Microstructure-based crystal plasticity modeling of cyclic deformation of Ti–6Al–4V

Ti–6Al–4V is a dual phase material with range of possible complex microstructures. It is well known that mechanical behavior of Ti–6Al–4V is significantly affected by its texture and microstructure morphology. A three-dimensional microstructure-based constitutive model for monotonic and cyclic deformation of duplex Ti–6Al–4V is developed and implemented. The model includes length scale effects associated with dislocation interactions with different microstructure features, and is calibrated using polycrystalline finite element simulations to fit the measured macroscopic responses (overall stress–strain behavior) of a duplex heat treated Ti–6Al–4V alloy subjected to a complex cyclic loading history. Representative microstructures are simulated using a three-dimensional finite element mesh with periodic boundary conditions imposed in all directions. The measured orientation and misorientation distributions of grains of this duplex Ti–6Al–4V are considered, and similar probability density distributions of the crystallographic orientations are assigned to the finite element mesh. The misorientation distributions are then fit using the simulated annealing method. Effects of microstructural features are examined and compared with the experimental data in terms of their influence on the material yield strength. The results are shown to be in good agreement with the experimental observations.     

Image-Based Inertial Impact Test for Characterisation of Strain Rate Dependency of Ti6Al4V Titanium Alloy

Experimental Mechanics - In the present work Image-Based Inertial Impact (IBII) tests are performed on Ti6Al4V material. The IBII test uses an impact on the edge of the specimen to generate a short...     

Novel Technique for Static and Dynamic Shear Testing of Ti6Al4V Sheet

Few shear test techniques exist that cover the range of strain rates from static to dynamic. In this work, a novel specimen geometry is presented that can be used for the characterisation of the shear behaviour of sheet metals over a wide range of strain rates using traditional tensile test devices. The main objectives during the development of the shear specimen have been 1) obtaining a homogeneous stress state with low stress triaxiality in the zone of the specimen subjected to shear and 2) appropriateness for dynamic testing. Additionally, avoiding premature specimen failure due to edge effects was aimed at. Most dimensional and practical constraints arose from the dynamic test in which the specimen is loaded by mechanical waves in a split Hopkinson tensile bar device. Design of the specimen geometry is based on finite element simulations using ABAQUS/Explicit. The behaviour of the specimen is compared with the more commonly used simple shear specimen with clamped grips. Advantages of the new technique are shown. The technique is applied to Ti6Al4V sheet. During the high strain rate experiments high speed photography and digital image correlation are used to obtain the local shear strain in the specimen. Comparison of experimental and numerical results shows good correspondence.     

Experimental and numerical investigation of the uncut chip thickness reduction in Ti6Al4V orthogonal cutting

The downsizing of traditional cutting (“macro-cutting”) to micro-cutting introduces changes in the cutting process. The uncut chip thickness decreases and the cutting edge radius of the tool cannot be neglected anymore. The minimum chip thickness phenomenon takes importance, as well as ploughing. The size effect appears and the influence of the microstructure grows. Determining the value of the uncut chip thickness is a major concern to produce high quality parts. This paper focuses on the determination of that value experimentally with a setup providing strictly orthogonal cutting configuration and a one-time machining of the surface, as well as numerically with a finite element model by only changing the value of the uncut chip thickness. Specificities of micro-cutting are highlighted experimentally and numerically. The cutting refusal is observed in both cases and the minimum chip thickness is estimated (at minimum 25 % of the cutting edge radius) with a good correlation.     

Multiaxial and non-proportional loading responses,anisotropy and modeling of Ti–6Al–4V titanium alloy over wide ranges of strain rates and temperatures

Results from a series of multiaxial loading experiments on the Ti–6Al–4V titanium alloy are presented. Different loading conditions are applied in order to get the comprehensive response of the alloy. The strain rates are varied from the quasi-static to dynamic regimes and the corresponding material responses are obtained. The specimen is deformed to large strains in order to study the material behavior under finite deformation at various strain rates. Torsional Kolsky bar is used to achieve shear strain rates up to 1000 s⁻¹. Experiments are performed under non-proportional loading conditions as well as dynamic torsion followed by dynamic compression at various temperatures. The non-proportional loading experiments comprise of an initial uniaxial loading to a certain level of strain followed by biaxial loading, using a channel-type die at various rates of loadings. All the non-proportional experiments are carried out at room temperature. Experiments are also performed to investigate the anisotropic behavior of the alloy. An orthotropic yield criterion [proposed by Cazacu, O., Plunkett, B., Barlat, F., 2005. Orthotropic yield criterion for hexagonal closed packed metals. International Journal of Plasticity 22, 1171–1194.] for anisotropic hexagonal closed packed materials with strength differential is used to generate the yield surface. Based on the definition of the effective stress of this yield criterion, the observed material response for the different loading conditions under large deformation is modeled using the Khan–Huang–Liang (KHL) equation assuming isotropic hardening. The model constants used in the present study, were pre-determined from the extensive uniaxial experiments presented in the earlier paper [Khan, A.S., Suh, Y.S., Kazmi R., 2004. Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys. International Journal of Plasticity 20, 2233–2248]. The model predictions are found to be extremely close to the observed material response.     

Optimization of cutting conditions for end milling of Ti6Al4V Alloy by using a Gravitational Search Algorithm (GSA)

Surface roughness is commonly used to indicate the quality of machine parts. Optimizing cutting parameters throughout the machining process is an important aspect for manufacturers, as it allows them to achieve a minimum surface value. During this study, a new optimization technique known as the gravitational search algorithm (GSA) was employed in order to achieve minimum surface roughness when end milling a Ti6Al4V alloy under dry cutting conditions, with both PVD coated and uncoated cutting tools. Regression models have been created based on the results of real experimental data. Through use of SPSS software, it was possible to formulate the objective (fitness) functions which were used in the GSA optimization for each cutting tool. A MATLAB code was then created to instigate the optimization process. The results indicated that high cutting speed and low feed rate and depth of cut could result in a minimum surface roughness value of (0.6255 μm), based on the objective function for the PVD cutting tool. Alternatively, surface roughness of around (0.4165 μm) could be achieved by using an uncoated tool on a lower feed rate, depth of cut and cutting speed. The same GSA technique was used in another case study optimized by Genetic algorithm (GA). The GSA achieved the same results, and proved that it is faster than GA: GSA could reach the optimum solution in the third iteration; GA could only reach it in the 67th.     

Mechanical behavior of titanium alloy Ti-6Al-4V with unprepared microstructure under jumpwise variations of the strain rate in the superplastic state

We present the results of extension tests with superplastic specimens made of structural titanium alloy with unprepared (coarse-grained) microstructure. The tests were performed at a constant temperature and constant or piecewise constant strain rate. It was shown that, in the case of a jumpwise decrease in the strain rate, the typical shape of the strain diagram depends on the test temperature. Some variations in the original microstructure are demonstrated.     

The effect of large deformation and material nonlinearity on gel indentation

A gel, an aggregate of polymers with solvents, has dual attributes of solid and liquid as solvent migrates in and out of the polymer network. Indentation has recently been used to characterize the mechanical properties of gels. This paper evaluates the effects of large deformation and material nonlinearity on gel indentation through theoretical modeling and finite element analysis. It is found that large deformation significantly affects the interpretation of the experimental observations and the classical relation between indentation force and depth has limitations for large deformation. The material nonlinearity does not play a very important role on indentation experiment so that the poroelasticity is a good approximation. Based on these observations, this paper proposes an alternative approach to measure the mechanical properties of gels, namely, uniaxial compression experiment.     

Effect of oxygen content and microstructure on the thermo-mechanical response of three Ti–6Al–4V alloys: Experiments and modeling over a wide range of strain-rates and temperatures

Results from a series of experiments on three different titanium alloys, under quasi-static and dynamic loading conditions are presented. The Ti–6Al–4V titanium alloys include the ELI version and two with higher oxygen contents. The strain-rates are varied from 10⁻⁶ to 3378 s⁻¹ while observations are made at temperatures from 233 to 755 K. The alloys initial and deformed photomicrographs and various deformation mechanisms responsible for the induced plastic deformation, are presented and discussed. Differences in the responses of these alloys are observed in terms of thermal softening, work hardening, and strain-rate and temperature sensitivities. The Khan–Huang–Liang (KHL) model is used to effectively simulate the observed responses obtained from these experiments. The model, with the constants determined from these experiments, is then used to predict strain-rate jump experimental results, and also high temperature dynamic experiments for one of the alloys; the predictions are found to be very close to the observations.     

Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part-I: A very low work hardening aluminum alloy (Al6061-T6511)

In the present study, the initial and subsequent yield surfaces in Al 6061-T6511, based on 10 με deviation from linearity definition of yield, are presented. The subsequent yield surfaces are determined during tension, free end torsion, and combined tension–torsion proportional loading paths after reaching different levels of strains. The yield surfaces are also obtained after linear, bi-linear and non-linear unloading paths after finite plastic deformation. The initial yield surface is very close to the von-Mises yield surface and the subsequent yield surfaces undergo translation and distortion. In the case of this low work hardening material, the size of the yield surfaces is smaller and negative cross-effect is observed with finite plastic deformation. The subsequent yield have a usual “nose” in the loading direction and flattened shape in the reverse loading direction; the observed nose is more dominant in the case of tension and combined tension–torsion loading than in torsional loading. The size of the yield surfaces after unloading is smaller than the initial yield surface but larger than subsequent yield surfaces obtained during prior loading, show much smaller cross-effect, and the shape of these yield surfaces depends strongly on the loading and unloading paths. Elastic constants (Young’s and shear moduli) are also measured within each subsequent yield surfaces. Evolution of these constants with finite deformation is also presented. The decrease of the two moduli is found to be much smaller than reported earlier in tension by Cleveland and Ghosh [Cleveland, R.M., Ghosh, A.K., 2002. Inelastic effects on springback in metals. Int. J. Plast. 18, 769–785]. Part-II and III [(Khan et al., 2009a) and (Khan et al., 2009b)] of the papers will include experimental results on annealed 1100 Al (a very high work hardening material) and on both Al alloys (Al6061-T6511 and annealed 1100 Al) in tension- tension stress space, respectively. The results for both cases are quite different than the ones that are presented in this paper.     

Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part II: A very high work hardening aluminum alloy (annealed 1100 Al)

Results are presented on the evolution of subsequent yield surfaces with finite deformation in a very high work hardening annealed 1100 aluminum alloy. In Part I [Khan, A.S., Kazmi, R., Stoughton, T., Pandey, A., 2009a. Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part 1: a very low work hardening aluminum alloy (Al-6061–T6511) 25, 1611–1625.] of this paper, similar results are presented for a very low work hardening aluminum alloy. Those results were very different from the present ones, and all the results were for proportional loading paths. The subsequent yield surfaces are determined in tension, free end torsion and combined tension–torsion proportional and non-proportional loading paths, using 10 με deviation from linearity definition of yield. Yield surfaces are also determined after linear, bi-linear, and non-linear unloading paths after finite deformation under tension, free end torsion, and combined tension–torsion loading. The initial yield surface is closer to the von-Mises surface and the subsequent yield surfaces show distortion, expansion, positive cross-effect, and “nose” in the loading direction. Additionally, the subsequent yield surfaces after non-proportional loading paths show shrinkage and compounded distortion. The yield surfaces after unloading depict strong anisotropy, positive cross-effect and exhibits different proportion of distortion in each loading conditions. The Young’s and shear modulus decrease with plastic deformation and this decrease is much less than those reported in the published literature.     

An experimental study of the effect of hardening on plastic deformation at notch tips in metallic single crystals

Experiments to measure the effect of hardening on the plastic deformation field near a notch tip in metallic single crystals were conducted. The specimens were cut from pure Cu and a CuBe alloy (with 1.8-2.0 wt% Be) FCC single crystals. The Cu-2.0wt%Be alloy was selected because its initial hardness and rate of hardening can be modified by heat treatment. The Vickers hardness of the specimens ranged from 87 to , while the hardening exponents ranged between 10 and 4.5. The experimental results were compared to analytical and numerical solutions from the literature. This comparison shows that the inclusion of elastic regions in the analytical solutions and anisotropic hardening in the numerical solutions results in better agreement with the experiments.     

Artificial neural network prediction to the hot compressive deformation behavior of Al–Cu–Mg–Ag heat-resistant aluminum alloy

The behavior of the flow stress of Al-Cu-Mg-Ag heat-resistant aluminum alloys during hot compression deformation was studied by thermal simulation test. The temperature and the strain rate during hot compression were 340-500 °C, 0.001 s⁻¹ to 10 s⁻¹, respectively. Constitutive equations and an artificial neural network (ANN) model were developed for the analysis and simulation of the flow behavior of the Al-Cu-Mg-Ag alloys. The inputs of the model are temperature, strain rate and strain. The output of the model is the flow stress. Comparison between constitutive equations and ANN results shows that ANN model has a better prediction power than the constitutive equations.     

The effect of shear deformation on the post-buckling behavior of imperfect nonlinear viscoelastic columns

Summary The post-buckling behavior of imperfect columns made of nonlinear viscoelastic materials is investigated, taking into account the effect of shear deformation. The material is modeled according to the Leaderman representation of nonlinear viscoelasticity. Solutions are developed, within the elastica and the shear deformation theories, in order to calculate the growth in time of the total deflection. The numerical results establish the importance of the shear and the nonlinear viscoelasticity effects, and of the h/ℓ ratio in the column post-buckling behavior. Accepted for publication 11 November 1996     

Multi-scale finite element simulation on large deformation behavior of wood under axial and transverse compression conditions

Acta Mechanica Sinica - Multi-scale finite element method is adopted to simulate wood compression behavior under axial and transverse loading. Representative volume elements (RVE) of wood...     

Impact of material processing and deformation on cell morphology and mechanical behavior of polyurethane and nickel foams

The cell morphology and mechanical behavior of open-cell polyurethane and nickel foams are investigated by means of combined 3D X-ray micro-tomography and large scale finite element simulations. Our quantitative 3D image analysis and finite element simulations demonstrate that the strongly anisotropic tensile behavior of nickel foams is due to the cell anisotropy induced by the deformation of PU precursor during the electroplating and heat treatment stages of nickel foam processing. In situ tensile tests on PU foams reveal that the initial main elongation axis of the cells evolves from the foam sheet normal direction to the rolling direction of the coils. Finite element simulations of the hyperelastic behavior of PU foams based on real cell morphology confirm the observation that cell struts do not experience significant elongation after 0.15 tensile straining, thus pointing out alternative deformation mechanisms like complex strut junctions deformation. The plastic behavior and the anisotropy of nickel foams are then satisfactorily retrieved from finite element simulations on a volume element containing eight cells with a detailed mesh of all the hollow struts and junctions. The experimental and computational strategy is considered as a first step toward optimization of process parameters to tailor anisotropy of cell shape and mechanical behavior for applications in batteries or Diesel particulate filtering.     

Thermal effect on the deformation of a flexible beam with large kinematical driven overall motions

The research investigates the transient longitudinal and transverse deformation of a planar flexible beam with large overall motions in a temperature field. With the increase of temperature, longitudinal deformation is caused by the thermal expansion in axial direction. Due to the coupling of longitudinal and transverse deformation, the transverse deformation is induced, which is significant in cases where temperature increases rapidly in a very short period. Furthermore, the transverse temperature gradient, which is caused by the temperature variation in the transverse direction, may lead to transverse deformation. Considering the thermal strain, equations of motion of a flexible beam with arbitrary large overall motion are derived based on virtual work principle. The high order terms of the strain tensor are taken into account, such that the geometric nonlinear deformation terms are included in the dynamic equations. Simulation results of a rotating beam are shown to reveal the thermal effect and nonlinear effect on the dynamic performance of the beam.     

Effects of size on the strength and deformation mechanism in Zr-based metallic glasses

We report results of uniaxial compression tests on Zr₃₅Ti₃₀Co₆Be₂₉ metallic glass nano-pillars with diameters ranging from ∼1.6 μm to ∼100 nm. The tested pillars have nearly vertical sidewalls, with the tapering angle lower than ∼1° (diameter >200 nm) or ∼2° (diameter ∼100 nm), and with a flat pillar top to minimize the artifacts due to imperfect geometry. We report that highly-localized-to-homogeneous deformation mode change occurs at 100 nm diameter, without any change in the yield strength. We also find that yield strength depends on size only down to 800 nm, below which it remains at its maximum value of 2.6 GPa. Quantitative Weibull analysis suggests that the increase in strength cannot be solely attributed to the lower probability of having weak flaws in small samples - most likely there is an additional influence of the sample size on the plastic deformation mechanism.