Instability of plastic flow in the directions of pure shear: II. Experimental

Two aspects of the phenomenon of plastic instability in direction of pure shear are examined, namely that the condition dσ = 0 (maximum in true flow stress) is necessary for localization of flow along characteristics as defined in continuum plasticity, and that fracture is initiated and propagates along characteristics. Two types of sheet specimens were employed, the standard-type flat sheet specimens, and specimens simulating both plane stress and plane strain. Grids were placed on gage sections and photographs were taken successively in the plastic range to enable strains to be calculated and instabilities to be observed and recorded. The principal variable in the flat specimen test was theW/T ratio (width to thickness). In the plane* strain specimens, both the gage length (constantW/T) and the strength level of the material (quenched and tempered AISI 4340 steel) were varied. A maximum in true flow stress is found consistently at the onset of instabilities. Fracture propagated consistently along the instability band-matrix interface. Variations in specimen geometry produces significant changes in stress state, directions of characteristics, and ductility. For a given specimen geometry, plane strain is more closely approached the higher the strength level of the material. In mixed mode fracture paths slant fracture is associated with the more embrittling stress state. Formerly with Metals and Ceramics Laboratory, Aerospace Research Laboratories, Wright-Patterson AFB     

Temperature changes in specimens in microplasticity tests

A tensile specimen and a gage assembly were designed to measure plastic strain at room temperature. The assembly mounts three capacitance strain gages 120 deg apart, and is held by ribs with a 45 deg included angle so as to define a 2 in. (5.08 cm) gage length. This novel construction eliminates spurious effects due to the fillets and shoulders of the specimen. The strain sensitivity is ±1 × 10⁻⁷. The cooling and heating of a specimen, accompanying the loading and unloading, respectively, in the elastic range, are shown to affect plastic strain readings in a manner not considered by other investigators of microplasticity. The thermal contributions to apparent strain in specimens of normalized 4340 steel and annealed Invar were determined and were found to be significant at strains less than 10^-5. Strain measurement techniques necessary for the exclusion of the thermal dimensional changes of the specimen from the measurement of very small plastic strains are discussed.     

Instability of plastic flow in the directions of pure shear: II. Experimental

Two aspects of the phenomenon of plastic instability in direction of pure shear are examined, namely that the condition dσ = 0 (maximum in true flow stress) is necessary for localization of flow along characteristics as defined in continuum plasticity, and that fracture is initiated and propagates along characteristics. Two types of sheet specimens were employed, the standard-type flat sheet specimens, and specimens simulating both plane stress and plane strain. Grids were placed on gage sections and photographs were taken successively in the plastic range to enable strains to be calculated and instabilities to be observed and recorded. The principal variable in the flat specimen test was theW/T ratio (width to thickness). In the plane* strain specimens, both the gage length (constantW/T) and the strength level of the material (quenched and tempered AISI 4340 steel) were varied. A maximum in true flow stress is found consistently at the onset of instabilities. Fracture propagated consistently along the instability band-matrix interface. Variations in specimen geometry produces significant changes in stress state, directions of characteristics, and ductility. For a given specimen geometry, plane strain is more closely approached the higher the strength level of the material. In mixed mode fracture paths slant fracture is associated with the more embrittling stress state.     

The variation of plastic anisotropy during straining

The relationship between length and width strain during a tensile test has been studied in detail for a wide range of low carbon steels. The data have been analyzed in terms of the conventionalr-value,r _e, the instantaneous r-value, r_i, and a linear regressionr-value,r _r. r_r is derived from a linear regression between width strain and length strain, as first suggested by Liu, using data obtained between yield and uniform elongation.r _r was found to be the most suitable method of characterizing the average anisotropic behavior, because its value is unaffected by the presence or absence of inhomogeneous yielding. There are reproducible variations of width strain from linear behavior which are not due to experimental error. These causer _e to vary with strain. No systematic increase or decrease ofr _e with strain was observed, in contrast to previous reports in the literature.     

Dynamic deformation behavior of ultrafine-grained low-carbon steels fabricated by equal-channel angular pressing

The dynamic deformation behavior of ultrafine-grained low-carbon steels fabricated by equal-channel angular pressing (ECAP) was investigated in this study. Dynamic torsional tests, using a torsional Kolsky bar, were conducted on four steel specimens, two of which were annealed at 480 °C after ECAP, and then the test data were compared in terms of microstructures, tensile properties, and adiabatic shear-band formation. The equal-channel angular pressed specimen consisted of very fine, equiaxed grains of 0.2 to 0.3 μm in size, which were slightly coarsened after annealing. The dynamic torsional test results indicated that maximum shear stress decreased with increasing annealing time, whereas fracture shear strain increased. Some adiabatic shear bands were observed at the gage center of the dynamically deformed torsional specimen. Their width was smaller in the equal-channel angular pressed specimen than in the 1-hour-annealed specimen, but they were not found in the 24-hour-annealed specimen. Ultrafine, equiaxed grains of 0.05 to 0.2 μm in size were formed inside the adiabatic shear band, and their boundaries had characteristics of high-angle grain boundaries. These phenomena were explained by dynamic recrystallization due to a highly localized plastic strain and temperature rise during dynamic deformation.     

Strain and the quantitative characterization of anisotropic microstructures

Microstructures exhibit both crystallographic and morphological anisotropy. The orientation distribution function (ODF) for P _L(t), the number of intersections per unit length of boundaries with test lines parallel to a unit vector. t. describes morphological anisotropy, the spatial distribution of internal interfaces that separate grains or phases. Weak anisotropy refers to a microstructure such that P _L(t) vs t is an ellipsoid. Coefficients of the direction cosines in the equation of the ellipsoid form a Cartesian tensor called the microstructural anisotropy tensor (MAT). This work develops a measure of internal total strain, the Eulerian finite grain strain tensor (EFGST), based on the MAT. The reference state for the EFGST is an isotropic network having the same surface area per unit volume, S _V, as the deformed specimen. Analysis of the deformation of the network of ferrite-ferrite boundaries in a specimen of 1020 steel deformed in uniaxial tension illustrates that the EFGST measured at the centroid of the gage section changes congruently with a similar measure of bulk deformation, both having principal axes aligned with those of the bulk deformation. However, the values of strain are not identical due to nonuniform deformation in the gage section after necking. CRAIG S. HARTLEY, formerly Program Manager, Air Force office of Scientific Research, Arlington, VA 22203.     

Effect of surface roughness on low-cycle fatigue behavior of type 304 stainless steel

The effects of surface roughness on the low-cycle fatigue life of Type 304 stainless steel at 593°C in air have been investigated. It is observed that, at a strain rate of 4 × 10⁻³ s⁻¹ and a total strain range of 1 pct, the fatigue life (N _f cycles) decreases with an increase in surface roughness. Information on crack growthvs strain cycles has been generated, as a function of surface roughness, by the measurement of striation spacing on fractured surfaces of specimens tested to failure. Crack propagation follows the Ina ∞N (wherea is the crack length afterN strain cycles) relation for longer specimen fatigue lives (N_f > 2700 cycles) and departs from Ina ∞N for shorter fatigue lives. A quantitative estimate is made of the number of cycles N_o(r) to generate a crack length equal to 0.1 mm (≈ 1 grain diam). The initial surface roughness significantly affects only the initiation component of specimen life time. The effect of roughness on crack initiation is described byN ₀ (R) = 1012R^−0.21, whereR is the surface roughness (root-mean-square value) in microns.     

Effect of temperature and strain distribution on martensitic transformation during uniaxial testing of AISI-304 stainless steel

A coupled finite element method has been used to determine the true plastic strain, effective strain, and temperature distribution inside the tensile specimen of AISI-304 austenitic stainless steel during uniaxial testing at low and high strain rates. The volume fraction of martensite has been computed along the gage length by employing Olson-Cohen analysis and using the value of a and β parameters from Heckers curve at the temperatures which were obtained by FEM analysis in different elements of the specimen. The results reveal that due to nonhomogeneous distribution of plastic strain and variation in temperature along the gage length, the volume fraction of martensite would be different near the end of gage length and the center of the specimen.     

Tension and compression testing of single-crystalline gamma Ti-55.5 pct Al

High-quality single crystals 6 to 10 mm in diameter of γ-Ti 55.5 pct Al have been grown using the optical float zone furnace technique. These crystals have been oriented and cut into microsample tension and compression specimens with a gage area of 250×250 μm and an effective gage length of 300 μm. These specimens have been deformed using a microsample testing machine which applies loads on the order of 50 N and measures strain using an interferometric strain/displacement gage. Stress-strain curves have been obtained for four different orientations and two temperatures and as a function of the sense of the applied load. Of special interest is the availability of tensile data for the resolved shear stress. Preliminary comparison of tension and compression microsample tests indicates that the tension-compression asymmetry is negligible at 500 K. This article is based on a presentation made in the symposium “Fundamentals of Gamma Titanium Aluminides,” presented at the TMS Annual Meeting, February 10–12, 1997, Orlando, Florida, under the auspices of the ASM/MSD Flow & Fracture and Phase Transformations Committees.     

Deformation textures of AA8011 aluminum alloy sheets severely deformed by accumulative roll bonding

A fully annealed AA8011 aluminum alloy sheet containing a number of large particles (∼5 μm) was severely deformed up to an equivalent strain of 12 by an accumulative roll-bonding (ARB) process. The texture evolution during the ARB process was clarified, along with the microstructure. The ARB-processed aluminum alloy sheets had a different texture distribution through the sheet thickness, due to the high friction between the roll and the material during the ARB process. The shear textures composed of {001} 〈110〉 and {111} 〈110〉 orientations developed at the sheet surface, while the rolling textures, including Cu {112} 〈111〉 and Dillamore {4,4,11} 〈11,11,8〉 orientations, developed at the sheet center. The textural change from a shear texture to a rolling texture at the sheet center during the ARB process contributed to an increase in the fraction of high-angle boundaries. Also, a large number of second-phase particles in the AA8011 alloy sheets weakened the texture. Up to the medium strain range (below ɛ=6.4), relatively weak textures developed, due to the inhomogeneous deformation around the second-phase particles; after the strain of 6.4, strong rolling-texture components, such as the Dillamore and Cu orientations, developed. This remarkable textural change can be explained by the reprecipitation of fine particles in grain interiors.     

The microstructural evolution of near beta alloy Ti-10V-2Fe-3Al during subtransus forging

The microstructural evolution of titanium alloys during subtransus isothermal forging (IF) has been effectively demonstrated using a testing methodology developed at Imperial College London. Double truncated cone specimen geometries were isothermally deformed at near β transus temperatures to obtain microstructural information for a range of strains within a single specimen. The methodology was applied to the near β alloy, Ti-10V-2Fe-3Al, to determine the effect of strain, strain rate, and IF subtransus temperature on microstructural evolution. An erratum to this article is available at .     

Analysis of Strain Rate Sensitivity of Ultrafine-Grained AA1050 by Stress Relaxation Test

Commercially pure aluminum sheets, AA 1050, are processed by accumulative roll bonding (ARB) up to eight cycles to achieve ultrafine-grained (UFG) aluminum as primary material for mechanical testing. Optical microscopy and electron backscattering diffraction analysis are used for microstructural analysis of the processed sheets. Strain rate sensitivity (m-value) of the specimens is measured over a wide range of strain rates by stress relaxation test under plane strain compression. It is shown that the flow stress activation volume is reduced by decrease of the grain size. This reduction which follows a linear relation for UFG specimens, is thought to enhance the required effective (or thermal) component of flow stress. This results in increase of the m-value with the number of ARB cycles. Strain rate sensitivity is also obtained as a monotonic function of strain rate. The results show that this parameter increases monotonically by decrease of the strain rate, in particular for specimens processed by more ARB cycles. This increase is mainly linked to enhanced grain boundary sliding as a competing mechanism of deformation acting besides the common dislocation glide at low strain rate deformation of UFGed aluminum. Recovery of the internal (athermal) component of flow stress during the relaxation of these specimens seems also to cause further increase of the m-value by decrease of the strain rate.     

Microstructural evolution and mechanical properties of the AA8011 alloy during the accumulative roll-bonding process

The investigation of the microstructure and mechanical properties has been conducted on an AA8011 alloy produced by a novel intense plastic straining process named accumulative roll bonding. The results show that an ultrafine-grained 8011 alloy, having a mean grain (or subgrain) size less than 1 μm, was successfully accumulative roll-bonded (ARB) at room temperature (RT-ARB) and at 200 °C (HT-ARB). The average grain (or subgrain) sizes of the RT-ARB and HT-ARB samples were reduced greatly from about 25.8 μm initially to 650 to 700 nm and 800 to 900 nm, respectively. After several cycles of accumulative roll bonding, most regions of this material were filled with ultrafine grains with high-angle boundaries. The ambient tensile strengths of the RT-ARB and HT-ARB samples increased with equivalent strain only up to the strain of 2.4. After that, the strengths of the RT-ARB samples nearly leveled off, and the strengths of the HT-ARB samples decreased with equivalent strain above the strain of 2.4. Furthermore, the elongation in both the RT-ARB and HT-ARB samples decreased greatly after the first cycle and then increased continuously with strain. The softening behavior happened in HT-ARB samples above a strain of 2.4, which is mainly attributed to the continuous recrystallization, dynamic recovery, and static recovery during and/or after the accumulative roll-bonding process.     

Constraint induced stresses and the hard surface-soft surface question in fatigue

Cu, 80-20 α-brass and 70-30 α-brass single crystals were cycled in a strain controlled tension-compression mode. Chemical polishing over the entire gage length of specimens in the grips at zero load and zero strain and reloading indicated no detectable difference in flow stress, or equivalently no significant difference in the resolved shear stress on the slip system. When half the gage length was electrolytically polished in specimens unloaded from tension to zero load, bending occurred in a manner indicating that the residual σ_zz stress was higher at the interior than at the surface. Unloading from compression to zero load indicated a reversal in residual σ_zz stress distribution. Finite element method (FEM) analysis, taking into account the slip behavior of a single crystal and the effect of end constraints occurring in the test, confirmed that there was little difference between the resolved shear stress on the slip system at the surface and the interior during deformation. The FEM calculations also indicated that the residual σ_zz stress was nonuniform, in agreement with the bending experiments. These results, therefore, indicate that a difference in flow stress between surface and interior is not necessary for bending to take place when half the gage length is electropolished.     

Effect of surface roughness on low-cycle fatigue behavior of type 304 stainless steel

The effects of surface roughness on the low-cycle fatigue life of Type 304 stainless steel at 593°C in air have been investigated. It is observed that, at a strain rate of 4 × 10^?3 s^?1 and a total strain range of 1 pct, the fatigue life (N _f cycles) decreases with an increase in surface roughness. Information on crack growthvs strain cycles has been generated, as a function of surface roughness, by the measurement of striation spacing on fractured surfaces of specimens tested to failure. Crack propagation follows the Ina ∞N (wherea is the crack length afterN strain cycles) relation for longer specimen fatigue lives (N_f > 2700 cycles) and departs from Ina ∞N for shorter fatigue lives. A quantitative estimate is made of the number of cycles N_o(r) to generate a crack length equal to 0.1 mm (≈ 1 grain diam). The initial surface roughness significantly affects only the initiation component of specimen life time. The effect of roughness on crack initiation is described byN ₀ (R) = 1012R^?0.21, whereR is the surface roughness (root-mean-square value) in microns.     

Elevated temperature plastic anisotropy of Ti-6AI-4V plate

The influence of temperature on the planar and normal anisotropy parameters (ΔR andR, respectively) for mill annealed, duplex annealed, and cross rolled Ti-6A1-4V plate was investigated from 25 to 704°C (77 to 1300°F). Both parameters were assessed in terms of the plastic strain ratio (R), ratio of width to thickness strain at maximum load (~0.065 longitudinal strain) in tensile specimens oriented at 0, 45, and 90 deg to the rolling direction, and correlated with texture and microstructure. With increasing temperature, plates characterized by alpha deformation type basal plane textures exhibited significantly larger anisotropy variations than plate with a beta transformation type texture. This behavior was related to the degree of textural randomness and to a thermally induced transition in primary deformation mode from twinning to slip. Depending on texture, the results strongly suggest that working temperature may be utilized advantageously to alter the plastic anisotropy of Ti-6A1-4V plate for improved formability in a given fabrication operation.     

Spatial and Temporal Characteristics of Propagating Deformation Bands in AA5182 Alloy at Room Temperature

The spatial and temporal characteristics of propagating deformation bands in the Al-Mg alloy AA5182 in O temper were studied experimentally at room temperature. Tensile tests were carried out on flat specimens at strain rates in the range from 10⁻⁵ to 10⁻¹ s⁻¹. Digital image correlation (DIC) and digital infrared thermography (DIT) were applied to monitor the propagating bands. It was found that the material exhibits a sharp yield point, and Lüders bands were seen at all the strain rates. Jerky flow took place all along the Lüders plateau. It thus seems that the Portevin–Le Chatelier (PLC) effect starts at incipient yielding and that there is no critical strain. At the end of the Lüders plateau, PLC bands immediately started to propagate back and forth along the gage section of the specimen. The work hardening of the material decreased consistently with increasing strain rate, while the flow stress on the Lüders plateau was rather unaffected by the strain rate. This indicates that the dynamic strain aging (DSA) mainly affects the strength of the interaction between mobile and forest dislocations. The strain to necking was found to decrease gradually with strain rate for this alloy, which is consistent with the lower work-hardening rate at the higher strain rates.     

Numerical analysis of the hot tension test

Plastic flow during the round bar, uniaxial tension test has been analyzed for conditions representative of the hot-working of metals. Two methods of analysis were employed: the finite element method and a simpler finite-difference technique using a so-called “direct equilibrium” approach. Variables which were investigated included material properties (strain-hardening exponents of 0 or 0. 1; strain-rate sensitivity exponents between 0. 02 and 0. 30) and sample geometry (gage length-to-diameter ratios between 4 and 15; samples with and without tapers from the fillet to the center of the gage section). Results were summarized in terms of nominal (engineering) stress-strain curves, axial strain distributions after the onset of rapid flow localization, and total elongations. A comparison of the results from the two types of numerical analyses were very similar. This similarity was interpreted to result from the similar degrees of stress triaxiality during neck formation which werepredicted via the finite element method andassumed (based on the Bridgman analysis) for the direct equilibrium approach. Total elongation predictions from the numerical models were compared to measurements and to a simple closed-form analytical solution contained in the literature. The numerical results showed good agreement with the measurements but differed greatly from the analytical solution, thereby quantifying the effect of the neglect of stress triaxiality in simple analytical models on predicted elongations.     

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     

A numerical analysis of the tensile test for sheet metals

The strain hardening, strain-rate hardening, and plastic anisotropy properties of metal sheets are normally determined in a tensile test during the nearly uniform deformation prior to the maximum load. Beyond this point, strain nonuniformity leading to a neck is poorly understood in terms of interaction of these material properties with changes in strain-rate and stress-state within the neck, and the resulting load-extension plot. Satisfactory modeling of this problem has been achieved by using a rigid/plastic constitutive law including strain hardening and strain-rate hardening. Progressive cessation of deformation starting from elements in the specimen fillet region toward the center is demonstrated. This effect is shown to generate a strain peak (neck) at the gage length center. The predicted load-extension plots and strain distributions in the neck agree well with experiments conducted on a number of test materials. This work provides a quantitative measure of the influence of various material parameters on tensile ductility and identifies the proper constitutive law for input into mathematical models of more complex forming operations. Formerly with Research Laboratories, General Motors Corporation, Warren, Ml.