Prediction Of Stress Relaxation Research Articles

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.

Sealing force prediction of elastomeric seal material for PEM fuel cell under temperature cycling

This paper is to study the sealing force of elastomeric seal material used for PEM fuel cell under temperature cycling. Stress relaxation and thermal stress of liquid Silicone rubber (LSR) seal material under temperature cycling is discussed. It is found that thermal expansion or contraction is the major contributor to the compressive stress developed in the LSR seal. The classical Maxwell model including the time-temperature shift can predict stress relaxation at a given temperature, but fail in calculation of thermal stress when there is temperature change. Experimental data show that material stiffness increased if the material had been aged at a higher temperature. This change of material stiffness was quantified experimentally and included in a modified Maxwell equation. The modified model appears to predict the sealing force accurately. A temperature profile was then used to demonstrate the sealing force development during startup, operation and shutdown periods of a PEMFC stack. Similar analysis can be applied to other polymeric materials under temperature variation which exhibit stress relaxation and material aging.

On the “elastic stiffness” in a high-cycle accumulation model — continued investigations

The high-cycle accumulation (HCA) model proposed by the authors can be used to predict permanent deformations or stress relaxation due to a large number (e.g., several millions) of load cycles with relative small strain amplitudes (<10−3). The predicted stress relaxation depends on the isotropic “elastic stiffness”, [Formula: see text], used in the HCA model. To calibrate the bulk modulus, K, the rate of pore pressure accumulation obtained from an undrained cyclic test and the rate of volumetric strain accumulation measured in a drained cyclic test are compared. Poisson’s ratio, ν, can be determined from the shape of the stress relaxation path measured in an undrained test with anisotropic consolidation stresses and strain cycles. Unfortunately, the calibration of K shown for a medium coarse sand in a previous paper by Wichtmann et al. in 2010 was affected by membrane penetration effects. Consequently, all further studies have been performed on a fine sand for which membrane penetration is negligible. The present paper reports on the new results. The strong pressure dependence of K and its independence from amplitude found in the previous study could be confirmed by the new tests. In addition, the new experimental results reveal a density dependence of K, while the bulk modulus is rather independent of stress ratio. Furthermore, for the first time Poisson’s ratio, ν, used in the HCA model has been calibrated based on tests performed with different amplitudes, densities, and initial stresses.

Modeling Stress-Relaxation Behavior of the Periodontal Ligament During the Initial Phase of Orthodontic Treatment

The periodontal ligament is the tissue that provides early tooth motion as a result of applied forces during orthodontic treatment: a force-displacement behavior characterized by an instantaneous displacement followed by a creep phase and a stress relaxation phase. Stress relaxation behavior is that which provides the long-term loading to and causes remodelling of the alveolar bone, which is responsible for the long-term permanent displacement of the tooth. In this study, the objective was to assess six viscoelastic models to predict stress relaxation behavior of rabbit periodontal ligament (PDL). Using rabbit stress relaxation data found in the literature, it was found that the modified superposition theory (MST) model best predicts the rabbit PDL behavior as compared to nonstrain-dependent and strain-dependent versions of the Burgers four-parameter and the five-parameter viscoelastic models, as well as predictions by Schapery's viscoelastic model. Furthermore, it is established that using a quadratic form for MST strain dependency provides more stable solutions than the cubic form seen in previous studies.

Recent Advances in Creep Modelling of the Nickel Base Superalloy, Alloy 720Li.

Recent work in the creep field has indicated that the traditional methodologies involving power law equations are not sufficient to describe wide ranging creep behaviour. More recent approaches such as the Wilshire equations however, have shown promise in a wide range of materials, particularly in extrapolation of short term results to long term predictions. In the aerospace industry however, long term creep behaviour is not critical and more focus is required on the prediction of times to specific creep strains. The current paper illustrates the capability of the Wilshire equations to recreate full creep curves in a modern nickel superalloy. Furthermore, a finite-element model based on this method has been shown to accurately predict stress relaxation behaviour allowing more accurate component lifing.

Stress Relaxation Continuum Damage Constitutive Equations for Relaxation Performance Prediction

Stress relaxation constitutive equations based on Continuum Damage Mechanics, Kachanov-Robatnov creep model, and stress relaxation equation has been developed by analyzing stress relaxation damage mechanisms and considering the relationship that stress relaxation is creep at various stresses. And, the constitutive differential equations were integrated to predict stress relaxation performance by using numerical analysis technique. In order to validate the approach, the predicted results are compared to the experimental results of uni-axial isothermal stress relaxation tests conducted on 1Cr10NiMoW2VNbN steel with the same temperature of creep tests. Good agreement between results of relaxation tests and the predicted results indicates that the developed constitutive models can be used in the relaxation behavior evaluation of high temperature materials.

Residual Stress Relaxation in CFRP Cross-ply Laminate

We measured residual stress relaxation in epoxy-based CFRP laminates and cyanate-based CFRP laminates. We estimated the residual stress in symmetric cross-ply laminates by measuring the curvature of unsymmetric cross-ply laminates and investigated the relaxation of the residual stress by measuring the curvature of unbalanced laminates in a nitrogen environment. Our experimental results demonstrated that the residual stress in both kinds of laminate can decay by approximately 15% after 500 hours at 40°C. The stress relaxation can be modeled by the power law model. Viscoelastic parameters were obtained by a quasi-static tensile test to predict stress relaxation. The validity of the prediction is discussed.

Creep behavior of the F82H steel under irradiation with 17 MeV protons at 300 °C

Although fusion blankets are exposed to severe irradiation, its rear side would stay at rather a modest condition. In this research, the irradiation-induced deformation of F82H IEA-heat steel at 300 °C was examined. A torsion creep apparatus with a strain resolution of ∼10 −7 was used with 17 MeV protons (2 × 10 −7 dpa/s). At the lowest stress of 30 MPa, deformation in the direction against applied stress was observed. This ‘negative creep’ was attributed to the increase in elastic modulus due to irradiation. Such an effect was compensated for each measurement based on the modulus data measured during irradiation. Stress exponent n of irradiation creep rates was 1.5, very close to that of creep strain at 5 dpa of pressurized tubes. The predicted stress relaxation was slower than that for 5% cold-worked Type 316L steel, resulting mainly from the difference in n, smaller and closer to unity in the latter.

Numerical simulations and experimental measurements of stress relaxation by interface diffusion in a patterned copper interconnect structure

We describe a series of experiments and numerical simulations that were designed to determine the rate of stress-driven diffusion along interfaces in a damascene copper interconnect structure. Wafer curvature experiments were used to measure the rate of stress relaxation in an array of parallel damascene copper lines, which were encapsulated in a dielectric, and passivated with an overlayer of silicon nitride or silicon carbide. The stress relaxation was found to depend strongly on the choice of passivation. Three-dimensional finite element simulations were used to model the experiments, and showed that this behavior is caused by changes in the diffusivity of the interface between the copper lines and the passivation. By fitting the predicted stress relaxation rates to experimental measurements, we have identified the interfaces that contribute to stress relaxation in the structure, and have estimated values for their diffusion coefficients.

Relaxation and creep phenomena in shape memory alloys. Part I: Hysteresis loop and pseudoelastic behavior

To describe the behavior of SMA we use a thermomechanical model, founded on a free energy which is a convex function with respect to the strain and to the martensitic volume fraction, and a concave one with respect to the temperature. The material parameters of the model are experimentally determined. In part I we prove that the model can describe the existence of the hysteresis loop and the pseudoelastic behavior of the SMAs. In Part II we show that the model can predict stress relaxation and strain creep during martensitic transformation, and we compare this predictions with the corresponding experimental results obtained by us.

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.

A Mechanical Equation of State for Inelastic Deformation of Iron: An Analytic Description

The applicability of two familiar analytic descriptions of micromechanical deformation as equations of state for polycrystalline iron is discussed. These equations are the power law and the relationship based on reaction rate theory. It is shown that the reaction rate description fails to describe adequately individual stress relaxation events without invoking undue complexity from use of adjustable parameters. Moreover, even in that case, this formulation lacks the predictive capability required in an equation of state. Conversely, the power law is found not only to describe stress relaxation data properly but also to provide the capability of predicting stress relaxation following initial deformation by different loading paths. It thus appears to represent an equation of state for the material.

Discussion of “Stress Relaxation in Tension of CA 172 Copper-Beryllium” by R. P. Goel

In a recent publication, R. P. Goel has attempted to predict the 40-year stress relaxation behavior of CA 172 copper-beryllium with the use of temperature accelerated tests. The stress relaxation data were collected at four temperatures between 25 and 181/sup 0/C for times up to about 1000 h. To predict stress relaxation after 40 years, the Arrhenius equation was used to compensate time with temperature. It is shown that for the data presented in the paper the method used to compensate time with temperature is unsound, and as a result large errors occur in estimating long-time behavior. This error leads to an underestimate of stress remaining at long times and could preclude the use of alternative materials or could lead to component overdesign. (JRD)

Use of Leicester's ?rheological model for mechano-sorptive deflections of beams?

The model for mechano-sorptive deformation proposed by Leicester is used to predict stress relaxation of wood drying under constraint from apparent creep of drying wood under constant load. The predictions are compared with measurements on four pairs of beams, one beam in each pair being tested under constant load, the other at constant deflection. Agreement was sufficiently close to demonstrate the value of the model.