Stress relaxation and creep of cork

The stress relaxation and creep behaviour of cork under compression were characterized in tests done with the compression axis parallel to each of the three principal directions in the tree (radial, tangential and axial). All stress relaxations lead to a linear variation of stress with the logarithm of time, the slopes being nearly independent of stress and direction of compression. Creep stresses in the range 0.36 to 1.72 MPa were used. The strain rate continuously decreases during creep, from initial values around 10^–4sec^–1 to 10-7 sec^–1 after 8 h, but its dependence on the creep stress and direction of compression is not simple, mainly because different deformation regimes may operate during a single creep test. Compression loading-relaxation-unloading cycles were imposed on specimens, with compression either in the radial or in the tangential direction, with the purpose of simulating the performance of a cork stopper. A work softening is observed, i.e. the resistance decreases in successive compressions, particularly between the first two. This is explained in terms of an increased undulation of the cell walls produced in the first compression.     

Stress intensity factor for the cylindrical interface crack between nonhomogeneous coaxial finite elastic cylinders

The problem of determining the stress intensity factor for a cylindrical interface crack between two dissimilar nonhomogeneous coaxial finite elastic cylinders under axially symmetric longitudinal shear stress is considered. The mixed boundary conditions lead to a pair of dual series equations which are reduced to a Fredholm integral equation of the second kind and then finally to a system of algebraic equations. Numerical values of the stress intensity factor are presented graphically.     

The correlation between creep deformation and stress relaxation in concrete

Summary The functional relation between creep deformation and stress relaxation can be represented by the Volterra integral equation. By substituting the creep function and the relaxation function into this equation and comparing coefficients it is possible to obtain an expression which relates the ultimate creep to the relaxed stress at time t=∞. The rate at which the stress decreases at the begenning of the experiment is proportional to the creep velocity, and the constant of proportionality is the modulus of elasticity. It is shown the half-life time of the relaxation process is always smaller than the corresponding half-life time of the creep process. The derived equations are compared with experimental results described in the literature.

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Résumé On peut traduire la relation entre fluage et relaxation par l'équation intégrale de Volterra. La substitution des fonctions ?fluage? et ?relaxation? dans cette équation et la comparaison des coefficients permet d'obtenir une expression qui relie le fluage final et la contrainte relachée au tempst=∞. Le taux de décroissance au début de l'expérience est proportionnel à la vitesse de fluage; la constante de proportionnalité est le module d'élasticité. On montre que la mi-temps du processus de relaxation est toujours plus petite que la mi-temps correspondance du processus de fluage. On compare les équations dérivées avec les résultats expérimentaux décrits dans la littérature.

     

Stress relaxation and creep on living cells with the atomic force microscope: a means to calculate elastic moduli and viscosities of cell components

In this work we present a unified method to study the mechanical properties of cells using the atomic force microscope. Stress relaxation and creep compliance measurements permitted us to determine, the relaxation times, the Young moduli and the viscosity of breast cancer cells (MCF-7). The results show that the mechanical behaviour of MCF-7 cells responds to a two-layered model of similar elasticity but differing viscosity. Treatment of MCF-7 cells with an actin-depolymerising agent results in an overall decrease in both cell elasticity and viscosity, however to a different extent for each layer. The layer that undergoes the smaller decrease (36-38%) is assigned to the cell membrane/cortex while the layer that experiences the larger decrease (70-80%) is attributed to the cell cytoplasm. The combination of the method presented in this work, together with the approach based on stress relaxation microscopy (Moreno-Flores et al 2010 J. Biomech. 43 349-54), constitutes a unique AFM-based experimental framework to study cell mechanics. This methodology can also be extended to study the mechanical properties of biomaterials in general.     

Stress relaxation in zirconium carbide. Report 2. Mechanisms of stress relaxation. The relationship of the processes of creep and relaxation

Mechanisms of stress relaxation in ZrC_1.00 (d=6–35 .m) in the area of the ductile-to-brittle transition temperature (1600–2200C) are considered. It is established that in the 1800–2000C range for ZrC_1.00 with grain sizes of 6 and 14–35 m, respectively, stress relaxation occurs as the result of pure grain boundary slip while at higher temperatures by intragranular cross slip. It is shown that creep in the steady stage and stress relaxation in ZrC_1.00 with grain sizes of 6–35 m are controlled by different physical processes, which makes impossible obtaining for these materials of data on stress relaxation by conversion with use of information on steady creep.Translated from Problemy Prochnosti, No. 2, pp. 55–60, February, 1994.     

Observation of the relation between uniaxial creep and stress relaxation of filled rubber

This paper presents an experimental evaluation of the stress relaxation and creep of filled rubber. A detailed study of the influence of different test programs, where the main variable was the load sequence on the creep and relaxation processes, is discussed. The final goal of the research is to find a method to predict stress relaxation from known creep, or vice versa, in a simple way that would give sufficiently accurate results over both primary and secondary creep regions. Therefore suggestion for converting the creep test result into a stress relaxation curve and vice versa is presented. The idea is based on the assumption that both processes (creep and stress relaxation) are the result of the same viscoelastic mechanism and that the stress relaxation can be treated as creep under decreasing stress. Experimental data shows these assumptions to be correct. For the conversion of the creep parameters into stress relaxation parameters a reverse stress-strain curve is needed, therefore factors affecting the unloading stress-strain curve are also presented. Finally, the transition from the suggested conversion to the final method will be discussed.     

Stress relaxation during thermal cycling of particle reinforced aluminium matrix composites

Two SiC-particle reinforced composites were produced by powder metallurgy using a 2124 Al-alloy matrix and two powder blending techniques: ball milling and wet blending. The effect of the blending route on the stress relaxation during thermal cycling is studied by in situ neutron diffraction based on the determination of the average stresses in the matrix and the particles. The thermal stresses in both composites partially relax by creep at T ? 90 °C. The higher creep resistance of the composite produced by ball milling reduces relaxation in comparison with the wet blended composite. This results in average axial compressive thermal stresses of ～?50 MPa and ～?10 MPa after heating to 230–300 °C in the matrices of the ball milling and wet blending composites, respectively, which relax at rates ?5 × 10^?9–3 × 10^?8 s^?1.     

The competition between the crack kinking away from the interface and crack propagation along the interface in elastic bicrystals

The problem analyzed is of the crack kinking away from the interface between the two different anisotropic materials. The attention is concentrated on the initiation of the crack kinking and the condition that the length of the crack segment that is leaving the interface is small in comparison to the crack segment that remains along the interface. The emphasis is placed to the application of the fracture mechanics concept for the interfacial crack that propagates dynamically between the two orthotropic materials. The simulations and calculations were done by application of the Mathematica ^® programming routine. The stress intensity factors and the energy release rate are obtained for the kinked crack, as functions of the corresponding values for the interfacial crack prior to kinking. The analysis was performed of the influence of anisotropy on the crack kinking versus crack propagating along the interface competition. Due to anisotropy the kinking is easier, i.e., it is easier for the crack to kink away from the interface into the “softer” of the two materials. The oscillatory index for the case of the dynamic crack growth along the interface between the two orthotropic materials increases with crack tip speed v and with increase of the difference in stiffnesses. The practical application of this analysis could be for the interface in the glued joints and protective coatings.     

On the direct estimation of creep and relaxation functions

Two alternative approaches for estimating linear viscoelastic material functions from a single experiment under random excitation are derived and analyzed. First, Boltzmann’s superposition integral is discretized into a system of linear equations. Due to the ill-posedness of the resulting matrix equation, Tikhonov’s regularization is introduced. Second, the integral is transformed into a recursive formula, using a Prony series representation of viscoelastic material functions, in which gradient-based optimization is applied. Numerical results are provided to compare and verify the applicability of the presented numerical procedures.     

Stress relaxation in beryllia

Beryllia beams were loaded at temperature in four-point bending to a deflection of 0.001 in. or 0.002 in. and the decrease in load necessary to maintain the deflection constant was measured as a function of time. The beryllia was fine-grained, in the range ～ 1 to 7μm, and the porosity varied between 3 and 21%. The test conditions covered a temperature range of 850 to 1240°C, experiments took from 10 min to 8 h: the loads used produced initial maximum outer fibre stresses of the order 3000 to 6000 psi. A method was developed for calculating the stress distribution in a beam at any time and this was used to analyse the results. The stress relaxation process was found to be stress-activated, and the conversion of elastic to plastic strain could be expressed as a creep law having the form $$\dot \in = k_0 exp \left( {\frac{{ - Q}}{{RT}}} \right) exp \left( {\frac{{Cv\sigma }}{{RT}}} \right)$$ . The activation energy was 100 ± 2 kcal mole^?1 and the activation volume was large, probably of the order of 10³ atoms. The rate constantk ₀ was approximately proportional to the fraction of intergranular porosity and inversely proportional to the cube of the grain diameter. It is suggested that the mechanism of grain boundary sliding is consistent with the observations.     

Stress dependence on stress relaxation creep rate during tensile holding under creep-fatigue interaction in 1Cr-Mo-V steel

A quantitative analysis of the stress dependence on stress relaxation creep rate during hold time under creep-fatigue interaction conditions has been conducted for 1Cr-Mo-V steel. It was shown that the transient behavior of the Norton power law relation is observed in the early stage of stress relaxation in which the instantaneous stress is relaxed drastically, which occurs due to the initial loading condition. But after the initial transient response in a 5 hour tensile hold time, the relations between strain rate and instantaneous stress represented the same creep behavior, which is independent of the initial strain level. The value of stress exponent after transition was 17 which is the same as that of the typical monotonic creep suggested from several studies for 1Cr-Mo-V steel. Considering the value of the activation energy for the saturated relaxation stage, it is suggested that the creep rate is related to instantaneous stress and temperature by the Arrhenius type power law.     

Harmonic generation at an unbonded interface—I. Planar interface between semi-infinite elastic media

An analysis is made of the nonlinear dynamics of a system composed of an unbonded planar interface separating two semi-infinite linear elastic media. The unbonded interface, by definition, cannot support tension and hence opens up in the tension phase of a propagating disturbance, if it is not already open. The opening and closing of the interface is the origin of the nonlinearity. This is perhaps the simplest nonlinear problem involving continuous media, since the problem reduces to the consideration of a pair of independent first order ordinary differential equations involving the center of gravity and width of the gap. In the case of an incident sinusoidal wave the second harmonic generation efficiency is determined as a function of the ratio of the ambient hydrostatic pressure to the stress amplitude of the incident wave.     

How interface size,density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

Matrix-inclusion composites are known to exhibit interaction among the inclusions. When it comes to the special case of inclusions in form of flat interfaces, interaction among interfaces would be clearly expected, but the two-dimensional nature of interfaces implies quite surprising interaction properties. This is the motivation to analyze how interaction among two different classes of microscopic interfaces manifests itself in macroscopic creep and relaxation functions of matrix-interface composites. To this end, we analyze composites made of a linear elastic solid matrix hosting parallel interfaces, and we consider that creep and relaxation of such composites result from micro-sliding within adsorbed fluid layers filling the interfaces. The latter idea was recently elaborated in the framework of continuum micromechanics, exploiting eigenstress homogenization schemes, see Shahidi et al. (Eur J Mech A Solids 45:41–58, 2014). After a rather simple mathematical exercise, it becomes obvious that creep functions do not reflect any interface interaction. Mathematical derivation of relaxation functions, however, turns out to be much more challenging because of pronounced interface interaction. Based on a careful selection of solution methods, including Laplace transforms and the method of non-dimensionalization, we analytically derive a closed-form expression of the relaxation functions, which provides the sought insight into interface interaction. The seeming paradox that no interface interaction can be identified from creep functions, while interface interaction manifests itself very clearly in the relaxation functions of matrix-interface materials, is finally resolved based on stress and strain average rules for interfaced composites. They clarify that uniform stress boundary conditions lead to a direct external control of average stress and strain states in the solid matrix, and this prevents interaction among interfaces. Under uniform strain boundary conditions, in turn, interfacial dislocations do influence the average stress and strain states in the solid matrix, and this results in pronounced interface interaction.     

Adhesive force between a spherical rigid particle and an incompressible elastic substrate

Adhesion between a spherical rigid particle and an incomprssible elastic substrate is studied on the basis of the Lennard–Jones (L–J) potential, and the aim is to explore limitations of the well-known Derjaguin approximation. A new expression of the adhesive force is derived, in which the contribution from the elastic deformation of the substrate is incorporated naturally. Numerical results show that the Derjaguin approximation is valid down to particle radii of the order of the interaction range.     

Prediction of arbitrary crack growth from the interface between two dissimilar elastic materials

Based on the universal laws of stress distribution around a crack edge, the general analysis of crack start from the interface is given. The solution for the original crack is assumed to be known. In order to classify different possible cases of crack growth beginning, both a slip-region ahead of the opening zone and a core region near the crack edge are introduced. The former provides non-overlapping of the crack surfaces and removes an undesirable oscillating stress field singularity which is produced mathematically at the assumption of a completely opening crack. The latter means that we consider the damage of an elementary volume (geometrical measure of the microstructure) as a discrete fracture operaton. Two asymptotical cases are studied: the slip-region is much smaller or much larger than the cross-section of the core region. Then the stress-strain state on the core region periphery qualitatively is the same as for a completely opening or shear interface crack, respectively. A characteristic crack opening appears instead of a characteristic length of the slip-region for a blunted crack. The angles of crack departure are predicted according to different known criteria of fracture. In passing, parametric, analysis of stresses and energy density angle distributions are given. Plane and penny-shaped cracks are examined as the illustration.     

Thermal stress intensities at an interface crack between two elastic layers

The thermal stress intensities (energy release rate and stress intensity factors) due to temperature changes are derived in closed-form for an interface crack between two elastic layers of dissimilar materials. The solutions are two-dimensional and tabulated over a wide range of material and layer thickness combinations. The tables serve as rapid evaluations of the thermal stress intensities for given temperature changes. A strain gauge technique is given for determining constraint coefficients which reflect the constraint conditions during the temperature changes. The solutions are compared with results from the literature. The stress intensities due to thermal and mechanical loads are generally superimposed. As an example of application, the solutions are utilized to obtain the complete thermal and mechanical stress intensities for a four-point bend specimen.