Mechanical Relaxation Processes Research Articles

Effect of the physical aging on the secondary β relaxation process in a La-based metallic glass

Dynamic mechanical relaxation processes, i.e., main (α) relaxation and secondary (β) relaxation, are important issues to understand mechanical deformation, atomic diffusion as well as glass transition phenomenon of metallic glasses. In current work, La68Ni15Al15Cu2 metallic glass was selected as a protocol glass system. Mechanical relaxation processes were probed by dynamic mechanical analysis. The effects of annealing at different temperatures were analyzed by Kohlrausch–Williams–Watts (KWW)-type equation. The Kohlrausch exponent βKWW reflects the deviation from a single Debye relaxation, indicating the fact that dynamics in metallic glass are actually heterogeneous originating from the structural heterogeneity. The effects of thermal treatments were also discussed, which provides a potential solution to tune the relaxation behaviors in metallic glasses.

The β relaxation process of La-based amorphous alloy: Effect of annealing and strain amplitude

The dynamic relaxation process of amorphous alloys is an important issue to understand the diffusion behavior, plastic deformation as well as glass transition phenomenon. In the current research, (La<sub>0.6</sub>Ce<sub>0.4</sub>)<sub>65</sub>Al<sub>10</sub>Co<sub>25</sub> amorphous alloy with a pronounced β relaxation process was selected as a model system to study the dynamic mechanical relaxation processes. Influence of driving frequency, physical aging and applied strain amplitude on the β relaxation of the La-based metallic glass was probed process using dynamic mechanical analysis. The experimental results demonstrated that the peak of the β relaxation process shifts to high temperature by increasing the driving frequency. Physical aging below the glass transition temperature induces a decrease of the intensity of the β relaxation process. The “defects” of amorphous alloy decreases during the physical aging process, which is ascribed to the glassy system shifts to more stable state induced by physical aging treatment. In parallel, the intensity of the β relaxation process of the amorphous alloy increases by increasing strain amplitude. The research sheds new light on further understanding the physical origin of β relaxation process of the amorphous alloy.

Evolution of the distribution of flow units of a metallic glass under cyclic loading

Dynamic mechanical relaxation processes (i.e., β relaxation and α relaxation) are closely connected with the mechanical and physical properties of metallic glasses. In the current work, the β relaxation of La60Ni15Al25 metallic glass was studied in sequential heating and cooling experiments by dynamic mechanical analysis. The values of the loss modulus peak were found to reach a relatively stable state during the progress of the heating-cooling cycles. The evolution of the flow unit distribution during thermal cycling was revealed by stress relaxation tests. The experimental results of stress relaxation were well described by a generalized Maxwell model, allowing the analysis of the underlying relaxation time and activation energy distributions. We also show here a suppressed relaxation behavior observed under repeated loading cycles, which is attributed to the annihilation of flow units and the modification of the relaxation time spectrum obtained in the framework of the generalized Maxwell model.

Analysis of the Relaxation Process of Welding Residual Stresses Using a Combined and Nonlinear Hardening Model

This article applies a combination of hardening models to analyze the relaxation process of residual stresses. The obtained results can be used to estimate the final stress state in welded structures after the load application. This work begins by modeling the evolution of residual stresses produced by the thermal cycle during welding process. Subsequently, this stresses obtained by finite element calculations will be subjected to a mechanical relaxation process. In order to ensure the accuracy of the relaxation model, the plastic behavior of the material has been integrated by modeling two non-linear hardening models, which are combined and applied in the same relaxation process. The results have made it possible to visualize the final state of the residual stress field after relaxations. Then these results are analyzed in order to assess the impact of plasticity on the relaxation process.

New insight into dynamic mechanical relaxation in N-butyl-N-(2-nitroxy-ethyl) nitramine plasticized nitrocellulose through molecular dynamic simulations

We performed dynamic mechanical analysis (DMA) on nitrocellulose (NC) plasticized by an insensitive plasticizer N-butyl-N-(2-nitroxy-ethyl)nitramine (Bu-NENA). NC/Bu-NENA blend shows two mechanical relaxation processes in the temperature ranges of − 50 to − 40 °C and 30 ~ 40 °C, and their variations with deformation frequencies were studied. To explore further the effect of temperature on relaxation, the binary mixture model of NC/Bu-NENA was constructed, and molecular dynamic simulations were conducted. The simulated mean square displacements (MSD) show abrupt increase in the temperature range of − 50 to − 40 °C and 30 ~ 40 °C, which are consistent with those of the two relaxation processes observed in the DMA curves. Moreover, the free volume (Vfree) and torsion energy obtained from molecular dynamic simulations exhibit distinct increase at the temperature above 30 °C and − 50 °C respectively, reflecting the sudden enhancements on the mobility of polymer chain elements and the rotation of molecular bonds. Furthermore, the radial distribution function (RDF) associated with the intermolecular interactions reveals that the intensities of both hydrogen bond and van der Waals forces decrease with the increase of temperature, which is responsible for the decrease of storage modulus at high temperature. These computational and experimental studies reveal guidance to strengthening the NC base propellants in broad temperature range.

Dynamic relaxation characteristics and stress relaxation behavior of Pd-based<sub> </sub>metallic glass

As a potential functional and structural material, high-entropy metallic glasses have aroused tremendous research interest in condense matter physics and mechanics. The correlation between macroscopic mechanic properties and microstructure heterogeneity of high-entropy metallic glasses is one of the most important scientific issues in glassy solids. In the present research, Pd<sub>42.5</sub>Cu<sub>30</sub>Ni<sub>7.5</sub>P<sub>20</sub> metallic glass and Pd<sub>20</sub>Pt<sub>20</sub>Cu<sub>20</sub>Ni<sub>20</sub>P<sub>20</sub> high-entropy metallic glass are selected as the model alloys. Dynamic mechanical analysis (DMA) and stress relaxation are used to investigate the influences of temperature and physical aging on dynamic mechanical relaxation process and microstructure heterogeneity of the model alloys. The dynamic mechanical analysis results demonstrate that the Pd<sub>42.5</sub>Cu<sub>30</sub>Ni<sub>7.5</sub>P<sub>20</sub> metallic glass and Pd<sub>20</sub>Pt<sub>20</sub>Cu<sub>20</sub>Ni<sub>20</sub>P<sub>20</sub> high-entropy metallic glass both exhibit evident <i>β</i> relaxation process. In addition, the atomic mobility of model alloys is reduced in these processes, and the <i>β</i> relaxation shifts toward higher temperatures. In the stress relaxation process, the Gibbs free energy is reduced due to the high configurational entropy. This is the potential reason that high-entropy metallic glass possesses higher activation energy. In parallel, high-entropy metallic glass is more difficult to activate and needs to break through a higher energy barrier. With the increase of physical aging time, the flow unit in high-entropy metallic glass becomes smaller. This also benefits from the high-entropy effects that bring sluggish diffusion into high-entropy metallic glass. The change of activation volume under physical aging of high-entropy metallic glass is less sensitive to stress relaxation than that of metallic glass.

Characteristic of dynamic mechanical relaxation processes in Cu46Zr46Al8 and La43.4Ce18.6Ni24Al14 metallic glasses

Dynamic mechanical relaxation processes are very important to understand physical and mechanical properties of metallic glasses. In the current work, dynamic mechanical behaviors of La43.6Ce18.4Ni24Al and Cu46Zr46Al8 metallic glasses were investigated by mechanical spectroscopy. Unlike Cu46Zr46Al8 metallic glass, La43.6Ce18.4Ni24Al14 glassy system shows an evident slow β relaxation process. In addition, physical aging below the glass transition temperature Tg induces a reduction of intensity of the β relaxation. Evolution of the concentration of “defects” of metallic glasses was analyzed in the framework of Interstitialcy theory. Our research provides a new insight on understanding of the correlation between the structural heterogeneity and β relaxation of metallic glasses.

Visco-elasticity and mechanical relaxation behavior in La-based metallic glasses

Dynamic mechanical relaxation process is one of the important issues to understand mechanical/physical properties of metallic glasses. In the current research, dynamic mechanical relaxation behavior of La62Al14(Cu5/6Ag1/6)20(Ni1/2Co1/2)4 and (La0.7Ce0.3)65Al10Co25 bulk metallic glasses were investigated by mechanical spectroscopy. Unlike the typical Zr- or Cu-based metallic glasses, (La0.7Ce0.3)65Al10Co25 metallic glass shows an evident β relaxation process. On the other hand, La62Al14(Cu5/6Ag1/6)20(Ni1/2Co1/2)4 metallic glass presents a “shoulder” relaxation process. Physical aging below the glass transition temperature Tg induces a decrease of the concentration of “defects”, which corresponds to a reduction of the intensity of the β relaxation. During aging process, the amplitude of β relaxation (△E") decreases, while the relaxation time (τβ) increases. In organic glasses, it was reported that the changes of In(τβ) and In(△Emax) are linearly correlated with In(τβ)=b-a In(△E"max), this correlation has also been found in metallic glass. This behavior is discussed in the framework of the asymmetric double well potential (ADWP) model, and U and △ are used to characterize ADWP. It is suggested that during the aging process, the U/△ ratio remains basically unchanged, which is close to the coefficient describing the linear correlation between In(τβ) and In(△Emax) (U/△~a).

APPLICATION OF ACOUSTIC PULSE ECHO-METHOD FOR THE INVESTIGATION OF DYNAMIC AND STRUCTURAL DYSLOCATION CHARACTERISTICS OF CRYSTALS

The multifunctional pulse equipment allowіng to use the method of amplitude-independent internal friction in the frequency range 7.5 to 232.5 MHz is described. Equipment gjves the possibility to investigate the peculiarities of the process of phonon-dislocation interaction in crystals, to carry out thermoactivation analysis of the process of dislocation of the dislocations about the stoppers under the action of temperature and elastic loading, to study processes of dislocation and mechanical relaxation in loaded samples in the quasi-elastic and plastic strain range.

Effects of high energy on steel structure in deformation

The author of the article investigates how microwave radiation affects the processes of active deformation and mechanical stress relaxation in stressed stainless steel specimen under the electric current and when vector E (of microwave radiation) moves in different directions along the axe of the specimen. When vector E of microwave radiation was oriented in a longitudinalis way and electric current was passed, the softening of metal increased from 22 to 30 %. Multi-criteria analysis of steel samples with electric current and samples with no electric current was made. Analysis findings showed that external energy deposition influenced greatly on deformation of steel crystals. The action of high-density electric current pulses and microwave radiation on a sample loaded above the yield strength increases the ductility of stainless steel, and its strength characteristics, the microstructure is modified. Phase composition of steel was also investigated. The studies showed that the content of martensitic and austenitic phases in steel changed significantly. Moreover, the results showed that there was an additional mechanism of electroplastic deformation in the crossed fields of microwave radiation and magnetic field of current.

Ionic glasses: Structure, properties and classification

Due to the absence of microstructure and virtually infinite compositional versatility, glassy materials are perfect candidates for rational methods to predict structure-property relationships. In the most common models of glass structure, a three-dimensional network backbone and less-localized interstitial species are taken as the fundamental constituents of a glass. Such theoretical frameworks break down for the wide range of glass-forming compositions in which covalent bonding does not percolate and, therefore, there is no network in the classical sense. Most prominently, this applies to the class of ionic glasses, presently emerging as a separate class of amorphous materials, which includes classical invert glasses, geometrically frustrated compounds, mixtures of simple salts and ionic liquids, and organic–inorganic hybrids. Here, we will critically review ionic glasses as a distinct group of materials in which structural predictions are complicated by the dominance of long-range bonding interactions which lack directionality. First, we will reassess Zachariasen’s and Hägg’s rules for conventional glass formation in an attempt to broaden the current understanding of glass formation to include ionic glasses. By reviewing the compositions and properties of many simple and complex glass-forming salts, we discern the commonalities shared by ionic glasses and their unique characteristics as compared to other classes of glass. Specifically, we discuss the importance of non-percolating topology to dynamic properties such as mechanical behavior, ionic conductivity, relaxation processes and crystallization. We also demonstrate the relevance of the adjacent fields of ionic liquids and amorphous metal organic frameworks, and highlight possibilities for fruitful interdisciplinary exchange. The structure of ionic glasses, being dominated by Coulombic interactions, lends itself to high compositional flexibility and therefore, creates significant opportunities in the search for optical materials with enhanced transmission windows, fast ion conductors, phase-change materials, or, e.g ., adapted solders, hermetic seals and dielectric insulators. • The field of ionic glasses is reviewed with a focus on structure and properties. • Classification criteria are proposed. • Invert, halide, oxoanionic, halide-oxide and superionic glasses are included. • Links are drawn to the adjacent fields of ionic liquids and metal organic framework glasses.

The Pioneers of the Mittag-Leffler Functions in Dielectrical and Mechanical Relaxation Processes

We start with a short survey of the basic properties of the Mittag-Leffler functions Then we focus on the key role of these functions to explain the after-effects and relaxation phenomena occurring in dielectrics and in viscoelastic bodies. For this purpose we recall the main aspects that were formerly discussed by two pioneers in the years 1930’s-1940’s whom we have identified with Harold T. Davis and Bernhard Gross .

DYNAMIC RELAXATION CHARACTERISTICS AND HIGH TEMPERATURE FLOW BEHAVIOR OF ZR-BASED BULK METALLIC GLASS 1)

Dynamic mechanical relaxation processes of amorphous alloys are very important to understand plastic deformation, glass transition phenomenon, diffusion behavior and crystallization. How to establish the correlation between mechanical properties and mechanical relaxation modes is one of key issues. In the current research, with the help of dynamic mechanical analysis (DMA), dynamic mechanical behavior of Zr$_{50}$Cu$_{40}$Al$_{10}$ bulk metallic glass from room temperature to supercooled liquid region was probed. In parallel, based on the uniaxial tensile tests, high-temperature flow behavior of Zr$_{50}$Cu$_{40}$Al$_{10}$ metallic glass around glass transition temperature were investigated. Dynamic mechanical behavior and high temperature deformation behavior were discussed in the framework of quasi-point defects theory. The results demonstrated that main $\alpha $ relaxation process of metallic glass can be well described by the quasi-point defects theory. Based on internal friction of Zr$_{50}$Cu$_{40}$Al$_{10}$ metallic glass, activation energy of elementary movement of atoms $U_\beta$ is 0.63 eV. In addition, correlation factor $\chi $ corresponding to concentration of the quasi-point defects in solid glass remains almost constant below the glass transition temperature. When the temperature above the glass transition temperature, the correlation factor $\chi $ increases by increasing the temperature (below the crystallization temperature). Finally, high temperature flow behavior in tensile mode near the glass transition temperature of Zr$_{50}$Cu$_{40}$Al$_{10}$ metallic glass was studied. The normalized viscosity decreases with increasing strain rate at low temperatures or high strain rates, indicating a non-Newtonian flow behavior. Whereas Newtonian flow behavior is observed at higher temperatures and lower strain rates. The apparent viscosity is affected by temperature and strain rate. High-temperature flow behavior of Zr$_{50}$Cu$_{40}$Al$_{10}$ metallic glass was described by stretched exponential function and free volume theory. Specifically, experimental master curve of the high temperature flow behavior of metallic glass is in good agreement with the prediction of the quasi-point defects theory, which provides a new insight on understanding of viscous effects during high temperature deformation of solid glasses.

Modeling the high frequency mechanical relaxation of simplified industrial polymer mixtures using dielectric relaxation results

The mechanical characterization of rubber materials at the frequencies relevant for the tire function during braking (about 1 MHz) is extremely challenging. On the other hand, dielectric relaxation experiments provide a suitable tool for the analysis of relaxation phenomena over a broad frequency range with high sensitivity. Here we show that by analyzing dielectric relaxation experiments in the framework of a simple model the mechanical relaxation of simplified industrial systems based on mixtures of a styrene butadiene rubber (SBR) with a polystyrene oligomer can be anticipated, at least for the SBR rich mixtures that are more relevant for development of tire polymers. The model needs the description of the dielectric and mechanical relaxation processes of the single components of the mixture and uses concepts and ideas introduced in the past for describing the segmental dynamics of athermal polymer blends. The model description of dielectric relaxation experiments on the mixtures provides a quantification of the thermal fluctuations of concentration in the blends. With this input, the mechanical relaxation of the mixtures are calculated using well established equations for the mechanical properties of composite materials. The present approach should be helpful in a rational design of the rubber material depending on the specific requirements.

A fractional calculus approach to study mechanical relaxations on hybrid films of Fe2O3 nanoparticles and polyvinyl butyral

Polymeric hybrid magnetic films composed of iron oxide nanoparticles and polyvinyl butyral (PVB) were synthesized and studied by a fractional calculus approach. Iron oxide nanoparticles were synthesized in situ from a polymeric hybrid precursor composed of Fe+2 and PVB. These polymeric hybrid magnetic films (PVB/Fe2O3) could carry out functions as actuators or sensors in electronic or mechatronic devices. But, for this purpose, it is required a study of the mechanical relaxation processes displayed in the polymer matrix. The synthesis of iron oxide nanoparticles into PVB was confirmed by HRTEM, XRD and FTIR analysis. The main goal of this work is the study of the effect of iron oxide nanoparticles on the α-relaxation for three PVB samples with a different mass average molar mass. Experimental measurements of the complex modulus, $$\left( {E^{*} = E^{{\prime }} + iE^{\prime \prime } } \right)$$, were obtained by dynamic mechanical analysis (DMA) to identify the α-relaxation for each analyzed sample. Experimental isochronal curves of $$E^{\prime }$$ and $$E^{\prime \prime }$$ were compared with theoretical curves of $$E^{\prime } \left( T \right)$$ and $$E^{\prime \prime } \left( T \right)$$ computed by the fractional Zener model (FZM). An agreement between experiments and fractional model predictions has been achieved. The effect of fractional parameters ($$a$$ and $$b$$) of the FZM was related to molecular motions associated with this relaxation process. The cooperative motions of chains segments were observed in all analyzed samples, and $$b > a$$; this means that when temperature increases, the molecular mobility (energy dissipation) also increases. The matching between PVB matrix and the Fe2O3/PVB films showed that Fe2O3 nanoparticles decreases the molecular mobility of PVB; this effect is more pronounced at temperatures above $$T_{\text{g}}$$.

Dislocation mechanisms of low-temperature acoustic relaxation in iron

An integrated approach to the study of the mechanisms of low-temperature dislocation relaxation during low-temperature cyclic deformations of crystalline materials has been developed and tested. The approach is based on the combined use of experimental methods of mechanical spectroscopy in wide frequency-temperature ranges and theoretical methods of statistical and thermoactivation analysis of experimental results. The efficiency of this approach was demonstrated by studying low-temperature relaxation resonances in iron crystals whose dislocation structure was varied by preliminary plastic deformation. In this study, the previous mechanical spectroscopy results for iron in the temperature range of 4 K < T < 150 K at vibrational frequencies of about 1 Hz and 105 Hz were supplemented by a detailed study of the temperature spectra of internal friction and the Young’s modulus of a single-crystal iron plate at intermediate frequencies of about 103 Hz. A two-mode dislocation relaxator model was suggested for interpreting the entire set of experimental results. Its first component is a linear segment of a dislocation line in a first-kind Peierls relief whose relaxation properties are determined by thermal activation of kink pairs. The second component is a chain of geometric kinks capable of thermally activated diffusion movement in a second-kind Peierls relief. Empirical estimates of the energy, force, inertial, and geometric characteristics of both components of such a relaxator have been obtained. This study complements the earlier analysis of the processes of mechanical relaxation in crystals caused by nucleation and movements of kinks on dislocation lines [a review: A. Seeger and C. Wüthrich, Nuovo Cimento B 33, 38 (1976)].

Method for calculating stress evolution in glass-metal composite taking into account structural and mechanical relaxation processes

Technological modes of annealing layered glass-metal composite material are investigated. A cylindrical glass-metal composite vessel with an internal glass cylinder is used as a model sample in the experimental studies of highly compressed fragile rocks mass. A mathematical model of the evolution of technological and residual stresses during its annealing is considered. The difficulty in modeling is due to the glass transition process and the elastic-plastic behavior of the metal. Structural and mechanical relaxation processes in glass are calculated using the Tula-Naariswami-Moynihan-Mazurin method, which is based on the concept of structural temperature, and the Boltzman-Volterra superposition principle. The dependence of viscosity and coefficient of linear temperature expansion on the structural temperature is taken into account. Elastic state in the stress space is limited by the surface of the Mises limit state for metal shell. In this paper, a finite-difference scheme for calculating structural changes and process stresses over the entire temperature treatment interval is proposed. To assess the accuracy of the developed calculation algorithm, we used an analytical solution of the problem with the Maxwell core in the absence of temperature-time analogy in glass and elastic deformation of the metal layer. Calculations of technological stresses in glass metal composite based on borosilicate glass and low carbon steel for various temperature regimes of annealing were carried out. The proposed mathematical model and calculation method can be used for evaluating residual stresses in the technology of applying glass coatings on metal pipes.

Differences in the viscoelastic properties between earlywood and latewood in the growth rings of Chinese fir as analyzed by dynamic mechanical analysis (DMA) in the temperature range between −120°C and 120°C

Abstract To clarify the viscoelasticity of earlywood (EW) and latewood (LW) within different growth rings of Chinese fir, the following data were determined: absolute dry density, percentage of tracheid cell wall, microfibril angle (MFA), modulus of elasticity (MOE), storage modulus (E′) and loss modulus (E″) within the 3rd and 6th growth rings (in heartwood, hW) and the 14th and 18th growth rings (in sapwood, sW). The E′ and E″ data were obtained by dynamic mechanical analysis (DMA) between −120°C and 120°C, at a heating rate of 1°C min−1 at the frequencies of 1, 2, 5 and 10 Hz under a dynamic load amplitude of 10 μm. All measured data were different between EW and LW. In the same growth ring, LW had a greater MOE and larger E′ than those of EW due to the higher density of LW. The MOE and E′ increased for both EW and LW with increasing tree age. The variation of MFA in different growth rings of EW influenced the MOE and E′. Both density and the MFA affected the MOE and E′ in LW. The profiles of E″ plots vs. DMA temperature reveal two maxima around −12°C (β mechanical relaxation process, βMRP) and 12°C (αMRP). The LW-MRP maxima are higher than those of EW, but in both cases increased with tree age. No frequency dependence was seen for the αMRP, whereas the loss peak temperature (LPT) of the βMRP increased with increasing frequency of DMA. Almost no difference in αLPT was observed between the four EW growth rings, and their βLPTs were similar. The LW-αLPT was almost the same in the four growth rings, but the hW-βLPT was higher than that of sW. In addition, the apparent activation energy (ΔH) of the hW-βMRP was greater than that of sW in both EW and LW, and the EW data>LW data in individual growth rings. These differences can be explained tentatively that hW and EW contain more extractives than sW and LW, and the deposited of extractives limit the motion of molecular segments within the cell walls.

Influence of Nanodisperse Metal Fillers on the Viscoelastic Properties and Processes of Mechanical Relaxation of Polymer Systems

The results of research into the viscoelastic properties and processes of mechanical relaxation of polyvinylchloride (PVC) containing Cu nanoparticles obtained by means of electroerosion crushing and electrohydraulic destruction of agglomerates of disperse Cu in the presence of an ultrasonic field are presented. It is shown that, in the case of longitudinal shear deformation at a frequency of 0.4 × 106 s–1 over a wide range of temperatures and content of ingredients, viscoelastic phenomena depending on structural changes in the PVC system occur. An analysis of quantitative results of the elastic and viscoelastic deformation of a body is carried out taking into account the energy and entropy components of interaction of the polymer and filler at their interface.

Phase Morphology, Thermal, Thermomechanical and Interfacial Properties of PP/SAN/SBS Blend Systems

ABSTRACTThe effect of styrene–butadiene–styrene content on morphology, melting, crystallinity, dynamic mechanical properties and relaxation processes of polypropylene/poly(styrene-co-acrylonitrile)/styrene–butadiene–styrene blends was investigated. Styrene–butadiene–styrene reduced the average size of dispersed particles and generated complex aggregates in the matrix. Morphology development examined by dynamic mechanical thermal analysis showed increased damping of poly(styrene-co-acrylonitrile) domains at high styrene–butadiene–styrene contents. All blends showed reduced crystallinity and melting point compared with neat polypropylene. Poorer nucleation effect of dispersed particles at high styrene–butadiene–styrene loadings was observed. Compatibilization accelerated the form relaxation of dispersed particles. Additional relaxation process probably due to styrene–butadiene–styrene chains was observed in blends containing 10% and higher styrene–butadiene–styrene content.