Stress Relaxation Conditions Research Articles

Viscous stress relaxation, characteristics, and numerical boundary conditions

AbstractThe anomalous infinite propagation speeds in the classical parabolic flow equations are removed by the inclusion of a small amount of fluid elasticity or viscous stress relaxation. The inclusion of such effects results in a hyperbolic system of equations with a complete set of characteristic equations. The directional characteristic equations are used to give insights into the appropriate boundary molecules to be used in finite difference numerical schemes. © 1994 John Wiley & Sons, Inc.

Strain hardening in Ni3 (Al, Hf)

A method of repeated stress relaxations is used to determine the strain-hardening that takes place during stress relaxation tests performed at different temperatures and for various crystallographic deformation axises. It is shown that strain hardening for stress relaxation conditions is substanbally higher than for constant strain-rate deformation conditions. This behaviour is found to be more and more pronounced with increasing temperatures. It is suggested that strain-hardening is not dislocation substructure dependent but is inherent to dislocation motion

Microplastic deformation of polycrystals during cyclic loading

A model of microplastic deformation of polycrystals during zero-start cyclic loading with tensions lower than the yield strength is proposed according to which during cycling, thermally activated movement of dislocations occurs under conditions of stress relaxation. Based on this model and the statistical theory of polycrystalline microdeformation, the accumulation of microplastic deformation is theoretically described as a function of the number of loading cycles and the stress amplitudes. It is theoretically proved that in the cycling process the microplastic deformation that accumulates over one cycle decreases as the number of cycles increases; up to the macroscopic elastic limit it is independent of the stress amplitude, and then sharply increases. Agreement of the theory with experimental data for spring alloys is observed in the density of mobile dislocations, which decreases during cycling.

Crack growth in brittle materials exhibiting primary creep

Engineering materials such as ferritic steels for turbine rotors and in weld heat affected zones exhibit substantial primary creep, and low failure strains (less than 1%), at low operating stresses. In components containing initial defects, the possibility of the growth of the defect by creep must be considered. This paper initially examines time and strain hardening primary creep under conditions of stress relaxation in uniaxial specimens. Uniaxial failure by damage accumulation during stress relaxation is also considered for a brittle ferritic steel representative of weld heat affected zone material. An approximate analysis is presented to obtain near crack tip stress and strain rate amplitudes for time and strain hardening primary creep. The amplitudes are found for the transient state from the initial elastic to the fully primary creep stresses. Characteristic times for the transition from small scale to large scale primary creep are determined for time and strain hardening creep. It is found that the strain hardening transient amplitude and characteristic times are greater than for the time hardening case. The derived transient amplitudes and characteristic times are used to determine crack initiation times assuming that near crack tip damage accumulation takes place. Crack initiation times are shorter in strain hardening than in time hardening primary creep. Subsequent crack growth using experimental crack growth rate data is explored. The growth of a crack relative to the growth of the small scale creep zone in both time and strain hardening primary creep is determined. Results show that for strain hardening primary creep in a creep brittle weld heat affected zone steel, the crack grows rapidly out of the transient creep stress field into the surrounding elastic field.

Analysis of axial and radial stress distribution in packing in stuffing-box seals taking account of stress relaxation.

An analytical approach to determine the axial and radial stress distribution in packing in stuffing-box seals is presented taking account of stress relaxation by means of a viscoelastic model. Radial-to-axial stress ratio and friction coefficient of the asbestos and graphite packing rings were experimentally determined, and they were found to be constant over time under the stress relaxation condition. Change of stress distribution with time in asbestos/graphite packing in stuffing-box seals is investigated by comparing the analytical results with the corresponding experimental results. The stress in packing decreases rapidly just after gland tightening and gradually decreases further with time, and it reaches an asymptotic value. The stress relaxation is reduced by repeated operation of gland tightening. This analytical model can simulate such behavior of packing as observed in actual packing installation.

Shear deformation of indium solder joints

Indium solder joint deformation has been investigated under conditions of shear loading and stress relaxation at room temperature. The deformation behavior was characterized as a function of strain, strain rate, joint thickness, and hold time. Implications of the results are discussed relative to thermal stresses and solder joint reliability in an electronic package. Work hardening during loading was found to increase with strain rate and volume fraction of intermetallics. The behavior was also dependent on the amount of work hardening and recovery that occurred in the prior stress relaxation cycle. The stress-strain rate characteristics during relaxation were found to be a function of the initial strain level and the spring constant of the assembly. It is shown how a material constitutive relation can be used with the assembly spring constant to calculate stress reduction over time. This procedure can be applied to any electronic assembly which undergoes stress relaxation during a constant temperature hold.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Rate‐dependent nonlinear constitutive equation of polypropylene

AbstractIn order to investigate the viscoelastic‐plastic properties of polymer solids and construct a constitutive equation for them, torsional tests were performed on polypropylene (PP) hollow cylinders. Testing was conducted under constant strain rate, abrupt change of strain rate, stress relaxation, creep, and cyclic loading conditions. The experimental data were compared with the numerical results derived from an overstress model. It is shown that the overstress theory explains the viscoelastic‐plastic properties of PP well, provided that the current strain is not below the maximum previous strain.

Biphasic indentation of articular cartilage—II. A numerical algorithm and an experimental study

Part I (Mak et al., 1987, J. Biomechanics 20, 703–714) presented the theoretical solutions for the biphasic indentation of articular cartilage under creep and stress-relaxation conditions. In this study, using the creep solution, we developed an efficient numerical algorithm to compute all three material coefficients of cartilage in situ on the joint surface from the indentation creep experiment. With this method we determined the average values of the aggregate modulus, Poisson's ratio and permeability for young bovine femoral condylar cartilage in situ to be H A = 0.90 MPa, ν s = 0.39 and k = 0.44 × 10 −15 m 4/Ns respectively, and those for patellar groove cartilage to be H A = 0.47 MPa, ν s = 0.24, k = 1.42 × 10 −15 m 4/Ns. One surprising finding from this study is that the in situ Poisson's ratio of cartilage (0.13–0.45) may be much less than those determined from measurements performed on excised osteochondral plugs (0.40–0.49) reported in the literature. We also found the permeability of patellar groove cartilage to be several times higher than femoral condyle cartilage. These findings may have important implications on understanding the functional behavior of cartilage in situ and on methods used to determine the elastic moduli of cartilage using the indentation experiments.

Prediction of the reliability of products made of polymer composites for conditions of creep and stress relaxation

Prediction of the reliability of products made of polymer composites for conditions of creep and stress relaxation

除荷過程中のクリープき裂伝ぱ

Crack propagation under sustaining or increasing load conditions in monotonic creep and time-dependent fatigue has been described successfully by the creep J-integral. This paper extends the creep J-integral concept to the crack propagation in decreasing load conditions. Because the J-integral can be originally defined for a linear or nonlinear elastic body even in an unloading condition although it can not for a plastic body, and because the creep J-integral in a creep body is analogous to the J-integral in an elastic one, the creep J-integral can be expected to be valid in the decreasing load (stress relaxation) condition when a unique stress-strain rate relation exists. Crack propagation tests of 0.16% carbon steel were carried out in creep and time-dependent fatigue conditions with the stress relaxation. As the result, the crack propagation rate had a good correlation with the creep J-integral for the stress relaxation period. In time-dependent fatigue, moreover, the crack propagation rate was correlated well with the creep J-integral (or creep J-integral range) independently of the stress waveform. These show the applicability of the creep J-integral concept for crack propagation during the stress relaxation.

Microscopically-Determined Static Recrystallization of Copper During Holding Without Stress or with Stress Relaxation After Hot Working

After deformation to 0.15 in the range 450–540°C and 1.8 × 10−3 to 1.8 s−l in compression or torsion, the recrystallization of ETP Cu determined microscopically is compared to the restoration measured mechanically during intervals of holding at the deformation temperature under both stress-free and stress-relaxation conditions. Recrystallization is initially much slower than softening, the difference being due to recovery, but finally they become equal at about 85%. TEM substructures sharpen considerably during intervals up to 100 s. Recovery and recrystallization occur more rapidly as strain rate and temperature rise in both modes of holding, but in stress relaxation the former is slowed down and as a result the latter is speeded up.

Microscopically-Determined Static Recrystallization of Copper During Holding Without Stress or with Stress Relaxation After Hot Working

Abstract After deformation to 0.15 in the range 450–540°C and 1.8 × 10−3 to 1.8 s−l in compression or torsion, the recrystallization of ETP Cu determined microscopically is compared to the restoration measured mechanically during intervals of holding at the deformation temperature under both stress-free and stress-relaxation conditions. Recrystallization is initially much slower than softening, the difference being due to recovery, but finally they become equal at about 85%. TEM substructures sharpen considerably during intervals up to 100 s. Recovery and recrystallization occur more rapidly as strain rate and temperature rise in both modes of holding, but in stress relaxation the former is slowed down and as a result the latter is speeded up.

Static recovery of copper during annealing and stress relaxation following hot deformation

After compression to 0.15 at 450 and 540 °C at rates between 1.8 × 10 −1 and 1.8 { su−3 s −1, the kinetics of softening and recovery of electrolytic tough pitch (ETP) copper held at the annealing temperature under both unloading and stress relaxation conditions were determined by mechanical testing and by transmission electron microscopy. Recovery occurs more rapidly at a higher strain energy (i.e. strain rate) or temperature (constant strain energy) but has more effect on the overall softening at a lower temperature and strain energy. Recovery occurs more slowly during stress relaxation than during unloading. The recovered metal exhibits a combination of a high strain-hardening rate and a high strength; as more recrystallization occurs, the strength decreases.

Relaxation stability and fatigue strength of thread elements made of VT6 alloy under cyclic load

1. A regularity of stress relaxation has been established for the investigated alloy under cyclic load, and a link was shown between the relaxation process intensity and cyclic as well as static stress components. An analytical description is given of the relaxation process at the steady stage, and a method has been put forward for assessing the relaxation stability of the material — the arbitrary relaxation stress limit — based on the change of the relaxation process intensity as a function of stress amplitude. 2. An evaluation of the contribution to the relaxation process of various structural elements of a threaded joint was carried out. It is shown that the highest specific contribution to the relaxation stress is that supplied by the working thread. Such a joint will work at tightening stresses σm = (0.5–0.7)σ0.2 and a cyclic load at normal temperature under the conditions of stress relaxation. 3. An evaluation of the service life of a material working under conditions of cyclic stress relaxation was carried out which takes into account its fatigue and relaxation characteristics; this evaluation is based on the linear hypothesis of the summation of fatigue damage.

Detailed examination of high-density polyethylene in the conditions of nonlinear creep and stress relaxation

Detailed examination of high-density polyethylene in the conditions of nonlinear creep and stress relaxation

A study of the viscoelastic behaviour of polybenzoxazole and polyimide under stress relaxation conditions

The mechanisms of isothermal stress relaxation during compression have been studied for the heat-resistant aromatic polymers, polybenzoxazole and polyimide. The relaxational transitions inside the limits of the glassy state and appreciably remote from the softening points, are features of these polymers. The regions of mechanical serviceability of these polymers have been evaluated.

Magnetic anisotropy in (Fe, Co) 75Si 15B 10 and (Fe 0.11Co 0.89) 72Mo 3Si 15B 10 metallic glass ribbons, induced by constant stress and constant strain annealing

The magnetic anistropy induced by constant tensile stress and constant torsional strain annealing has been studied for liquid quenched alloys of the compositions (Fe x Co 1− x ) 75Si 15 B 10 ( x = 0.1−1.0) and (Fe 0.11Co 0.89) 72Mo 3Si 15B 10. Within a certain annealing temperature range (depending on composition, pre-annealing time, applied stress and stress-annealing duration) the induced easy axis is perpendicular to the ribbon axis. After subsequent stress relief the easy axis turns parallel to the ribbon axis. The easy ribbon axis anisotropy produced in this way reveals a similar composition dependence as the anisotropy obtained by magnetic field annealing, but the anisotropy constant may be up to one order of magnitude larger, depending on the stress annealing conditions. In contrast to the field anneal induced anisotropy, the stress anneal induced anisotropy can be made permanent in the sense that it still remains after subsequent stress relief. It is furthermore shown that constant strain annealing induced anisotropy can be deduced from the properties observed after constant stress annealing, and a method for selecting proper stress relaxation conditions, with the purpose of obtaining maximum magnetic softness (isotropy) is proposed.

Determination of Stress Relaxation by Damping Measurements

Abstract The conventional determination of the stress relaxation properties of metals and their alloys is tedious and time-consuming. The method of predicting stress relaxation in metal strips subjected to uniform bending is based on the work per cycle required to maintain a constant strain energy level for the specimen. The change of the work per cycle with time or the number of cycles has been considered. The data obtained by damping measurements agree very well with a limited number of static stress relaxation measurements. The proposed method of predicting stress relaxation by damping measurements is simple and fast and should be particularly useful for data recorded at or close to room temperature.

The effects of temperature, pressure and volume on the stress relaxation properties of low density polyethylene (LDPE)

The results of examining the low-density polyethylene (LDPE) under conditions of creep and stress relaxation in isothermal, isobaric and isochoric regimes are described. The results have shown that pressure, temperature and volume are parameters which are present in the equation of state as independent variables; stress relaxation is therefore a function of all 3 parameters. The effect of the volume on the relaxation time can be accounted for by the addition of a fourth item in the exponent of the Aleksandrov-Lazurkin-Gurevich equation τ = τ 0 exp [ U 0−γ 1σ i+γ 2σ m+γ 2θ RT ] . The effective activation energies and activation volumes of the polymer were determined by processing the experimental results.

Optical studies of void formation and healing in styrene-isoprene-styrene block copolymers

Void formation is shown to be a significant response of styrene-isoprene-styrene block copolymers under conditions of tensile stress relaxation. When brought to zero stress, these voids are observed to close and heal, restoring the original mechanical properties of the undamaged material. Dark-field optical microscopy and light-transmission photometry have been used to study void formation and healing in the size regime appropriate to optical techniques. As meaured from a reference state of damage, healing was found to increase with time and temperature in the zero-stress state, with an apparent activation energy of 9 kcal/mole. The Mie theory of particle scattering was used to analyze changes in void size and size distribution during the healing process. The results are discussed in terms of possible mechanisms for healing.