Showing papers on "Strain hardening exponent published in 1990"
TL;DR: In this article, a model is proposed, which quantitatively takes into account the above effects, and the ultimate tensile properties of different particulate and short fibre filled thermoplastic composites are analysed using the proposed model equation.
444 citations
TL;DR: In this article, the constitutive equations of soil thermoplasticity were analyzed in light of the thermomechanical tests on three clays and the results showed a strong dependence of the elastic domain on temperature.
Abstract: Experimental results obtained from thermomechanical tests on three clays are analyzed in light of the constitutive equations of soil thermoplasticity presented in a companion paper. Heating and cooling drained tests at constant isotropic stress show a strong dependence of the elastic domain on temperature. Thermal sensitivity of elastic domain was found to be different in overconsolidated and in normally consolidated clays. Thermoplastic strain hardening builds up to compensate for thermal softening in normally consolidated clays at plastic compression during drained heating, if the constant stress is imposed. Triaxial compression tests at constant elevated temperatures show an increase in ductility and a decrease in dilatativity at high temperatures. Undrained heating tests show a significant water pressure buildup. At constant principal stress difference, the water pressure growth leads to an effective stress drop and an eventual failure at the critical state line. A temperature‐rate‐dependent non‐assoc...
328 citations
TL;DR: In this article, the plastic flow of polycarbonate (PC) was examined by obtaining true stress-strain data over a range of strain rates at room temperature through homogeneous, uniaxial, constant strain rate compression testing to strains as high as 125 percent.
Abstract: In this investigation, the plastic flow of polycarbonate (PC) was examined by obtaining true stress-strain data over a range of strain rates at room temperature through homogeneous, uniaxial, constant strain rate compression testing to strains as high as 125 percent. Uniaxial compressive loading conditions give rise to a planar molecular orientation process which results in the observed strain hardening in compression. Uniaxial tensile tests on PC were also conducted. The necked region of the tensile specimen is being cold drawn resulting in a uniaxial state of orientation. Therefore, the observed macroscopic strain hardening in uniaxial tension distinctly differs from that obtained In uniaxial compression, giving different stress-strain curves. The major differences experimentally obtained between the large strain response in compression and tension indicate a need for an orientation-based model of the strain hardening process. The experimental program also acts to uncouple the effects of strain softening and strain rate providing more accurate data for future modeling of the true strain softening process. A constitutive law which directly relates the strain hardening response to the state of molecular network stretch in the polymer is used to model and analyze the experiments. The model is found to simulate the observed rate dependent yield and post yield strain softening and hardening of the compressive data over the entire range of strain rates very well. The model is then utilized in a finite element analysis of the tensile tests on PC. Numerical results compared favorably with the experimental data including: load vs, contraction curves, natural draw ratio, and the axial stress-strain response of the cold drawing region.
237 citations
TL;DR: In this article, a thermoplastic version of the critical state model is proposed to model the plastic behavior of soils and shales due to heating and loading under constant elevated temperature.
Abstract: Plastic behavior of soils and shales due to heating and loading under constant elevated temperature is discussed in terms of a thermoplastic version of the critical state model. Rules for dependence of the yield surface on temperature in the elastic states and at yielding are proposed. The elastic domain is assumed to shrink during heating (thermal softening) and to expand during cooling, when the stress state is elastic. In a plastic state thermal softening occurs simultaneously with the plastic strain hardening. At a constant stress state, thermal softening may entirely be compensated by plastic strain hardening leading to thermal consolidation. Loading and unloading criteria are given to determine whether the soil response is thermoelastic or thermoplastic. As opposed to isothermal plasticity, stress rate excursions inside the current yield surface are admissable plastic processes, when temperature grows, even if strain hardening occurs. Also, outside stress rate excursions at the softening side may generate plastic strain, when cooling occurs. Thermally induced plastic strain rate non-associativity is discussed as well. Direct and inverse incremental strain-stress-temperature relationships are formulated. An analysis of the experimental results of thermomechanical testing of saturated clays is given in a companion paper.
230 citations
151 citations
TL;DR: In this article, the dependence on temperature and strain rate is shown to fit the sinh and Arrhenius functions, and the relationship between grain size, substructure, hot ductility, and stress is discussed.
149 citations
TL;DR: The material exhibited superplastic elongation (>150%) in a tension test at temperatures from 1000° to 1100°C and at strain rates from 7.2×10−5 to 3.6 × 10−4 s−1 as mentioned in this paper.
Abstract: Dense and translucent hydroxyapatite polycrystals (Ca10(PO4)6(OH)2 with a grain size of 0.64 μMm) were obtained by hot isostatic pressing at 203 MPa and 1000°C for 2 h in argon. The material exhibited superplastic elongation (>150%) in a tension test at temperatures from 1000° to 1100°C and at strain rates from 7.2×10−5 to 3.6 × 10−4 s−1. Extensive strain hardening was observed. The stress exponent of the yield stress was larger than 3.
100 citations
TL;DR: In this article, the effects of an electric current on dislocation mobility and mechanical properties at low homologous temperatures (T < 0.5Tm) reveal a polarity effect and yield an electron wind force in some agreement with theory.
Abstract: Investigations of the effects of an electric current on dislocation mobility and mechanical properties at low homologous temperatures (T < 0.5Tm) reveal a polarity effect and yield an electron wind force in some agreement with theory. An external directcurrent electric field has been reported to influence the creep rate of unalloyed metals at high homologous temperatures. During superplastic deformation of the 7475 Al alloy, such a field has been found to decrease the flow stress, reduce strain hardening, increase strain-rate hardening, reduce grain boundary cavitation and reduce grain growth. The effects of the field were polarity dependent and extended to the center of 1–2 mm thick specimens. No significant effect of the field on the flow stress occurred at low homologous temperatures. This suggests that the field influences atomic mobility through vacancy generation and/or migration. The occurrence of an uneven electron density at the interfaces between phases and at grain boundaries has been proposed as a factor, but this idea needs further consideration.
98 citations
TL;DR: In this article, a method of converting the carbon fiber Raman frequency versus strain data into stress-strain curves in both tension and compression, is demonstrated, and values of fibre stress and fibre modulus at failure in compression compare exceptionally well with corresponding estimates deduced from full composite data.
Abstract: Spectroscopic-mechanical studies have been conducted on a range of carbon fibres by bonding single filaments on the top surface of a cantilever beam. Such a loading configuration allows the acquisition of the Raman spectrum of carbon fibres and the derivation of the Raman frequency strain dependence in tension and compression. Strain hardening phenomena in tension and strain softening phenomena in compression were closely observed. The differences in the slopes of the Raman frequency versus applied strain curves in tension and compression respectively, have been used to obtain good estimates of the compression moduli. A method of converting the fibre Raman frequency versus strain data into stress-strain curves in both tension and compression, is demonstrated. Values of fibre stress and fibre modulus at failure in compression compare exceptionally well with corresponding estimates deduced from full composite data. The mode of failure in compression has been found to depend upon the carbon fibre structure. It is demonstrated that certain modifications in the manufacturing technology of PAN-based fibres can lead to fibres which show resistance to catastrophic compressive failure without significant losses in the fibre compressive modulus.
90 citations
75 citations
TL;DR: In this paper, the Avrami equation was used to describe the rate of softening in a 300 series austenitic stainless steels, tested in the range 1200-900°C and 0.1 to 5.0 s-1.
Abstract: The mechanical torsion data in the form of flow curves and strain hardening rates from both as-cast and worked 300 series austenitic stainless steels, tested in the range 1200-900°C and 0.1 to 5.0 s-1, have been analysed to deepen understanding of dynamic softening mechanisms. The critical strain for dynamic recrystallization (DRX) is determined from the downward inflection of the strain hardening rate-stress curves, and completion of DRX is taken from the start of the steady-state regime. The rate of softening can be described by means of the Avrami equation with a mean k value of 1.27. These conclusions, based upon mechanical data, have been confirmed by optical metallographic methods. The peak strain (e p) at which there is about 30% DRX is shown to be a function of the Zener-Hollomon parameter (Z) and the original grain size (D0). The transition from multiple-peak grain coarsening to single-peak grain refinement behaviour has been determined. While the DRX grain size is a linear function of th...
TL;DR: In this paper, a phenomenologically based time and rate-dependent bounding surface model is introduced which can be classified among the unified creep-plasticity theories, motivated mainly by experimental behaviors over a wide range of strain rates with particular emphasis on the behavior of metals under nonproportional loading.
Abstract: A phenomenologically based time- and rate-dependent bounding surface model is introduced which can be classified among the unified creep-plasticity theories. The model is motivated chiefly by experimental behaviors over a wide range of strain rates with particular emphasis on the behavior of metals under nonproportional loading where bounding surface theories have found success in modeling rate-independent behavior. In addition, a micromechanical interpretation is given for two kinematic hardening variables which lead to the rate-dependent bounding surface interpretation. The definition of the image point for the directional indices of kinematic hardening is left unspecified to maintain generality. The distinction between instantaneous rate sensitivity and rate sensitivity of material hardening is discussed and a framework for partitioning material rate sensitivity is presented. The relationship of the model to previously proposed formulations is discussed. Asymptotic and parametric behaviors of the model are examined with reference to experimentally observed behavior. A rate-independent idealization of the theory is obtained as a limiting, special case of the more general rate-dependent bounding surface framework.
TL;DR: Slow strain rate testing (SSRT) was initially developed as a rapid, ad hoc laboratory method for assessing the propensity for metals and environments to promote stress corrosion cracking as discussed by the authors, and it is now clear, however, that there are good theoretical reasons why strain rate, as opposed to stress per se, will often be the controlling parameter in determining whether or not cracks are nucleated and, if so, are propagated.
Abstract: Slow strain rate testing (SSRT) was initially developed as a rapid, ad hoc laboratory method for assessing the propensity for metals and environments to promote stress corrosion cracking. It is now clear, however, that there are good theoretical reasons why strain rate, as opposed to stress per se, will often be the controlling parameter in determining whether or not cracks are nucleated and, if so, are propagated. The synergistic effects of the time dependences of corrosion-related reactions and microplastic strain provide the basis for mechanistic understanding of stress corrosion cracking in high-pressure pipelines and other structures. However, while this may be readily comprehended in the context of laboratory slow strain tests, its extension to service situations may be less apparent. Nevertheless, laboratory work involving realistic stressing conditions, including low-frequency cyclic loading, shows that strain or creep rates give good correlation with thresholds for cracking and with crac...
TL;DR: In this paper, an internal state variable model for dislocations interacting with interstitial carbon atoms and with other dislocation interactions was proposed to analyze the deformation microstructures of nickel-carbon alloys.
Abstract: Analysis of the strain-rate sensitivity of the yield stress and the strain-rate sensitivity of strain hardening in annealed and quasi-statically and dynamically prestrained Ni270, Ni-510 wt ppm (0.25 at.%) C, and Ni-1900 wt ppm (0.92 at.%) C is presented. Measurements in compression are analyzed according to an internal state variable model where for a given obstacle type the state variable represents the stress required for deformation at 0 K. State variables are defined for dislocations interacting with interstitial carbon atoms and for dislocations interacting with other dislocations. The application of a power law to combine the contributions of separate obstacles is investigated. Evolution of the mechanical threshold stress characterizing dislocation/dislocation interactions is analyzed using a modified Voce equation. The Stage II hardening rate is shown to be insensitive to the carbon concentration, while the hardening at large strains is strongly dependent on the carbon concentration. Dynamic strain aging is found to influence both the temperature and strain-rate dependent yield stress and the hardening rate in the nickel-carbon alloys. Deformation microstructures are characterized using transmission electron microscopy, and the measured dislocation cell size is correlated with the internal state variable characterizing dislocation/dislocation interactions.
TL;DR: In this article, zero-to-tension load controlled tests at stress rates differing by three orders of magnitude were performed on annealed AISI Type 304 stainless steel.
Abstract: Uniaxial zero-to-tension load controlled tests at stress rates differing by three orders of magnitude were performed on annealed AISI Type 304 stainless steel. The maximum stress was determined either as the stress reached in displacement control at one per cent strain (History I), or as the stress reached after a 1050 s relaxation test at one per cent strain (History II). The tests of History III were identical to those of History I, except that the specimens were subjected to cyclic hardening prior to the start of the ratchetting test. The ratchet strain accumulations in Histories I and II are significant and depend on stress rate. A stress rate decrease increases the accumulated ratchet strain. The final ratchet strain accumulation is independent of stress rate sequence. In History II, no ratchet strain was found at any stress rate. If the steel had behaved in a rate-independent fashion, no ratchet strain accumulation should have been found in any of the tests. They were performed with an MTS servohydraulic, computer controlled testing machine, a clip on-extensometer and digitized data acquisition.
TL;DR: In this article, large deformation, three-dimensional finite element analysis has been used to study the blunting of a mode I crack tip in a thin elastic-plastic sheet.
Abstract: Large deformation, three-dimensional finite element analysis has been used to study the blunting of a mode I crack tip in a thin elastic-plastic sheet. The near tip stress and deformation fields were analyzed, and the results compared with two-dimensional plane stress solutions. A double shear band was found ahead of the crack tip which created a three-dimensional zone extending several sheet thicknesses before the crack. This mechanism leads to an irregular blunt tip shape at the midplane of the sheet. Distinct differences in crack tip shape and the deformation fields were found between the perfect plasticity solution and the strain hardening solution. The analysis was also compared with experimental results obtained by other investigators.
TL;DR: Vickers hardness tests were conducted on samples of copper and aluminium in a cold rolled or annealed condition to determine the apparent hardness variation in the load range 15 g to 20 kg as mentioned in this paper.
Abstract: Vickers hardness tests were conducted on samples of copper and aluminium in a cold rolled or annealed condition to determine the apparent hardness variation in the load range 15 g to 20 kg. The variation was greatest for the soft specimens. Lubrication with an extreme-pressure lubricant was effective in reducing the hardness values to a virtually constant level for each metal. It is therefore reaffirmed that the hardness variation is attributable to friction and that strain hardening propensity is important in governing the magnitude of the variation. Comparison of these findings with data previously reported for similar tests on iron suggests that the phenomenon is probably an indentation size effect.
TL;DR: The importance of the role of plastic spin in the rate-dependent response of materials at large deformations is discussed in this paper, where an isotropic/kinematic hardening and an orthotropic viscoplastic model are used to analyze the stress-strain response under simple shear and biaxial loading at different rates.
TL;DR: In this paper, a small-strain analysis of a stationary crack in an elastic-plastic solid is performed by finite element analysis under small-scale yielding conditions, and the normalized stresses ahead of the crack tip are plotted as functions of the normalized radial distance to the tip for several combinations of prescribed mode 1 and III elastic K fields.
Abstract: WITHIN THE context of the small-strain approach, combined mode I and III near-tip fields of a stationary crack in an elastic-plastic solid are obtained by finite element analysis under small-scale yielding conditions. To investigate the behavior of the near-tip fields, the normalized stresses ahead of the crack tip are plotted as functions of the normalized radial distance to the tip for several combinations of prescribed mode 1 and III elastic K fields. The angular variations of the normalized stresses at a fixed radial distance deep within the plastic zone are also plotted for several combinations of remote mode I and III elastic K fields. These plots show an unmistakeable pattern : the in-plane stresses are more singular than the out-of-plane shear stresses. Over a certain distance, the near-tip in-plane stresses can be said to be more singular than r- ’ ‘“+ ‘) while the near-tip out-of-plane shear stresses are less singular than r- I’(“+ I), where I is the radial distance to the tip and n is the strain hardening exponent of the material. lmpli~tions of these features as they relate to three-dimensional engineering fracture analyses are discussed.
TL;DR: In this paper, the authors investigated the behavior of the material system over two length scales which are physically relevant, namely, distances comparable to the dominant plastic zone and the crack tip opening displacement.
Abstract: In previous analyses [1, 2, 13], and full-field computational investigations, we found that the near tip plastic fields of cracks on a bimaterial interface do not have a separable form of the HRR type. Nevertheless they appear to be nearly separable in an annular region well within the plastic zone. Asymptotically, as the crack tip is approached, the material system responds like that of a plastically deforming solid bonded to a rigid substrate; in particular, the stress and strain fields in the more compliant (lower hardening) material behave like those of a material with identical plastic properties bonded to a rigid substrate. Furthermore, the asymptotic fields of the interface crack bear strong similarities to mixed mode HRR fields for the homogeneous medium characterized by the plastic properties appropriate to the more (plastically) compliant material. In this investigation, we elucidate the behaviour of the material system over two length scales which are physically relevant, namely, distances comparable to the dominant plastic zone and the crack tip opening displacement. The latter is approximately given by the plastic zone size times and the relevant yield strain. Over length scales comparable to the dominant plastic zone, the stress fields are governed by the characteristics of the weaker (lower yield strength) material. On the other hand, the near tip plastic fields are governed by the strain hardening characteristics of the more plastically compliant (lower hardening) material.
TL;DR: In this paper, the same Taylor relation was applied to steady-state structures of 304 stainless steel and showed that the dislocation density increases with the strain rate and temperature, which is consistent with the Taylor relation.
Abstract: Previous elevated-temperature experiments on 304 stainless steel clearly show that the density of dislocations within the subgrain interior influences the flow stress at a given strain rate and temperature. A re-evaluation shows that the hardening is consistent with the Taylor relation if a linear superposition of solute hardening (τ
0, or the stress necessary to cause dislocation motion in the absence of a dislocation substructure) and dislocation (αGbϱ
1/2) hardening is assumed. The same Taylor relation is applicable to steady-state structures of aluminium if the yield stress of annealed aluminium is assumed equal toτ
0. New tests on aluminium deforming under constant-strain-rate creep conditions show a monotonic increase in the dislocation density with strain. This and the constant-stress creep trends are shown to be possibly consistent with Taylor hardening.
TL;DR: In this article, a method of experimental and theoretical treatment of the curve is proposed allowing to obtain information concerning the influence of crystal microstructure on the coefficients of the dislocation density evolution.
Abstract: Using the equation of the dislocation density evolution which includes the process of dislocation multiplication at obstacles of dislocation and nondislocation origin and the process of dislocation annihilation, the strain hardening curves of some f.c.c. and b.c.c. metallic crystals and polycrystals are analysed. A method of experimental and theoretical treatment of the curves is proposed allowing to obtain information concerning the influence of crystal microstructure on the coefficients of the evolution equation. Particular attention is given to receive quantitative data of the process of dislocation annihilation at temperatures lower than 0.4Tm, Tm is the melting temperature. It is found that the annihilation coefficient of dislocations in f.c.c. metals changes approximately linearly with temperature in this temperature region.
TL;DR: In this paper, slip line field solutions for several commonly used fracture mechanics specimens are summarized from these solutions analytic expressions of the plastic η¯¯¯¯ p� factors are derived These results are then compared with those obtained using the EPRI's finite element analyses for power law strain hardening materials.
Abstract: Slip line field solutions for several commonly used fracture mechanics specimens are summarized From these solutions analytic expressions of the plastic η
p
factors are derived These results are then compared with those η
p
factors obtained using the EPRI's finite element analyses for power law strain hardening materials in order to assess the extent to which they can be approximately applied in J-integral tests with these specimens containing both deep and shallow cracks It appears that in the deep crack specimens the η
p
factors are approximately equal for all hardening materials implying that the η
p
factors derived from slip line field solutions are accurate enough for J-integral evaluation In the shallow crack specimens, with the exception of the double-edge cracked panels and pure bend specimens, the η
p
factors do not agree very well and reasons for the discrepancies are discussed
TL;DR: In this article, a phenomenological rate-independent plasticity theory with combined isotropic and kinematic hardening has been formulated to represent their experiments and other results in the literature.
TL;DR: In this paper, the effect of the relative inability of the adhesive to transmit shear on formability of the sheet and conformity to the tool profile is discussed, and it is shown that high forming speed is favorable to the forming of steel sheet laminate bonded with a viscoplastic polymeric adhesive, which in turn increases the transverse stiffness of sheet laminates, although it increases springback.
TL;DR: In this paper, a theoretical framework for a constitutive model for the dynamic finite plastic deformation of rate-dependent single fcc crystals is developed, based on a high strain-rate single crystal plasticity model and a visco-plastic power law.
TL;DR: In this article, a constitutive relation for simple shear of an elastic-plastic material containing a periodic array of cracks is developed based on finite element analysis and slip-line field solutions for interacting cracks.
Abstract: A constitutive relation for simple shear of an elastic-plastic material containing a periodic array of cracks is developed. The relation is based on finite element analysis and slip-line field solutions for interacting cracks in simple shear. Typical shear stress-strain curves display a peak in the nominal shear stress due to competition between strain hardening of the matrix and material softening due to rotation and stretching of cracks with deformation. The effect of nonuniform crack distributions on localization behavior is studied by determining the critical conditions for which the shear strain in a band of cracks becomes unbounded relative to that in the surrounding, uncracked material. The results show that the strain to localization depends strongly on the ratio of crack length to crack spacing, crack orientation, crack-face friction and matrix hardening. The results are helpful to understanding shear localization under confining pressures, where voids adopt a crack-like morphology.
01 Nov 1990-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this paper, the effects of an externally applied d.c. electric field of 2 kV cm−1 on the superplastic deformation behavior of 7475 Al alloy were studied.
Abstract: The effects of an externally applied d.c. electric field of 2 kV cm−1 on the superplastic deformation behavior of 7475 Al alloy were studied. The flow stress and strain hardening exponent of superplastic deformation were reduced by the electric field while the strain rate sensitivity exponent was increased. No appreciable change in elongation occurred. The possible reasons for these effects are discussed in terms of the influence of an electric field on microstructure and deformation mechanism.
TL;DR: In this article, a numerical analysis of plasticity-induced fatigue crack closure based upon the finite difference method is presented, which permits modelling easily fatigue crack growth as well as contacts between fracture faces, without requiring sophisticated algorithms.
TL;DR: In this article, the authors analyzed the dominant singularity solutions of the stress and strain field near an interface crack in a pure power-hardening bimaterial and showed that the crack stress singularity is −1/(nII+1) for hardening power of nI and nII(nI
Abstract: Analytical and numerical analysis of the dominant singularity solutions of the stress and strain field near an interface crack in a pure power-hardening bimaterial indicates that the crack stress singularity is −1/(nII+1) for hardening power of nI and nII(nI