β brass bicrystal stress-strain relations

The stress-strain relations of three isoaxial and one nonisoaxial bicrystal whose grain boundaries are parallel to the stress axis have been studied. From one set of isoaxial bicrystals it has been possible, for a given strain, to determine the average stress in the grain boundary deformation zone from the relationship where σ _T is the applied stress, σ _b is the single crystal flow stress for the given strain, andV _gb is the volume fraction of grain boundary deformation zone. was determined from measured values of σ _T , σ _b , andV _gb . From these data and it was possible to extrapolate to the grain boundary to obtain σ _gb , the grain boundary stress. From the nonisoaxial bicrystal series containing a hard and a soft component, it was possible to determine at a given strain the stresses in each component and therefore the stress-strain relations from the relationship where and are the average stress in the hard and soft components respectively, andV _H andV _S are the corresponding volume fractions. The remaining two isoaxial bicrystal series were used to evaluate strengthening effects of bicrystal boundaries. YII-DER CHUANG, formerly Graduate Student, Department of Metallurgy and Materials Sciences, School of Engineering, New York University, Bronx, N. Y. 10453 This paper is based on a thesis submitted by Yii-der Chuang in partial fulfillment of the requirements for the Ph.D. degree in metallurgy at New York University, New York, N. Y.     

Simultaneous hardening and softening in a nonisoaxial β brass bicrystal

Nonisoaxial beta brass bicrystals, consisting of a hard (H) orientation, close to <110>, and a soft (S) orientation near the center of the stereographic triangle, were compressed in both continuous and interrupted tests, which permitted slip line observations to be made, in order to ascertain why in previous work⁵ a similarH-S combination had shown much greater hardening in theH component. Stress-strain behavior of each component was determined by methods developed earlier.⁵ TheH component initially hardened rapidly with strain, and at 0.5 pct strain, hardened more slowly. TheS component revealed lower strength and strain hardening than the unbonded single crystal up to 1.5 pct plastic strain, after which hardening was much more rapid. From slip line observations considerations of the effect of secondary stresses, and examination of slip systems providing least work at the grain boundary, it appears that the reduced flow strength of theS component is due to pile-up stresses from theH component. Changes in strain hardening rate in bothH andS components were related to the onset or cessation of heavy slip associated with serrated yielding. where Taek Dong Lee was formerly a Graduate Student. This paper is based on a thesis to be submitted by Taek Dong Lee in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Polytechnic Institute of New York.     

Plastic behavior of 70/30 brass sheet

The plastic yield behavior of strip annealed 70/30 brass sheet has been investigated using several experimental techniques. Proportional path, stress-strain relations were measured in two strain states using a recently devised plane-strain test and a standard sheet tensile test. Based on these data, 70/30 brass exhibits a dramatic departure from Hill's plasticity models. Particularly notable is the lower work-hardening rate in plane strain. A second series of tests was carried out by deforming first in plane-strain tension and subsequently in uniaxial tension. The relative orientation of the principal strain directions in the two strain paths strongly affected the transient yielding behavior, but the original work-hardening pattern and plastic anisotropy were approached after an additional effective strain of ∼0.04. These observations are consistent with a two yield-surface model;i.e., one an underlying, proportional path yield surface and one an instantaneous, transient yield surface.     

Yielding behavior of prestrained interstitial-free steel and 70/30 brass

The yielding behavior of interstitial-free (IF) steel and 70/30 brass prestrained in plane strain tension and subsequently strained in uniaxial tension has been investigated experimentally. Upon reloading in uniaxial tension, brass exhibited a negative transient (decrease in flow stress) and steel exhibited a positive transient (increase in flow stress). When the yield stress is defined by the offset method, the positive transient is difficult to model using conventional yield theories as elastic deformation is thought to occur outside the original yield or loading surface. In this work, the yield point was defined using the axial strainvs transverse strain curve as measured with biaxial resistance strain gages. The curve has an initially linear elastic portion; the slope then gradually changes until the linear plastic slope is reached. The intersection of the elastic and plastic slopes is defined as the yield point. Using this alternate definition, the yielding behavior of the prestrained metals was investigated. The yield stress for both prestrained brass and steel was found to be lower than the expected monotonic stress. Compared to previous research based on a traditional definition of yield point, this result is unexpected in prestrained steel and shows that yielding does occur inside the loading surface. The positive transient may, therefore, be modeled using conventional yield theories provided that the yield surface is defined using this alternate technique.     

Flow stress model considering the transformation-induced plasticity effect and the inelastic strain recovery behavior

On the basis of continuum mechanics and the Mori-Tanaka mean field theory, a micro-mechanical flow stress model that considered both the transformation-induced plasticity (TRIP) effect and the inelastic strain recovery behavior of TRIP multiphase steels was presented. The relation between the volume fiaction of constituent phases and plastic strain was introduced to characterize the transformation-induced plasticity effect of TRIP steels. Loading-unloading-reloading uniaxial tension tests of TRIP600 steel were carried out and the strain recovery behavior after unloading was analyzed. From the experimental data, an empirical elastic modulus expression is extracted to characterize the inelastic strain recovery. A comparison of the predicted flow stress with the experimental data shows a good agreement. The mechanism of the transformation-induced plasticity effect and the inelastic recovery effect acting on the flow stress is also discussed in detail.     

Dislocation structures in the strain localized region in fatigued 85/15 brass

The correlation between the formation of extrusions and the dislocation structures in polycrystalline 85/15 brass subjected to a long term stress cycling with a low strain amplitude in vacuum was examined by means of transmission electron microscopy. The overall dislocation structures consisted of two types of structures,i.e., copper-type and 70/30 brass-type. Within them the strain localized regions bounded by two closely located active slip layers were frequently observed. In these boundary layers appeared a fringe pattern which was suggestive of intensive slip. Extrusions were formed in close association with the two closely located layers, and the initiation and growth of fatigue cracks occurred along one of them. On the basis of these observations, the mechanism of extrusion formation and of fatigue crack initiation are discussed.     

High strain plane-strain deformation of 70-30 brass in a channel die

Parallel-piped samples of 90 and 4 μm grain size 70-30 brass have been deformed in plane-strain in a channel die up to a true strain of 2.3. Optical and electron metallography and X-ray diffraction have been used to determine the development of microstructure and texture with strain. The stress-strain data have been obtained by measuring the specimen dimensions and the load after each increment of 0.1 true strain. At low strains 70-30 brass deforms mainly by slip and at slightly higher strains by a combination of slip and twinning. At medium strains shear bands form. The average angle which they make with the compression plane and also their density increases with strain. The strain at which they form and their angle is different for the two grain sizes examined. The stress-strain curves show three distinct hardening stages. At low and high strains the rate of work hardening is high, while at medium strains the rate is low. Shear bands form when the rate of work hardening is low but positive and continue to form at high strains under a high rate of work hardening.     

Transient tensile behavior of interstitial-free steel and 70/30 brass following plane-strain deformation

The transient behavior of interstitial-free (IF) steel and 70/30 brass which results from an abrupt change in strain state has been investigated experimentally and modeled analytically. After a plane-strain prestrain, reloading in uniaxial tension results in a negative stress transient for brass and a positive stress transient for IF steel. The strain behavior during the stress transient was studied by measuring the local axial and transverse strains using resistance strain gages. The monotonic data exhibited a constant plastic strain ratio, whereas the prestrain data showed decreasing plastic strain ratios with increasing axial strain for both IF steel and brass. A simple analysis of the transient was performed by modifying Hill's nonquadratic yield surface to allow variable plastic anisotropy (via r) during the transient. By choosing an appropriate variation ofr, the stress transient could be reproduced. The predicted variations in strain ratios by the model agreed qualitatively with measurements for brass but were of the opposite sign to measurements for steel. Although not conclusive, this result suggests that the normality condition is violated during a stress transient induced by an abrupt change in strain path. A.B. DOUCET, formerly A.E. Browning, Graduate Research Associate, Department of Materials Science and Engineering, The Ohio State University     

The effect of grain size and plastic strain on slip length in 70-30 brass

Polycrystalline 70−30 brass of varying grain size has been studied. Measurements were made of slip line lengths on the polished surface of specimens which had undergone different plastic strains. A relation between the slip line length and the grain size and plastic strain was found based on experimental data using a multiple regression technique. Qualitative agreement was found between the observed slip lengths and slip lengths calculated from a published work-hardening model. The effect of the boundary on slip behavior was observed, and both passive and active types of obstruction to slip by boundaries are suggested. H. DONG, formerly with Carnegie-Mellon University, is now with Jilin Institute of Engineering, Changchun, China. A. W. THOMPSON     

The strain dependence of the flow stress-grain size relation for 70:30 brass

The grain size dependence of the stress-strain behavior of annealed 70:30 brass was evaluated using room temperature tensile tests. The resulting data, which covered × 10^-5 to 4 × 10^-1, were analyzed in terms of the conventional Hall-Petch stress-grain size equation, σ_∈ = σ_O∈ +k∈l-1/2, and, also, in terms of the extended Hall-Petch equation previously proposed for 70:30 brass, σ_є = σ0y+ A Є _p + β(є _p /l ^1/2 +kl ^−1/2 The lattice friction stress, σ0_∈, increased linearly with plastic strain over nearly the full strain range. The lattice friction stress for the initiation of plastic flow, σ0_y, was evaluated using two alternative double extrapolation procedures. Both extrapolation techniques, which involved the macrostrain behavior, gave the same σ0_y value of 3.4 kg/mm², which agreed with the σ0_∈ value determined directly in the microstrain region (∈ <-10^-3). Large grain size specimens, which yielded homogeneously, exhibited a kx2208; value of only 0.2 kg/mm^3/2 at a plastic strain of 1 × 10^-5; however this small kx2208; increased rapidly with increasing microstrain. For the small grain size specimens, which yielded via a Luders extension,kε was essentially constant at 0.8 kg/mm^3/2 for all microstrains; however, kx03B5; did increase in the macrostrain region to a maximum value of 1.6 kg/mm^3/2. When consideration was given to a grain size dependent increase in dislocation density, an intrinsic grain boundary resistance to plastic flow of approximately 0.7 kg/mm^3/2 was obtained. This paper is based upon a thesis submitted by W. L. Phillips in partial fulfillment of the requirements of the degree of Doctor of Philosophy at University of Maryland.     

Formability behavior of brass alloy sheet: the role of twins in microstructure

Quantitative understanding of the process and formability parameters involved in grain size and the formation of annealing twins after plastic straining is important in the control of the manufacturing process. There is a synergistic effect of strain and temperature on the density of annealing twins. Formability of brass alloy sheets was studied after annealing of 65% cold worked (CW) samples at different temperatures (300–600°C). Tensile, deep drawing and Erichsen tests were carried out at room temperature to evaluate formability of alloy. Effect of annealing temperature on density, distribution and size of twins is investigated. It was shown that annealing of brass alloy resulting in formation of annealing twins which at higher annealing temperature were reduced by increasing grain size. Best deep drawability would be achieved by annealing at moderate temperature 400–450°C which microstructure consists of fine grain and twin bands. Work hardening exponent of samples was calculated based on the tensile test data and correlated with stretch ability of annealed brass sheets. It was found that the sheets annealed at 600°C possess best ductility and high average n-value.     

Compression testing techniques to determine the stress/strain behavior of metals subject to finite deformation

We have investigated techniques to conduct a valid single-increment compression experiment to large strains, ε ≈ 1.0. Our investigation included experiments with many different lubricants, specimen-end geometries, five different materials, and temperatures of 22 °C, 315 °C, and 600 °C. We found that for materials with a work-hardening exponent greater than 0.15 and a slightly positive strain-rate sensitivity, the best technique was to cut concentric grooves into the ends of the compression sample and to use polished platens and a molybdenum-disulfide greasebase lubricant. This technique gave valid stress/strain data and uniform displacement fields (as determined by metallography of the deformed specimen cross sections). At all temperatures, satisfactory results were also obtained using a MOLYKOTE spray lubricant. We investigated both well-lubricated experimental conditions (the concentric specimen grooves and Molygrease lubrication and TEFLON sheet lubrication) as well as poor lubrication conditions. The poorest lubrication was achieved by using a set of platens which had grooves cut in them to prevent any expansion by the ends of the specimen during deformation. Up to a compressive strain of 0.5, the load/displacement data from all of these lubrication conditions were almost identical. This was the case for materials with a work-hardening exponent >0.15. Despite the similarity of the “average” stress/strain data to ε = 0.5 for all lubrication conditions, metallographic cross sections showed that the deformation was nonuniform for the poorly lubricated experiments. The results of the experiments show that a single increment compression test can be used to obtain accurate constitutive behavior of many materials to large deformations, ε ≈ 1.0. In addition, we have found that the compression test is relatively insensitive to lubrication conditions for many materials through moderate deformations,ε ≈ 0.5.     

H65黄铜ECAP变形规律和第二相取向演变的数值模拟

采用Deform-2D有限元软件模拟H65黄铜ECAP变形实验, 分析H65黄铜ECAP变形规律及第二相取向的演变, 并结合H65黄铜ECAP变形实验验证H65黄铜ECAP变形过程中第二相取向的演变.结果表明:ECAP变形过程可分为开始变形载荷逐渐增加,逐渐变形载荷增加迅速,变形稳定载荷一定范围内波动,退出变形载荷减小迅速4个阶段;试样中心的等效应变分布随挤压道次的增加而逐渐趋于稳定,并集中在试样的3~9 mm区域内;偶数道次挤压,可以获得等效应变较均匀的变形件;模具内角转角处是裂纹优先产生的地方.第二相取向的演变模拟与实验基本一致,即试样中心水平第二相,经奇数道次挤压后,大约与水平正方向呈约30 °规则的分布在基体中;经偶数道次挤压后,心部和边部的取向各不相同.试样中心竖直第二相,各道次挤压后,取向基本保持不变.      

Social stress and eating behavior.

Responds to issues raised by E. R. Bauer (1971), stating that research findings cast considerable doubt on the postulated relationship between social stress and the eating behavior of obese individuals. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Yield strain behavior of trabecular bone

If bone adapts to maintain constant strains and if on-axis yield strains in trabecular bone are independent of apparent density, adaptive remodeling in trabecular bone should maintain a constant safety factor (yield strain/functional strain) during habitual loading. To test the hypothesis that yield strains are indeed independent of density, compressive (n = 22) and tensile (n = 22) yield strains were measured without end-artifacts for low density (0.18 +/- 0.04 g cm(-3)) human vertebral trabecular bone specimens. Loads were applied in the superior-inferior direction along the principal trabecular orientation. These 'on-axis' yield strains were compared to those measured previously for high-density (0.51 +/- 0.06 g cm(-3)) bovine tibial trabecular bone (n = 44). Mean (+/- S.D.) yield strains for the human bone were 0.78 +/- 0.04% in tension and 0.84 +/- 0.06% in compression; corresponding values for the bovine bone were 0.78 +/- 0.04 and 1.09 +/- 0.12%, respectively. Tensile yield strains were independent of the apparent density across the entire density range (human p = 0.40, bovine p = 0.64, pooled p = 0.97). By contrast, compressive yield strains were linearly correlated with apparent density for the human bone (p < 0.001) and the pooled data (p < 0.001), and a suggestive trend existed for the bovine data (p = 0.06). These results refute the hypothesis that on-axis yield strains for trabecular bone are independent of density for compressive loading, although values may appear constant over a narrow density range. On-axis tensile yield strains appear to be independent of both apparent density and anatomic site.     

Thermal stress and strain in a metal matrix

The stresses and strains, induced by coefficient of thermal expansion (CTE) mismatch, are analyzed for a metal matrix composite (MMC) with a spherical reinforcement particle. The spherical reinforcement particle is found to be in a hydrostatic stress state and remains in the elastic state. The stresses and strains are largest, and plastic deformation occurs in the matrix adjacent to the reinforcement particle. Accordingly, the reinforcement particle/matrix interface becomes a potential crack initiation site under thermal cycling. The critical internal pressure for plastic deformation is less than two-thirds of the yield stress of the matrix material and decreases with increasing range of thermal cycle.     

Equivalent strain and stress history in torsion tests

Bulk and plane torsion tests are being used in industry to determine the flow curve of metals up to very high plastic strains. Despite their wide usage the experimental results obtained in torsion tests are still not being evaluated uniformly. Differences arise basically due to the conversion of the measured angle of twist into the corresponding equivalent strain. This paper shows that the often used equivalent strain expression by Nádai and Davis as well as Eichinger is invalid, since the so-called redundant shear during torsion deformation has been ignored. Also, the histories of different stress measures such as the convected and rotated stress tensors are computed to discuss the reasons for differences between the flow curves obtained from torsion and simple tension tests.