Quasi-static Conditions Research Articles

Variational free energy based macroscopical modeling of ferroelectroelasticity

In this paper, a thermodynamically consistent minimum-type variational model for ferroelectric materials in a macroscopical continuum approach is presented. The motivation for this results from the lack of models in the literature that have on the one hand a Helmholtz free energy based variational structure and on the other hand are able to represent all important characteristic phenomena of ferroelectrics under quasi-static conditions. First of all, a unified variational theory for the material response of dissipative electro-mechanical solids in line with the framework of the generalized standard materials (GSM) is outlined. A macroscopic ferroelectric model with microscopically motivated internal state variables representing the switching processes taking place at the material microscale is adapted to the above mentioned variational structure. Additionally, a mixed variational principle for the global electro-mechanical boundary value problem is introduced in order to embed the Helmholtz free energy based local theory in a suitable finite element formulation. The solution processes for the resulting local and global variational problems is described in detail to enable easy implementation. The capability of the presented methods to reproduce the real behavior of ferroelectric systems is demonstrated by numerical examples. Here, a comparison to experimental results from the literature is a particular focus.

Irregular and stepwise behaviour of hydraulic fracturing: insights from linear cohesive crack modelling with maximum stress criterion

There is growing evidence that fracture advancement in saturated and dry porous media may be smooth or stepwise. In the stepwise behaviour, there are also pressure oscillations in saturated porous materials, as predicted by Biot’s theory. The type of behavior depends on the specifications of the problem and material properties. Not all the adopted numerical models are capable of capturing stepwise behaviour. While non-local fracturing models are perfectly adapted to capture the stepwise behaviour, it is shown that cohesive models are also capable to model such a behaviour. In fact, it is necessary to satisfy a consistency condition for the numerical solution; in other words, the fracture advancement/time-stepping algorithm must not impose a constraint on the tip advancement speed. This is peculiar to cohesive models because there the unit of fracture advancement is specified beforehand, while in other models, such as peridynamics, it is an outcome of the analysis. In inhomogeneous media, it can be expected to capture irregular results from hydraulic fracturing (HF); however, homogeneous media can also show such behaviour as presented herein. In this study, the eXtended Finite Element Method (XFEM) is used in conjunction with a cohesive crack model to investigate the stepwise or irregular behaviour of HF in homogeneous saturated porous media both under quasistatic and dynamic conditions. The results clearly show that the extent of irregularity depends directly on the intensity of dynamic effects in the problem. Moreover, fracture forerunning is one of the reasons of the stepwise fracture growth in the solutions. Although the results are obtained by XFEM, the conclusions are not restricted to this particular numerical method, and the findings can provide useful insights into the necessary aspects of the numerical algorithms for dynamic HF modelling.

Comparative analysis of small size non-pneumatic tires and pneumatic tires - radial stiffness and hysteresis, selected parameters of the contact patch

Nowadays, non-pneumatic tires are becoming an increasingly likely alternative to pneumatic tires. The function of compressed air has been taken over by the belt and the elastic structure (materials used and shape of the components). The research presented in the paper was carried out in quasi-static conditions. The research's aim was to compare the radial stiffness, hysteresis and selected parameters of the contact patch of two non-pneumatic tires and four pneumatic tires used interchangeably in ATVs/UTVs. Analizowane opony niepneumatyczne charakteryzują się większą sztywnością radialną niż opony pneumatyczne tego samego rozmiaru. The analyzed non-pneumatic tire with a cellular structure has the highest hysteresis of the radial characteristics of the tested wheels and the highest values of the unit pressure in the area of contact patch. The paper also verified two methods of calculating the contact patch length of non-pneumatic tires.

Comparative Study of the Relationship between Microstructure and Mechanical Properties of Aluminum Alloy 5056 Fabricated by Additive Manufacturing and Rolling Techniques.

In recent years, additive manufacturing of products made from 5000 series alloys has grown in popularity for marine and automotive applications. At the same time, little research has been aimed at determining the permissible load ranges and areas of application, especially in comparison with materials obtained by traditional methods. In this work, we compared the mechanical properties of aluminum alloy 5056 produced by wire-arc additive technology and rolling. Structural analysis of the material was carried out using EBSD and EDX. Tensile tests under quasi-static loading and impact toughness tests under impact loading were also carried out. SEM was used to examine the fracture surface of the materials during these tests. The mechanical properties of the materials under quasi-static loading conditions exhibit a striking similarity. Specifically, the yield stress σ0.2 was measured at 128 MPa for the industrially manufactured AA5056_IM and 111 MPa for the AA5056_AM. In contrast, impact toughness tests showed that AA5056_AM KCVfull was 190 kJ/m2, half that of AA5056_IM KCVfull, which was 395 kJ/m2.

Comparative study on the effect of test temperature on tensile and charpy impact properties of Ti–5Al–1V–1Sn–1Zr-0.8Mo alloy

Impact toughness is a critical indicator to prevent catastrophic failure, especially at low service temperature. At present, most strategies to strengthen and toughen Ti alloys are proposed under the quasi-static tensile deformation condition. In fact, whether these strategies can be directly extended to improve impact toughness is still controversial due to the high loading rate and the existing of pre-notch during Charpy impact deformation condition. In this work, we found that, even though the yield strength and elongation of Ti–5Al–1V–1Sn–1Zr-0.8Mo alloy increase simultaneously with the decrease of test temperature under tensile deformation condition, the impact toughness still decreases gradually with the decreasing of deformation temperature under Charpy impact deformation condition. This phenomenon indicates that the successful strengthening and toughening strategies under quasi-static tensile deformation may fail under impact deformation. Finally, the reasons behind this phenomenon are explained based on the comparison of surface deformation morphologies under different deformation conditions, and the corresponding deformation mechanisms are established.

Magnetic Circuit Optimization and Physical Modeling of Giant Magnetostrictive Actuator

Due to the excellent performance, giant magnetostrictive actuator is used in the active vibration isolation control system. However, its hysteresis nonlinear dynamic model is too complex for engineering practical applications, so it is necessary to establish an accurate and easy-to-use model. Based on Simulink/Simcape, a magnetic circuit model and a nonlinear dynamic physical model of the giant magnetostrictive actuator are developed. In the optimization of the magnetic circuit, the uniform distribution and the magnetic energy utilization of the giant magnetostrictive actuator are taken as the optimization objective, and the design criteria of the magnetic circuit are given. The hysteresis performance between the current and the magnetization is analyzed by simulating the magnetic circuit model. From the perspective of energy conservation, a linear magnetostrictive model which can reflect the effects of the frequency doubling and preload is established. Finally, the accuracy of the nonlinear dynamic physical model for the giant magnetostrictive actuator is verified by an experiment. The results show that the physical model agrees well with the experiment results not only under the quasistatic operating conditions but also under dynamic operating conditions. The error of the output displacement of the GMA under step response is less than 0.6 μm.

Dynamic three-point bending tests under high loading rates

The theory of dynamic three-point bending tests under high-loading rates is developed for the first time with account for structural vibration. Analytical solutions for dynamic normal (flexural) and shear stresses are derived. To study the dynamic effect, dynamic factors for both types of stresses are defined and investigated by employing a dimensionless characteristic time and a strain rate. It is found that both dynamic factors attenuate with respect to the characteristic time and, therefore, the quasi-static time thresholds and loading conditions are obtained. In addition, the dominant failure mode is studied for potential application in brittle materials in terms of normal-to-shear stress ratio, which is oscillatory in contrast to the quasi-static case. The developed theory is verified with a split Hopkinson bar test together combined with digital image correlation as well as finite-element simulations. The findings of this study can provide a guideline for test design, such as selection of specimen geometry and loading rate. As the theory provides a modal decomposition of dynamic normal and shear stresses, it can also be used in the field of structural health monitoring.

Identification of the Constitutive Parameters of Viscosity and the Prediction of the Cutting Force of S32760 Duplex Stainless Steel under a High Strain Rate

The mechanical properties of S32760 duplex stainless steel under dynamic loading conditions at high strain rates are significantly different from those under quasi-static conditions. As a result of large strain, high strain rate, and high temperature, the analysis of the cutting process needs to factor in the influence of the viscous behavior of the material on the plastic deformation process. Based on the viscous effect of the two phases and the mixing rule, a mechanical threshold stress (MTS) constitutive model of S32760 duplex stainless steel considering the viscous effect is established to analyze the effect of strain rate on flow stress. An inverse identification method of the constitutive parameters based on Oxley's theory is proposed. The constitutive parameters of S32760 duplex stainless steel were reversely modified using an equal shear zone model and an orthogonal cutting experiment. The results show that the viscosity of the austenite phase was greater than that of the ferrite phase, and the strain rate had the greatest influence on the viscosity effect in the constitutive model. The prediction error of the constitutive model constructed in this manuscript was less than 4%, which had high accuracy.

The Transient Evolution of Flow Due to the Excitation Pulse in Oscillating Drop Experiments in Microgravity Electromagnetic Levitation

In oscillating drop experiments, surface oscillations in a molten sample are captured and analyzed to determine the surface tension and viscosity of a melt without the need to contact the liquid sample. In electromagnetic levitation, surface oscillations are initiated using an excitation pulse in the electromagnetic field. The variation in the electromagnetic force field drives rapid acceleration in the melt while also changing the flow pattern. During the quasi-static flow conditions prior to the excitation pulse, the flow displays a “positioner-dominated” flow pattern with 4 recirculation loops in the sample hemisphere. However, the accelerating flow of the excitation pulse transitions into a “heater-dominated flow” pattern in which there are only 2 recirculation loops in the sample hemisphere. Following the excitation pulse, the flow rapidly slows and quickly returns to the conditions present before the excitation pulse. For many combinations of parameters, the transition in the flow pattern results in a very complicated variation in velocity with time; that variation is the topic of this paper.

High strain-rate deformation analysis of open-cell aluminium foam

This study investigated the high-strain rate mechanical properties of open-cell aluminium foam M-pore®. While previous research has examined the response of this type of foam under quasi-static and transitional dynamic loading conditions, there is a lack of knowledge about its behaviour under higher strain rates (transitional and shock loading regimes). To address this gap in understanding, cylindrical open-cell foam specimens were tested using a modified Direct Impact Hopkinson Bar (DIHB) apparatus over a wide range of strain rates, up to 93 m/s. The results showed a strong dependency of the foam's behaviour on the loading rate, with increased plateau stress and changes in deformation front formation and propagation at higher strain rates. The internal structure of the specimens was examined using X-ray micro-computed tomography (mCT). The mCT images were used to build simplified 3D numerical models of analysed aluminium foam specimens that were used in computational simulations of their behaviour under all experimentally tested loading regimes using LS-DYNA software. The overall agreement between the experimental and computational results was good enough to validate the built numerical models capable of correctly simulating the mechanical response of analysed aluminium foam at different loading rates.

Ultrafast antiferromagnet rearrangement in Co/IrMn/CoGd trilayers

Antiferromagnets offer great potential for high-speed data processing applications, as they can expend spintronic devices from a static storage and gigahertz frequency range to the terahertz range. However, their zero net magnetization makes them difficult to manipulate and detect. In recent years, there has been a lot of attention given to the ultrafast manipulation of magnetic order using ultra-short single laser pulses, but it remains unknown whether a similar scenario can be observed in antiferromagnets. In this work, we demonstrate the manipulation of antiferromagnets with a single femtosecond laser pulse in perpendicular exchange-biased Co/IrMn/CoGd trilayers. We study the dual exchange bias interlayer interaction in quasi-static conditions and competition in ultrafast antiferromagnet rearrangement. Our results show that, compared to conventional ferromagnetic/antiferromagnetic systems, the IrMn antiferromagnet can be ultrafast and efficiently manipulated by the coupled CoGd ferrimagnetic layer, which paves the way for potential energy-efficient spintronic devices.

Quasi-static and dynamic mechanical characterization of clay and ballistic soap

Ballistic gelatin, soap, and clay are three human simulated target materials commonly used in the field of wound ballistics research. Currently, there are more studies on ballistic gelatin’s mechanical properties, but rarely on clay and soap. In this paper, the mechanical properties of clay and soap materials were tested by using universal material testing machine and Hopkinson bar, respectively, and their stress-strain curves were obtained under different temperatures (4°C, 15°C, and 25°C) from quasi-static to dynamic loading. The test results showed that the clay material was sensitive to temperature and strain rate in quasi-static conditions, its stress-strain curves showed nonlinear strengthening characteristics, and the stress always increased without strength decrease during the loading process; the dynamic compression mechanical properties of clay were significantly higher than the quasi-static mechanical properties, showing obvious strain rate strengthening effect. In quasi-static compression experiments, the stress-strain curves of soap material showed bilinear elastic-plastic material characteristics; when the strain was less than 0.1, it was insensitive to temperature and strain rate, and only when the strain was more significant than 0.1 did it show a certain temperature and strain rate correlation. The dynamic compressive mechanical properties of soap are significantly higher than the quasi-static mechanical properties, showing a significant strain-rate strengthening effect. The stress of soap at the same strain rate is slightly less than that of clay. These results not only help provide more accurate material parameters for relevant numerical calculations but also help to provide references for the development of new bionic materials.

Modelling mesh independent failure loads of a soft strain-softening clay using a rate dependent model

If no regularisation method is used during finite element modelling of strain-softening (brittle) materials, results become mesh dependent: manifesting as very thin shear bands whose thickness and orientation depends on the mesh discretisation. The objectives of this paper were to determine if mesh independent results were achieved, and to track the evolving width of the shear band when considering naturally occurring properties of soft clays, including a rate dependent stress-strain-strength relationship. The constitutive model included a destructuration process and strain-rate dependency, and the analyses allowed for local pore water flow. A bearing capacity problem was loaded to failure. Analyses were conducted with different mesh discretisation, loading rates and permeabilities. The results demonstrated mesh independent failure loads, and the strain-softening occurred in zones with thickness independent of mesh size. Local pore water flow delayed the initiation of strain softening and resulted in higher failure loads. The softening zones grew in thickness to over one meter, reinforcing that the finite element method is suitable for the determination of the bearing capacity of strain-softening sensitive clays. In conclusion, the rate dependent constitutive model is a promising method for regularising strain localisation in soft brittle clays under quasi-static loading conditions.

Studying the rate-dependent specific absorption rate in magnetic hyperthermia through multiscale simulations

In this work, the issue of whether the dynamic magnetic properties of monodispersed magnetic colloids, modeled using micromagnetic simulations, can be extrapolated to analyze magnetic particle hyperthermia data, i.e., specific absorption rate (SAR) values acquired at high frequencies of excitation fields, is addressed. Micromagnetic finite difference simulations were performed using the Object Oriented Micromagnetic Framework (OOMMF) software package in order to obtain the dynamic hysteresis loops under a 24 kA/m alternating magnetic field amplitude and for various frequencies (50–765 kHz). In OOMMF, the finite difference method was used to find the solution of the nonlinear Landau–Lifshitz Gilbert (LLG) equation, which describes the nanoparticles’ magnetization motion when applying an effective magnetic field. To create a system of randomly oriented magnetite nanoparticles having a certain volume fraction (0.02%) that coincides with the experimentally utilized concentration of 1 mg/ml, we start with a perfect simple cubic lattice with a large lattice spacing so that the particle–particle distance is large enough to neglect dipolar interactions (non-interacting nanoparticles). The system under study is a set of 40-nm magnetite nanoparticles with a lognormal size distribution. The simulations were performed assuming quasistatic conditions, an approach that is reasonable for ferromagnetic-like behavior. It is worth noting that the code considers not only the uniaxial anisotropy Ku but also the cubic magnetocrystalline one Kc as well. Kc is usually neglected in literature because the uniaxial contribution dominates, but this is not the case for magnetite since Ku = 9 kJ/m3 and Kc = −11 kJ/m3. Moreover, such an inclusion seems quite reasonable since the magnetocrystalline anisotropy is always present yet with a relative contribution. The SAR values at each frequency were determined after calculating hysteresis losses via the area of the simulated hysteresis loops. Interestingly, SAR values at low frequencies followed an exponential increase trend with a frequency indicating a deviation from the linear behavior usually reported in the literature. To validate our approach, we employed a coupled electromagnetic-thermal model based on COMSOL Multiphysics simulations that provides an accurate estimation of the magnetic field and temperature distribution within the ferrofluid. The time-dependent temperature curves are obtained after 30 min of magnetic particle hyperthermia treatment for the same alternating magnetic field amplitude used in OOMMF simulations (30 mT) and for two representative frequency values. One in the low (300 kHz) and one in the high (765 kHz) frequency regimes. The numerical curves were compared to the corresponding experimental ones and found to be in good agreement. Our findings provide new insight into the validity of dynamic micromagnetic simulation to analyze the frequency behavior of SAR within the framework of LLG and indicate that anisotropy selection plays a key role in the reliability of simulations.

Experimentally validated axisymmetric simulation for thermo-fluid performance of an active flat-plate solar water heater at low flow rates

ABSTRACT In this work, the thermo-fluid performance of a liquid flat-plate collector (FPC) has been analyzed using experimental and computational methods. A closed-loop active flat-plate solar water heater (AFPSWH) was tested under quasi-static and laminar flow operating conditions, where a maximum instantaneous collector efficiency of 62.82% and an outlet temperature of 45.2°C were attained in the winter with flow rates of 0.012 and 0.004 kg/s, respectively. Raising the flow rates from 0.004 kg/s to 0.008 and 0.012 kg/s reduces the energy loss parameter [FRUL] by 23.77% and 34.61%, whereas the absorbed energy parameter [FR(τα)n] improves by 10.48% and 21.55%, respectively. The suggested axisymmetric numerical model was validated with outcomes of an in-house developed lab scale experimental setup, with less than 1.5% deviations for all studied cases. In addition, the overall thermal efficiency of the solar thermal system (STS), Nusselt number (Nu), and friction factor (f) have been analyzed for a comprehensive understanding of the system’s thermo-fluid performance.

A comparative study of different constitutive models to predict the dynamic flow behaviour of a homogenised AT61 magnesium alloy

In the present work, phenomenological and physical models were established to predict the plastic flow behaviour of homogenised AT61 magnesium alloy. The models were developed using experimental data obtained from compression experiments under quasi-static and dynamic loading conditions over a wide range of strain rates (10−4–4000 s−1) and temperatures (25–250 °C). The quasi-static and high strain rate compression experiments were performed on a universal testing machine and a split Hopkinson pressure bar, respectively. Several types of basic and modified (m-) constitutive models, including Johnson-Cook (JC), Khan-Huang-Liang (KHL), and Zerrilli-Armstrong (ZA), were calibrated to predict the plastic flow behaviour of an AT61 alloy. The prediction capabilities of these constitutive models were compared statistically in terms of average relative error and correlation coefficient. It was noticed that the predictions of the models JC, m-JC, and m-KHL were quite similar to the experimental findings; however, ZA model deviates more from the experimental data.

Effect of ZnO-decorated electrospun veils on the damage tolerance of CFRP laminates

In this work, multifunctional carbon fiber reinforced polymer (CFRP) laminates were manufactured by interleaving electrospun veils decorated with ZnO nanorods (NRs) (CFRP_NY_ZnO). The laminates were tested under dynamic (low velocity impact at 5.0 J and 7.5 J) and quasi-static (pre- and post-impact four-point bending tests) loading conditions. The delamination resistance of CFRP_NY_ZnO was compared with those of CFRP (without veils) and CFRP_NY (with four non-decorated veils) laminates. At 5.0 J, ZnO NRs enhanced the delamination resistance (the lowest delaminated area was around 232.3 ± 38.7 mm2) due to additional energy consuming mechanisms. When the impact energy was increased (7.5 J), the debonding of ZnO NRs from the nanofibers was promoted and a rapid failure propagation was observed (increase in delaminated area of about 27% with respect to CFRP_NY). In quasi-static condition, ZnO NRs proved to be effective in increasing flexural strength (914.4 MPa (±18.8 MPa)) and modulus (83.6 GPa (±0.3 GPa)) of the laminate with respect to CFRP and CFRP_NY and in preventing laminate stiffness losses even after impacts at 5.0 J and 7.5 J.

Experimental investigation of the quasi-static and dynamic compressive behavior of polymer-based 3D-printed lattice structures

Because additive manufacturing (AM) allows the creation of complex structures that can be tailored or optimized based on mechanical and material specifications, it is increasingly used for various applications. Among others, it gives access to new designs of lightweight shields exhibiting good capabilities for absorbing dynamic loads and kinetic energy. In the present work, the quasi-static and dynamic compressive behavior of 3D polymeric lattice structures manufactured by the fused deposition modeling (FDM) process were evaluated. Two different materials were considered: ABS (Acrylonitrile Butadiene Styrene) and Tough-PLA (PolyLactic Acid). First, the tensile quasi-static mechanical properties of precursor filaments and 3D-printed dog-bone specimens were evaluated. Through these tests, it was observed that the printing process and orientation have a significant effect on the mechanical behavior of AM-produced samples. Then, quasi-static and dynamic compressive tests were conducted on AM-produced cylindrical specimens using two distinct printing topologies. The dynamic tests were performed with a split Hopkinson pressure bar (SHPB) apparatus. The results indicated that the compressive strength increases with the loading rate, indicating a strain rate sensitivity of the studied materials. Finally, three different 3D lattice structures were experimentally evaluated against crushing at two different deformation rates. It was noted that the geometrical design and relative densities of these structures have major effects on their energy absorption capability. However, no clear correlation seems to exist between energy absorption capabilities under quasi-static and dynamic loading conditions.

Unexpected departure from seismic laws with largest labquakes on model granular materials

In an effort to understand the most devastating natural earthquakes, we present a series of largest laboratory quakes on model granular materials under triaxial compression in fully drained and quasi-static shearing conditions. These largest labquakes can lead to a complete loss of normal and tangential stresses and even a destruction of the granular structure. The repeated spontaneous stick–slip frictional failures under uncontrolled triggering stress reproduce the traditional statistical seismic relations (Gutenberg–Richter, Omori–Utsu, inter-event times and productivity) with unexpected deviations created by biggest detected stick–slip motions in laboratory. A surprising long quiescent period results from these lab-quakes, contrasting the presence of numerous aftershocks following the majority of natural earthquakes. We also identify the appearance conditions of these unexpected granular instabilities. This work would have practical implications in improving qualitatively our understanding of the potentially highest magnitude earthquakes.

Deformation induced phase transition in brass under shock compression

Dual-phase brass, owing to its designability in terms of performance, is of great importance among multiphase alloys and has been widely applied for thousands of years. Its deformation behavior is critical for various applications. However, most investigations are conducted under quasi-static conditions, and the deformation behaviors under high-strain rate conditions, which are common in impact and detonation, are rarely considered. Here, the deformation behavior and structure evolution of brass under high-strain rate compression were investigated (>106 s−1). The α→β phase transition caused by the accumulation of stacking faults as the dominant deformation was revealed, which is different from the mechanism of deformation-twin growth with low-strain rates in previous studies. Furthermore, deformation under high-strain rate compression produce more low-angle grain boundaries, which is in contrast to the reported high-angle grain boundaries that are easier to form at low-strain rates. High-strain rate compression can lead to the α→β phase transition, inducing brass hardening. These results are helpful for understanding the reinforcement and failure mechanisms of dual-phase alloys.