Steady-state Deformation Research Articles

An approximation to the PTT viscoelastic model for gas assisted injection moulding simulation

An approximation to the Phan-Thien Tanner (PTT) constitutive model is developed with the aim of giving low-cost simulation of Gas Assisted Injection Moulding (GAIM) while incorporating important viscoelastic characteristics. It is shown that the developed model gives a response typical of full viscoelastic models in transient and steady-state uniaxial and constant shear rate deformations. The model is incorporated into a 3D finite element GAIM simulation which uses the ‘pseudo-concentration’ method to predict residual polymer, and applied to published experimental results for a Boger fluid and a shear-thinning polystyrene melt.It is shown that the simulation gives a very good match to published results for the Boger fluid which show increasing Residual Wall Thickness (RWT) with increasing Deborah number. Against the shear-thinning polymer, the quality of match depends upon which of two ‘plausible’ relaxation times is chosen; qualitatively different results arise from two different means of estimating a single relaxation time. A ‘multi-mode’ approach is developed to avoid this uncertainty. It is shown that the multi-mode approach gives decreasing RWT with increasing Deborah number in agreement with the published experimental results, and avoids the issues that arise from estimating a single relaxation time for a molten polymer.

A theoretical computational model of a plate in hypersonic flow

A theoretical model of an elastic panel in hypersonic flow is derived to be used for design and analysis. The nonlinear von Kármán plate equations are coupled with 1st order Piston Theory and linearized at the nonlinear steady-state deformation due to static pressure differential and thermal loads. Eigenvalue analysis is applied to determine the system’s stability, natural frequencies and mode shapes. Numerically time marching the equations provides transient response prediction which can be used to estimate limit cycle oscillation amplitude, frequency and time to onset. The model’s predictive capability is assessed by comparison to an experiment conducted at a free stream flow of Mach 6. Good agreement is shown between the theoretical and experimental natural frequencies and mode shapes of the fluid–structure system. Stability analysis is performed using linear and nonlinear methods to plot stability, flutter and buckling zones on a free stream static pressure vs temperature differential plane.

Numerical study on the effect of rheological parameters on the droplet deformation process in Newtonian and non-Newtonian two-phase systems using extended finite element method

In the present study, attempts were made to study the effect of rheological parameters on the drop deformation process. For this purpose, both Newtonian and non-Newtonian (Carreau-Yasuda model) were considered and extended finite element method (XFEM) along with level-set method (LSM) were used to simulate the process. The result showed that in Newtonian-Newtonian systems, there was no shear stress overshoot (maximum) during the deformation process and the shear stress increased monotonically until it reached a steady-state, whereas, it exhibited an overshoot (maximum) for non-Newtonian systems. Results also showed that the increase of the wall confinement parameter (R/H) would increase the droplet deformation monotonically for studied viscosity ratios. It was further observed that the steady-state deformation parameter (Dss) was increased as Ca increased from 0.2 to 0.8 for viscosity ratio (λ) between 0.5 and 2.5.

Compressive creep behavior of a γ-TiAl based Ti–45Al–8Nb–2Cr-0.2B alloy: The role of β(B2)-phase and concurrent phase transformations

The primary and steady-state compressive creep deformation behavior of an as-cast high Nb containing γ-TiA1 alloy having remnant β(B2)-phase has been studied over the temperature range of 750–850 °C at constant initial applied stress levels between 75-200 MPa. The creep curves derived over the entire creep testing conditions show a prominent primary creep regime which is attributed to the presence of dislocation debris of the coarse γ-grains at the colony boundaries. The stress and temperature dependence of the steady-state creep rate follows the Norton-Bailey power law and the corresponding average value of the stress exponent and apparent activation energy are estimated to be 3.6 and 375 kJ/mol, respectively. The average value of the stress exponent in conjunction with the dislocation substructure of the crept samples suggests that the kinetics of creep deformation within the studied experimental conditions is controlled by the non-conservative motion (climb) of dislocations. Further misorientation analyses of the phase-resolved EBSD maps imply that for most of the conditions creep strain is carried by the γ-TiAl phase. Consequently, contrary to the commonly believed idea, the β(B2)-phase does not appear to deteriorate the creep resistance of the present alloy below suitable combinations of temperature and stress. Beyond these conditions, the concurrent deformation of γ-TiAl and β(B2)-phases is found to enhance the steady-state creep rate. In addition, characteristics of the dynamic transformation of β(B2) phase into γ and α2 phases during creep and its effect on the steady-state creep rate are further considered. Finally, the application potential of the present alloy is compared through a composite plot of Larson-Miller parameter with several other potential alloys reported in the literature.

Effect of thermal gradient on the deformation of a rotating composite disk

Sherby’s law is used in present study to calculate effect of impressive linear thermal gradient on secondary stage of deformation behaviour of rotating composite disk. Mathematical model is used to explain the steady state deformation behaviour inside the rotating isotropic composite disk in presence of linear thermal gradient along radial as well as tangential direction. The deformation that occurs due to long period of time in the composite disk with constant temperature has been compared with thermal graded disk using MATLAB. The effect of creep is reduced in the presence of thermal gradient.

Dynamic Recrystallization in Austenitic Stainless Steel during Hot Working with Decreasing Deformation Temperature

Abstract The deformation microstructures and the mechanical properties of an advanced austenitic stainless steel subjected to hot forging with a decrease in deformation temperature from 1,323 to 1,073 K were studied. The deformation microstructures were characterized by the development of dynamic recrystallization (DRX), leading to a decrease in the mean grain size from 11 to 1 μm as temperature decreased. Two DRX mechanisms, i.e., discontinuous and continuous ones, operated concurrently during the hot compressions. Corresponding true flow stress gradually increased approaching a steady-state deformation during each compression. The grain refinement was accompanied by an increase in the dislocation density, resulting in significant strengthening. The yield strength increased from about 600 MPa to almost 1,000 MPa as revealed by tensile tests at room temperature. Both the grain-size strengthening and the dislocation strengthening contributed to the overall strength of the processed steel samples with DRX microstructures.

Faraday instability of a liquid layer on a lubrication film

The Faraday instability in a system of two conjugated immiscible liquid layers with disparate thicknesses is investigated. The top layer is relatively thick and undergoes short-wavelength instabilities, while the bottom layer is thin and undergoes long-wavelength instabilities. The two layers are coupled by the kinematic and dynamic relations at the interface. Through linear stability analysis, a lubrication effect, which significantly reduces the destabilization threshold, is identified. Especially when the vibration frequency is low, the lubrication effect is seen to influence the transition between the harmonic and subharmonic instability modes. It is studied how far the system with two layers can be approximated by a single-layer system with a Navier-slip boundary condition at the bottom. In corresponding experiments it is found that the time-periodic excitation of the system creates a steady-state deformation of the bottom layer. This indicates nonlinear dynamics of the system and the violation of reversibility. The excellent agreement between experimental and theoretical results for the onset of the instability underpins the validity of the linear stability analysis.

Anisotropy in Sand–Fibre Composites and Undrained Stress–Strain Implications

Among the plethora of studies on anisotropy in fibre-reinforced sands, there exist conflicting views on effects on the steady-state deformations of initial packing. These conflicting views are further confused by strictly limited experimental evidence on flow in complex loading environments where the principal stresses rotate whereby shearing and torsional stresses combine, and when extension in soil relieves the compressive stresses. In the heuristic of intrinsically anisotropic nature of the soil and in recognition of the inability of placement methods to overcome such anisotropy, this paper aims to use the orientation of principal stress and soil initial packing state combined as proxy parameters to further the knowledge of plastic behaviour in fibre-reinforced sands. This study furthers the knowledge of the dependency of steady states on anisotropy in composite geomaterials. In doing so, the direction of principal stress orientation is varied from 15° to 60° (from vertical axis), taking an intermediate principal stress ratio of 0.5 and 1.0 and two initial confining pressures. Twenty-four undrained torsional shear tests are conducted using a hollow cylindrical torsional shear apparatus. Under compression and plain strain conditions, torsional stresses limit the improvements in soils’ undrained shear strength upon fibre reinforcement. Extension in soil remarkably increases fibres’ contribution to betterment of undrained strength. Fibres are least effective under low isotropic confining pressures and also for certain ranges of torsional stresses.

Magnetization and Deformation of a Drop of a Magnetic Fluid in an Alternating Magnetic Field

The magnetization and slow steady-state deformation oscillations of a droplet of a magnetic fluid in an alternating magnetic field are investigated theoretically. The drop is suspended in another magnetic fluid with which it is immiscible. The change in the magnetic field is so slow that approximations of a quasi-stationary magnetic field and a quasi-steady flow can be used.

Numerical study of droplet deformation in shear flow using a conservative level-set method

This paper is concerned with a numerical study on the behavior of a single Newtonian droplet suspended in another Newtonian fluid, all subjected to a simple shear flow. Conservative finite-volume approximation on a collocated three-dimensional grid along with a conservative Level-set method are used to solve the governing equations. Four parameters of capillary number (Ca), Viscosity ratio (λ), Reynolds number (Re) and walls confinement ratio are used to physically define the problem. The main focus of the current study is to investigate the effect of viscosity on walls critical confinement ratio. In this paper, the phrase critical is used to specify a state of governing parameters in which divides the parameter space into the subcritical and supercritical regions where droplets attain a steady shape or breakup, respectively. To do so, first, we validate the ability of proposed method on capturing the physics of droplet deformation including: steady-state subcritical deformation of non-confined droplet, breakup of supercritical conditioned droplet, steady-state deformation of moderate confined droplet, subcritical oscillation of highly-confined droplet, and the effect of viscosity ratio on deformation of the droplet. The extracted results are compared with available experimental, analytical and numerical data from the literature. Afterward, for a constant capillary number of 0.3 and a low Reynolds number of 1.0, subcritical (steady-state) and supercritical (breakup) deformations of the droplet for a wide range of walls confinement in different viscosity ratios are studied. The results indicate the existence of two steady-state regions in a viscosity ratio-walls confinement ratio graph which are separated by a breakup region.

Effects of Original Microstructure on Hot Deformation Behavior and Microstructure of a P/M Ni-Base Superalloy

The hot deformation behavior and microstructure of a powder metallurgy (P/M) Ni-base superalloy with different original microstructure were studied by isothermal compression tests. The isothermal compression tests were conducted on Gleeble-3500D simulator with the temperature range of 1000°C~1100°C and the strain rate of 0.001s-1~0.1s-1. The results showed that the flow stress of the specimens with fine grains (10μm) and ultrafine grains (3μm) gained by hot extruding (HEX) were much less than the that with the average grain diameter of 30μm by hot isostatic pressing (HIP). At the strain rate of 0.001s-1，the as-HIPed specimens with the average grain diameter of 30μm showed steady-state deformation at 1100°C only， whereas the as-HEXed specimens with the average grain diameter of 10μm and 3μm showed steady-state deformation both at 1050°C and 1100°C. The flow stress showed decreasing trend as the average grain diameter decreasing. The activation energy of hot deformation decreased form 622.79 kJ·mol-1 to 302.36 kJ·mol-1 as the average grain diameter decreased from 30μm to 3μm. When the as-HEXed specimen with the average grain diameter of 3μm was deformed at the condition of (1050°C, 0.001s-1), the flow stress was lower than that at the condition of (1100°C,0.001s-1), and the former also gained much finer and uniform grain, the later gained mixed grains.

Quasi-Static and High Strain Rate Simple Shear Characterization of Soft Polymers

The simple shear response of soft polymers under large deformation (>50%) and strain rates spanning 10−3 – 103 s−1 is characterized by developing quasi-static and split-Hopkinson pressure bar based single-pulse dynamic simple shear experiments rooted in continuum mechanics fundamentals. Cross-linked polydimethylsiloxane (PDMS) is chosen as a model material. By examining the evolution of stress, strain and strain rate, the latter two parameters measured using two-dimensional digital image correlation (DIC), it is demonstrated that dynamic simple shear deformation consists of four distinct stages: momentum diffusion, inertia effect, steady-state material response, and strain rate decay. By isolating the unsteady and steady-state deformation stages, inertia-free material response is captured under a uniform strain rate. It is shown that the shear response of PDMS is nearly linear with a weakly rate-sensitive shear modulus in the investigated strain rate range. Further, by analyzing the DIC strain-field and comparing the kinematic experimental results with those predicted by classical continuum mechanics, it is demonstrated that the proposed experiments not only achieve a nearly theoretical simple shear state that is uniform across the specimen, but also allow for post-test validation of individual experiments based on these criteria.

Thermal monitoring and thermal deformation prediction for spherical machine tool spindles

Machine tool operations and processing can cause temperature changes in various components because of internal and external thermal effects. Thermal deformations caused by thermal effect in machine tools can result in errors in processing size or shape and decrease processing precision. Thus, this paper focuses on the analysis of heating during machine tool spindle?s high speed operation, which is the heat source that causes component and structural deformation. In this paper, thermal monitoring was used to build a thermal error prediction model. Temperature change around the spindle was measured with a DS18B20, then multiple regression analysis was used to establish the relationship between thermal deformation quantity and temperature fields at specific points. Finally, finite element analysis was used to build the thermal error model. A solution for the correlation coefficient was obtained using the least squares method. The result of this study verified that finite element analysis can predict front bearing and rear bearing temperature rise, and is consistent with laboratory results. The error in thermal steady-state deformation prediction was less than 2 ?m. This information can be used by the controller to effectively compensate the processing and improve processing precision.

Creep behavior and deformation mechanisms of a novel directionally solidified Ni-base superalloy at 900 °C

A novel directionally solidified Ni-base superalloy with excellent creep-rupture strength has been developed. By means of measurement of the creep properties and microstructural observations, the variations of the creep deformation behavior and corresponding deformation mechanisms of the new superalloy with the applied stress are investigated at 900 °C. As the applied stress increases from 300 to 375 MPa, the steady-state creep rate increases gradually, whereas the creep-rupture life decreases. Transmission electron microscope observations on the crept specimens reveal that dislocation climb plays an important role in the steady-state creep deformation, and the process which two matrix dislocations with different Burgers vectors combine into one a〈001〉 dislocation and subsequently shear through γ′ precipitates operates more actively with increasing the applied stress. Based on the experimental observations, the reasons that account for the variation of the creep properties with the applied stress are discussed.

A novel ferritic steel family hardened by intermetallic compound G-phase

In this paper, G-phase precipitation and the resulting hardening effect on Fe-20Cr-3Ni-1Mn-3Si ferritic alloys by the addition of Ti, Nb, Ta and Zr were individually studied by electron microscopy and atom probe tomography, combined with thermodynamic and first principle calculations. The high resolution scanning electron and transmission electron microscopy observations confirmed that four kinds of Ni16M6Si7 (M=Ti, Nb, Ta and Zr) G-phase particles were distributed uniformly in the matrix of the four alloys aged at 560–860 °C. The 3D-APT results revealed the formation of the four different nanoscale precipitates, with the highest number density (6.05 × 1023 m−3) and smallest radius (1.64 ± 0.45 nm) in the Ti added alloy. The nanoscale sized precipitates stability (~3 nm for Ti added alloy; ~5 nm for Nb added alloy and Zr added alloy; ~25 nm for Ta added alloy) was attributed to their particular cube-cube orientation relationships, which led to a very low interfacial energy. The effects of the G-phase on precipitation hardening and quasi steady-state deformation resistance were examined. The 560 °C-aging hardening experiments suggested a rapid precipitation process of the nano-particles. The peak hardness values of the four alloys are in the descending order: Ti ˃˃ Nb > Ta ˃˃ Zr. The 660 °C quasi steady-state deformation experiments showed threshold stresses of 110 and 140 MPa in cases of the Nb and Ti added alloys, which were higher than that of the previously reported B2-NiAl strengthened steels and commercial heat-resistant steels. By using the formation of nanoscale G-phase precipitates, a new ferritic steel family with very high strength and creep resistance has been proposed. Further alloy optimization is in progress.

Deep Transient Slow Slip Detected by Survey GPS in the Region of Atacama, Chile.

We detected a long‐term transient deformation signal between 2014 and 2016 in the Atacama region (Chile) using survey Global Positioning System (GPS) observations. Over an ∼150 km along‐strike region, survey GPS measurements in 2014 and 2016 deviate significantly from the interseismic trend estimated using previous observations. This deviation from steady state deformation is spatially coherent and reveals a horizontal westward diverging motion of several centimeters, along with a significant uplift. It is confirmed by continuous measurements of recently installed GPS stations. We discard instrumental, hydrological, oceanic, or atmospheric loading effects and show that the transient is likely due to deep slow slip in the transition zone of the subduction interface (∼40‐ to 60‐km depth). In addition, daily observations recorded by a continuous GPS station operating between 2002 and 2015 highlight similar transient signals in 2005 and 2009, suggesting a recurrent pattern.

Concentrated sources on the interface of diffusive bimaterial media: The steady-state deformation

While the fundamental solutions of concentrated forces and dislocations in purely elastic media are available for various applications, solutions in the corresponding diffusive materials have seldom been derived due to the involved complexity. In this paper, in terms of the cylindrical system of vector functions and under the assumption of steady-state deformation, we derive analytically the elastic and diffusive fields induced by the concentrated forces and dislocations which are located on the interface of a transversely isotropic and diffusive bimaterial space. Solution of the concentrated diffusive source has been also derived. These solutions can further be reduced to the corresponding isotropic bimaterial case and the transversely isotropic full-space case. Based on the newly derived solutions, field quantities induced by different concentrated dislocation sources are presented numerically to demonstrate the effect of the diffusive coefficients, material heterogeneity, and dislocation types on the induced fields.

Electrohydrodynamics of a liquid drop in AC electric fields

The aim of this study is to gain a detailed understanding of the behavior of a liquid drop in AC electric fields at finite Reynolds number. A front-tracking/finite difference method, in conjunction with Taylor–Melcher leaky dielectric model, is used to solve the governing electrohydrodynamic equations. The evolution of the flow field and the drop deformation are studied for three representative fluid systems, corresponding to the three regions of the deformation–circulation map. It is shown that for the range of the physical parameters used here, the relaxation time during which the drop settles to its quasi-steady-state deformation is essentially the same as that predicted by the creeping flow solution. Furthermore, the mean (time-independent) deformation is well represented by its steady-state deformation in the corresponding DC field in a root-mean-square sense. The evolution of the flow field shows formation of closed vortices that cross the drop surface and move toward the ambient fluid or the drop, in line with the motion of the drop surface. The evolution of the kinetic energy of the flow field with time is investigated, and the correlations between the minimum and the maximum kinetic energy and the state of the drop deformation are explored.

Electrohydrodynamics of confined two-dimensional liquid droplets in uniform electric field

In this study, the electrohydrodynamics of viscous droplets in a confined domain under the action of a uniform electric field is investigated numerically. Considering both the phases to be perfect dielectric or leaky dielectric, two-dimensional numerical simulations are performed to obtain the shape deformation of droplets placed between two parallel plate electrodes. The aim of this study is to show the effect of domain confinement on the droplet morphology and temporal droplet deformation. Perfect dielectric systems always deform into a prolate shape, and the magnitude of deformation is augmented or reduced in a confined domain depending on the electrical permittivity ratio. For leaky dielectric systems, the electrical conductivity ratio comes into play and the droplet can attain an oblate or prolate shape depending on the size of the droplet relative to the channel height. A regime diagram is constructed to show the impact of domain confinement on the droplet shape. Additionally, the steady-state deformation parameter undergoes some non-monotonic variation with domain confinement for the leaky dielectric systems. The domain confinement can significantly decrease the droplet deformation and thereby suppress the droplet breakup phenomenon for few leaky dielectric systems. The domain confinement markedly affects the temporal evolution of the droplet deformation. The temporal evolution of the droplet shape shows that the droplet deforms more sluggishly toward its final steady configuration in a confined domain when the inertial effects are negligible. The oscillations in droplet deformation at the finite inertial regime are also suppressed in a confined domain. Finally, the interaction of two droplets is also studied, which shows that coalescence and detachment of the droplet pairs take place at a slower rate in a confined domain with respect to an unbounded domain. Thus, the present study shows the possibility of modulating the droplet morphology by tuning the domain confinement, which can be of potential use in designing droplet-based microfluidic devices.

A Modified Back Propagation Artificial Neural Network Model Based on Genetic Algorithm to Predict the Flow Behavior of 5754 Aluminum Alloy.

In order to predict flow behavior and find the optimum hot working processing parameters for 5754 aluminum alloy, the experimental flow stress data obtained from the isothermal hot compression tests on a Gleeble-3500 thermo-simulation apparatus, with different strain rates (0.1–10 s–1) and temperatures (300–500 °C), were used to construct the constitutive models of the strain-compensation Arrhenius (SA) and back propagation (BP) artificial neural network (ANN). In addition, an optimized BP–ANN model based on the genetic algorithm (GA) was established. Furthermore, the predictability of the three models was evaluated by the statistical indicators, including the correlation coefficient (R) and average absolute relative error (AARE). The results showed that the R of the SA model, BP–ANN model, and ANN–GA model were 0.9918, 0.9929, and 0.9999, respectively, while the AARE of these models was found to be 3.2499–5.6774%, 0.0567–5.4436% and 0.0232–1.0485%, respectively. The prediction error of the SA model was high at 400 °C. It was more accurate to use the BP–ANN model to determine the flow behavior compared to the SA model. However, the BP–ANN model had more instability at 300 °C and a true strain in the range of 0.4–0.6. When compared with the SA model and BP–ANN model, the ANN–GA model had a more efficient and more accurate prediction ability during the whole deformation process. Furthermore, the dynamic softening characteristic was analyzed by the flow curves. All curves showed that 5754 aluminum alloy showed the typical rheological characteristics. The flow stress rose rapidly with increasing strain until it reached a peak. After this, the flow stress remained constant, which demonstrates a steady flow softening phenomenon. Besides, the flow stress and the required variables to reach the steady state deformation increased with increasing strain rate and decreasing temperature.