Calculations of forming limit

The method of calculating the shape of forming limit diagrams (FLDs) using a high-exponent yield criterion with the Marciniak and Kuczynski (M-K) analysis has been extended to include the effects of changing the strain paths and applied to aluminum alloy 2008 T4. Calculations incorporating abrupt path changes agreed with the general trends found experimentally. If the first stage of strain is under biaxial tension, the subsequent FLD shifts to the right and down with respect to the original FLD, whereas it shifts to the left and up when the first stage of strain is in uniaxial tension. Calculations introducing gradual strain-path changes, characteristic of stretching over a hemispherical dome, predict that the minimum of the FLD shifts to the right.     

Effect of matrix constitutive behavior and inclusions on forming limits of Fe-42 pct Ni alloy sheet

The effects of matrix constitutive behavior and nonmetallic inclusions on forming limit strains have been examined with five laboratory heats of Fe-42 pct Ni alloy. The inclusion volume fraction was varied between approximately 0.01 and 1.59 pct by proper selection of Mn, S, and O contents. Each ingot was processed into 0.38-mm-thick sheets and heat treated to the recovered or the recrystallized condition. Forming limit strains were obtained from uniaxial tensile, plane-strain tensile, and hydraulic bulge tests by circle grid analysis. In any strain path, the limit strain increased with increasing the strain hardening exponent, n. The forming limit strains on the right-hand side of the forming limit diagram (FLD) decreased with inclusion volume fraction, while no effects of the inclusion volume fraction were observed on the left-hand side. A decrease in the slope of the FLD on the right-hand side due to an increase in the inclusion volume fraction qualitatively agrees with the theoretical calculation by Graf and Hosford, which was conducted on the basis of the Marciniak-Kuczynski (M-K) theory.     

Room Temperature Shear Band Development in Highly Twinned Wrought Magnesium AZ31B Sheet

Failure mechanisms were studied in wrought AZ31B magnesium alloy after forming under different strain paths. Optical micrographs were used to observe the shear band formation and regions of high twin density in samples strained under uniaxial, biaxial, and plane strain conditions. Interrupted testing at 4?pct effective strain increments, until failure, was used to observe the evolution of the microstructure. The results showed that shear bands, with a high percentage of twinned grains, appeared early in the samples strained under biaxial or plane strain tension. These bands are similar to those seen in uniaxial tension specimens just prior to failure where the uniaxial tensile ductility was much greater than that observed for plane strain or biaxial tension conditions. A forming limit diagram for AZ31B, which was developed from the strain data, showed that plane strain and biaxial tension had very similar limit strains; this contrasts with materials like steel or aluminum alloys, which typically have greater ductility in biaxial tension compared to plane strain tension.     

Forming response of retained austenite in a C‐Si‐Mn high strength TRIP sheet steel

TRIP sheet steels typically consist of ferrite, bainite, retained austenite, and martensite. The retained austenite is of particular importance because its deformation‐induced transformation to martensite contributes to excellent combinations of strength and ductility. While information is available regarding austenite response in uniaxial tension, less information is available for TRIP steels with respect to the forming response of retained austenite in complex strain states. Therefore, the purpose of this work was to study the austenite transformation behaviour in different strain paths by determining the amount of retained austenite before and after forming. Forming experiments were performed on a high strength 0.19C‐1.63Si‐1.59Mn TRIP sheet steel 1.2 mm in thickness in two different strain conditions, uniaxial tension (ε₁ = ‐2ε₂) and balanced biaxial stretching (ε₁ = ε₂). Specimens were formed to strains ranging from zero to approximately 0.2 effective (von Mises) strain. Specimens were tested both longitudinally and transverse to the rolling direction in uniaxial tension, and subtle mechanical property differences were found. The volume fraction of austenite, determined with X‐ray diffraction subsequent to forming, was found to decrease with increasing strain for both forming modes. Some modification in the crystallographic texture of the ferrite was observed with increasing strain, in specimens tested in the balanced biaxial stretch condition. This trend was not evident in the uniaxial tensile test results. Slight differences were found in the transformation behaviour of the austenite when formed in different strain conditions. More austenite transformed in specimens tested parallel to the rolling direction than transverse to the rolling direction in uniaxial tension. The amount of austenite transformed during biaxial stretching was determined to be greater than the amount transformed in uniaxial tension for specimens tested transverse to the rolling direction at an equivalent von Mises strain. The amount of austenite that transformed in biaxial tension, however, was comparable to the amount of austenite that transformed in specimens tested longitudinal to the rolling direction in uniaxial tension.     

On the influence of strain-path changes on fracture

Abrupt changes in strain path between uniaxial and equibiaxial tension are shown to have a large effect on plane-strain ductility. Data for titanium sheets, both with and without hydrides, show that a significant ductility enhancement occurs at a final strain state of plane-strain tension following multi-stage deformation sequences comprised of uniaxial and equibiaxial tension. While the dependence of ductile fracture on both accumulated damage and strain hardening suggests that failure strains should be sensitive to a nonproportional strain-path history, the detailed cause(s) of the present effect is not known.     

Effects of strain path changes on the formability of sheet metals

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. AMIT K. GHOSH, formerly with General Motors Research Laboratories     

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Forming limit diagram (FLD) of cold- rolled TRIP steel was established by experiments. The microstructures of samples before and after deformation were examined by metalloscopy and scanning electron microscopy and at the same time the contents of retained austenite after different strain ratios were measured by X- ray diffraction. The results show that the ultimate strain under plane strain state(FLD0) is 0. 397. With the strain ratio increasing, strain path changes from uniaxial stretching to plane strain and then biaxial stretching and the transformation amount of residual austenite increases gradually. Compared with dual- phase steel, the higher FLD0of TRIP steel is ascribed to TRIP effect and necking area is wider during deformation.     

Influence of strain path on the forming-limit curve in aluminum

The influence of a two-stage strain path on the forming-limit curve (FLC) in aluminum has been investigated. Uniaxial tensile straining followed by orthogonal uniaxial tensile straining decreases the forming-limit strains. Equibiaxial tensile straining followed by uniaxial tensile straining increases the forming-limit strains in the region of plane-strain deformation. Uniaxial tensile straining followed by biaxial tensile straining increases the forming-limit strains in the region of biaxial tensile deformation in some cases. The texture evolution related to the deformation along the two-stage strain path was observed.     

Biaxial deformation of 70-30 brass: Flow behaviors,texture, microstructures

70-30 brass tubes have been tested in combinations of tension/internal pressure and in pure torsion. The flow properties, from these loading conditions, were measured from yield until local necking. We found that the pure hoop tension, plane strain, and torsion flow curves were 15 pct lower than those in uniaxial tension and balanced biaxial tension when compared on the basis of a von Mises effective stress-strain criterion. Microstructures, at a von Mises strain of 0.4, were examined; no differences were observed between plane strain, torsion, and uniaxial tension deformation modes. Based on the microstructural measurements, we estimate that at most 13 pct of the deformation at an effective strain of 0.40 was by twinning. The initial texture and final textures, after balanced biaxial and uniaxial tension, were measured by pole figure analysis. The initial texture was qualitatively consistent with measured flow stress levels of the axisymmetric deformation modes (uniaxial tension, balanced biaxial tension, and hoop tension). A crystallographic effective stress-strain criterion was also applied to the torsion data. This method of analysis gave results which were better than the von Mises criterion.     

Punch-stretching behavior of a 2014 aluminum alloy in the temperature range 250° to 500 °C

The influence of forming temperatures in the range 250° to 500 °C on the performance of a 2014 aluminum alloy in punch stretching has been investigated. In tests at moderate strain rates within the 250° to 450 °C range, the biaxial stretching limits of annealed sheets were greatly superior to the room-temperature values. Limiting depths of pressing increased with increasing temperature in the range 250° to 400 °C as a result of improvement in both limit strains and strain distribution, but increasing deformation temperature above ~400 °C caused the limit strains to decrease as a result of cavitation at high strains. Under comparable conditions of temperature and extension rate, such cavity growth was more rapid in equibiaxial stretching than in uniaxial or plane-strain stretching. At 500 °C with a punch speed of 0.083 mm s^-1, the thickness strain which could be applied in biaxial stretching without significant cavitation damage was less than 0.4. Thus, susceptibility to cavitation imposes an important restriction on opportunities for combining solution treatment with a hot stretch-forming operation when using an alloy based on Al-4 pct Cu.     

不同应变方式下TRIP钢中残余奥氏体的体积分数随应变量的变化

对TRIP钢板在单向拉伸、双向拉伸和平面应变3种应变方式下残余奥氏体的体积分数随应变量变化的规律进行了实验研究。结果表明：在变形过程中，残余奥氏体的体积分数随应变量的增加而减小；该变化量不仅与应变量有关，还与应变方式有关；平面应变时变化最大，双向拉伸次之，单向托伸下变化最小。还对同一零件不同区域残余奥氏体的含量对零件形状精度的影响进行了讨论。     

Development of forming limits for superplastic formed fine grain 7475 AI

Forming limits in conventional sheet metal forming are given by strain levels obtainable prior to the onset of a localized neck or tear in the sheet. While the external appearance of such a neck is not observed in superplastic metals until strains become quite large, the formation of internal cavities could dictate the tolerable levels of strain in formed components. In this paper, these useful strain limits for a superplastic 7475 Al alloy have been explored. The approach used was to establish the influence of strain state (uniaxial, plane strain, and balanced biaxial) on the inception and growth characteristics of cavities and to correlate the extent of cavitation with material properties. Based on these data, it was then possible to establish strain states for which little or no loss in properties was observed, and thereby to define forming limits for superplastic forming this material. These results, coupled with comparisons against strains developed in actual parts as well as analytically predicted strains, show that a wide range of structural parts can be superplastically formed within the constraints of the recommended forming limits.     

plane-strain work hardening and transient behavior of interstitial-free steel

Stress transients resulting from abrupt changes in strain path have been shown to be important to subsequent formability. In order to investigate whether these transients result from strain aging or related interstitial effects, two-stage experiments were performed on Armco interstitial-free steel After a prestrain in plane-strain tension, the material was strained in uniaxial tension in the direction of zero initial extension. The stress-strain curve in plane strain was found to deviate markedly from that predicted by usual plasticity theory (Hill’s theory withM = 2.0). Comparison of monotonie curves from uniaxial and plane-strain tension using a newly-developed, self-consistent calculation suggested that IF steel follows Hill’s new theory with constantM ≈ 2.9. After the change from plane strain to uniaxial tension, positive stress transients (flow stress exceeds the monotonie flow stress) were measured. This form of transient agrees with ones measured for other steels. It therefore appears that the origin of the transient phenomenon is independent of interstitial content, and that static strain aging is not the mechanism by which these stress transients occur. Formerly A. E. Browning, Graduate Research Associate, Department of Metallurgical Engineering, The Ohio State University     

Strain hardening and instability in biaxially streched sheets

This work is concerned with the origins of the two different patterns of failure limits in biaxially stretched sheets which were recently described in Ref. 1: the brass-type in which the limit strain is insensitive to strain state, and that of ferritic steel in which the limit strain increases as the imposed strain-ratio, ρ = ε₂/ε₁, changes from zero (plane-strain tension) toward unity (balanced biaxial tension). An earlier proposal that different slip modes,i.e. wavy in ferrite vs planar in brass, might have contributed to these failurelimit differences was found not to be valid. There were two parts to the main experimental program: the prestraining of small sheets by proportional loading on different paths betweenρ = 0 andρ = 1, followed by tension testing, and a more direct measurement of strain hardening and instability between ρ ≅ — 1/2 (uniaxial tension) andρ = 0. The principal finding was that the overall hardening rate, essentially as it appeared in the material’s effective stress-strain curve, changed with the loading path. Inα brass it decayed as p was increased from ∼—1/2 to 1; in ferritic steel it increased; and in aluminum it was affected very little. Such changes in hardening rate cause similar changes in the material’s capacity for stable flow. The stable flow, in turn, is the base to which a quasistable-flow increment (whenρ is >0) is added in reaching the observed failure limit. Thus a base ofρ-dependent height can account for the failure-limit patterns. There is still no explanation for the ρ dependence of the hardening rate. AMIT K. GHOSH, formerly Graduate Student, Massachusetts Institute of Technology, Cambridge, Mass. 02139, This paper is based upon a thesis submitted by AMIT K. GHOSH in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology.     

The influence of biaxial prestrain on the tensile properties of three aluminum alloys

We have investigated the influence of planar biaxial prestrain on the subsequent tensile behavior of three aluminum alloys. The flow stability encountered in the uniaxial stage is explained in terms of the reduced tensile hardening following biaxial prestraining. A critical stress value approximately equal to the nonprestrained ultimate tensile strength is shown to be the controlling factor for the onset of failure.     

面内双轴循环载荷下304不锈钢的力学行为

为研究面内双轴载荷下304不锈钢材料的力学行为,运用有限元方法对十字形试样尺寸进行了设计与优化,在自主设计的面内双轴疲劳试验系统上对304不锈钢进行了单轴拉伸、双轴比例加载和非比例圆路径下的力学试验。结果表明,比例加载条件下304不锈钢的棘轮应变累积最小,圆路径下材料的棘轮应变最大,而单轴加载的棘轮应变累积介于比例载荷与圆路径之间。进入棘轮应变稳定增长阶段,圆路径对应的棘轮应变率高于单轴与比例加载,说明圆路径使304不锈钢的损伤失效进程加速。     

Stretch forming and fracture of strongly textured Ti alloy sheets

The influence of plastic anisotropy and R -value on the stretch forming and fracture behavior of strongly textured Ti-6A1-4V and Ti-5Al-2.5Sn sheets has been examined utilizing sheet specimens with a wide range of R -values but with similar work hardening and strain-rate sensitivity characteristics. The results indicate that a high R -value and difficult through-thickness slip enhance the forming limit as well as fracture strains when the minor strain in the plane of the sheet is negative, this effect being most pronounced at uniaxial tension. At plane strain, the R -value has little or no influence on the limit or fracture strain. A direct determination of the effect of R -value on the biaxial stretch forming characteristics of Ti-6-4 sheet is precluded by the intervention of fracture prior to localized necking when the minor strain is positive. The influence of plastic anisotropy on both the localized necking and the fracture behavior can be generally understood in terms of the difficulty of attaining critical thickness strains as through-thickness slip becomes more difficult.     

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.     

用正电子寿命法研究深冲钢板不同变形路径中的微观缺陷

本文应用正电子寿命法研究了深冲钢板在单向拉伸、平面应变和等双向拉伸变形过程中的位错和微空洞增长机制。结果表明,深冲钢板的宏观失稳及成形极限与板材内部的微观缺陷的产生及发展密切相关;当变形路径不同时,缺陷的增长速率不同;当应变量小于0.2～0.35时,材料内的微观缺陷以位错增长机制为主,且平面应变的缺陷增长速率最大,当应变量大于0.2～0.35时,微空洞的形核及增长速率加快,对板材集中失稳起到促进作用。