modifying the translational rule in a non-linear, kinematic hardening model, it is shown that some phenomena occuring during cyclic loading can be simulated: stress relaxation for cycles with prescribed strain amplitude superposed upon fixed strain, axial strain accumulation for asymetric stress cycle, cyclic hardening or softening. It is also shown that the variation of hardening modulus along the yield surface after plastic prestrain is fairly well described by the present model. The accumulation and relaxation phenomena depend on additional material function which can be determined from uniaxial loading-unloading or cyclic loading tests.
56 citations
TL;DR: In this article, the elastic and the fully plastic solutions were used to interpolate behavior from the small-scale yielding range to the fully-plastic range and the relations between the J-integral, load point displacement, crack opening displacement, and the applied load were developed.
Abstract: General procedures are proposed which utilize the elastic and the fully plastic solutions to interpolate behavior from the small-scale yielding range to the fully plastic range. The relations between the J-integral, load point displacement, crack opening displacement, and the applied load thus developed, are applicable to test configurations and cracked bodies in general. To assess the accuracy of the estimated relationships, a detailed numerical investigation, which employs an accurate finite element approach, is carried out for a particular configuration under antiplane shear. The results obtained from the full numerical calculations, for values of the applied load well into the fully plastic range, are in excellent agreement with the estimated results.
45 citations
TL;DR: The recorded load time histories showed marked nonlinearities in the stress strain behavior of some specimens including plastic deformation and strain hardening effects, thus emphasizing that the fracture energy alone is an incomplete representation of the tensile impact behaviour of bone.
43 citations
39 citations
TL;DR: In this paper, an exact asymptotic expansion is given for the initial post-bifurcation behavior of a perfect plate compressed into the plastic range, and the imperfection sensitivity is studied through an asymptic analysis of the behavior of the hypoelastic plate that results from neglecting the effect of elastic unloading.
38 citations
TL;DR: In this paper, the authors examined the strain-hardening behavior of spheroidized steels in terms of continuum and quasi-continuum models based on the requirement that continuity be maintained at various boundaries in the two-phase polycrystals.
35 citations
TL;DR: In this article, the work hardening coefficients of Type 316 stainless steel niobium and 1100 aluminum alloy are measured in tensile tests and the significance of the experimental results is discussed in terms of the concept of the mechanical equation of state for plastic deformation.
29 citations
TL;DR: In this paper, the strain-hardening parameters of steel, copper and brass were determined by uniaxial and balanced baoxial tensile tests and the results showed that the stress-strain relationship of steel was well described by the Hollomon equation while, the Voce equation was valid for copper and Brass.
Abstract: The strain-hardening parameters of steel, copper and brass were determined by uniaxial and balanced biaxial tensile tests. The stress-strain relationship of steel was well described by the Hollomon equation while, the Voce equation was valid for copper and brass. Thus the use of then-value as a measure of strain-hardening ability is justified for steel only and uniform strains have to be used for copper and brass. The uniaxial and biaxialn-values of steel were found to be equivalent. However, the stress-strain relationships of copper and especially brass were observed to be stress-state dependent. Forming limit diagrams of the materials were constructed using hydraulic bulging and tensile tests. The FLDs were also calculated using the plastic instability conditions and the strain-hardening parameters determined.
23 citations
TL;DR: In this article, the relative importance of various parameters in the floating-plug tube drawing process was investigated, and a kinematically admissible velocity field was assumed for the deformation process.
Abstract: The upper-bound technique has been used to investigate the relative importance of the various parameters in the floating-plug tube-drawing process. A kinematically admissible velocity field is assumed for the deformation process, and the solution takes into account the position of the plug in the deformation zone, redundant work, friction, and strain hardening. The proposed mode of deformation is substantiated by experimental evidence and by comparison of theoretical and experimental values af the drawing stress.
TL;DR: In this paper, a model is proposed which can account for both the magnitude of h and its observed stress dependence, assuming that dislocations, activated by a stress increment within subboundaries, can traverse the subcell diameter, d. The observed behaviour of h is dependent on the relationship between d and stress, and on the friction stress, σo, of the material.
Abstract: The strain-hardening parameter h, measured during creep by means of small stress increments, is usually found to have values of 0.1–2G, where G is the shear modulus. Depending on material, the value can be stress-independent or can vary as the reciprocal of the stress. A model is proposed which can account for both the magnitude of h and its observed stress dependence. In the model it is assumed that dislocations, activated by a stress increment within subboundaries, can traverse the subcell diameter, d. The observed behaviour of h is dependent on the relationship between d and stress, and on the friction stress, σo, of the material.
01 Jan 1976
TL;DR: In this paper, a two-dimensional elastic-plastic computer program was adapted to calculate problems in plane stress as well as plane strain geometry, and a simulation of a tension test of a flat aluminum plate pulled to failure was calculated with the modified two dimensional program.
Abstract: In the study of ductile fracture it is useful to simulate fracture on the computer under plane stress conditions. In general, this is a three dimensional problem. Presented here is a method for adapting a two dimensional elastic-plastic computer program to calculate problems in plane stress as well as plane strain geometry. A simulation of a tension test of a flat aluminum plate pulled to failure is calculated with the modified two dimensional program. The results are compared with a fully three dimensional calculation. Finally a comparison is made with an experiment to demonstrate the effectiveness of the computational methods for studying fracture of work hardening materials.
TL;DR: In this paper, a model for the thickness effect on K c has been developed on the basis of these observations and is in fair agreement with experimental results, showing that void nucleation, void growth, and void coalescence are dominant microstructural events that control ductility and therefore fracture toughness.
Abstract: For most technical materials the dominant mechanism resisting crack extension is plastic deformation. Continuum mechanics analysis shows that fracture toughness, in addition to depending on Young's modulus, flow stress, strain hardening exponent, and yield strain, should be nearly proportional to the effective fracture ductility obtained for the stress state characteristic for the region ahead of the crack; plane stress or plane strain. The original equation for plane-strain fracture toughness-equibiaxial ductility is refined to include the effects of strain hardening. Such a correlation has been experimentally confirmed for steels; K I c was found to be proportional to the effective equibiaxial ductility. A model for the thickness effect on K c has been developed on the basis of these observations and is in fair agreement with experimental results. The dominant microstructural events that control ductility, and therefore fracture toughness, are void nucleation, void growth, and void coalescence. Void nucleation at an inclusion-matrix interface is governed by the value of the interface strength-flow stress difference and is, consequently, temperature sensitive. Models for void growth mechanisms show the void coalesence strain to be a strong function of the nuclei density but rather insensitive to temperature. Qualitative relationships are presented which give some insight into the microstructural causes for ductility and fracture toughness transitions (or their absence in face-centered-cubic materials) with temperature, and can serve for the development of new high-toughness materials.
TL;DR: In this article, an equation has been derived which will permit plane-strain fracture toughness, K I c, to be calculated from a knowledge of uniaxial tensile properties.
Abstract: An equation has been derived which will permit plane-strain fracture toughness, K I c , to be calculated from a knowledge of uniaxial tensile properties. After corrections for constraint and strain hardening the plane-stress rigid plastic crack opening displacement expression was found to describe accurately experimental crack opening displacement for the plane-strain condition. The crack tip strain distribution was measured and found to be compatible with an r - 1 strain distribution within a small region ahead of the crack tip. A length parameter was identified and shown to be proportional to mean-free ferrite path in steels. From the proposed behavior of crack tip instability, it was possible to better understand the observed trend of decreasing fracture toughness with increasing yield strength and how this trend can be altered by control of the microstructure.
TL;DR: In this paper, the effect of back-stress hardening on cyclic deformation was investigated for a quenched and tempered low alloy steel which contained cementite particles, and the initial slopes of the cyclic stress-strain curves for several steels were demonstrated to coincide with the theoretical work-hardening rates calculated on the basis of back stress hardening due to the included carbide particles.
Abstract: Low cycle fatigue was considered in relation to back-stress hardening. Cyclic stress-strain behaviours under controlling strain and stress conditions were investigated for a quenched and tempered low alloy steel which contained cementite particles. The cyclic stress-strain states obtained by the two prescribed tests were uniquely described using a parameter which reflected the cumulative reversible plastic work associated with the back-stress hardening. It was suggested that the effect of back-stress hardening on cyclic deformation should appear directly on the cyclic stress-strain curves defined as the loci of the tips of stable hysteresis loops. The initial slopes of the cyclic stress-strain curves for several steels were demonstrated to coincide with the theoretical work-hardening rates calculated on the basis of back-stress hardening due to the included carbide particles. Finally, the Manson-Coffin law was explained from the view that the surface damage would progress in parallel with the structure change in the bulk according to the persistency of slips resulting from the reversible back-stress hardening.
TL;DR: Stress-strain curves obtained at constant cross-head velocity tensile tests of Ti-6Al-4V sheets at different temperatures show different behavior as discussed by the authors, suggesting that necking occurs at various locations along the gauge length.
01 Jan 1976
TL;DR: In this article, it is shown that the Bailey-Orowan approach to simultaneous strain hardening and recovery is in conflict with experimental results on the work-hardening behavior of many fcc mono-and polycrystals, and therefore should not be used in creep theories either.
Abstract: It is shown that the Bailey-Orowan approach to simultaneous strain hardening and recovery is in conflict with experimental results on the work-hardening behavior of many fcc mono- and polycrystals, and therefore should not be used in creep theories either. A more promising approach is the superposition of strain hardening and strain softening, a term used for mechanically rather than thermally activated recovery processes. The strain-rate dependence of the mechanical properties is then characterized by two exponents m and n, one for the isostructural flow stress and one for the strain-softening process. The latter dominates steady-state creep up to temperatures of about 0.6 of the melting point, and can, by extrapolation, even explain high-temperature creep.
TL;DR: In this paper, a computational scheme is presented for the analysis of a certain class of problems involving creep of metals at elevated temperatures, where the high temperature nonelastic behavior of materials is assumed to obey a new mechanical equation of state type constitutive relation recently proposed by Hart.
01 Jan 1976
TL;DR: In this paper, the tangent stiffness and pseudo force forms of the equations of motion are derived within the context of a total Lagrangian formulation, and the small strain formulations and computational procedures of the mechanical sublayer model and combined kinematic-isotropic hardening as used in the general purpose structural analysis program AGGIE I are presented Several sample problems are then presented along with recommended guidelines for use of the two plasticity models.
Abstract: The tangent stiffness and pseudo force forms of the equations of motion are first derived within the context of a total Lagrangian formulation After a brief discussion of available incremental theory plasticity models, the small strain formulations and computational procedures of the mechanical sublayer model and combined kinematic-isotropic hardening as used in the general purpose structural analysis program AGGIE I are presented Several sample problems are then presented along with recommended guidelines for use of the two plasticity models
TL;DR: In this paper, a cyclic mechanical equation of state at high temperature is discussed from some experimental results on random and periodic cycling of two high temperature steels, where stress relaxation as recovery opposing strain hardening the shape of the high temperature hysteresis loop is described.
TL;DR: In this paper, the authors determined the rupture conditions of a part-through crack in a relatively thin plate or tube by using conformal mapping to determine the aperture at the center of the crack.
Abstract: This study is concerned with the determination of the rupture conditions of a part-through crack in a relatively thin plate or tube. Zones at the bottom of the crack and at the crack-tip, which have become plastically deformed are replaced by equivalent constraining efforts exerted on the rest of the structure that is assumed to deform elastically. A subsequent elastic analysis, utilizing conformal mapping in which the appropriate boundary conditions are introduced, allows one to determine the aperture at the center of the crack. Two rupture criteria are considered. First, the stress in the connecting ligament at the center of the crack is equal to the rupture stress of the material. Second, the opening at the center of the crack is a critical material characteristic. Experimental verifications were conducted on A106B steel and on AISI 304 steel at 540°C which predicted the point of bursting of tubes within 15% and 10% respectively in 90% of the cases.
TL;DR: In this paper, the authors examined the supporting evidence for surface layer control of cyclic hardening and found that critically depend upon an assessment of the stress to initiate plastic flow after a cycling and surface removal procedure.
TL;DR: In this article, a review of the theoretical work dealing with the title problem and some experiments on circular plates under uniform edge compression are described, and the experimental results are compared with the predictions of the applicable theories.
Abstract: Theories describing postbuckling and postyielding of circular plates under uniform edge compression have been published by several authors in recent years. There is, however, no experimental verification available for any of these theoretical approaches. The present paper reviews the theoretical work dealing with the title problem and describes some experiments on circular plates under uniform edge compression. The experimental results are compared with the predictions of the applicable theories. The importance of material strain hardening and the phenomenon of ‘jamming’ of plastic hinges is discussed.
TL;DR: In this paper, the deformation of Hastelloy alloy C-276 was studied and the relationship between flow stress, strain, strain rate and temperature was examined and the mechanical equation of state was developed.
Abstract: High temperature deformation of Hastelloy alloy C-276 was studied. Hot compression tests were carried out at 1900, 2000, 2050 and 2100°F and at strain rates ranging from 10s3 to 1 set-I. The relationship between flow stress, strain, strain rate and temperature was examined and the mechanical equation of state was developed. Stress, strain and strain rate behavior at 2100°F was found to be markedly different from that at 1900 and 2000°F. The material showed a high degree of strain hardening at 2100°F. The activation energy for the deformation of Hastelloy alloy C-276 was found to be 109 Kcal/mole which is much higher than the activation energy for self-diffusion of nickel. It is suggested that dynamic recrystallization could be the rate-controlling mechanism. Microstructure examination revealed that recrystallization was promoted by higher temperature and higher deformation speed.
01 Jan 1976
TL;DR: In this article, a new equation describing recovery creep is proposed, where e is the strain and is the eventual steady creep rate, where r is the recovery rate and h is the hardening coefficient.
Abstract: A new equation describing recovery creep is , where e is the strain and is the eventual steady creep rate. From one form of the equation, namely , the McVetty-Garofalo, two forms of logarithmic, and Andrade creep equations are obtained with n = 1,2, and 5/2 respectively. From another form, namely , Li's, Akulov's and McLean's equations are obtained. These and other equations which are obtained are thus systematically related to each other. The physical bases of several derivations are also shown to be similarly related.During the deceleration from the initial creep rate to the final rate , there develops not only a balance between the rate of recovery, r, and the strain hardening coefficient, h, so that , but also a decrease in r and an increase in h which prolongs primary creep. This paper shows how to take into account the changes in r and h, and that equations which do so, whether implicitly or explicitly, describe experimental creep strain/time curves quite well.It is thus shown that behind the presen...
TL;DR: In this article, the shape of the strain hardening curves of alloy mono-and polycrystals is analyzed; it is shown that it depends substantially on the stress level τF.
Abstract: A brief review is given of the peculiarities of the strain hardening of face-centered cubic (fee) alloys as compared with pure metals. The fundamental equations connecting the strain hardening characteristics to the quantitative characteristics of the dislocation structure and the slip trace picture are considered in application to alloys with a high friction stress of a nondislocation nature τF. The shape of the strain hardening curves of alloy mono- and polycrystals is analyzed; it is shown that it depends substantially on the stress level τF.
01 Jan 1976