Logarithmic Stress Relaxation Research Articles

Strain Stiffening And Soft Glassy Rheology In A Generalized Sliding Filament Model

Despite their enormous complexity and structural diversity, most biological materials show a remarkably similar viscoelastic phenomenology: nonlinear elasticity, power-law or logarithmic stress relaxation, and plastic length adaptation. Here we present a simple model based on Huxley's sliding filament model to demonstrate that such behavior can arise from generic structural properties, independent of the actual molecular constituents of the system. We compare the model predictions to data from active and passive microrheological experiments on epithelial cells and fibroblasts, smooth muscle tissue, and extracellular matrix protein networks.The material is represented by an uniaxial arrangement of infinitely stiff filaments crosslinked with parallel elastic elements that have a distribution of attachment angles. When the system is sheared or stretched, elements start to align, leading to strain stiffening due to a geometric recruitment of springs. The elastic elements have force-dependent average lifetimes described by energy traps with a broad distribution of energy trap depths. Broken links can reattach at random positions and attachment angles after unbinding. Such nanoscale structural rearrangements lead to viscous flow and plastic length adaptation on a macroscopic scale. Due to a broad distribution of energy trap depths, the system displays power law stress relaxation and soft glassy rheology.The model is capable of qualitatively reproducing experiments, and gives quantitative agreement for creep compliance, stress stiffening and plasticity in the case of cell microrheology. These results suggest that recruitment and dynamic unbinding of elastic elements are the common mechanism underlying the mechanical behavior of many complex biological materials from single cells to whole tissues.

Logarithmic relaxation due to minimization of interactions in the Burridge-Knopoff model

The time evolution of macroscopic quantities describing the relaxation of complex systems often contains a domain with logarithmic time dependence. This logarithmic behavior at the macroscopic level is often associated with strongly interacting elements at the microscopic level, whose interactions depend significantly on their history. In this paper we show that stress relaxation in the Burridge-Knopoff (BK) model of multicontact friction behaves logarithmically, when the model is in, or close to, the solitary state where the elements move independently. For this regime we present an automaton that allows us to follow the decay of stress relaxation over the entire range where it behaves logarithmically in time. We show that our model can be mapped onto a system of noninteracting elements subject to a uniform distribution of forces, for which logarithmic stress relaxation is derived analytically.

The effects of solvent type on the concentration dependence of the compression modulus of thermoreversible isotactic polystyrene gels

AbstractSolutions of isotactic polystyrene in either trans‐decalin or 1‐chlorodecane were transformed into gels by quenching from a high temperature (ca. 180°C) to −20°C. The relaxation modulus in compression of these gels was measured over a range of concentrations of from 0.04 g/g to 0.40 g/g. At 22°C, the gels show a double logarithmic stress relaxation rate, m, which is higher than for PVC and gelatin gel systems. 120 s isochronal modulus concentration diagrams exhibit non‐power law behavior, i.e., not only is the general trend such that the double logarithmic slope decreases with increasing concentration, but there are also regions in which abrupt changes in modulus occur over narrow ranges in concentrations. These features in the concentration dependence of the modulus are less pronounced than those found previously1 in isotactic polystyrene/cis‐decalin gels. The behavior is interpreted to be inconsistent with a fringed micelle picture of the gel structure. Preliminary results are reported indicating that polymer fraction and temperature of gel formation can significantly affect the modulus of the gels.

Stress relaxation in cobalt between 15 and 300 K

Abstract The slope of the logarithmic stress–relaxation curve for a well-annealed cobalt polycrystal of 99·999% purity has been measured as a function of the initial stress level from which relaxation at constant strain was allowed to start at a given temperature between 15 and 300 K. A pronounced undulation was observed in the plot of the relation between the inverse of the stress sensitivity of the relaxation rate and temperature, with a maximum and a minimum at about 75 and 50 K, respectively. The ‘classically unexpected’ behaviour below about 80 K seems to arise from the progressive inhibition of dynamic recovery process as T→0 K, which necessitates the use of stresses higher than that applied in the basic equations describing the mode of deformation.

Stress relaxation in nickel at 15 to 300 k

Logarithmic stress relaxation was studied in 99.999% polycrystalline nickel at natural strains of up to 8% at 15. 25, 40, 50, 77, 150 and 295 K. The structural and activation characteristics of the stress relaxation were investigated theoretically by a tentative model. The temperature dependence of the yield stress was interpreted by a theoretical model which provided an agreement with the expérimental results. The activation energies, i.e.1.15 ± 0.2 eV, deduced from a single barrier model of logarithmic stress relaxation, i.e. u 0 ~ k × (T 0+AT 2)[m+2.3 (dσ 0 ds] (where T 0 and A are constants), allows for “quantum” effects below T ⩽ 70 K, favours cross-slip and also the dynamic “recovery” as the rate determining process. For temperatures 77 and 150K, the activation energies obtained from equation, s = 2.3 kT σ 0 (u 0 - mkT ) , suggest that vacancy formation by jogged dislocations is a rate determining process except at 295 K, where the thermal “recovery” process occurs due to dislocation/dislocation intersection.

Yield-stress and stress relaxation measurements in cobalt

Yield stress of polycrystalline cobalt (5N) was studied in the temperature range 15–300 K and interpreted by a theoretical model which provided an agreement with experimental results. Logarithmic stress relaxation was also studied in polycrystalline cobalt at natural strains of up to 8% at 15, 25, 40, and 55 K. Activation energies, i.e., 1.27±0.35 eV, deduced from a single barrier model of logarithmic stress relaxation, i.e., u0=k(T0+AT2)×[m+2.3 (dσ/ds)c] where T0 and A are constants), which allows for ‘‘quantum’’ effects below T≤70 K, favors vacancy formation and dynamic recovery as the rate determining process. The occurrence of structural effects such as ‘‘strain enhancement’’ (semiempirical fact) at low temperatures, suggests that a single barrier model is not sufficient to explain the ‘‘anomalies’’ appertaining to the temperature dependence of the yield stress and of the accompanying modes of plastic deformation. However, both quantum and structural effects seem to play an important role in the determination of low temperature deformation peculiarities.

Reduced‐variable mechanical characterization of styrene‐butadiene rubber with varying crosslink density, temperature, and finite strain states

AbstractA single master logarithmic stress relaxation curve of reduced modulus as a function of reduced time is established for a styrene‐butadiene rubber (SBR) system, accounting for the effects of crosslinking density, temperature, and time. The results from recent tests involving uniaxial and various biaxial strain states at finite strain levels may be represented by a unique strain‐energy function W of the Valanis‐Landel separable symmetric type, where the λi are principal extension ratios. These two representations demonstrate that the mechanical response of whole families of elastomeric materials may be predicted once a single member of the family is fully characterized.

Stress Relaxation in PZT

Time‐dependent deformation in the sonar transducer ceramic, PZT, was studied by stress‐relaxation techniques. Logarithmic stress relaxation was not observed but the data could be treated in terms of an analysis of thermally activated deformation by Reed‐Hill and Dahlberg. The room‐temperature activation energy and activation volume of the rate‐controlling deformation mechanism were measured as 25 kcal/mol and 7000 Å3, respectively. A dislocation model of the domain processes responsible for deformation, consistent with the experimental data, is presented.

The effect of the magnitude of the stress exponent on the time span of logarithmic stress relaxation and creep

representing the dependence of the shear strain rate y on the shear stress T is extensively used in the study of plastic deformation. It has been found that the stress exponent n is a quantity which characterizes several plastic properties of theoretical and engineering interest. 1,2,3,4 For example, Johnston has shown1 that the yield drop exhibited in constant strain rate tests and the delay time observed in constant stress creep is controlled by the magnitude of the stress exponent n. Because both tests are controlled by the same thermally activated process the two effects are interrelated.5 Studies by Faucher, Aggarwal and Krausz6 have indicated that the behavior exhibited in constant loading rate tests is also strongly affected by the magnitude of the stress exponent. It was found that when the stress exponent is large the sow stress increases only slightly over a long period of loading time while when n is sm all the stress increase is very steep. Experimental observations indicate that superplastic behavior is also characterized by the stress exponent. It has been established empirically7,8 that the smaller is n the greater is the elongation. The relation between the stress exponent and superplasticity was explored in a theoretical study9,lO and it was shown that when both deformation and fracture are controlled by Newtonian sow (n = 1) the material is ideally superplastic. The stress exponent is, therefore, a me aningful characteristic quantity. It is the purpose of this communication to report the results of a study in which the effect of the magnitude of the stress exponent on the extent of the logarithmic stress relaxation and creep period was investigated.

Stress relaxation in nickel at 20–300°k

Logarithmic stress relaxation was studied in 99.999% polycrystalline nickel at natural strains of up to 25% at 20, 77, 200 and 293°K. The activation energy of 1,4 ± 0.2 eV associated with the process suggests that vacancy formation by jogged dislocations is rate determining. At room temperature significant loss or immobilisation of dislocations during relaxation appears to be facilitated by crossslip.

Microplasticity in α-uranium

Logarithmic stress-relaxation in α-uranium strips extended up to 5% at 200°–386°K is shown to be controlled by a mechanism with an energy barrier of 1.0 eV, numerically equal to about 0.57 times the activation energy of self-diffusion. This result, in conjunction with analyses of the kinetics of debris formation by moving dislocations, as observed in thin foils of the metal by electron transmission microscopy, is consistent with a model in which relaxation arises from residual glide of screw dislocations in the prominent (010)[100] glide system, the dislocations being subjected to a frictional drag by vacancy generating jogs of the 1 2 [110] type.

Creep and stress relaxation in alpha-brass at low temperatures

Abstract Creep of vacuum annealed polycrystalline 65/36 alpha-brass was studied at constant stress in the range 77–30°k, close to the yield point, at elongations not exceeding 3%. The tensile strain σ increased logarithmically with time, and the characteristic strain 8cr ≡ de/d log10 t, given by the slope of the creep curves in semi-logarithmic representation, decreased approximately linearly with increasing temperature, from 29 × 10−4 at 77°k to 11 × 10−4 at 300°k. The creep was correlated with logarithmic stress relaxation, and the relation 8Cr = - 8rel/χ was established. where χ ≡ d[sgrave]/d σ in the coefficient of work-hardening, and 8 rel≡ d[sgrave]/d log10 t the slope of the corresponding curve obtained with stress relaxation at constant elongation. Both the creep and the relaxation are ascribed to a process of residual slip propagation in which the migration of edge disclocations impeded by the drag of conservatively moving jogs is rate determining. The driving force on the jog is the component of the line tension of the dislocation, which impels the jog in the direction of its Burgers vector; the effective stress on the dislocation is the difference between that necessary to tear it from its looked site and the stress, due to the intragranular sub-structure, which opposes its movement through the lattice in the unlocked state. At temperatures exceeding about 300°k, when dislocation locking is weak, both 8cr and 8rel tend to very small values.