Plastic Flow Stress Research Articles

Grain-size effect on plastic flow stress of nanolaminated polycrystalline aluminum/graphene composites

Nanolaminated metal/graphene composites can have many special mechanical properties, thanks to a high density of interfaces. Even though the interface effect is a key mechanism for the propagation of dislocations in nanolaminated metal/graphene composites, it is not well understood. In this paper, simulations of the molecular dynamics of nanolaminated polycrystalline aluminum/graphene (PAl/Gr) composites are performed. The results provide insight into the grain-size effect on plastic flow stress of nanolaminated PAl/Gr composites and the underlying mechanism. Extended dislocations are found to dominate the plastic deformation of the PAl/Gr composites. Both the PAl/Gr interface and the Al grain boundaries (GBs) interact with the dislocations. Three dislocation propagation forms are observed in the PAl/Gr nanolaminated composite based on the Al grain-size. By decreasing the laminate thickness, the dislocation-GB interaction can transition to a dislocation-graphene interaction. When the Al layer thickness is smaller than the in-plane grain size, the strain-hardening capability is increased due to greater ability of the dislocation/graphene-interface to store dislocations than the GBs. Besides, geometrically necessary dislocations are induced because of the deformation gradient between the graphene and Al grains, which lead to back-stress strengthening and thus strain hardening. Accordingly, a confined layer slip mechanism, which considers back-stress, is used to predict the flow stress of the PAl/Gr composites.

Quantification of porosity and microstructure and their effect on quasi-static and dynamic behavior of additively manufactured Inconel 718

The objective of this investigation is to quantify the evolution of microscopic features, including porosity, precipitates, and grain structure with respect to post-processing heat-treatments and their influence on the quasi-static and dynamic behavior of additively manufactured Inconel 718 built by laser powder bed fusion technique. In laser powder bed fusion, porosity, phase formation, and grain configuration could arise from different sources, including building powder or from the processing (e.g., laser pattern and solidification). The effect of these microscopic features on mechanical properties has drawn the scientific community's attention to developing thermal post-processing procedures targeting porosity closure, microstructural recrystallization, and precipitation of strengthening phases, thus improving material performance. One major challenge is to understand whether one can generalize the effect of certain microscopic features on mechanical properties under different states of stress and whether observed trends remain the same across strain rates? To address these questions, a comprehensive characterization agenda, which includes X-ray Micro-Computed Tomography, Scanning Electron Microscopy, Electron Backscatter Diffraction and mechanical testing at two strain rates (10−4 s−1 and 103 s−1) were implemented on as-built, stress relieved, hot isostatically pressed, and solution treatment plus aging test samples. Results show that, for the given specimen size, precipitate morphology and distribution changes from heat-treatment have a more significant effect than the porosity. In addition, it is demonstrated that there is a considerable enhancement in the magnitude of the plastic flow stress after applying the stress relief heat-treatment, while the subsequent heat-treatments do not have the same effect. When the state of stress is changed to compression, a different trend is observed that is relatively consistent increases in the magnitude of the flow stress. However, an opposite observation is seen under dynamic loading conditions indicating compressive mechanical behavior is more sensitive to the underlying microstructure than tensile behavior. Furthermore, strengthening mechanisms as a result of implemented heat-treatment is also discussed.

A compact plane stress yield function formulation

The construction of anisotropic yield function by introducing linear transformations is a common practice with many phenomenological yield criteria. Based on the K1 − K2 representation method of principle stresses (represented by Barlat89 yield function), a compact 13-parameter plane stress function is proposed. The new yield function consists of five different linear transformations, and is designed to have a certain symmetry in both the overall structure and the distribution of linear transformation matrix components. The new 13-parameter yield function is applied to predict the yield surfaces (loci), plastic strain rate directions, flow stresses and r-values for both fcc and bcc materials. Compared with the yield functions of Yld2004-18p and CPB06ex2 (both reduce to 14 parameters in symmetric plane stress condition), the new yield function can achieve similar prediction accuracy with fewer parameters.

Visco‐elasto‐plastic constitutive model of adhesives under uniaxial compression in a range of strain rates

ABSTRACTDetermining the constitutive model of adhesives enables the prediction of the mechanical response of hybrid structures in which the adhesive is used. In this study, the stress–strain behavior of a two‐component structural adhesive was first measured in uniaxial compression experiments at the strain rates ranging from 0.001 to 2600 s−1 for developing a constitutive model. It was found that the compressive response, including elastic modulus, yield strength, and plastic flow stress, is substantially influenced by the strain rate. In plastic deformation, the strain rate sensitivity is not constant but varies with the rate; moreover, strain softening and hardening dominate the plastic deformation at low and high strains, respectively. A visco‐elasto‐plastic constitutive model was then proposed for the adhesive, integrating the strain rate sensitivity that was quantified by empirical equations. The model which was validated can reliably represent the strain rate dependent compressive behavior of the adhesive. © 2020 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48962.

Статистические закономерности развития локализации деформации при пластическом течении в сплаве АМг6

The laws governing the development of localization of plastic deformation under the conditions of manifestation of the effect of space-time heterogeneity (the Portevin-Le Chatelier effect) were investigated. Compression tests were carried out on cylindrical specimens of the aluminum alloy AMg6 with a constant strain rate of 0.4 –1.7 ·10 − 1 s−1, inclined by 2° from the vertical. This shape of the specimens determines a preferential direction for the formation of slip bands that allows for achieving large strains (up to 80 %) without failure. Calorimetric studies of samples of the AMg6 alloy with varying degrees of deformation were carried out using a STA “Jupiter” 449 calorimeter. Statistical distributions of the intervals between the plastic flow stress fluctuations were analyzed and two critical points were found that indicate a change in the mechanisms of plastic deformation. The transition through the first critical point corresponds to the formation of multiple regions of localized plasticity. The further plastic flow of the studied alloy reveals multiscale signs of localization of plastic deformation over the rest of the plastic flow curve. At the stage of developed plastic flow, the maximum level of stored energy is observed during deformation. The transition through the second critical point is associated with the formation of nuclei of macroscopic failure, which is accompanied by the release of the stored strain energy and a decrease in calorimetric effects. The form of the probability density function of the intervals between the plastic flow stress fluctuations and the probability density function of the flow stress fluctuations confirm the self-similar nature of multiscale correlations of these quantities, similar to that observed for a closed turbulent flow of fluids between two rotating disks in the Karman experiment with large Reynolds numbers.

Study on Dynamic Mechanical Properties and Constitutive Model Construction of TC18 Titanium Alloy

In order to investigate the static and dynamic mechanical properties of TC18 titanium alloy, the quasi-static stress–strain curve of TC18 titanium alloy under room temperature was obtained by DNS 100 electronic universal testing machine (Changchun Institute of Mechanical Science Co., Ltd., Changchun, China). Meanwhile, the flow stress–strain curves under different temperatures and strain rates are analyzed by split Hopkinson pressure bar (SHPB) device with synchronous assembly system. On the basis of the two experimental data, the JC constitutive model under the combined action of high temperature and impact load is established using the linear least squares method. The results show the following: the yield strength and flow stress of TC18 titanium alloy increase slowly with the increase of the strain rate, and the strain value corresponding to the yield strength is reduced. With the increase of strain, the flow stress increases at first and then decreases at different temperatures. The strain value corresponding to the transition point rises with the temperature increase, and the corresponding stress value remains basically unchanged. With the increase of experimental temperature, the flow stress shows a downward trend, and the JC constitutive model can predict the plastic flow stress well.

Micro-CT based finite element modelling and experimental characterization of the compressive mechanical properties of 3-D zirconia scaffolds for bone tissue engineering

The present study aims at developing a computational framework with experimental validation to determine the mechanical properties of zirconia foams for bone tissue engineering. A micro-CT based finite element model that allows characterizing the mechanical property of such cellular structures is developed. Micro-CT images are filtered to vanish noises and smooth boundaries before constructing 3D zirconia foams using an adaptive Body-Centered Cubic background lattice. In addition to micro-CT images, the local material property at the scaffold struts is measured using a micro-indentation test, which shows a considerable difference with that of common zirconia owing to the manufacturing process. The computational model also takes the plastic deformation of material into account employing the Voce law, a nonlinear isotropic hardening law, as well as Von-mises yield criterion. Zirconia foams with different pore sizes are manufactured using the replica method and their mechanical properties determined experimentally. Such experimental outcomes are to validate and demonstrate the capability of the developed model, which can be used for pre-operational evaluations and preclinical tests of zirconia scaffolds. The stress magnitude and distribution within the scaffold as well as plastic strains and flow stress of the zirconia scaffold are computed and analysed. Using the proposed approach, a deep insight into the association of macroscopic behaviour of the scaffold to microscopic features, e.g. strut waviness, Plateau border, thickness variation of cells, irregularity, microstructural variability, imperfections and strut's material property associated with to the manufacturing procedure, can be gained.

Finite element analysis of deep drawing

With the advancement of technology, aiming for achieving a greater lightness and smaller size of 3C products, parts processing technology not only needs to explore the basic scientific theory of materials but also needs to discuss the process of deep drawing numerical and the plastic deformation. This study is based on the square shape of the deep drawing numerical simulation, and aluminum alloy plastic flow stress was input into the finite element method for simulation of plastic deformation in the aluminum alloy friction, mold clamping force, and frequency, as well as amplitude in the influence of forming mechanism and the drawing ratio of aluminum alloy. Finite element analysis software has the function of grid automatic rebuild, which can rebuild the broken grid in the analysis into a complete grid shape, which can avoid the divergence caused by numerical calculation in the analysis process. The greater the obtained error value, the best plastic parameters can be found.

The size dependent strength of Fe, Nb and V micropillars at room and low temperature

The strength of focussed ion beam (FIB) machined [001] orientation single crystal micropillars of body centred cubic structured (bcc) metals Fe, Nb and V, with diameters 200–5000 nm, have been measured at 296 K and 193 K using nanoindentation equipment. The metals have similar critical temperatures for screw dislocation mobility, Tc, close to 350 K. All three metals deform on the (110) plane at both test temperatures and show very similar behaviour of the plastic flow stress, σp, normalised by the shear modulus resolved on the slip plane, μ, as a function of pillar diameter, d, normalised by the Burgers vector, b. At room temperature all metals show a size effect on strength described by power law relation σp/μ=A(d/b)n with n ≈ −0.6 and this is shown to mirror the behaviour of face centred cubic metals. At 193 K the three metals show a higher strength and larger size exponent n ≈ −0.3 and again their normalised flow data is very similar. The behaviour is consistent with the observation that the deformation size effect in bcc materials converges to that seen with face centred cubic (fcc) structure metals as testing temperature approaches Tc. The temperature and size dependence of the experimental data shows similarity with the prediction of strength models based on the geometric confinement of dislocation sources (the single dislocation arm model) and a temperature dependent friction stress. However the model cannot consistently capture the behaviour for the three metals studied.

Some issues concerning the use of a single, material specific length scale parameter in theories of higher order strain gradient plasticity

Higher order strain gradient plasticity theories extend conventional ones with a view to explain the observed elevation of plastic flow stress in micron-sized structures. The essential elements of this modifications are the definition of a measure of plastic strain gradients, introduction of a conjugate higher order stress and introduction of one or more length scale parameters. We adopt a particular elasto-viscoplastic version of the higher order strain gradient theory based on a single scalar length scale parameter, formulate a large deformation based Finite Element model capable of handling strain gradients and higher order boundary conditions and simulate for three different materials, two sets of experiments where size effects manifest. The experiments differ in the level of plasticity that is induced during deformation — ranging from the order of the yield strain to approximately ten times its value. The materials, namely Cu, Al and Ni, have grain sizes that differ widely. We determine the scalar length scale parameter by demanding that the simulations match the experimental load deformation responses closely. The results indicate that single, scalar length scale parameter based higher order strain gradient theories cannot describe experimental observations across a wide range of geometries, boundary conditions, and plastic strain levels. The length scale is not intrinsic to the material but depends on the level of plastic strain induced by the deformation and also possibly on the number of grains involved in the deformation.

Effect of SLM Build Parameters on the Compressive Properties of 304L Stainless Steel

Selective laser melting (SLM) is well suited for the efficient manufacturing of complex structures because of its manufacturing methodology. The optimized process parameters for each alloy has been a cause for debate in recent years. In this study, the hatch angle and build orientation were investigated. 304L stainless steel samples were manufactured using three hatch angles (0°, 67°, and 105°) in three build orientations (x-, y-, and z-direction) and tested in compression. Analysis of variance and Tukey’s test were used to evaluate the obtained results. Results showed that the measured compressive yield strength and plastic flow stress varied when the hatch angle and build orientation changed. Samples built in the y-direction exhibited the highest yield strength irrespective of the hatch angle; although, samples manufactured using a hatch angle of 0° exhibited the lowest yield strength. Samples manufactured with a hatch angle of 0° flowed at the lowest stress at 35% plastic strain. Samples manufactured with hatch angles of 67° and 105° flowed at statistically the same flow stress at 35% plastic strain. However, samples manufactured with a 67° hatch angle deformed non-uniformly. Therefore, it can be concluded that 304L stainless steel parts manufactured using a hatch angle of 105° in the y-direction exhibited the best overall compressive behavior.

Flow stress of open-celled aluminum foams based on current density and the optimal foam for energy absorption

Aiming to reveal a fundamental property of open-celled foams under large plastic deformation, the present study proposes and examines a hypothesis, that is, a piece of open-celled foam after being compressed to a certain strain without wall fracture can be regarded as a fresh piece of foam characterized by its current density. As an immediate deduction of this hypothesis, the mechanical property of open-celled foam is completely determined by its current density regardless its initial density. The proposed hypothesis is successfully verified by our experimental data. It is shown that the plastic flow stress (expressed in true stress) of a piece of open-celled foam is independent of its initial density and can be predicted by a power function of its current relative density. Based on the power function, the specific energy absorbed by the aluminum foam can be predicted merely from the initial and the final densities of the foam, instead of integrating the measured stress-strain curve, which greatly simplifies the material design for engineering applications. Then an optimization method is proposed to determine the foam with the optimal initial density for absorbing a specified energy. The optimal foam will produce the minimal stress during the energy absorption compared to those with other magnitudes of density. All the analytical predictions are verified by the experimental results.

Thermomechanical behavior of laser metal deposited Inconel 718 superalloy over a wide range of temperature and strain rate: Testing and constitutive modeling

The lack of comprehensive insight and accurate description on the dynamic thermomechanical behaviors in high-temperature and high-strain-rate loading environment could be one of the major obstacles to extend the laser metal deposited (LMD) Inconel 718 to engineering applications in aeroengine. In this study, to obtain in-depth understanding of plastic flow behavior of the LMD Inconel 718, uniaxial compressive experiments were conducted over a wide range of temperature (298–1273 K) and strain rate (0.001–5300/s). Based on a great number of experimental results, not only the anisotropy of compressive property, but the dependence of the plastic flow stress on temperature and strain rate were investigated systematically. The flow stress of the as-deposited alloy in laser scanning direction is higher than that in depositing direction, which is attributed to the columnar grains epitaxially growing along the build direction and featuring the high length-diameter ratio within the as-deposited sample. Since the small-size precipitates in the under-aged (as-deposited) Inconel 718 alloy could be cut by the moving dislocations directly during plastic deformation, they have various effect on the interaction between moving dislocations and interstitial elements at different strain rate. The third-type of strain aging (3rd SA) effect, exhibiting an anomalous bell-shaped flow stress vs. temperature relation, was observed more apparently than that in the post-aged Inconel 718 reported by other literatures. As for the strain-rate effect, the flow stress of the alloy exhibits inconspicuous strain-rate sensitivity over the range of strain rate below ∼103/s, while increases sharply with the strain rate once it exceeds ∼103 /s. Finally, taking into account the mechanical anisotropy, as well as the anomalous temperature and strain rate sensitivities of the flow stress, we developed a constitutive model based on a physical frame. In this model, an anisotropy component was introduced to consider the effective size of columnar grains in the corresponding loading direction, the strain rate hardening was enhanced as the strain rate gets close to a certain level, and a normal distribution with temperature was used to describe the 3rd SA effect. The developed model was shown to be able to accurately reproduce the plastic flow behavior of the LMD Inconel 718 over a wide range of temperature and strain rate.

Surface modification of Al6061-SiC surface composite through impregnation of graphene, graphite & carbon nanotubes via FSP: A tribological study

Fabricating high wear resistance Al matrix composite without sacrificing its ductility and thermal properties is a critical issue in the designing of Al-based composites. In present study, a detailed wear mechanism of Al-SiC surface composite modified by the impregnation of Graphene, Graphite & carbon nanotubes through friction stir processing (FSP) is documented. The results revealed that with SiC and graphene nanoplatelets (GNP) reinforcements the friction coefficient and specific wear rate decreased by ~34% and ~50% as compared to as-received Al6061 alloy respectively. On the other hand, combination of SiC and carbon nanotubes (CNT) reinforcements severely deteriorates the wear resistance of the composite. The layered structure, large specific surface area and the wrinkled morphology of the graphene flakes are the primary reasons for the increased wear resistance. The exfoliation of GNP to few layered graphene (FLG) under the effect of plastic flow stresses during FSP also contributes significantly to the improvement of surface properties. The abrasion is identified as the dominant wear mechanism in Al-SiC-Graphite & Al-SiC-GNP hybrid composite. Whereas, delamination due to adhesion with the counter surface is the leading mechanism in Al-SiC-CNT hybrid composite. Various characterization strategies such as microstructural characterization through SEM, interfacial study through TEM and phase analysis through XRD corroborate the results. Finally, GNP is identified as the best reinforcement among the carbon family for improvement in wear resistance of Al6061-SiC surface composite.

Real-time nanoscale observation of deformation mechanisms in CrCoNi-based medium- to high-entropy alloys at cryogenic temperatures

Abstract Technologically important mechanical properties of engineering materials often degrade at low temperatures. One class of materials that defy this trend are CrCoNi-based medium- and high-entropy alloys, as they display enhanced strength, ductility, and toughness with decreasing temperature. Here we show, using in situ straining in the transmission electron microscope at 93 K (−180 °C) that their exceptional damage tolerance involves a synergy of deformation mechanisms, including twinning, glide of partials and full dislocations, extensive cross-slip, and multiple slip activated by dislocation and grain-boundary interactions. In particular, massive cross-slip occurs at the early stages of plastic deformation, thereby promoting multiple slip and dislocation interactions. These results indicate that the reduced intensity of thermal activation of defects at low temperatures and the required increase of applied stress for continued plastic flow, together with high lattice resistance, play a pivotal role in promoting the concurrent operation of multiple deformation mechanisms, which collectively enable the outstanding mechanical properties of these alloys.

Modelling of serrated chip formation processes using the stabilized optimal transportation meshfree method

Numerical modelling of chip formation is important for a better understanding thus for an improvement of the high speed metal cutting process. The challenge in the modelling of chip formation lies in capturing the shear band formation, the material separation and the tool-chip interaction accurately. Mostly, some assumptions are made when modelling the material separation and the serrated morphology generation, which leads to an unrealistic prediction of the chip formation. In this work, both the serrated morphology on the chip upper surface and the material separation at the chip root are treated using a ductile fracture model. Additionally, a recently developed Galerkin type meshfree scheme, the stabilizedoptimal transportation meshfree (OTM) method is applied as a numerical solution method in combination with a material point erosion approach. This enables the modelling of material separation and serrated morphology generation of the cutting process in a more realistical and convenient way. The frictional contact force exerted by the cutting tool is imposed on the workpiece using a predictor-corrector strategy. The shear band formation is described by the thermal softening term in the Johnson–Cook plastic flow stress model. Using this model, it can be demonstrated that thermal softening is the main cause for the shear band formation. However, this phenomenon is under-predicted by the Johnson–Cook flow stress model. Additionally, it can be seen that the Johnson–Cook fracture model shows limitations in capturing the fracture on the chip upper surface. Thus, a supplementary condition for the stress triaxiality is applied. This condition allows a more accurate measurement of the chip size, like chip spacing, peak and valley. These improvements are demonstrated by comparing the calculated chip morphology, cutting force and chip formation process with experimental results.

Microstructure and mechanical anisotropy of CoCrW alloy processed by selective laser melting

We have investigated the correlation between the microstructure and mechanical anisotropy of biomedical CoCrW alloy processed by selective laser melting (SLM). A phase analysis revealed that the as-SLM CoCrW alloy consisted of mostly the γ-fcc phase and little ε-hcp phase. The as-SLM CoCrW microstructure featured the rotated cube texture, a strong <100> texture along the building direction (BD) and a weaker <110> texture along the front direction. To investigate the mechanical anisotropy, the external loading was applied either perpendicular or parallel to the BD (i.e., horizontal loading (⊥BD) or vertical loading (//BD), respectively). The rotated cube texture leads to a higher elastic modulus (~ 2.4 times), plastic flow stress, and microhardness in the horizontal loading. Macroscopic plastic anisotropy was elucidated by the Taylor factor analysis of polycrystalline aggregate. Strain-induced martensite transformation (SIMT) occurring in the horizontal loading (ef = 6.9%) is responsible for significantly reduced elongation to fracture compared to the vertical loading (ef = 32.8%). In the fatigue crack growth experiment, the threshold stress intensity range in the vertical loading is ~ 32% higher compared to the horizontal loading, leading to a retarded fatigue crack growth rate. A vertically elongated columnar granular structure due to the epitaxial grain growth along the BD results in anisotropic behavior of the fatigue crack growth.

Modelling of the mechanical response of Zr–Nb and Ti–Nb alloys in a wide temperature range

This article presents the results of modeling the mechanical behavior of Zr–Nb and Ti–Nb alloys in a range of strain rates from 0.001 to 1000 1/s and temperature range 297–1273 K. A modification of constitutive equations describing the mechanical response of fine-grained and coarse-grained Zr–1Nb and Ti–13Nb–13Zr alloys in a wide temperature range is proposed. It was shown that the phase transition between the hexagonal closed packed and body-centered cubic crystal structure at elevated temperatures leads to a sharp change in strain rate sensitivity of the yield strength of Zr–Nb and Ti–Nb alloys. The proposed modifications of constitutive equations make it possible to describe the strain hardening and the strain rate sensitivity of the plastic flow stress over a wide temperature range in the coarse-crystalline and ultrafine-grained Zr–Nb and Ti–Nb alloys. The results can be used for engineering analysis of structural elements of technical systems and design of manufacturing technologies for biomedical products.

A Comprehensive CFD Model for Dual-Phase Brass Indirect Extrusion Based on Constitutive Laws: Assessment of Hot-Zone Formation and Failure Prognosis

A numerical method for the precise calculation of temperature, velocity and pressure profiles of the α-β brass indirect hot extrusion process is presented. The method solves the Navier–Stokes equations for non-Newtonian liquids with strain-rate and temperature-dependent viscosity that is formulated using established constitutive laws based on the Zener–Hollomon type equation for plastic flow stress. The method can be implemented with standard computational fluid dynamics (CFD) software, has relatively low computational cost, and avoids the numerical artifacts associated with other methods commonly used for such processes. A response surface technique is also implemented, and it is thus possible to build a reduced order model that approximately maps the process with respect to all combinations of its parameters, including the extrusion speed and brass phase constitution. The reduced order model can be a very useful tool for production, because it instantaneously provides important quantities, such as the average pressure or the temperature of hot-spots that are formed due to the combined effect of die/billet friction and the generation of heat from plastic deformation (adiabatic shear deformation heating). This approach can assist in the preliminary evaluation of the metal flow pattern, and in the prediction and prevention of critical extrusion failures, thus leading to subsequent process and product quality improvements.

Development of interfacial stress during selective laser melting of TiC reinforced TiAl composites: Influence of geometric feature of reinforcement

In this work, interfacial stress evolution behavior of TiC reinforced TiAl composites fabricated by selective laser melting were investigated, based on a meso-scale finite element model solely including a single reinforcing particle. The results implied that stress concentration always emerged where the maximum temperature gradient existed. As the laser beam successively moving from the left side of powder bed to the right side, the matrix around TiC particle underwent a solid-to-liquid-to-solid transfer process, as a result of which the interface located at left side and right side of TiC particle experienced a transformation from a compressive stress to a tensile stress. But the top edge of TiC particle always suffered from the tensile stress. Two different types of reinforced particle, namely sphere-shaped particle and cubic particle, were analyzed in this work. For the sphere-shaped one, the calculated plastic flow stress in the interface was higher than the corresponding simulated Von Mise stress during the solidifying period, while the opposite result was obtained for the cubic one. It indicated that higher thermal shock resistance could be obtained for sphere-shaped TiC reinforced composites which was further verified by the experiment results.