Correlation of Cooperatively Localized Rearrangement on the ＂Fluidized Domain＂ of Polymers to Their Nonexponentially Viscoelastic Behaviors at Double Aging Processes （I）： A Set of Reduced Universal Equations on the Stress Relaxation Modulus and Creep Comp

Based on the structure of glass （or liquid） polymers consisting of α-domain, β-co-domain, and entanglement constituent chain networks, and the nonexponentially viscoelastic behavior, a “heterophase fluctuation” model was proposed. It was found that the dynamics of cooperative rearrangement on the “fluidized domain” has a great shear rate, domain size, and temperature dependences. When the shear rate, domain size, and temperature dependences were taken account into the cooperatively localized rearrangement on the fluidized domain by the degradation of primary α-domain and the reformation of secondary β-co-domain constituent chains. A new dynamic theory of cooperatively localized rearrangement on the fluidized domain constituent chains with different size and different network chain length during physical and mechanical aging was established. The total viscoelastic free en-ergy of deformation resulting from the change in conformations of α-domain, β-co-domain, crytallite, crosslinked, and trapped entanglement constituent chains during aging processes was calculated by the combining method of kinetics and statistical mechanics. The constitu- tive equations and reduced stress relaxation modulus and creep compliances for three types of polymers were also derived. Finally, two reduced universal equations on creep compliance and stress relaxation modulus with a non-linear and two nonexponential parameters α and β were theoretically derived from the dynamic theory and a statistically extended mode coupling theory for double aging effects of polymers was developed. Results show that the two reduced universal equations have the same form as Kohlraush-Williams-Watts （K-W-W） stretched exponential function. The nonlinearity and the nonexponentiality are, respectively, originated from the memory effects of nonthermal and thermal history. The correlation of nonlinearity, α and β to the aging time, aging temperature, and the mesomorphic structure of fluidized domains was also established.

Effect of grain size on high-temperature stress relaxation behavior of fine-grained TC4 titanium alloy

In order to analyze the effect of grain size on stress relaxation(SR) mechanism,the SR tests of TC4 alloy with three kinds of grain size were performed in a temperature range of 650-750℃.A modified cubic delay function was used to establish SR model for each grain size.A simplified algorithm was proposed for calculating the deformation activation energy based on classical Arrhenius equation.The grain size distribution and variation were observed by microstructural methods.The experimental results indicate that smaller grains are earlier to reach the relaxation limit at the same temperature due to lower initial stress and faster relaxation rate.The SR limit at 650℃ reduces with decreasing grain size.While the effect of grain size on SR limit is not evident at 700 and 750℃ since the relaxation is fully completed.With the increase of grain size,the deformation activation energy is improved and SR mechanism at 700℃ changes from grain rotation and grain boundary sliding to dislocation movement and dynamic recovery.

Stress Relaxation of Grouted Entirely Large Diameter B-GFRP Soil Nail

One of the potential solutions to steel-corrosion-related problems is the usage of fiber reinforced polymer （FRP） as a replacement of steel bars. In the past few decades, researchers have conducted a large number of experimental and theoretical studies on the behavior of small size glass fiber reinforce polymer （GFRP） bars （diameter smaller than 20 ram）. However, the behavior of large size GFRP bar is still not well understood. Particularly, few studies were conducted on the stress relaxation of grouted entirely large diameter GFRP soil nail. This paper investigates the effect of stress levels on the relaxation behavior of GFRP soil nail under sustained deformation ranging from 30% to 60% of its ultimate strain. In order to study the behavior of stress relaxation, two B-GFRP soil nail element specimens were developed and instrumented with fiber Bragg grating （FBG） strain sensors which were used to measure strains along the B-GFRP bars. The test results reveal that the behavior of stress relaxation of B-GFRP soil nail element subjected to pre-stress is significantly related to the elapsed time and the initial stress of relaxation procedure. The newly proposed model for evaluating stress relaxation ratio can substantially reflect the influences of the nature of B-GFRP bar and the property of grip body. The strain on the nail body can be redistributed automatically. Modulus reduction is not the single reason for the stress degradation.

Effects of Periodic Temperature Changes on Stress Relaxation of Chemically Treated Wood

In order to clarify the relationship between the microstructural changes and the rheological behaviors of four chemically treated woods (delignified wood, hemicellulose-removed wood, DMSO swollen and decrystallization treated wood), the stress relaxation of wood with three different moisture contents was determined during periodic temperature changes. The experi- mental results show that after wood relaxation for 4 h at 25 °C, the stress decays sharply when the temperature increases and 2 h later the stress recovers again when the temperature drops back to the original point. The additional stress relaxation, produced after tem- perature begins to increase, is mainly caused by the thermal swelling, molecular thermal movement and the break of a part of residual hydrogen bonds. The number of hydrogen bonds and the size and amount of cavities in various treated woods greatly affect the magnitude of the additional relaxed stress and the recovery stress.

Residual stress relaxation in typical weld joints and its effect on fatigue and crack growth

Many factors influence the fatigue and crack growth behavior of welded joints. Some structures often undergo fairly large static loading before they enter service or variable amplitude cyclic loading when they are in service. The combined effect of both applied stress and high initial residual stress is expected to cause the residual stresses relaxation. Only a few papers seem to deal with appropriate procedures for fatigue analysis and crack growth by considering the combined effect of variable amplitude cyclic loading with residual stresses relaxation. In this article, some typical welded connections in ship-shaped structures are investigated with 3-D elastic-plastic finite element analysis. The effect of residual stress relaxation, initial residual stress, and the applied load after variable amplitude cyclic loading is revealed, and a formula for predicting the residual stress at hot spot quantitatively is proposed. Based on the formula, an improved fatigue procedure is introduced. Moreover, crack growth of typical weld joints considering residual stresses relaxation is studied.

Stress Relaxation of Paraffin Wax Emulsion/Copper Azole Compound System Treated Wood

[Objective] An approach of stress relaxation was proposed in present work to investigate the interactions among the waterproof agent,preservative and wood.[Method] Paraffin emulsion waterproof using natural surfactants was prepared at different concentrations of 0.5% and 2.0%,which were added into two concentrations（0.3%,0.5%） of copper azole（CA） to obtain compound systems,and one-time fullcell process was applied to treat the sapwood of Pinus spp.with a size of 10 mm（L） ×10 mm（R） ×10 mm（T）.[Result] Compressive stress relaxation behaviors at two moisture levels and room temperature were measured and the results were as follows：1） compared with control group,the stress relaxation of compound system treated groups reduced,whether at oven-dried state or air-dried state.2） Under oven-dried condition,CA could weaken the relaxation of treated samples and this effect became greater with increasing concentration of preservative,but an increase in the concentration of paraffin emulsion would slightly promote the relaxation of compound system treated samples.While under air-dried condition,both CA and paraffin wax emulsion lowered the relaxation which was inversely related to the concentrations of both agents.[Conclusion] The results were expected to shed new light on the various macroscopic properties of the compound system treated wood at a microscopic level,and to provide favorable scientific evidences and theoretical supports for the manufacture of waterproofing preservative-treated wood.

Transverse relaxation characteristic and stress relaxation model considering molecular chains of HTPB coating based on pre-strained thermal aging

In order to accurately describe the transverse relaxation characteristic and stress relaxation modulus of HTPB coating during pre-strain thermal aging process,a one month thermal aging test was carried out at70C with pre-strain of 0%,3%,6%and 9%,respectively.The low-field1 H NMR and stress relaxation modulus tests were carried out for HTPB coating at different aging stages.The stress relaxation model considering the molecular chains was proposed according to the changes of crosslinking chain and dangling chain of HTPB coating during pre-strain aging.The results showed that with the increase of aging time,the decay rate of transverse relaxation curve became faster,the transverse relaxation time decreased,the value of combined parameter q Mrl increased,the proportion of crosslinking chain decreased,while the proportion of dangling chain increased.Moreover,the stress relaxation modulus increased,the crosslinking network structure of HTPB coating became denser and the degree of crosslinking increased.At the initial aging stage,the pre-strain will destroy the crosslinking network structure of HTPB coating to a certain extent.With the increase of aging time,the effect of pre-strain will gradually weaken and the influence of aging on materials will gradually increase.The correlations between the stress relaxation model considering the molecular chains and the test results were more than 0.9950,which can accurately describe the stress relaxation modulus of HTPB coating during the pre-strain thermal aging process.

Stress Relaxation and Sensitivity Weight for Bi-Directional Evolutionary Structural Optimization to Improve the Computational Efficiency and Stabilization on Stress-Based Topology Optimization

Stress-based topology optimization is one of the most concerns of structural optimization and receives much attention in a wide range of engineering designs.To solve the inherent issues of stress-based topology optimization,many schemes are added to the conventional bi-directional evolutionary structural optimization(BESO)method in the previous studies.However,these schemes degrade the generality of BESO and increase the computational cost.This study proposes an improved topology optimization method for the continuum structures considering stress minimization in the framework of the conventional BESO method.A global stress measure constructed by p-norm function is treated as the objective function.To stabilize the optimization process,both qp-relaxation and sensitivity weight scheme are introduced.Design variables are updated by the conventional BESO method.Several 2D and 3D examples are used to demonstrate the validity of the proposed method.The results show that the optimization process can be stabilized by qp-relaxation.The value of q and p are crucial to reasonable solutions.The proposed sensitivity weight scheme further stabilizes the optimization process and evenly distributes the stress field.The computational efficiency of the proposed method is higher than the previous methods because it keeps the generality of BESO and does not need additional schemes.

Constitutive modeling and springback prediction of stress relaxation age forming of pre-deformed 2219 aluminum alloy

Stress relaxation ageing behavior of pre-deformed AA2219 is studied through stress relaxation age experiments and finite element(FE) simulation. The results show that the stress can promote the process of ageing precipitation, and shorten the time to reach the peak strength. Meanwhile,the residual stress and yield strength increase along with the increase in the initial stress. Based on microstructure evolution and ageing strengthening theory,a unified constitutive model is established and incorporated into the FE simulation model through a user subroutine. It is found that the relative error of the radius is 3.6% compared with the experimental result and the springback is 16.8%. This indicates that the proposed stress relaxation ageing constitutive model provides a good prediction on the springback of such stiffened panel during its ageing process.

Stress relaxation behavior and life prediction of gasket materials used in proton exchange membrane fuel cells

Silicone rubber gaskets are employed to keep fuel gases and oxidation in their own zones. Due to the viscosity and elasticity, the assembly force could relax when the silicone rubber is compressed in a proton exchange membrane fuel cell. In this work, the stress relaxation behavior of silicone rubber samples is studied under different temperatures and simulated operating conditions. The results show that the stress relaxes exponentially with time at 25% strain level, especially at higher temperature or with higher acid concentration solution. The three-term Prony series can simulate the viscoelastic behavior well, and the Master curves are established by applying a time–temperature superposition method to estimate the life of the samples. It can save approximately 50% and 78% of the test time when an operating temperature and acid solution are chosen appropriately.

Stress Relaxation of Chemically Treated Wood during Processes of Temperature Elevation and Decline

In order to clarify the effect of drying on structural changes of DMSO swell treated and DEA-SO2-DMSO decrystallization treated Chinese fir （Cunninghamia lanceolate） wood, the stress relaxation of treated oven-dry specimens during the processes of temperature elevation and reduction and that of treated wet specimens at constant temperature were determined. A stress decrease process and a stress increase process were observed in all stress ratio curves of wood during the processes of decreasing temperature. Untreated wood, during the process of temperature reduction under higher initial temperature conditions and during the process of temperature elevation, has a larger stress decrease than treated woods. In a wet state this trend is reversed. It indicated that the drying set made treated woods have a smaller increase in fluidity of wood constituents with increasing temperature. Some bonding between decrystallization reagents and wood molecules may occur.

Stress relaxation analysis of single chondrocytes using porohyperelastic model based on AFM experiments

Based on atomic force microscopy technique, we found that the chon- drocytes exhibits stress relaxation behavior. We explored the mechanism of this stress relaxation behavior and concluded that the intracellular fluid exuding out from the cells during deformation plays the most important role in the stress relax- ation. We applied the inverse finite element analysis technique to determine nec- essary material parameters for porohyperelastic （PHE） model to simulate stress relaxation behavior as this model is proven capable of capturing the non-linear behavior and the fluid-solid interaction during the stress relaxation of the single chondrocytes. It is observed that PHE model can precisely capture the stress re- laxation behavior of single chondrocytes and would be a suitable model for cell biomechanics.

Uniqueness of rate-dependency, creep and stress relaxation behaviors for soft clays

This work focuses on the uniqueness of rate-dependency, creep and stress relaxation behaviors for soft clays under one-dimensional condition. An elasto-viscoplastic model is briefly introduced based on the rate-dependency of preconsolidation pressure. By comparing the rate-dependency formulation with the creep based formulation, the relationship between rate-dependency and creep behaviors is firstly described. The rate-dependency based formulation is then extended to derive an analytical solution for the stress relaxation behavior with defining a stress relaxation coefficient. Based on this, the relationship between the rate-dependency coefficient and the stress relaxation coefficient is derived. Therefore, the uniqueness between behaviors of rate-dependency, creep and stress relaxation with their key parameters is obtained. The uniqueness is finally validated by comparing the simulated rate-dependency of preconsolidation pressure, the estimated values of secondary compression coefficient and simulations of stress relaxation tests with test results on both reconstituted Illite and Berthierville clay.

Stress relaxation of Si/Si_(1-x)Ge_x/Si structure prepared by ion implantation and subsequent annealing process

The stress relaxation of 74Ge＋-implanted （100） silicon wafers was investigated. The implantation energy as a function of Si/Si1-xGex/Si struc-ture fluence and two kinds of thermal annealing were reported. The stress and stress relaxation after thermal annealing were calculated on the basis of Raman analysis, and were compared with those obtained from the calculation of virgin Si.

STRESS RELAXATION BEHAVIOUR OF TITANIUM

Studies of stress relaxation were carried out on commercially pure titanium.It was found that the stress relaxation behaviour relates closely to the level of deformation.The amount of re- laxed stress (?)σ_R is independent of the amplitude of stress dip in a certain range of deformation.However,it depend on the stress level at which stress relaxation begins in a cer- tain relaxation time t_R.Both back(critical)stress σ_c and flow stress σ_o vary with the strain in a similar manner.The effective stress on dislocations σ~* increases with increasing strain under low strains,but keeps constant under higher strains.

Thickness dependence of viscoelastic stress relaxation of laminated microbeams due to mismatch strain

Time-dependent behaviors due to various mismatch strains are very important to the reliability of micro-/nano-devices.This paper aims at presenting an analytical model to study the viscoelastic stress relaxation of the laminated microbeam caused by mismatch strain.Firstly,Zhang’s two-variable method is used to establish a mechanical model for predicting the quasi-static stress relaxation of the laminated microbeam.Secondly,the related analytical solutions are obtained by combining the differential method and the eigenvalue method in the temporal domain.Finally,the influence of the substrateto-film thickness/modulus ratio on the relaxation responses of the laminated microbeam subject to a step load of the mismatch strain is studied.The results show that the present predictions are consistent with the previous theoretical studies.Furthermore,the thickness dependence of stress relaxation time of the laminated microbeam is jointly determined by the intrinsic structural evolution factors and tension-bending coupling state;the stress relaxation time can be controlled by adjusting the substrate-to-film thickness/modulus ratio.

STRESS RELAXATION AND RELIABILITY EVALUATION OF SODA-LIME GLASS

Stress relaxation of glass is a dualism effect, it often lead to strength degradation in strengthened glass, but on the other hand, it improves the reliability and stress-uniformity of glasses. In this work, stress relaxation of soda-lime glass was investigated using three-point bending tests at 400-560℃ which is near the brittle to ductile transition temperature, for enhancing the safety of glass productions and exploring the most economic anneal process. The experimental results show that the speed of stress relaxation increases but the ultimate stress decreases with increasing temperature. The stress uniformity of the glass samples before and after anneal was examined using spherical indentation at arranged testing points. It indicates that the scatter of the local strength measured by the Hertzian indentation is smaller in the anneal glass than in initial specimen, so that the estimated Weibull modulus for the anneal specimen is higher. Furthermore, the strength evaluation by Hertzian indentation and statistical analysis was presented.

Microstructural and Microhardness Variation of Amorphous Fe_(78)Si_9B_(13) Alloy during Bend Stress Relaxation

The amorphous Fe78Si9B13 ribbons were bend stress relaxed at various temperature well below the crystallization temperature （Tx） for different time. The effect of pre-annealing on the subsequent bend stress relaxation was examined. The variation of the microstructure and microhardness during bend stress relaxation process was studied using X-ray diffraction （XRD）, atomic force microscopy （AFM） and Vickers microhardness test,respectively. Curvature radius of the amorphous Fe78Si9B13 ribbons decreased with increase bend stress relaxation temperature and time. The microhardness of the stress relaxed specimens increased with time at 300℃ due to the forming of nanocrystals during bend stress relaxation. The pre-annealing reduced the decrease rate of the curvature radius of stress relaxed specimens.

Indenter Size Effect on Stress Relaxation Behaviors of Surface-modified Silicon:A Molecular Dynamics Study

Long-lasting constant loading commonly exists in silicon-based microelectronic contact and can lead to the appearance of plastic deformation.Stress relaxation behaviors of monocrystalline silicon coated with amorphous SiO_(2)film during nanoindentation are probed using molecular dynamics simulation by varying the indenter’s size.The results show that the indentation force(stress)declines sharply at the initial and decreases almost linearly toward the end of holding for tested samples.The amount of stress relaxation of SiO_(2)/Si samples indented with different indenters during holding increases with growing indenter size,and the corresponding plastic deformation characteristics are carefully analyzed.The deformation mechanism for confined amorphous SiO_(2)film is depicted based on the amorphous plasticity theories,revealing that the more activated shear transformation zones(STZs)and free volume within indented SiO_(2)film promote stress relaxation.The phase transformation takes place to monocrystalline silicon,the generated atoms of Si-II and bct-5 phases within monocrystalline silicon substrate during holding are much higher than those for smaller indenter.

EFFECT OF INITIAL GRAIN SIZE ON STATIC RECRYSTALLIZA-TION SOFTENING IN Cr STEEL USING STRESS RELAXATION TECHNIQUE

Effect of initial grain size (I.G.S.) on static recrystallization softeningin Cr steel (0.77 wt. percent Cr) has been investigated through the use of interrupted hotcompression tests and stress relaxation curves from Gleeble 1500. Initial grain sizes were variedbetween 20 and 93 microns. Stress strains curves for Cr steel for different initial grain sizes andrecrystallization times have been highlighted. Similar observation was made for metadynamicrecrystallization with shorter retardation times. Statically recrystallized grain size alsoincreased as initial grain size increases. It is found that the values of initial grain size havesignificant effects on the mean flow stress and static recrystallization kinetics as well as thepeak strain values to initiate dynamic recrystallization.