Showing papers on "Strain hardening exponent published in 1978"
TL;DR: In this article, structural instability due to strain-softening (i.e., declining branch of the stress-strain diagram) is presented, and the existence of a lower limit on the size of this region permits ductility, along with its dependence on the structure size and stored energy, to be predicted by a stability analysis.
Abstract: Analysis of structural instability due to strain-softening (i.e., declining branch of the stress-strain diagram) is presented. In a continuum, strain-softening is impossible; it can exist only in a heterogeneous material. Failure occurs by unstable localization of strain or beam curvature, in which the stored strain energy of the structure is transferred into a small strain-softening region whose size is several times the aggregate size, or the spacing of reinforcement, or the depth of the beam. The existence of a lower limit on the size of this region permits ductility, along with its dependence on the size and stored energy, to be predicted by a stability analysis. Calculations of limit loads and moment redistributions in strain-softening beams and frames must include instability checks of possible curvature localization. The same applies to finite element analyses of reinforced concrete structures with account of tensile cracking, and predictions of limit loads of these structures which are questionable because they depend on the size of the finite elements.
467 citations
TL;DR: In this paper, the problem of elastic spring-back is investigated and transient free surface solutions are demonstrated for stretch forming and deep drawing, which is shown to be capable of dealing with boundary friction and strain hardening.
297 citations
199 citations
TL;DR: In this article, the lateral compression of circular tubes to large deformations is examined and the discrepancy between the theories and experiments reported previously is attributed in the main to an inadequate modelling of the stationary plastic hinges which are produced in the tube as it deforms.
181 citations
01 Jan 1978
TL;DR: In this paper, the bending deformation component was isolated by replacing the shoulders and bead of the drawbead by rollers, which reduced the friction to a negligible value and good agreement was found between the measured and calculated frictional components.
Abstract: During sheet metal forming on a double-action press, drawbeads on the blankholder supply a restraining force which controls the flow of metal into the die. As metal is drawn through the drawbead, the restraining force has two components, bending deformation and friction. In this study, these components were separated and analyzed. Drawing load, clamping load and strain were measured for sheet steels and aluminums which were drawn through a short section of simulated drawbead. The bending deformation component was isolated by replacing the shoulders and bead of the drawbead by rollers which reduced the friction to a negligible value. The experimental data is analyzed in terms of the materials effects which must be included in a mathematical model of drawbead forces. It was found that an isotropic hardening assumption would not adequately model the strain hardening but that a kinematic hardening assumption that takes cyclic hardening into account is necessary. It is also shown that strain rate hardening must be modeled for steel but not for aluminum. Friction is adequately represented by a coefficient of friction, µ. Experimental values of µ were obtained. Drawbead forces were calculated employing these experimental coefficients of friction and good agreement was found between the measured and calculated frictional components.
156 citations
TL;DR: In this article, the effects of a change in strain path on the deformation characteristics of aluminum-killed steel and 2036-T4 aluminum sheets have been studied and the form-ing limit diagram of steel was found to decrease with prestrain at a much faster rate than that of aluminum.
Abstract: The effects of a change in strain path on the deformation characteristics of aluminum-killed steel and 2036-T4 aluminum sheets have been studied. These sheets were pre-strained various amounts in balanced biaxial tension and the resulting uniaxial proper-ties and forming limits for other loading paths were determined. In comparison to uni-axial prestrain the steel was found to suffer a more rapid loss in uniform strain upon the strain path change from biaxial to uniaxial. In contrast, the uniform strain in aluminum does not drop as rapidly after the same change. In keeping with this behavior, the form-ing limit diagram of steel is found to decrease with prestrain at a much faster rate than that of aluminum. Such effects can be explained in terms of the transition flow behavior of the metals occurring upon the path change. Thus, the path change produces strain soften-ing and premature failure in steel, while causing additional strain hardening and consequent flow stabilization in aluminum.
147 citations
TL;DR: For elastic-plastic sheets under biaxial stretching localized necking is investigated in this article assuming that the material follows a kinematic hardening rule, and it is found that the forming limit curves predicted by kinematicshardening are in far better agreement with experimental results than the similar curve predicted by standard flow theory with isotropic hardening, which may be considered as a simple model of a solid that develops a vertex on the yield surface.
104 citations
TL;DR: In this paper, the effects of cementite particles and subgrain boundaries on the work-hardening behavior of spheroidized carbon steels were investigated by making direct measurements of residual internal stresses.
Abstract: The effects of cementite particles and subgrain boundaries on the work-hardening behaviour of spheroidized carbon steels were investigated by making direct measurements of residual internal stresses. These internal stresses developed due to plastic incompatibilities between elastic particles and the surrounding elastic–plastic matrix. A continuum analysis of these internal stress fields, based upon a multiple slip model, was found to be in good accord with the experiments regarding its predictions of the Bauschinger effect. The internal stresses appear to saturate in the plastic strain range of ∼ 3–5% where a transition in strain-hardening behaviour was observed (double-n behaviour), and to contribute approximately 20% to the total work-hardening. The cementite-particle-pinned subgrain boundaries, formed during a post-quench annealing treatment, were found to lower the internal stress levels, thus indicating that they assisted the relaxation processes of entrapped Orowan loops by acting as sources...
53 citations
01 Jan 1978
TL;DR: In this article, a review of these properties for several materials is presented in an attempt to show their importance on the necking behavior, and the dependence of the patterns of behavior upon the mode of stretching (in-plane and punch stretching) is discussed.
Abstract: Considerable interest exists in understanding the levels of maximum useful strains achievable prior to localized necking (forming limits) and their dependence on the imposed stress-state. Marciniak’s model of imperfection growth has successfully explained the rise in forming limit as the imposed strain-ratio (e2/e1) is increased from zero (plane strain) toward unity (balanced biaxial tension). Experimental studies on formability of various materials have, however, revealed basic differences in behavior, such as the “brass-type” and the “steel type”, exhibiting respectively, zero and positive dependencies of forming limit upon the strain-ratio. Such results cannot be reconciled without proper attention to the details of strain hardening and strain-rate hardening behaviors of these materials, particularly as functions of strain and strain-ratio. A review of these properties for several materials will be presented in an attempt to show their importance on the necking behavior. Furthermore, the dependence of the patterns of behavior upon the mode of stretching (in-plane and punch stretching) is discussed. Some results of a Marci niak-type model of material imperfection are also considered.
47 citations
TL;DR: In this article, the true stress-strain relations for PVC under plane strain compression and under uniform extension in tension have been determined, in each case true stresses increase with strain as orientation hardening sets in, and attempts have been made to relate the orientation-hardening process to three types of function: (1) a first order reaction process; (2) a power law function after Bahadur); (3) Rivlin-Mooney stored energy relationships.
TL;DR: In this article, single-crystal CdTe specimens were deformed in compression at 25°, 200°, 300°, and 500°C to various levels of plastic strain and to failure.
Abstract: Single-crystal CdTe specimens were deformed in compression at 25°, 200°, 300°, and 500°C to various levels of plastic strain and to failure. Deformation characteristics at each temperature are given as curves of shear stress vs shear strain and the effect of test temperature on deformation behavior is examined. The dislocation structure of the CdTe samples deformed at high temperatures is examined using transmission electron microscopy. The relation between the deformation properties and the corresponding microstructure in CdTe is explored using previously developed models to describe metallic and nonmetallic crystalline materials.
TL;DR: In this paper, a vanadium-strengthened SAE 980X steel and a GM 980X ferrite matrix were evaluated by scanning electron microscopy after biaxial and uniaxially deformation, and it was concluded that the higher work-hardening coefficient of the Ferrite matrix and the deformable martensite phase combine to give GM 980x its superior formability.
Abstract: Variations in the strain hardening behavior of GM 980X and a vanadium-strengthened SAE 980X steel were investigated as a function of strain. Changes in the microstructural deformation characteristics of the two steels were evaluated by scanning electron microscopy after biaxial and uniaxial deformation. Plastic deformation was found to occur in the SAE 980X steel by deformation of the ferrite matrix, while in GM 980X it occurred by deformation of both the ferrite and martensite phases. The GM 980X ferrite matrix was found to have a much higher work-hardening rate than that of the SAE 980X steel. Failure occurred in the SAE 980X steel when the ferrite was highly strained. In GM 980X it occurred after more extensive deformation had occurred, and the martensite phase was also highly strained. It was concluded that the higher work-hardening coefficient of the ferrite matrix and the deformable martensite phase combine to give GM 980X its superior formability.
TL;DR: In this article, experimental results of load relaxation studies of a commercial metallic glass as a function of temperature are reported, which suggest that metallic glasses exhibit deformation behavior with flow laws similar to those governing plastic deformation in crystalline solids.
01 Jan 1978
TL;DR: In this paper, the maximum strain that the sheet metal can suffer in stretch-forming processes is limited by the phenomena of strain localization and fracture, which are strictly connected with the stability loss of the workpiece.
Abstract: The maximum strain that the sheet metal can suffer in stretch-forming processes is limited by the phenomena of strain localization and fracture. Both are strictly connected with the stability loss of the workpiece. Different possible modes of instability are discussed in the paper. Also the post-stability stages of the forming process are analyzed. It is shown that the limit strain depends mostly upon the rate of strain-localization process that occurs in the unstable stage. The influences of stress ratio, material properties (strain hardening ability, strain rate sensitivity, temperature sensitivity, inhomogeneity) and the forming conditions (friction, surface pressure) on the strain concentration process and on the limit strain are analyzed.
TL;DR: In this article, the effect of unequal interface friction between tup-billet and billet-anvil contact surfaces on the strain distribution and hence the billet profiles as it is deformed to its final shape, together with the variations in tup and anvil loads and energy consumption is predicted theoretically using a numerical technique.
TL;DR: In this article, the role of cyclic hardening in crack nucleation at high strain amplitudes was investigated, and it was concluded that strain incompatibility is most responsible for the crack formation process in high strain fatigue, irrespective of the state of hardening.
TL;DR: For metastable austenitic steel, plastically deformed at −160°C under conditions of linear and plane stress states, an analytical expression for stress-strain curves describing the strain hardening of the austenite and the resistance of the developed martensite to deformation was obtained in this article.
Abstract: 1.
For metastable austenitic steel, plastically deformed at −160°C under conditions of linear and plane stress states, we obtained an analytical expression for stress-strain curves describing the strain hardening of the austenite and the resistance of the developed martensite to deformation. It was shown that, due to the effect of the type of stress state on the structure of the steel, the hypothesis of a single stress-strain curve for the investigated ratios of principal stresses is not satisfied.
2.
In biaxial tension, in contrast to uniaxial tension, dislocation density in the austenite increases and the development of martensite transformation is inhibited, resulting in a change in the numerical values of the stress-strain diagram parameters and a reduction in the ductility of the steel.
3.
The established dependences of the stress-strain diagram parameters on the type of stress state, taking into account the decisive structural characteristics of the steel, may be used to calculate flow stresses in biaxial tension from data obtained in mechanical and structural studies of the steel in uniaxial tension.
TL;DR: In this article, a special class of hardening response functions for small deformation of elastic-plastic materials, its application to isotropic metals, and comparison of the theoretical results with experimental cyclic stress-strain curves for two different metals are discussed.
Abstract: : This paper is concerned with a special class of hardening response functions for small deformation of elastic-plastic materials, its application to isotropic metals, and comparison of the theoretical results with experimental cyclic stress-strain curves for two different metals. The theoretical development is carried out within the scope of the existing purely mechanical theory for the 'rate-independent' response of elastic-plastic materials, which admits the existence of a single loading function, as well as certain accepted idealizations. After summarizing the basic equations for small deformation, detailed attention is given to the development of a special form of the hardening response function, motivated mainly by the observation that the stress-strain curves for uniaxial cyclic loading of a fairly large class of metals attain -- after several cycles -- the so-called saturation hardening.
TL;DR: In this article, the authors established microscopic ductile fracture processes in a fracture-tough superalloy, Inconel 718, aged to five strength levels, with a fracture toughness of 120 MPa-m1/2.
Abstract: Two microscopic ductile fracture processes have been established in a fracture tough superalloy, Inconel 718, aged to five strength levels. At yield strengths less than 800 MPa, the mechanism is a slow tearing process within large pockets of inhomogeneous carbides and nitrides, giving rise to plane strain fracture toughness (KIC)values greater than 120 MPa-m1/2. At yield strengths greater than 900 MPa, the mechanism involves fracture initiation at carbides and nitrides followed by off crack plane void sheet growth nucleated at the Laves (σ) phases. Here, the fracture toughness drops to about 80 MPa-m1/2. A Mode I normal strain growth model for low yield strength conditions and a shear strain void sheet model for high yield strength ones are shown to model KIC data obtained from a J-integral evaluation of compact tension results.
TL;DR: In this paper, true stress-true strain tensile data have been obtained for titanium modified type 316 stainless steel in the solution annealed condition and after exposure to a flowing sodium environment at temperature of 700, 650, 600 and 550°C.
TL;DR: In this article, the effect of one-sided reinforcement on the ultimate strength was evaluated on six beams containing mid-depth rectangular holes which were reinforced by welding horizontal bars to one side of the web.
Abstract: Tests are described on six beams containing mid-depth rectangular holes which were reinforced by welding horizontal bars to one side of the web. The objective was to evaluate the effect of one-sided reinforcement on the ultimate strength. Particular reference was made to beams with slender webs and to the effect of moment-to-shear ratio. The efficiency of the one-sided reinforcement was judged on the basis of the predicted capacity of a symmetrically reinforced beam with the same reinforcement area. It was found that, due to strain hardening, the ultimate strength achieved was in some cases equal to this predicted strength and, on the basis of such results, suggestions relating to design are made.
TL;DR: Crack growth resistance curves have been determined for crack-divider laminates in which layers of 2024-T3 aluminum alloy are adhesively bonded to layers of 7075-T6 alloy.
TL;DR: In this article, a model for corrosion-fatigue crack propagation (CFCP) was proposed, which is modified in an attempt to explain a number of curious behaviors of CFCP, including Poisson contraction, strain hardening, ligament surface attack/annihilation, and stress relaxation.
TL;DR: In this paper, the behavior of solution annealed material was examined through biaxial stress experiments conducted at room temperature under radial loadings (√3τ = σ) in tension-torsion stress space and the effects of both stress limited monotonic loading and strain limited cyclic loading were determined on the size, shape, and position of yield loci corresponding to a small offset strain (10 microstrain) definition of yield.
TL;DR: In this paper, a modified form of slip-line field solution was used to explain the variation of longitudinal stress ahead of notch tips in strain hardening materials, and the results of elastic-plastic stress analyses for notched bars.
Abstract: Using the results of elastic-plastic stress analyses for notched bars, it is shown that a modified form of slip-line field solution can satisfactorily explain the variation of longitudinal stress ahead of notch tips in strain hardening materials.