Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet

Various self-consistent polycrystal plasticity models for hexagonal close packed (HCP) polycrystals are evaluated by studying the deformation behavior of magnesium alloy AZ31B sheet under different uniaxial strain paths. In all employed polycrystal plasticity models both slip and twinning contribute to plastic deformation. The material parameters for the various models are fitted to experimental uniaxial tension and compression along the rolling direction (RD) and then used to predict uniaxial tension and compression along the traverse direction (TD) and uniaxial compression in the normal direction (ND). An assessment of the predictive capability of the polycrystal plasticity models is made based on comparisons of the predicted and experimental stress responses and R values. It is found that, among the models examined, the self-consistent models with grain interaction stiffness halfway between those of the limiting Secant (stiff) and Tangent (compliant) approximations give the best results. Among the available options, the Affine self-consistent scheme results in the best overall performance. Furthermore, it is demonstrated that the R values under uniaxial tension and compression within the sheet plane show a strong dependence on imposed strain. This suggests that developing anisotropic yield functions using measured R values must account for the strain dependence.     

FeCrAl合金材料织构对其宏观力学本构关系的影响研究

FeCrAl合金具有优良的高温抗氧化性和耐辐照性能,是事故容错核燃料包壳的重要候选材料. 其在加工过程和热处理过程中易形成α纤维织构（<110>//RD）和γ纤维织构（<111>//ND）,会影响材料的宏观力学性能与深加工成形能力. 本研究针对具有不同织构的多晶FeCrAl合金,建立了代表性体元模型, 使用晶体塑性有限元方法,在ABAQUS/Explicit中模拟材料单轴加载下的宏观应力应变曲线,分析不同织构对FeCrAl合金宏观力学本构关系的影响. 计算结果表明,对于具有α织构、γ织构和晶粒无择优取向的材料,在轧向上的应力应变曲线差异较小. γ织构会引起材料强烈的各向异性,在轧面法向上的屈服强度远高于轧向和横向上的屈服强度,这是因为晶粒的<111>方向平行于加载方向,滑移系难以启动. 提高γ纤维织构的比例,将增大轧面法向上的屈服强度. 本研究可以为优化FeCrAl合金材料织构、加工条件和材料力学性能提供参考.     

FeCrAl合金材料织构对其宏观力学本构关系的影响研究

FeCrAl合金具有优良的高温抗氧化性和耐辐照性能,是事故容错核燃料包壳的重要候选材料. 其在加工过程和热处理过程中易形成α纤维织构（<110>//RD）和γ纤维织构（<111>//ND）,会影响材料的宏观力学性能与深加工成形能力. 本研究针对具有不同织构的多晶FeCrAl合金,建立了代表性体元模型, 使用晶体塑性有限元方法,在ABAQUS/Explicit中模拟材料单轴加载下的宏观应力应变曲线,分析不同织构对FeCrAl合金宏观力学本构关系的影响. 计算结果表明,对于具有α织构、γ织构和晶粒无择优取向的材料,在轧向上的应力应变曲线差异较小. γ织构会引起材料强烈的各向异性,在轧面法向上的屈服强度远高于轧向和横向上的屈服强度,这是因为晶粒的<111>方向平行于加载方向,滑移系难以启动. 提高γ纤维织构的比例,将增大轧面法向上的屈服强度. 本研究可以为优化FeCrAl合金材料织构、加工条件和材料力学性能提供参考.     

Effect of temperature on the fracture modes of BHW-35 steel under mode-II loading

Finite element method (FEM) has been used to analyze the stress and strain fields and the stress tri-axial levels around the tip of the crack under mode- II loading. The results show that: under mode- II loading, the direction of the maximum tensile stress and that of the maximum tri-axial levels (R _o ) exist at an angle of –75. 3° from the original crack plane; the maximum shear stress andR _o = 0 exist along the original crack plane.Mode- II loading experiment using BHW-35 steel at different temperatures show that there are two kinds of fracture mode, opening mode (or tensile mode) and sliding mode (or shear mode). A decrease in temperature causes the fracture mode to change from shear mode to tensile mode. For BHW-35 steel, this critical temperature is about –90 C. Actually, under any kind of loading mode (mode I . mode II , mode III or mixed mode), there always exist several kinds of potenital fracture modes (for example, opening mode, sliding mode, tearing mode or mixed mode). The effect of temperature under mode- II loading is actually related to the change of the elastic-plastic properties of the material.     

Texture development and plastic anisotropy of B.C.C. strain hardening sheet metals

A Taylor-like polycrystal model is adopted here to investigate the plastic behavior of body centered cubic (b.c.c.) sheet metals under plane-strain compression and the subsequent in-plane biaxial stretching conditions. The <111> pencil glide system is chosen for the slip mechanism for b.c.c. sheet metals. The {110} <111> and {112} <111> slip systems are also considered. Plane-strain compression is used to simulate the cold rolling processes of a low-carbon steel sheet. Based on the polycrystal model, pole figures for the sheet metal after plane-strain compression are obtained and compared with the corresponding experimental results. Also, the simulated plane-strain stress—strain relations are compared with the corresponding experimental results. For the sheet metal subjected to the subsequent in-plane biaxial stretching and shear, plastic potential surfaces are determined at a given small amount of plastic work. With the assumption of the equivalence of the plastic potential and the yield function with normality flow, the yield surfaces based on the simulations for the sheet metal are compared with those based on several phenomenological planar anisotropic yield criteria. The effects of the slip system and the magnitude of plastic work on the shape and size of the yield surfaces are shown. The plastic anisotropy of the sheet metal is investigated in terms of the uniaxial yield stresses in different planar orientations and the corresponding values of the anisotropy parameter R, defined as the ratio of the width plastic strain rate to the through-thickness plastic strain rate under in-plane uniaxial tensile loading. The uniaxial yield stresses and the values of R at different planar orientations from the polycrystal model can be fitted well by a yield function recently proposed by Barlat et al. (1997b).     

Anisotropic responses, constitutive modeling and the effects of strain-rate and temperature on the formability of an aluminum alloy

Finite deformation anisotropic responses of AA5182-O, over a wide range of strain-rates (10⁻⁴ to 10⁰ s⁻¹) and temperatures (293-473 K) are presented. The plastic anisotropy parameters were experimentally determined from tensile experiments using specimens from sheet material. Using the experimental results under plane stress conditions, the anisotropy coefficients for Barlat’s yield function (YLD96) were calculated at different strain-rates and temperatures. The correlations obtained from YLD96 are in good agreement with the observed experimental results. The strain-rate sensitivity of AA5182-O alloy changed from negative at 293 K to positive at 473 K. Khan-Huang-Liang (KHL) constitutive model is shown to correlate the observed strain-rate and temperature dependent responses reasonably well. The material parameters were obtained from the experimental responses along the rolling direction (RD) of the sheet. Marciniak and Kuckzinsky (M-K) theory was used to obtain the theoretical strain and stress-based forming limit curves (FLCs) at different strain-rates and temperatures. The experimental result from the published literature is compared with the FLCs from the current study.     

Initiation and growth of wrinkling due to nonuniform tension in sheet metal forming

An experimental investigation was conducted on the initiation and growth of wrinkling due to nonuniform tension using the Yoshida buckling test. The initiation of wrinkling was detected by strain gages mounted on both surfaces of the samples in the loading and transverse directions. The bifurcation of aluminum auto body sheets appeared to be smooth and much less abrupt than that observed in a steel sheet. A special fixture was designed to, perhaps for the first time, continuously measure the in situ growth of the buckle heights so that the rates of buckle growth were monitored as functions of strain and stress in the loading direction. In contrast to what is commonly believed, it was found that the buckle height is not predominantly determined by the material yield strength, and lower averager value does not increase the rate of buckle growth. Crystallographic texture components and pole figures of the test materials were also measured, and the relationship of plastic anisotropy with wrinkling behavior was investigated by experiments with specimens aligned in the rolling direction, the transverse direction and 45-deg to the rolling direction of the sheet materials.     

Failure modes of specimens containing surface flaws under cyclic torsion

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such a torsional loading may initiate yielding at the outer radius of the shaft or in the fillets. The methods for predicting turbine-shaft fatigue life due to transient loading depent upon the mode of crack growth from an undetected crack. The most common location for the existence of a crack is the fillets or shoulders of the shaft. Specimens were designed from AISI 4340 steel with two diametrically opposed flat surfaces. Initial defect orientations of 0 deg, 45 deg and 90 deg with respect to the sepcimen axis on the fillet were studied. The specimens were subjected to cyclic torsion with zero mean torque and with a torque amplitude necessary to cause yielding at the outer radius of the specimen. When initial defects were aligned with a plane of maximum shear stress (0 deg and 90 deg), the cracks propagated along that plane. For 45-deg defects (aligned to a plane of maximum tensile stress) the crack still propagated along the plane of maximum shear. However, the number of cycles to initiate and to propagate the crack to failure for 45-deg defects were (two to three times) larger than those for 0-deg and 90-deg defects. Mode II and Mode III crack-growth rates were measured from specimens containing 0-deg and 90-deg defects. It was found that the crack-growth rate in Mode II was higher than in Mode III. However, all the specimens failed due to reduction of the net cross section, mostly attributed to Mode III crack growth. Similar results were obtained from specimens of turbine-shaft material (A469 steel), and 2024 aluminum with different rolling directions. Fatigue-crack-growth rates in Mode III were measured from circumferentially notched bar. They were found to be a unique function of ΔK _III alternating stress intensity in Mode III. It was found that the mechanism of crack growth is produced by the formation and linkage of elongated cavities at the crack tip.     

Spatiotemporal Thermal Inhomogeneities During Compression of Highly Textured Zirconium

Using a focal plane array infrared camera, the heat generated during large strain compression (at a rate of 1 s⁻¹) is used to study the characteristics of plastic flow for hcp zirconium. Heat generation during plastic flow in a reference material, copper, was seen to develop uniformly both at the lower (40 μm/pixel) and higher (8 μm/pixel) magnifications used in this study. The thermomechanical response of Zr, however, was seen to depend on the loading direction with respect to the specimen texture. Highly textured zirconium compressed along nonbasal oriented grains results in a homogeneous thermal response at both scales. However, compression along basal (0001) oriented grains shows evidence of inhomogeneous deformation at small strains that lead to macroscale localization and failure at large strains. The conversion of plastic work into heat is observed to be a dynamic process, both in the time-dependent nature of the energy conversion, but also in the passage of waves and ‘bursts’ of plastic heating. Basal compression also showed evidence of small scale localization at strains far below macroscale localization, even below 10%. These localizations at the lower strain levels eventually dominate the response, and form the shear band that is responsible for the softening of the macroscopic stress–strain curve.     

Large Strain Shear Compression Test of Sheet Metal Specimens

A hybrid experimental-computational procedure to establish accurate true stress-plastic strain curve of sheet metal specimen covering the large plastic strain region using shear compression test data is described. A new shear compression jig assembly with a machined gage slot inclined at 35° to the horizontal plane of the assembly is designed and fabricated. The novel design of the shear compression jig assembly fulfills the requirement to maintain a uniform volume of yielded material with characteristic maximum plastic strain level across the gage region of the Shear Compression Metal Sheet (SCMS) specimen. The approach relies on a one-to-one correlation between measured global load–displacement response of the shear compression jig assembly with SCMS specimen to the local stress-plastic strain behavior of the material. Such correlations have been demonstrated using finite element (FE) simulation of the shear compression test. Coefficients of the proposed correlations and their dependency on relative plastic modulus were determined. The procedure has been established for materials with relative plastic modulus in the range 5?×?10^?4?<?(E _p /E)?<?0.01. It can be readily extended to materials with relative plastic modulus values beyond the range considered in this study. Nonlinear characteristic hardening of the material could be established through piecewise linear consideration of the measured load–displacement curve. Validity of the procedure is established by close comparison of measured and FE-predicted load–displacement curve when the provisional hardening curve is employed as input material data in the simulation. The procedure has successfully been demonstrated in establishing the true stress-plastic strain curve of a demonstrator 0.0627C steel SCMS specimen to a plastic strain level of 49.2 pct.     

Texture gradient simulations for extrusion and reversible rolling of FCC metals

A texture simulation method is described for some complex plane strain deformation paths during hot shaping of FCC metals. The method employs both finite element calculations and a polycrystal plasticity model based on the Relaxed-Constraints (RC) Taylor hypothesis and a viscoplastic constitutive law. We have considered the {111}<110> slip systems and the {100}, {110}, {112} <110> non-octahedral slip systems. The finite element codes simulate the strain paths of material flow during a shaping process. The local velocity gradients, expressed in the macroscopic reference coordinates, are rewritten in the local flow line coordinates using a kinematic analysis for steady-state flow. Secondly, for the different deformation paths, the RC polycrystal plasticity model is used to numerically simulate the local deformation texture evolutions as a function of depth. Texture simulations are carried out for two deformation processes combining hot compression and shear: extrusion and reversible rolling. For extrusion, the simulated pole figures and ODFs show the typical texture variations through the thickness of an extruded 6082 aluminium alloys, i.e. (β-fibre in the centre and a TD rotated copper component near the surface. It is shown that hot reversible rolling should develop a strong pure shear texture {001}<110> near the surface.     

Characterization of Anisotropic Polymeric Foam Under Static and Dynamic Loading

An orthotropic polymeric foam with transverse isotropy (Divinycell H250) used in composite sandwich structures was characterized at various strain rates. Uniaxial experiments were conducted along principal material axes as well as along off-axis directions under tension, compression, and shear to determine engineering constants, such as Young??s and shear moduli. Uniaxial strain experiments were conducted to determine mathematical stiffness constants, i. e., C _ij . An optimum specimen aspect ratio for these tests was selected by means of finite element analysis. Quasi-static and intermediate strain rate tests were conducted in a servo-hydraulic testing machine. High strain rate tests were conducted using a split Hopkinson Pressure Bar system built for the purpose using polymeric (polycarbonate) bars. The polycarbonate material has an impedance that is closer to that of foam than metals and results in lower noise to signal ratios and longer loading pulses. It was determined by analysis and verified experimentally that the loading pulses applied, propagated along the polycarbonate rods at nearly constant phase velocity with very low attenuation and dispersion. Material properties of the foam were obtained at three strain rates, quasi-static (10^?4 s^?1), intermediate (1 s^?1), and high (10³ s^?1) strain rates. A simple model proposed for the Young??s modulus of the foam was in very good agreement with the present and published experimental results.     

Study of a drawing-quality sheet steel. I: Stress/strain behaviors and Lankford coefficients by experiments and micromechanical simulations

The sheet-metal industry uses Lankford coefficients and the forming-limit curve, FLC, as standards for characterizing a sheet’s ability to be stretched and deep drawn. Investigators have recently made significant advances in computer codes that predict these measures of formability. However, complete experimental data sets that provide input properties and verification data for the simulations rarely exist for a single material. The current investigation focused on obtaining such data for a single drawing-quality steel sheet. Measurements intended for the calibration and initial verification of the simulation code include uniaxial-tension tests, through-thickness and plane-strain compression experiments, and quantitative texture – orientation distribution function – evaluations, while a comparison between measured and simulated Lankford coefficients, Part I, and an FLC, Part II, provide a rigorous verification of the computer simulations. In order to initially verify the simulations, we performed through-thickness and plane-strain compression measurements. A key experimental result was that the flow curve in free, through-thickness compression – an experiment that corresponds to biaxial stretching – lies 18% above the uniaxial tensile data. The plane-strain compression curve is another 11% above the free-compression stress/strain data. We measured the Lankford coefficients, as a function of angle to the rolling direction, for the same steel sheet, finding the maximum values in and at 90° to the rolling direction, 1.59 and 1.89 respectively. A minimum Lankford coefficient of 1.19 was measured at 45° to the rolling direction. For calibrating a rate-dependent visco-plastic self-consistent polycrystal model we needed only to measure the material’s initial texture and to fit power-law and saturation-hardening laws to our tensile data. This kept the set of adjustable parameters to a minimum. Without other adjustments to the model, we predicted the correct stress levels in the free and channel-die compression experiments as well as values of Lankford coefficients. These successes indicate that the polycrystal model should be capable of simulating the entire FLC, Part II.     

Grain orientation fragmentation in hot-deformed aluminium: Experiment and simulation

Grain orientation fragmentation is studied in a set of 176 individual grains of an aluminium polycrystal deformed in plane strain compression at 400 °C to a strain of $\epsilon =1.2$. Experimental observations were made by EBSD at successive strains of 0, 0.42, 0.77 and 1.2 on the internal surface of a split sample. Statistics of the in-grain orientation spreads were computed based on approximately 3000 orientation measurements per grain. A high-resolution finite element simulation (about 1000 elements per grain) was carried out on a polycrystal whose grains were assigned the initial experimental crystal orientations. The experimental and simulation results were compared in terms of the fractions of grains that exhibit fragmentation and the lattice orientations of the fragmenting grains. The numbers of fragmented grains increase with strain, reaching values of 10% in the experiment (2-D characterization) and 20% in the simulation (3-D characterization) at $\epsilon =1.2$. For both experiment and simulation, fragmentation is more likely in grains whose lattice is symmetrically oriented with respect to the loading axes. Under plane strain compression, the orientations of the fragmented grains coincide with regions of orientation space in which the reorientation velocity field in the plane perpendicular to the reorientation velocity direction is unstable.     

Modeling the mechanical response of rolled Zircaloy-2

An elastoplastic self-consistent model has been implemented to perform a systematic study of the response of rolled Zircaloy-2 subjected to mechanical loading. The intergranular stresses induced by cooling the material from 898 K to room temperature are calculated, accounting for the experimental texture, and compared with experimental data. The elastoplastic response in tension and compression along the rolling and the transverse directions of the sheet is predicted and compared against the results of uniaxial tensile and compressive tests performed in the same material. The role of the internal stresses on the yield stress and the elastoplastic transition is analyzed, and information about the active deformation systems in the individual grains is inferred from the comparison. Indirect inference of the parameters describing the deformation mechanisms is the only available means, because it is not possible to grow single crystals of these alloys. The results of this study demonstrate the adequacy of self-consistent schemes for predicting intergranular stresses and the significance of the latter on the mechanical behavior of the material.     

Application of Laser Deposition to Mechanical Characterization of Advanced High Strength Steels Subject to Non-Proportional Loading

Background

Characterization of hardening and fracture limits of advanced high strength steels (AHSSs) undergoing strain path changes (SPCs) are particularly challenging for plane strain condition, which commonly occurs in sheet metal forming. There is a need for a simple, engineering-friendly method to characterize materials subjected to complex loading paths that mimic stress conditions in actual forming processes.

Objective

Experimental additive manufacturing techniques have been applied to reinforce AHSS specimens subjected to SPCs in order to broaden capabilities for characterizing hardening behavior and fracture limits.

Methods

Hardening curves subject to SPCs (e.g. uniaxial tension or equi-biaxial tension followed by plane strain) have been obtained with a programmable biaxial tensile testing system using cruciform-shaped specimens with load-bearing arms reinforced by laser deposition. A notched specimen selectively reinforced by laser deposition was newly designed to characterize fracture limits subjected to SPCs ending with plane strain condition.

Results

Complex loading histories were successfully enabled by applying laser deposition technology. Results show that both hardening behavior and fracture limits of a TRIP-assisted steel and a dual-phase steel are dependent on loading history.

Conclusions

It appears that the laser deposition technique can be used for material characterization under specific SPCs. Hardening behavior of AHSSs under SPCs ending with plane strain is quite different from traditional uniaxial tension-uniaxial compression tests. For materials sensitive to SPCs, multi-step forming can be a great option to reach the targeted forming shape.

     

A crack in a piezoelectric layer bonded to a dissimilar elastic layer under transient load

Summary  A piezoelectric layer bonded to the surface of an elastic structure is considered. The piezoelectric and the elastic layers are infinite along the x-axis and have finite thickness in the y-direction. The polarization direction of the piezoelectric material is along the y-axis. By means of the method of singular integral equations, the solution in a Laplace transform plane is demonstrated. Laplace inversion yields the results in the time domain. Numerical values of the crack tip fields under in-plane transient electromechanical loading are obtained. The influence of layers thickness on stress and electric displacement intensity factors is investigated. Received 16 March 2000; accepted for publication 16 August 2000     

High temperature damage model for carbon–carbon composites

A damage model for carbon–carbon orthotropic composite materials is introduced with a special attention to the thermo-mechanical effects. The internal variables of damage are identified from tension–compression tests according to each fiber direction and from shear tests in each orthotropy plane. The influence of the temperature is taken into account from typical experimental stress–strain curves given for different values of the temperature. The finite element model was implemented in ABAQUS^® using an implicit time incremental scheme. Finally, a significant numerical simulation of a thermo-mechanical loading with damage is presented.     

Nucleation and Growth Behavior of Twin Region Around Yield Point of Polycrystalline Pure Ti

The aim of the present study is to investigate the nucleation and growth behavior of twin region around yield point of polycrystalline pure Ti under deformation. Firstly, we prepare commercial polycrystalline pure Ti plate, and investigate the microstructure and pole figures using an Electron Backscatter Diffraction Patterns device. Secondly, tensile specimens are cut out from 0°, 30°, 45° and 90° relative to plate rolling direction. Then, we measure the macroscopic stress–strain curve, local strain distribution and nucleation and growth of twin region arising in specimens under uniaxial tensile loading. Results show the anisotropic characteristics in those behaviors. Those could be related to c axis in hcp lattice. However, detailed anisotropic mechanism may have something to do with several interactions between slips and twins arising in its body. It is also understood that the avalanche behavior of twin region nucleation occurs as a result of larger twin region formation, with inhomogeneous small twin region nucleation in transient process. Finally, we could suppose the bridge mechanism of deformation behaviors from macroscale to microscale for polycrystalline pure Ti under deformation.