Kinetics Of Stress Relaxation Research Articles

Time-temperature-transformation diagrams from isoconversional kinetic analyses applied to the processing and reprocessing of vitrimers

In this study, we extend the application of Time-Temperature-Transformation (TTT) diagrams, typically employed to describe thermoset processing, to address both the processing and reprocessing of vitrimers. To that end, we have used thermal analysis methods to characterize the reactions governing curing and the thermoforming of a disulfide-containing epoxy vitrimer. The resulting diagrams, which account for adverse processing effects such as degradation and vitrification, exclusively rely on predictions derived from isoconversional methods. Notably, we introduce, for the first time, the application of isoconversional methods to the modeling of stress relaxation kinetics. Using these diagrams, we have identified the conditions for safe curing and thermoforming of the vitrimer. Predictions have been experimentally validated, confirming the robustness and versatility of model-free kinetic analyses.

Strain-dependent transition of the relaxation dynamics in metallic glasses

Non-exponential relaxation is pervasive in glassy systems and intimately related to unique thermodynamic features, such as glass transition and aging; however, the underlying mechanisms remain unclear. The time scale of non-exponential relaxation goes beyond the time limit (nanosecond) of classic molecular dynamics simulation. Thus, the advanced time scaling atomistic approach is necessary to interpret the relaxation mechanisms at the experimental timescale. Here, we adopted autonomous basin climbing (ABC) to evaluate the long-time stress relaxation. At the same time, based on the energy minimization principle, we carried out simulations at continuum levels on the long-time stress relaxation kinetics of Cu–Zr metallic glass over timescales greater than 100 s. Combined with atomistic and continuum models, we demonstrate that a strain-dependent transition from compressed to stretched exponentials would happen, consistent with recent experimental observations on metallic glasses. Further examination of the spatial and temporal correlations of stress and plastic strain reveals two predominant driving forces: the thermal energy gradient governs in the compressed regime and leads to a release of the local internal stress; in the stretched regime, the strain energy gradient rules and causes long-range structural rearrangements. The discovery of the competition between two driving forces advances our understanding of the nature of aging dynamics in disordered solids.

Micromechanical characterizations and viscoelastic modeling reveal elastic and viscoelastic heterogeneities in ovarian tissue and the significant viscoelastic contribution to the apparent elastic modulus determined by AFM indentation.

Ovarian follicles develop in a highly regulated mechanical microenvironment and disruptions to the microenvironment may cause infertility. However, the viscoelastic properties of the ovarian tissue are not well studied. Here, we characterize both the elastic and viscoelastic properties of ovarian tissue from both reproductively older and younger domestic cats using atomic force microscopy (AFM) indentation and viscoelastic models of stress relaxation. Importantly, our analyses reveal the apparent elastic modulus obtained from the conventional AFM indentation measurement is significantly higher than the intrinsic elastic modulus and insignificantly different from the equivalent elastic modulus that is the summation of the intrinsic elastic modulus and the viscoelastic contribution to modulus at time 0. Interestingly, the ovarian cortex of both reproductive age groups has a higher apparent/intrinsic modulus than that of the medulla. Furthermore, two different kinetics of stress relaxation are identified with rate constants of ∼1s and ∼20-40s, respectively. Moreover, the rate constant of the slow kinetics is significantly different between the cortex and medulla in the reproductively older ovaries. Finally, these mechanical heterogeneities appear to follow the heterogeneous distribution of hyaluronic acid (HA) in the ovary. These findings may be invaluable to the development of biomimetic follicle culture for treating infertility. STATEMENT OF SIGNIFICANCE: This study investigates not only elastic but also the viscoelastic heterogeneity in both reproductively younger and older ovarian tissues for the first time. Further, by combining AFM indentation measurement and viscoelastic modeling, we show the apparent elastic modulus conventionally reported in the literature for AFM indentation measurement is the summation of the intrinsic elastic modulus and a significant viscoelastic contribution to the modulus at time 0. This is an important consideration for others who use this method to quantify biomaterial properties. In addition, the possible connection between the mechanical and compositional heterogeneities is explored. These findings may be invaluable for designing biomaterials to recapitulate the mechanical environment of the ovary and possibly many other organs for biomimetic tissue engineering.

Mechanically Strong, Autonomous Self‐Healing, and Fully Recyclable Silicone Coordination Elastomers with Unique Photoluminescent Properties

The combination of excellent mechanical performances, high reprocess efficiency, and wide-range tunability for functional dynamic siloxane materials is a challenging subject. Herein, the fabrication of mechanically strong, autonomous self-healing, and fully recyclable silicone elastomers with unique photoluminescent properties by coordination of poly(dimethylsiloxane) (PDMS) containing coordination bonding motifs with Zn2+ ions is reported. Salicylaldimine groups, which are introduced into the polysiloxane backbone via mild Schiff-base reaction, coordinate with zinc ions to form elastomeric networks The obtained supramolecular elastomers have excellent mechanical properties, with the optimized tensile strength up to 10.0MPa, which is unprecedented among the reported thermoplastic polysiloxane-based elastomers. Both mechanical properties and stress relaxation kinetics are tunable via adjusting the length of PDMS segments or the molar ratio of metal versus salicylaldimine. Furthermore, these elastomers can be conveniently healed and recycled to regain their original mechanical properties and integrity under mild conditions. In addition, this new kind of polysiloxane also exhibits coordination-enhanced fluorescence, showing great promise for preparing photoluminescent elastomers or coatings.

Kinetics of intrinsic stress in nanocrystalline films

Conventional polycrystalline materials acquire high levels of intrinsic mechanical stress (ranging from MPa to a few GPa) during preparation and use, but this stress decays quickly (~minutes) to small residual values (~kPa) under standard resting conditions. Nanocrystalline materials reach similar or even higher levels of intrinsic stress, but surprisingly retain a significant portion of this stress over much longer time scales (~hours). This behavior directly contradicts current theoretical models that predict stress relaxation through diffusive currents. Diffusive currents, which flow mainly on the surfaces of grains, are expected to produce faster relaxation kinetics when the stress to be released is higher. In this work, we study the kinetics of intrinsic stress relaxation in nanocrystalline films and identify the limitations of this process as a preliminary step towards designing a strategy for high-stress stabilization in nanostructured systems.

Deformations of microindentations on glassy epoxy mixed with silica nanoparticles

The change in the deformation properties of epoxy polymers after the addition of silica nanoparticles has been studied. It was shown that the addition of nanoparticles results in the polymer structural changes similar to the plasticization effect (increased mobility of the polymer chain). Nature of the stress relaxation kinetics significantly changed. In particular, for polymer with 1.6 wt% of nanoparticles, a complete recovery of the microindentation effect was observed (healing of indentation). The change in the activation energy of thermally stimulated relaxation of frozen inelastic deformations in an epoxy polymer was determined. The volume of atoms delocalization of the modified resin was estimated.

Stress relaxation in ultrafine-grained copper at low homologous temperatures

The temperature and rate sensitivity of the flow stress in ultrafine-grained (UFG) copper prepared by equal-channel angular hydroextrusion was studied. Tensile tests and stress relaxation tests were carried out in the temperature range of 77 to 295 K. It was established that, with increasing temperature, the flow stress decreases monotonously, and the activation volume reaches a maximum of ∼190b3 at a temperature of ∼(200 ± 20) K. The results of the experiment are discussed in terms of two thermally activated plastic deformation mechanisms, namely the intersection of “forest” dislocations and dynamic recovery, which are capable of significantly distorting stress relaxation kinetics in UFG copper.

Studying the Effect of Grain Size on Whisker Nucleation and Growth Kinetics Using Thermal Strain

To understand how and why Sn whiskers nucleate, measurements were performed in which the thermal expansion mismatch was used to induce strain in the samples. The current work focuses on the effect of grain size by studying samples with a thickness of 8 μm to compare with previous studies on 2.5 μm samples. The stress evolution during cycles of heating is determined by monitoring the resulting curvature in the sample. At the same time, the number of whisker nuclei are measured with optical microscopy which enables the relationship between film stress and nucleation rate to be quantified, where the stress relaxation kinetics depend on the grain size. The rate of stress relaxation is greater in the thick samples than the thin samples for the same heating cycle and the final stress after relaxation is smaller for the thicker samples. The whisker volume evolution was determined by using short sequences of heating and then measuring the size of different features after each interval in the scanning electron microscope. This enabled quantification of the relationship between film stress and whisker growth rate. The growth rate depends on the stress above the final stress, similar to our previous results for the thinner samples. The whisker nucleation kinetics in the 8 μm samples can also be explained with the same model used for the 2.5 μm samples. However, the stress-dependent activation energy is shifted to lower values.

Modeling of stress relaxation kinetics of amorphous Fe0.7Nb0.1Zr0.1Ti0.1 alloy powder: A novel approach based on differential thermal analysis

In this study, the stress relaxation of amorphous Fe0.7Nb0.1Ti0.1Zr0.1 alloy was investigated by differential thermal analysis (DTA) to enhance the soft magnetic properties. Amorphous Fe0.7Nb0.1Zr0.1T0.1 alloy was produced by mechanical alloying technique using the mixture of pure elements and without adding metalloids. It was found that the stress relaxation process follows the Johnson-Mehl-Avrami model and the mechanism was volume diffusion control with three dimensional growth of the nuclei. The relation of stress relaxation progress (α), with time was proposed as: dαdt=βdαdT=3.04exp−4312RT1−α−ln1−α0.37. The final achieved microstructure leads to higher saturation magnetization and lower coercivity that are favorable for soft magnetic applications.

Elastic precursor wave decay in shock-compressed aluminum over a wide range of temperature

The effect of temperature on the dynamic flow behavior of aluminum is considered in the context of precursor wave decay measurements and simulations. In this regard, a dislocation-based model of high-rate metal plasticity is brought into agreement with previous measurements of evolving wave profiles at 300 to 933 K, wherein the amplification of the precursor structure with temperature arises naturally from the dislocation mechanics treatment. The model suggests that the kinetics of inelastic flow and stress relaxation are governed primarily by phonon scattering and radiative damping (sound wave emission from dislocation cores), both of which intensify with temperature. The manifestation of these drag effects is linked to low dislocation density ahead of the precursor wave and the high mobility of dislocations in the face-centered cubic lattice. Simulations performed using other typical models of shock wave plasticity do not reproduce the observed temperature-dependence of elastic/plastic wave structure.

Role of Self-Organization of Dislocations in the Onset and Kinetics of Macroscopic Plastic Instability

The present paper examines two aspects of the problem of critical conditions of jerky flow in alloys, or the Portevin–Le Chatelier (PLC) effect. Recent development of dynamic strain aging (DSA) models proved their capacity to qualitatively reproduce complex non-monotonic behavior of the critical strain, providing that the parameters of theory are allowed to depend on strain. Experimental measurements of such strain dependences have been realized for the first time and used to revise the predictions of the critical strain and stress relaxation kinetics upon abrupt strain-rate changes. On the other hand, it is usually omitted from consideration that the PLC stress serrations can last very short time in comparison with the characteristic time of stress transients. The development of stress drops was studied with the aid of the acoustic emission (AE) technique. It is shown that such macroscopic instabilities are caused by clustering of AE events which otherwise occur all the time, including the periods of smooth plastic flow. The role of synchronization of dislocation avalanches in the development of abrupt stress serrations and its relationship with the predictions of the local DSA models is discussed.

Stress relaxation in pre-stressed aluminum core–shell particles: X-ray diffraction study, modeling, and improved reactivity

Stress relaxation in aluminum micron-scale particles covered by alumina shell after pre-stressing by thermal treatment and storage was measured using X-ray diffraction with synchrotron radiation. Pre-stressing was produced by annealing Al particles at 573K followed by fast cooling. While averaged dilatational strain in Al core was negligible for untreated particles, it was measured at 4.40×10−5 and 2.85×10−5 after 2 and 48 days of storage. Consistently, such a treatment leads to increase in flame propagation speed for Al+CuO mixture by 37% and 25%, respectively. Analytical model for creep in alumna shell and stress relaxation in Al core-alumina shell structure is developed and activation energy and pre-exponential multiplier are estimated. The effect of storage temperature and annealing temperature on the kinetics of stress relaxation was evaluated theoretically. These results provide estimates for optimizing Al reactivity with the holding time at annealing temperature and allowable time for storage of Al particles for different environmental temperatures.

Viscoelastic behavior and model simulations of poly(butylene adipate-co-terephthalate) biocomposites with carbon nanotubes: Hierarchical structures and relaxation

Poly(butylene adipate- co-terephthalate) (PBAT) biocomposites containing carbon nanotubes (CNTs) were prepared by melt compounding. The linear viscoelasticity of composites, including creep, creep recovery and stress relaxation in the solid state, and dynamic shear flow in the molten state, were studied and then further described by the viscoelastic models, aiming at exploring relaxation of hierarchical structures of CNTs and obtaining structural parameters of CNTs in PBAT matrix. The results reveal that CNTs are dispersed mainly as flocs or small aggregates in PBAT, which is further confirmed by the structural parameters of CNTs obtained through model simulations on the dynamic rheological responses of composites. The presence of CNTs retards overall kinetics of creep and stress relaxation of PBAT. This is attributed to highly restrained viscoelastic and viscoplastic deformation of PBAT chain coils, rather than slightly confined elastic deformation of chain segments because the chain coils is in the same size-scale with the CNT flocs.

Characteristics of stress relaxation kinetics of La60Ni15Al25 bulk metallic glass

The β relaxation typically plays an important role in the plastic deformation of glassy materials. Compared with amorphous polymers, most of the metallic glasses do not show evident β relaxation based on mechanical spectroscopy. However, La60Ni15Al25 bulk metallic glass (BMG) exhibits a prominent β relaxation process, which could be an ideal model alloy to investigate the correlation between the β relaxation and mechanical behavior of metallic glasses. In this work, compressive properties and stress relaxation at high temperature (below glass transition temperature Tg) were studied. Stress relaxation of La60Ni15Al25 BMG was measured by uniaxial compressive tests and mechanical spectroscopy around both α and β relaxation temperature domain. At higher temperatures and sufficiently low strain rate, the flow behavior of the La60Ni15Al25 BMG could be simulated by a master curve, showing that the behavior is independent of temperature, especially on the proximity of the β relaxation process. Because the existence of the β relaxation, a high value of the activation volume for the plastic deformation could be ascribed to the existence of a specific atomic arrangement in the La60Ni15Al25 BMG. It is found that compressive stress relaxation kinetics parameter remains temperature independent below Tg.

Electromigration induced stress evolution under alternate current and pulse current loads

Stress evolution in a metal line embedded in a rigid confinement caused by the arbitrary wave-form time-dependent current loads is resolved by a direct analytic solution of the one-dimensional (1-D) Korhonen's equation. Electromigration induced stress buildup and relaxation kinetics resulted by time-dependent current density are obtained as functions of the relevant physical parameters. A novel methodology for physics based conversion between the time-dependent and effective DC current densities is developed based on a condition of equal void nucleation times resulted by these currents. It is shown that in the case of high frequency currents, with periods much smaller than the characteristic time of stress evolution, the stress buildup is proportional to the pulse duty factor. It is demonstrated that very short metal lines with preexisted thermal voids loaded with symmetrical bi-directional currents can demonstrate a notable resistance increase when a specific temperature oscillation is generated in the line by active devices of the integrated circuit.

Research into structure and rheological and relaxation properties of nanocrystalline beryllium at temperatures of hot rolling and research into stress relaxation kinetics in different sorts of beryllium

Rheological and relaxational properties of distillate and technical beryllium were studied. It was shown that strengthening and thermal softening processes in nanocrystalline beryllium significantly differ from the same processes in distillate and technical beryllium. Thermal softening in distillate and technical beryllium takes place only at the holding time between deformations; in case of nanocrystalline beryllium, thermal softening takes place during the deformation process. It was considered that beryllium plastic deformation at 400–500°C involves an additional mechanism of deformation and stress relaxation: twinning; this mechanism increases the metal plasticity.

Investigation of structure, rheological and relaxation properties, and stress relaxation kinetics in nanocrystalline beryllium at hot rolling temperatures

Rheological and relaxation properties of high-purity nanocrystalline beryllium are obtained at hot rolling temperatures. It is shown that full stress relaxation in nanocrystalline beryllium occurs only upon deformation. A pause between deformations caused by repeated compressions does not affect the stress-strain curve or the final grain size. It is established that initially nanocrystalline beryllium (with grain sizes of 30–40 nm) converts into fine-crystalline one (with grain sizes of 5–6 μm) after hot plastic deformation at T = 700–800°C. The results are necessary for the creation of nondestructive technology to produce the thinnest foil from nanocrystalline beryllium.

Residual Stress in Ferrite and Austenite after Rolling and Recovery Processes

The relation between residual stresses occurring in plastically deformed material and after subsequent annealing is of practical and theoretical importance. In the present work the X-ray multi-reflection method was applied to determine residual stresses and their orientation distribution in rolled and annealed ferrite and austenite steel samples. An important decrease of the first- and the second-order residual stresses was observed during recovery and recrystallization processes. Diffraction peak width was also studied and correlated with stress variation during annealing. Different kinetics of stress relaxation in ferrite and austenite were explained by different levels of stacking fault energy and different types of intergranular interactions occurring in these materials.

Altering the Mechanical Properties of Sn Films by Alloying with Bi: Mimicking the Effect of Pb to Suppress Whiskers

Stress is believed to be the main driving force for whisker formation in Sn coatings on Cu. This suggests that whiskering can be suppressed by enhancing stress relaxation in the Sn layer, which is believed to be the reason why Sn-Pb alloys do not form whiskers. However, Pb is no longer acceptable for use in electronics manufacturing. As an alternative, we used pulsed plating to create Sn-Bi coatings with an equiaxed microstructure similar to that of Sn-Pb alloys. An optical wafer curvature technique was used to measure stress relaxation kinetics in Sn, Sn-Pb and Sn-Bi alloy thin films during thermal cycles. The results show that Sn-Bi films have significantly enhanced stress relaxation relative to pure Sn films. Comparison between Sn-Bi samples with equiaxed and columnar microstructures shows that both microstructure and alloy composition play a role in enhancing the stress relaxation.

Kirkendall Effect during Grain Boundary Interdiffusion in Polycrystalline Thin Films

We consider the kinetics of chemical interdiffusion along the grain boundaries in stressed thin metal film attached to inert substrate. We show that the kinetics of stress relaxation in the film can be either accelerated or slowed down if compared with the same kinetics in a single-component film, depending on the difference of intrinsic GB diffusion coefficients of the two components. In the case of faster matrix atoms the tensile stress in the film significantly increases beyond its initial value at the beginning of interdiffusion process, while in the case of faster diffuser atoms the compressive stresses develop in the film at the intermediate stages of stress evolution.