Strain Rate Gradient Research Articles

Regularization of softening plasticity with the cumulative plastic strain-rate gradient

We propose a novel variational framework to regularize softening plasticity problems. Specifically, we modify the plastic dissipation potential term by adding a contribution depending on the cumulative plastic strain-rate gradient. We formulate the evolution of the so-obtained strain-rate gradient plasticity model with an incremental variational principle. The time-discretized evolution equations are deduced from the corresponding first-order optimality conditions. To investigate the model, the problem of a bar in traction is studied. Analytical solutions are explicitly derived, and characterized by exponential localization profiles. Contrary to other regularization strategies, no spurious spreading of the plastic localization band is observed. A first numerical implementation in 1D and 2D plane strain conditions is proposed based on conic programming solvers and validated against the analytical predictions. Numerical results on plane strain von Mises plasticity show that the proposed framework leads to mesh-independent results and efficient control of plastic localization bands.

Small-scale computational fluid dynamics modelling of the wave induced ice floe-grease ice interaction in the Antarctic marginal ice zone

Computational sea ice models have been developed to simulate sea ice formation, melt and motion characteristics on a regional scale. However, the highly dynamic sea ice behaviour in the Antarctic marginal ice zone (MIZ), the area where sea ice and ocean waves interact, still eludes reliable prediction. This is due to the complex sea ice composition consisting of relatively small and mobile ice floes governed by collision and fracture mechanisms. To improve the accuracy of sea ice models, the realistic sea ice distribution needs to be accounted for at a high resolution so that key aspects defining the interplay of ice motion and wave propagation can be suitably distinguished. In this work a computational fluid dynamics model based on the small-scale continuum approach has been developed to simulate the dynamics of a heterogeneous sea ice cover. The model makes use of a realistic sea ice layout and studies the mechanical behaviour of sea ice as affected by wave forcing and the specific material properties of ice floes and grease ice. Taking advantage of the continuum approach paired with a heterogeneous sea ice cover, the floe-grease ice interaction is elucidated by discussing detailed temporal and spatial distributions of the mechanical response of sea ice. Results show that the interplay between waves and the ice floe collision behaviour is directly controlled by sea ice inertia, where the frequency and severity of ice floe collisions increase with the wave period. Furthermore, the interaction of grease ice with ice floes through form drag at the interface leads to high localised grease ice strain rate gradients and low viscosity values due its shear thinning characteristics.

Size effects in a power law creeping layer under compression or shear, and implications for deformation mechanisms of lithium films

The axisymmetric compression of a power law creeping metallic sandwich layer of micron-scale thickness is analysed. Account is taken of the elevation in flow strength due to the presence of a spatial gradient in plastic strain rate. Numerical and analytical solutions reveal that the average compressive traction is enhanced by a combination of strain rate gradients and plastic constraint. A similar size effect is predicted for simple shear of the creeping sandwich layer. The difference in responses for compression and shear is traced to the different profiles of shear strain rate through the thickness of the layer. The sensitivity of compressive and shear strengths to the choice of higher-order boundary condition is explored, and good agreement with recent experiments on compression and shear of a thin sandwich layer of lithium is achieved by assuming fully clamped higher-order boundary conditions and a material length scale on the order of 3−5μm in the strain gradient-based creep theory.

Hot Tear Formation During the Casting of Al–Zn Binary Alloys

The hot tearing susceptibility of Al–Zn binary alloys with solute contents of Al–0.5%Zn, Al–1%Zn, Al–2%Zn, and Al–4%Zn, with all compositions being in wt%, is investigated through physical experiments and numerical simulation. The temperature at the hot spot, the designed critical point for hot tearing, and the load at the end of the test bar are measured and compared with the simulation results. The test samples with 0.5 and 1.0% Zn show hot tears while those with 2.0 and 4.0% Zn have no sign of such tearing. The correlation between solid fraction, strain, stress, and hot tearing indicator is revealed using the simulation results of the Al–1%Zn and Al–4%Zn alloys. Just before solidification, the Al–1%Zn alloy is found to have not only a much higher strain rate at the hot spot of the test bar than that of the Al–4%Zn alloy, but also a higher strain gradient along the longitudinal direction. It is believed that both the high strain rate and high strain gradient are attributable to the formation of hot tears in the Al–1%Zn alloy.

Dynamic Response of Rock-like Materials Based on SHPB Pulse Waveform Characteristics.

Rock-like brittle materials under dynamic load will show more complex dynamic mechanical properties than those under static load. The relationship between pulse waveform characteristics and strain rate effect and inertia effect is rarely discussed in the split-Hopkinson pressure bar (SHPB) numerical simulation research. In response to this problem, this paper discusses the effects of different pulse types and pulse waveforms on the incident waveform and dynamic response characteristics of specimens based on particle flow code (PFC). The research identifies a critical interval of rock dynamic strength, where the dynamic strength of the specimen is independent of the strain rate but increases with the amplitude of the incident stress wave. When the critical interval is exceeded, the dynamic strength is determined by the strain rate and strain rate gradient. The strain rate of the specimen is only related to the slope of the incident stress wave and is independent of its amplitude. It is also determined that the inertia effect cannot be eliminated in the SHPB. The slope of the velocity pulse waveform determines the strain rate of the specimen, the slope of the force pulse waveform determines the strain rate gradient of the specimen, and the upper bottom time determines the strain rate of the specimen. It provides a reference for SHPB numerical simulation. A dynamic strength prediction model of rock-like materials is then proposed, which considers the effects of strain rate and strain rate gradient.

A convective model for poro-elastodynamics with damage and fluid flow towards Earth lithosphere modelling

Devised towards geophysical applications for various processes in the lithosphere or the crust, a model of poro-elastodynamics with inelastic strains and other internal variables like damage (aging) and porosity as well as with diffusion of water is formulated fully in the Eulerian setting. Concepts of gradient of the total strain rate as well as the additive splitting of the total strain rate are used while eliminating the displacement from the formulation. It relies on that the elastic strain is small while only the inelastic and the total strains can be large. The energetics behind this model is derived and used for analysis as far as the existence of global weak energy-conserving solutions concerns. By this way, the model of Lyakhovsky et al. (Appl Geophys 171:3099–3123, 2014; J Mech Phys Solids 59:1752–1776, 2011) is completed to make it mechanically consistent and amenable for analysis.

On the microstructural evolution pattern of 300 M steel subjected to surface cryogenic grinding treatment

In the present work, an ultrahigh strength 300 M steel was treated by the surface plastic deformation with surface cryogenic grinding treatment (SCGT) technique. The SCGT was carried out by rotational grinding wheel embedded with numerous zirconium corundum abrasive grits, which contributes to a decreasing distribution of strain, strain rate and strain gradient from the treated surface to the matrix. The depth-dependent microstructural evolution was systematically evaluated from micrometer to nanoscale and in particular, the deformation mechanisms and texture alternation were addressed. It was identified that the microstructural evolution starts from the formation of dislocation structures, that is subsequently followed by the distorted microstructures featured as the origination and evolution of ultrafine laminates and ultrafine grains in the form of dislocation activities. Nanocrystalline was generated in the topmost surface region and nanoparticle precipitates induced by the SCGT process occur within a few microns of the treated surface. In SCGT, a very high strain rate of over 10 6 s −1 and a strain gradient of over 0.2 μm −1 were induced on the topmost surface of 300 M steel sample, which impels the martensite-matrix lamella extended into the elongated structure and finally transformed into the nanosized grains during processing. A dislocation slip-dominated process that was supplemented by the mechanical twinning governs the microstructural evolution pattern during the SCGT process, the nucleus of dynamic recrystallization initiated from the pre-existing dislocation cells were observed, and the transformation from martensite to austenite was effectively suppressed. The increase of grain size from nanoscale to submicron and finally microscale contributes to a decrease of microhardness by 25.6% (from 7.8 GPa at the treated surface to 5.8 GPa at a depth of over 100 μm from the processed surface). • Gradient microstructures are observed after being subjected to the SCGT process • Nanoparticle precipitates induced by the SCGT process appear within a few microns of the treated surface • A dislocation slip-dominated process governs the microstructural evolution pattern • The relationship between the microstructural evolution and microhardness is analyzed

Modeling the pyrolysis of preceramic polymers: A kinetic study of the polycarbosilane SMP-10

A material model was developed to predict changes in mass, density and thus volume of cured preceramic polymers for CMC matrices as they pyrolyze into ceramics. Because part warpage and delaminations are most likely to occur when matrix strain rates and strain rate gradients are the highest, the ability to accurately predict changes in a matrix material’s volume is essential to determining the processing conditions that will efficiently minimize composite scrap rates. Experimental and model analysis of the SiC forming polycarbosilane, SMP-10, revealed that volume shrinkage is initially driven by mass loss, is quickly dominated by density’s contribution, and has both temperature and time at temperature dependencies, where density is not a simple function of mass yield. While material density is rarely reported in the open literature, the ability to predict changes in density is essential to accurately predicting the volume yield of preceramic polymers used in ceramic matrix composites.

A High-Throughput Forging Technique and Its Application in the Optimization of the Deformation Conditions

Abstract The high-throughput (HT) forging technique is introduced for speeding up the research on the forming property of materials. The core concept of the HT forging technology is to assign two influencing factors to multiple samples simultaneously. By se4tting gradients with different factors in the vertical direction and the horizontal direction, all the samples will be forged at different deformations and HT experimentation will be achieved. HT forging equipment was designed and developed to accomplish the 5 by 6 HT experimentation by establishing a temperature gradient in the vertical direction and a strain or a strain rate gradient in the horizontal direction. A simplified experiment with 5CrNiMoV steel to verify the reliability and efficiency was carried out. Combined with the analysis of microstructure, the relatively excellent deformation condition for the steel was the temperature of 1,000°C and strain rate of 1s−1. For obtaining the optimum deformation condition, more specimens should be forged in the HT equipment. It evidenced that the HT forging technique and the HT equipment would be favorable for analyzing the property and optimize the forming process rapidly.

Microstructural evolution in friction self-piercing riveted aluminum alloy AA7075-T6 joints

Friction self-piercing riveting (F-SPR) is an emerging technique for low ductility materials joining, which creates a mechanical and solid-state hybrid joint with a semi-hollow rivet. The severe plastic deformation of work materials and localized elevated temperatures during the F-SPR process yield complex and heterogeneous microstructures. The cut-off action of the work materials by the rivet further complicates the material flow during joint formation. This study employed the F-SPR process to join AA7075-T6 aluminum alloy sheets and systematically investigated the microstructural evolutions using electron backscatter diffraction (EBSD) techniques. The results suggested that as the base material approached the rivet, grains were deformed and recrystallized, forming two distinct fine grain zones (FGZs) surrounding the rivet and in the rivet cavity, respectively. Solid-state bonding of aluminum sheets occurred in the FGZs. The formation of FGZ outside the rivet is due to dynamic recrystallization (DRX) triggered by the sliding-to-sticking transition at the rivet/sheet interface. The FGZ in the rivet cavity was caused by the rotation of the trapped aluminum, which created a sticking affected zone at the trapped aluminum/lower sheet interface and led to DRX. Strain rate gradient in the trapped aluminum drove the further expansion of the sticking affected zone and resulted in grain refinement in a larger span.

A meshfree computational framework for the numerical simulation of the solid-state additive manufacturing process, additive friction stir-deposition (AFS-D)

In this work, a fully coupled thermo-mechanical meshfree approach is developed for the first time to simulate a solid-state layer-by-layer additive manufacturing process, Additive Friction Stir-Deposition (AFS-D). The meshfree method in this present work uses a Lagrangian reference frame, which permits tracking of material point history. A solid mechanics formulation is used, allowing the resolution of both elastic and plastic strains. An explicit dynamics time stepping scheme is used to ensure that the code is robust for the large level of non-linearity native to the AFS-D process. In this present work, a description of the meshfree method will first be described. Then a new thermo-mechanical joining contact algorithm will be introduced. Following that, a description of the experimental setup for the AFS-D model calibration experimental one layer deposition cases is explained. Subsequently, the simulation model and results for three different parameter sets will be detailed and compared against the experimental results. Finally, temperature and strain rate gradients are revealed across the entire deposition elucidating spatial-temporal flow phenomena in the AFS-D process.

Stress recovery for the particle-in-cell finite element method

The particle-in-cell finite element (PIC-FE) method has been widely used in geodynamic numerical modelling due to its efficiency in dealing with large deformations without the requirement of remeshing. However, material deformation within a Eulerian mesh frame will mix particles of contrasting strength properties (e.g., viscosity in Stokes problems) in a single element requiring some form of averaging to project particle properties to integration points. The numerical solutions are thus dependent on the way how the particle properties are projected to the integration points. An intra-element property discontinuity may introduce severe stress oscillations along the interfaces. In this study, we assess three preprocessing methods to smooth the viscosity contrast within one element. For simplified models with analytical solutions, the accuracy and convergence rate in L2 norm are systematically studied with ensembles. It is found that using higher-order quadrature elements does not improve the convergence rate for either the velocity or stress solution, both close to one. Additionally, the convergence rate of the maximum stress error, which exists adjacent to the mixed-material elements, is much less than one for all cases studied here. Comparing each component of the stress tensor, we find that the stress tensor component with the highest strain rate gradient across the material interface produces the maximum stress error. Such errors can be reduced by averaging the particle properties to the Gaussian quadrature point with an inverse-distance-weighted harmonic mean.

The Influence of Shear Angles on the Split Hopkinson Shear Bar Testing

Dynamic material characterization is one of important factors in the development of modern transportation industry to overcome two main challenges, i.e. lightweight and crashworthy vehicles. The most commonly used apparatus to characterize the material in high strain rates is the Hopkinson bar. The Hopkinson bar can be conducted into several loading conditions such as compression, tension, shear, torsion and multiaxial. This paper focuses on the split Hopkinson shear bar testing, especially on the effect of the shear angles on generating the shear stress – shear strain curves, shear strain rates, and final shear strains. Four geometries of specimen were studied, i.e. circular hat-shaped (CHS), flat hat-shaped (FHS), punch (P) and double-notch (DN). This research is conducted with three main considerations, i.e. the same kinetic energy (7.34 Joule), the same shear area (±25 mm2), and the shear angles were varied as ±2.5°, 5°, 7.5°, 10° and 15°. This study shows that each testing has its own advantages and disadvantages and they generate different strain rate, strain rate gradient, final strain, and shear stress – shear strain relations which is not desirable. In term of shear angles, authors recommend using a shear angle of appoximately 5°. This shear angle generates the best purity on the shear loading among other shear angles and also the flow stress variation (among four tests) are quite acceptable ±16.4%.

Analysis of contact conditions and its influence on strain rate and temperature in friction stir welding

In friction stir welding (FSW), the real contact conditions between the tool and the workpiece and the range of strain rates experienced remain quite unclear. In this work, a coupled 3D thermo-mechanical numerical model was used to simulate the FSW process. A Parametric finite element analysis of the evolution of the contact conditions, strain rates and temperatures with the processing parameters, tool dimensions and base material plastic properties was conducted. The numerical model was able to capture the evolution of the mixed slipping/sticking contact conditions with the welding time and welding parameters. The temperature and strain rate gradients obtained in the numerical simulations were validated with experimental data, by calculating the grain size distribution, in the stirred volume, using the Zener-Hollomon parameter. Full sticking, full slipping and mixed slipping-sticking contact domains were identified in a process parameters chart. It was found that, meanwhile the temperature and the sticking fraction evolve in the same way with the processing parameters, the strain rate is mainly determined by the tool rotation speed, varying from an average of 68 to 324 s−1, when the tool rotation speed is increased from 300 to 1200 rpm. The contact conditions and the base material plastic properties were also found to mutually influence the material flow. In full sticking contact, high strength materials, with high strain rate sensitivity, may display a similar flow pattern to that of low strength materials. However, coarser and more uniform grain structures may result from the welding of high strength materials, as a result of the narrower range of strain rates experienced during welding combined with high heat input.

Low formability and reduction of area in twinning-induced plasticity steels despite their excellent tensile elongation

The mechanism for low formability and reduction of area (RA) in twinning-induced plasticity (TWIP) steels despite their excellent tensile elongation has been investigated in an attempt to understand and increase their formability. In metals, RA is strongly dependent on the post-necking elongation (PE) rather than uniform elongation (UE); in this study, UE and PE had 9% and 91% contributions to RA, respectively. Between the two representative ductility indicators in tensile tests, the RA is typically higher than the total elongation (TE) in conventional metals. However, the RA of TWIP steels was lower than the TE because TWIP steels had a higher UE and lower PE. This was attributed to the higher strain hardening exponent (n) and lower strain rate sensitivity (m) of TWIP steels. This indicates that TWIP steels have a higher resistance to fracture by the strain gradient, but a lower resistance to fracture by the strain rate gradient. In this study, the small and/or negative m value of TWIP steels reduced the RA value and formability in spite of their higher elongation. The negative m value led to a strain concentration at the necking region, leading to localized necking without diffuse necking followed by shear cracks, resulting in the lower RA and formability. Consequently, it is necessary to increase the m value of TWIP steels in order to increase the formability.

On the microstructural evolution pattern toward nano-scale of an AISI 304 stainless steel during high strain rate surface deformation

In the present investigation, an austenitic AISI 304 stainless steel was subjected to high strain rate surface deformation by Pipe Inner-Surface Grinding (PISG) technique. The depth-dependent deformation parameters (strain, strain rate and strain gradient) were evaluated and the microstructures were systematically characterized. Microstructural evolution from millimeter- to nano-scale was explored, with special attention paid to the localized deformation. Microstructural evolution begins with the formation of planar dislocation arrays and the twin-matrix lamellae, which is followed by the localized deformation characterized by the initiation and the development of shear bands. A twinning-dominated process that was supplemented with dislocation slip-dominated one governed the microstructural evolution inside shear bands. The twin-matrix lamellae transform into extended/lamellar structure and finally the nano-sized grains. Austenitic grains were substantially refined and martensitic transformation was effectively suppressed, of which the underlying mechanisms were analyzed.

A Modified Hockett-Sherby Law Enabling the Description of the Thermomechanical Behaviour of the AA6061-T6

The use of warm temperatures in the forming process enhances the aluminium alloys formability and reduces the springback effect, when compared with room temperature conditions. However, in order to be able to design warm forming processes it is necessary to describe the influence of temperature and strain rate on the mechanical behaviour of the material. This work presents the procedure adopted to identify the parameters of a thermomechanical Hockett-Sherby type law, for the EN AW 6061-T6 aluminium alloy, based on previously reported results from experimental uniaxial tensile tests performed on a Gleeble machine [1]. The experimental data were analysed, in order to obtain the true stress-plastic strain curves, for a temperature range between room temperature and 200°C, at three different strain rates. A classical identification procedure was applied to identify the parameters of a modified Hockett-Sherby type law, which describes the dependence of the initial yield stress on temperature. A multi-step procedure is proposed, in combination with a gradient-based method, in order to enable the selection of an initial solution prone to lead to a feasible set of parameters. The identified parameters were used to perform the numerical analysis of the uniaxial tensile tests, taking into account the non-isothermal conditions, which occur in the Gleeble device. The analysis of these tests highlights that the non-isothermal conditions promote the increase of the strain rate in the centre of the specimen. However, the presence of the strain rate gradient along the specimen length seems to have a small impact in the classical analysis of the experimental data, as long as it is based on an effective gauge length that presents a uniform deformation.

Influence of inter-object relations on the microstructural evolution during hot upsetting of a steel billet determined by numerical simulation

AbstractThe aim of this work was to study the effect of the interaction between tools and workpiece on the plastic behavior and microstructural evolution of a carbon steel during hot deformation of a cylinder with diameter of 600 mm and height of 1 000 mm. The metallurgical processing was simulated applying the finite elements method. Temperature, deformation and strain rate gradients, recrystallized volume fraction, and grain size distribution were determined using this technique. The data obtained shown that the level of friction and the heat transfer between tools and material have strong influence on the deformation and microstructure gradients, creating large grain size heterogeneities.

Edge flame propagation statistics in igniting monodisperse droplet-laden mixtures

The effects of droplet diameter, overall (i.e., liquid+gaseous phases) equivalence ratio, and turbulence intensity on the edge flame propagation statistics for localized forced ignition of uniformly dispersed n-heptane droplet-laden mixtures under homogeneous isotropic decaying turbulence have been analyzed based on direct numerical simulations data. It has been found that the edge flame structure becomes increasingly prominent for large overall equivalence ratios and droplet diameters. Although the mean edge flame speed has been found to be positive and its most probable value remains comparable to the theoretical value for laminar edge flames in purely gaseous mixtures, the mean values have been found to decrease and the probabilities of finding locally negative edge flame speeds have been found to increase with increasing turbulence intensity. The marginal probability density function and curvature and strain rate dependences of the edge flame speed have been found to be principally governed by the displacement speed of the fuel mass fraction isosurface intersecting the stoichiometric mixture fraction isosurface. The displacement speed of the stoichiometric mixture fraction isosurface has also been found to influence the local scalar gradient dependences of the edge flame speed in this configuration, especially for large droplets. The displacement speed of the fuel mass fraction isosurface Sd has been found to be principally governed by leading order contributions of the reaction and molecular diffusion components and the evaporation contribution remains weak in comparison to these leading order contributors. The local edge flame speed exhibits nonlinear curvature and strain rate dependences and its variation with the magnitudes of both fuel mass fraction and mixture fraction gradients has been found to be nonmonotonic for all cases considered here. The correlations of the edge flame speed with curvature, strain rate, and scalar gradient have been found to be qualitatively similar to the corresponding statistics reported in the existing literature for edge flames in purely gaseous mixtures. Additionally, the curvature and tangential strain rate dependences of the edge flame speed have been found to be dependent on the droplet size and overall equivalence ratio, and these dependences become weak for cases with large droplets.

Scalar predictors of premixed gas ignition by a suddenly-starting hot jet

Hot-jet ignition is usually designed to reduce emissions in lean-burn combustion engines, and has potential in enabling novel pressure-gain combustion. Inspired by our experimental observations related to wave-rotor combustion chamber ignition, this work employs a numerical method to examine the sudden injection of a hot jet into a quiescent mixture of CH4–H2-air and the subsequent ignition. The goal is to provide the range of thermo-physical scalars that are supportive of successful ignition. The evolution of scalar fields is evaluated using large-eddy simulation (LES). The temporal evolution of mixture fraction, the squared gradient of mixture fraction (as indicative of scalar dissipation rate), strain rate, and intermediate species are investigated in order to find the appropriate physical conditions which support ignition. Independent distribution of stain rate and squared gradient of mixture fraction, especially in the leading head vortex, shows the necessity of correlated scalar analysis of the ignition process. Experimental and numerical methods are then employed to provide the qualitative and quantitative understanding of ignition process for fuels with two distinct hydrogen contents. Results show the meaningful difference in spatial distribution of local ignition as hydrogen content of the fuel increases.