Load Relaxation Curves Research Articles

Statistical-Probabilistic Approach to the Lifetime and Strength Degradation of E-Glass Filaments and Bundles under Constant Tensile Loading in Water

The present paper discusses the statistical features of static fatigue for E-glass multifilament tows in water. In such an aggressive environment, the glass fibres are sensitive to slow crack propagation from micron-sized flaws. Rupture and interrupted static fatigue tests under constant deformation in water, as well as tensile tests in inert environments on tows after fatigue were carried out on E-glass fibre tows that comprised around 2000 single filaments. The slow crack growth constants and the fast fracture statistical parameters for filaments were extracted from the outcome of experiments on tows, i.e., the load relaxation curves during fatigue and stress-strain curves during the tensile tests. These parameters provide a pertinent data base for the prediction of several characteristics in various conditions of fatigue for filaments and tows including statistical distributions of lifetimes and residual strengths, strength degradation during fatigue, size effects on lifetime and tow residual behaviour. Equations for calculation of filament lifetime and residual strength, and tow tensile behaviour were based on the model of slow crack growth and Weibull statistical distribution. Calculations using strength-probability-time relations provided insight into static fatigue behaviour of tows in water. Validity of the approach was assessed by the comparison of experimental and predicted tow residual behaviours.

Determination of an average quasi-linear viscoelastic model for the mechanical behavior of rat cervix

The objective of this study was to determine an average quasi-linear viscoelastic model for the mechanical behavior of rat cervix. The average model is applicable at defined displacement rates for virgin and pregnant tissues in the last trimester of pregnancy. After preconditioning, the displacement of 2 mm was applied to the distal halves of five pregnant rat’s cervices and 1 mm to the five virgin samples circumferentially. Uniaxial tension tests were employed at the displacement rates of 0.01, 0.1 and 1 mm/s randomly and were held for 10 min while the tissues were relaxed. Tensile and load-relaxation curves were well described by a quasi-linear viscoelastic model. Two average quasi-linear viscoelastic models were fitted to all 30 curves obtained from experiments for virgin and pregnant tissues. The average quasi-linear viscoelastic model coefficients were extracted using the average model equations. Cervical tissue is strongly viscoelastic. Determination of an average viscoelastic model of rat cervix may lead to a more precise description of the mechanical behavior of the virgin and pregnant tissues in the assessment of cervical insufficiency.

THE EFFECT OF DISPLACEMENT RATE ON VISCOELASTIC PROPERTIES OF RAT CERVIX

Determining the viscoelastic response of cervix at different displacement rates can provide sufficient information for the normal mechanical behavior of the tissue in assessment of cervical insufficiency. The objective of this study was to investigate the effect of displacement rate on viscoelastic properties of rat cervix. Different displacement rates were employed to measure the tensile and load-relaxation properties of cervices from virgin and 16 days post-conception pregnant rats. After preconditioning, the displacement of 2[Formula: see text]mm was applied to the distal halves of five pregnant rat’s cervices and 1 millimeter to the five virgin samples circumferentially. Uniaxial tension tests were employed at the displacement rates of 0.01, 0.1 and 1 mm/s randomly and were held for 10 min while the tissues were relaxed. Tensile and load-relaxation curves were well described by a quasi-linear viscoelastic model. Statistical analysis revealed significant correlation between the change in displacement rate and the elastic response, as well as the viscous response of the virgin samples. For pregnant samples, though, the correlation was found significant between the displacement rate and the elastic response of the tissue. Virgin tissue is strongly viscoelastic. Quantitative measurements of cervical mechanical properties will lead to a more accurate assessment of cervical insufficiency and prediction of preterm birth.

Development of a finite element model of decompressive craniectomy.

Decompressive craniectomy (DC), an operation whereby part of the skull is removed, is used in the management of patients with brain swelling. While the aim of DC is to reduce intracranial pressure, there is the risk that brain deformation and mechanical strain associated with the operation could damage the brain tissue. The nature and extent of the resulting strain regime is poorly understood at present. Finite element (FE) models of DC can provide insight into this applied strain and hence assist in deciding on the best surgical procedures. However there is uncertainty about how well these models match experimental data, which are difficult to obtain clinically. Hence there is a need to validate any modelling approach outside the clinical setting. This paper develops an axisymmetric FE model of an idealised DC to assess the key features of such an FE model which are needed for an accurate simulation of DC. The FE models are compared with an experimental model using gelatin hydrogel, which has similar poro-viscoelastic material property characteristics to brain tissue. Strain on a central plane of the FE model and the front face of the experimental model, deformation and load relaxation curves are compared between experiment and FE. Results show good agreement between the FE and experimental models, providing confidence in applying the proposed FE modelling approach to DC. Such a model should use material properties appropriate for brain tissue and include a more realistic whole head geometry.

Mechanical and structural changes of the rat cervix in late-stage pregnancy

Dysregulated remodeling of the cervix precedes preterm birth, a major cause of infant mortality and morbidity. The goal of this work was to identify changes in the mechanical properties of the cervix in late gestation. The tensile and load relaxation properties of cervices from rats 15–21 days (full term) post-conception were measured. Stiffness and load at 25% circumferential strain decreased with gestational age and correlated with the initial circumference of the cervix. Load–relaxation curves were accurately described by a seven parameter quasi-linear viscoelastic model, where three parameters associated with stiffness and load capacity decrease with gestational age and correlate with initial circumference. Time-dependent parameters did not depend on age or structure. Mechanical properties correlated with water content, but unexpectedly not with measures of collagen content, solubility, or organization. Quantitative measurements of cervical stiffness and structure will lead to a more accurate description of cervical remodeling and prediction of preterm birth.

Determination of the internal stress and dislocation velocity stress exponent with indentation stress relaxation test

Indentation stress relaxation tests were carried out on high-purity polycrystalline copper specimens at room temperature with a flat cylindrical indenter. The experimental results showed that the resulting load-time relaxation curves can be described by a power law, which coupled an internal stress and an integral constant between the effective stress and relaxation time. Then the internal stress, integral constant, and dislocation velocity stress exponent can be extracted from load relaxation curves. The derived values from this way were consistent with the results of conventional uniaxial compression stress relaxation tests. These agreements are not only useful to understand deformation (dislocation) mechanisms under the indenter, but also exhibit an attractive potential of measuring nano/micromechanical properties of materials by indentation test.

Similarity and scaling in creep and load relaxation of single‐crystal halite (NaCl)

This work explores the physical basis for Hart's mechanical equation of state in high‐temperature plasticity. The experiments seek to identify a possible microstructural basis for the “hardness” parameters associated with load relaxation curves. The experiments also seek to examine the microstructural basis for scaling in load relaxation data and to explore the relationship between creep and load relaxation. Constant stress creep and load relaxation tests were conducted on [100] oriented single crystals of halite at 700°C and stresses between 0.6 and 3 MPa. Load relaxation tests were performed at 400°C up to a stress level of 13 MPa. After testing, specimens were sectioned, and dislocation densities and subgrain size distributions were measured. Results at 700°C reveal that distributions of subgrain size in crystals crept at different stress levels are similar to each other; that is, they have the same shape but different average subgrain sizes depending on stress level. Hardness curves obtained from load relaxation experiments at different levels of work hardening were found to correspond to different average subgrain size. Load relaxation data from 700°C and 400°C belong to a single‐parameter family of curves, with hardness curves translating onto each other with a scaling slope m = 0.33 ± 0.05. Subgrain size distributions generated in creep are statistically identical to those from load relaxation. The hardness parameter, σ*, specified as the (apparent) high‐strain rate limit of stress in the load relaxation data, is approximately 50Gb/DI, where G is the shear modulus, b is the Burgers vector, and DI is the mean intercept subgrain diameter. During creep under constant stress the subgrain size evolves until a steady value is approached. The experimental data lend credence to Hart's interpretation that load relaxation data represent (nearly) constant “structure” with subgrain size playing the role of the structural variable.

Viscoelastic properties of canine temporomandibular joint disc in compressive load-relaxation

The present study was designed to investigate the mechanical properties and load-relaxation of these discs in compression. Eight discs were used for the experiments. Compression was applied to specimens up to the specified strain, and a series of load-relaxation tests was conducted on each specimen from 0.25% strain to 2.0% strain with 0.25% intervals. The load-relaxation was monitored over a period of 2 min. The elastic moduli of the canine articular discs were 30.9 and 15.8 MPa at t=0 and 120 sec, respectively, and the discs exhibited near-linear elastic characteristics at each time within a 2-min period. At all strains, the time-dependent load-relaxation curves showed that the load decreased markedly for the initial 30 sec, after which it levelled off after 120 sec with a steady non-zero level. This relaxation feature can be well represented by Kelvin’s model. It is concluded that the canine temporomandibular joint disc can be represented as a linear viscoelastic material, and that it plays an important part as a stress absorber under compression.

Analysis of load-relaxation in compressed segments of lumbar spine

Load-relaxation was measured in 12 segments of human cadaveric lumbar spine. Each segment consisted of an intact intervertebral disc attached to half of its adjacent vertebrae with the posterior elements removed. Six specimens were each compressed at six different strains (corresponding to initial loads of 0.5-2.5 kN) and, for each strain, the load-relaxation was measured for a period of 20 min at room lemperature. These load-relaxation curves were used to plot three isochrones for each specimen. All isochrones were linear (r values in the range 0.95–099). This result indicated that a linear model could be used to represent load-relaxation. Four specimens were tested at a single strain (corresponding to an initial load of about 2 kN) at 37°C for a period of 4–6 h. Load was plotted against the logarithm of time. The resulting plots did not show any peaks, indicating that relaxation effects did not predominate at any particular times during loa-relaxation. However, it was possible to model the load-relaxation as a simple linear system which can be represented as two Maxwell elements in parallel. These elements were characterized by relaxation times of 16 ± 8 min and 4.6 ± 0.8 h. Fourier transformation of the load-relaxation curves showed a gradual increase in the storage modulus and a gradual decrease in the loss modulus for frequencies of about 1 Hz and above. At these frequencies, the spine cannot function as a shock-absorber in pure compression.

Superplastic deformation behavior of 8090 aluminum-lithium alloy

The superplastic deformation behavior of crystalline materials has generally been described phenomenologically by a power law relation between the two external variables, stress ({sigma}) and strain rate ({dot {epsilon}}). A new approach for structural superplasticity has been made in this study by taking the dislocating glide mechanism as the major accommodation process for grain boundary sliding (GBS) instead of the generally accepted high temperature diffusion process. For the purpose of generating a proper relationship between {sigma} and {dot {epsilon}}, a series of load relaxation tests has been carried out at temperatures ranging from 470 C to 530 C after obtaining the required grain sizes through a thermomechanical treatment. The load relaxation test provides the flow data in a much wider range of strain rate with minimal microstructural change during the test. The flow curves of 8090 Al-Li alloy have consequently been analyzed systematically based on the internal deformation theory described. From the analysis of load relaxation test results for 8090 Al-Li alloy with d = 10{mu}m, the following important results are obtained. (1) The load relaxation curves at high temperatures consists of the plastic strain rate ({dot {alpha}}) and the grain boundary sliding rate ({dot g}). (2) The plastic flow more » curves of log {sigma}{sup 1} vs. log {dot {alpha}} can precisely be described by Eq. (3) for 8090 Al-Li alloy. (3) The grain boundary sliding appears to be a Newtonian viscous flow process characterized by Eq. (5) with M{sub g} = 1.0. (4) The condition {Sigma}{sub g} {le} {sigma} {le} {sigma}* must be satisfied for the superplastic deformation of crystalline materials. « less

The application of Hart's state variable description of inelastic deformation to Carrara marble at T < 450°C

An attempt has been made to determine if the material parameters in constitutive equations for inelastic deformation which fully accommodate the deformation history dependence of inelastic properties can be evaluated with sufficient accuracy at elevated confining pressures for such equations to be of interest in characterizing geological materials. Accordingly, a large number of constant displacement rate and load relaxation experiments (or variants thereof) have been conducted on Carrara marble at 200 MPa confining pressure in the temperature range 120 to 400°C, and the results have been interpreted in terms of Hart's state variable description of inelastic deformation. The observed mechanical behavior conforms to Hart's description, with a changeover at about 250°C from deformation rate controlled by dislocation glide controlled processes (as represented by concave upward () load relaxation curves), to rate control by strongly thermally activated processes (as represented by concave downward relaxation curves). All relaxation curves generated at a given temperature may be superposed by a translation in fixed direction in the () plane. This defines a master relaxation curve which represents what any individual relaxation curve would look like if it could be determined over a sufficiently wide range of strain rates. For Concave downward relaxation curves the master curve extends over 9 orders of magnitude of strain rate and, in consequence, substantially eases the problem of extrapolating the laboratory data to geological strain rates. The success of Hart's description in accounting for the mechanical behavior means that it is possible to avoid the steady state approximation both in the experimental evaluation of inelastic flow laws and in the application of those flow laws in geophysical modeling problems. Moreover, it provides a simple method of quantifying the mechanical state of a material and thereby is of potential significance for the problem of correlating microstructural observations with mechanical properties.

Load relaxation in steel fibres embedded in cement matrices

Twenty-four hour load relaxation curves were obtained from single fibre pull-out specimens with 60 and 80% of the peak pull-out load applied as the initial load. Two fibre types, hooked and crimped, and two matrices, cement paste and microsilica cement paste, were investigated. Tests were conducted at the ages of 1, 7 and 28 d. Two test temperatures of 22°C and 100°C were chosen Relaxation, as defined by the percent reduction in the applied initial load, was found to decrease with age and was found to increase with the applied initial load; microsilica addition resulted in a reduced relaxation. Hooked fibres were found to relax more than the crimped fibres. A high temperature of 100°C was found to significantly increase the relaxation. After 24 h of relaxation, the specimens, in general, had a poorer pull-out performance as measured by the peak pull-out load and the pull-out energy, compared to the virgin specimens.

Load relaxation in steel fibres embedded in cement matrices

Twenty-four hour load relaxation curves were obtained from single fibre pull-out specimens with 60 and 80% of the peak pull-out load applied as the initial load. Two fibre types, hooked and crimped, and two matrices, cement paste and microsilica cement paste, were investigated. Tests were conducted at the ages of 1, 7 and 28 d. Two test temperatures of 22°C and 100°C were chosen Relaxation, as defined by the percent reduction in the applied initial load, was found to decrease with age and was found to increase with the applied initial load; microsilica addition resulted in a reduced relaxation. Hooked fibres were found to relax more than the crimped fibres. A high temperature of 100°C was found to significantly increase the relaxation. After 24 h of relaxation, the specimens, in general, had a poorer pull-out performance as measured by the peak pull-out load and the pull-out energy, compared to the virgin specimens.

Load relaxation studies of germanium

A series of compressive load relaxation experiments were conducted on germanium single crystals in the temperature range 400 to 885° C. The curvature of the logσ-log\(\dot \in \) data obtained from load relaxation tests changes from concave upward to concave downward as the test temperature increases at fixed stress level, or as the strain level increases at fixed temperature. At intermediate temperatures, ∼600° C, the transition from concave upward to concave downward curvature happens on a single relaxation curve. These observations are consistent with the two-branch rheological model proposed by Hart to explain the deformation behaviour of metals and were analysed in terms of this model. The transition from concave upward to concave downward curvature could be moved to higher temperature by doping germanium with gallium, which decreases the dislocation glide velocity relative to that in pure germanium. The transition could be shifted to lower temperature by compressing samples along [1\(\bar 1\)1] rather than [1\(\bar 1\)0] because the [1\(\bar 1\)1] orientation favours cross-slip while the [1\(\bar 1\)0] orientation does not. Dislocation dipoles and straight dislocations dominated the microstructure of samples which had concave upward logσ-log\(\dot \in \) curves, while well-developed dislocation cell structures dominated the microstructure of samples which yielded concave downward curves. The observed changes in the curvature of the load relaxation curves and the dislocation structure both indicate the increased importance of dislocation climb with increasing temperature. When compared through the Orowan equation, the load relaxation results are in good agreement with published stress-dislocation velocity data.