Thermodynamic model of creep at constant stress and constant strain rate

A thermodynamic model has been developed that describes the entire creep process, including primary, secondary, and tertiary creep, and failure for both constant stress (CS) tests ($\text{σ =}\text{const.}$) and constant strain rate (CSR) tests ($\text{? =}\text{const.}$), in the form of a unified constitutive equation and unified failure criteria. Deformation and failure are considered as a single thermoactivated process in which the dominant role belongs to the change of entropy. Failure occurs when the entropy change is zero. At that moment, the strain rates in CS tests reach the minima and stress in CSR tests reaches the maximum (peak) values. Families of creep (? vs t) and stress-strain (σ vs ?) curves, obtained from uniaxial compression CS and CSR tests of frozen soil, respectively (both presented in dimensionless coordinates), are plotted as straight lines and are superposed, confirming the unity of the deformation and failure process and the validity of the model. A method is developed for determining the parameters of the model, so that creep deformation and the stress-strain relationship of ductile materials such as soils can be predicted based upon information obtained from either type of test.     

Effective creep behavior and complex moduli of fiber- and ribbon-reinforced polymer-matrix composites

This paper examines the influence of the cross-sectional aspect ratio (the thickness-to-width ratio, denoted by ) and volume concentration, c₁, of 2-D randomly oriented elliptic cylinders on the overall anisotropic creep and complex moduli of a viscoelastic composite. With such a microgeometry it is first shown that two Maxwell or two Voigt constituents generally do not make a Maxwell or a Voigt composite, but under the conditions that the ratios of the shear modulus to the shear viscosity are equal for both constituents and that both Poisson's ratios remain unchanged in the course of deformation, a Maxwell and a Voigt composite can be constructed. The transversely isotropic creep compliances are then examined as the cross-sectional shape of the elastic elliptic cylinders changes from a circular one ( = 1) to that of a long, thin ribbon ( → 0). Along all five loading directions the ribbon-reinforced composite consistently gives rise to the strongest creep resistance, and as the aspect ratio increases the creep resistance also continues to weaken, with the traditional circular fibers providing the poorest reinforcement. The real and imaginary parts of the five independent complex moduli are also investigated as a function of and c₁, and the loading frequency ω. It is found that the real parts of the complex moduli all increase with increasing ω, and as ω → ∞ these moduli all approach their respective elastic moduli. The imaginary parts of the complex moduli show two distinct trends; one is marked by a monotonic decrease with increasing c₁, and the other shows an initial increase before it decreases to zero. Finally, the complex plane/strain bulk moduli associated with various cross-sectional shapes are examined in light of the Gibiansky-Milton bounds, and it is found that all the theoretical results lie literally on the boundary of the bounds.     

The mechanical response of Hysol 4183 under constant strain rate loading and creep

Mechanics of Time-Dependent Materials - A comprehensive mechanical characterization of a polymer named Hysol 4183 subjected to either constant nominal strain rate loading or creep was carried out....     

Long-term prediction of creep strains of mineral wool slabs under constant compressive stress

The results obtained in determining the creep strain of mineral wool slabs under compressive stress, used for insulating flat roofs and facades, cast-in-place floors, curtain and external basement walls, as well as for sound insulation of floors, are presented. The creep strain tests were conducted under a compressive stress of σ _c =0.35σ _10%. Interval forecasting of creep strain was made by extrapolating the creep behaviour and approximated in accordance with EN 1606 by a power equation and reduced to a linear form using logarithms. This was performed for a lead time of 10 years. The extension of the range of the confidence interval due to discount of the prediction data, i.e. a decrease in their informativity was allowed for by an additional coefficient. Analysis of the experimental data obtained from the tests having 65 and 122 days duration showed that the prediction of creep strains for 10 years can be made based on data obtained in experiments with durations shorter than the 122 days as specified by EN 13162. Interval prediction of creep strains (with a confidence probability of 90%) was based on using the mean square deviation of the actual direct observations of creep strains in logarithmic form to have the linear trend in a retrospective area.     

Interface diffusion-induced creep and stress relaxation in unidirectional metal matrix composites under biaxial loading

Analytical solutions are developed for interface diffusion-induced creep and stress relaxation in unidirectional metal matrix composites under biaxial transverse loading. The driving force for the interface diffusion is the normal stress acting on the interface, which is obtained from rigorous Eshelby inclusion theory. The solutions are a function of the applied stress, volume fraction and radius of the reinforced-fiber, the modulus ratio between the fiber and the matrix, specially, exhibit a strong dependence of creep rate and stress relaxation behavior on the biaxial stress ratio. Moreover, the solution for the interface stress presented in this study also gives some insight into the relationship between the interface diffusion and interface slip. For the application of the solutions in the realistic composites, the scale effect is taken into account by detailed finite element analysis based on a unit cell model.     

Cumulative creep damage for unidirectional composites under step loading

The creep lifetime prediction of unidirectional composite materials under step loading, based on constant loading durability diagram, is analyzed for the two-step creep loading condition. For this purpose different nonlinear cumulative-damage laws are revisited and applied to predict creep lifetime. One possible approach to accounting for damage accumulation is provided by the continuum-damage mechanics (CDM). However, the CDM lifetime expression obtained for constant loading condition presents some drawbacks. Specifically, the upper stress range is not accommodated by CDM form. A?modification of CDM is proposed, forcing the CDM to capture the short-term creep failure. It is proven that this modified CDM (MCDM) does not yield the same predictions as the Linear Cumulative-damage law (Miner??s law). Predictions obtained from the nonlinear cumulative-damage laws are compared against synthetic lifetime generated by a micromechanical model that simulates unidirectional composites under two-step creep loading condition. Comparable deviations from Miner??s law are obtained by the nonlinear cumulative-damage laws.     

Submicron diameter nickel filaments and their polymer-matrix composites

Discontinuous nickel filaments of diameter 0.4 m and having a carbon core of diameter 0.1 m were fabricated by electroplating nickel on discontinuous carbon filaments. They exhibited a grain size of 0.016 m and electrical resistivity of about 5 × 10^–6 ·cm. In an amount as low as 7 vol.% in a polymer (polyether sulfone) matrix, they resulted in a composite exhibiting electromagnetic interference shielding effectiveness of 87 dB and reflection coefficient 0.95 at 1–2 GHz, tensile strength 52 MPa, tensile ductility 1.0%, and density 1.87 g/cm³.     

Corrosion cracking of metals at constant stress and constant strain rate

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 1, pp. 31–38, January–February, 1989.     

Reference stress approach for predicting creep deformation of metal matrix composites

Abstract

A sound, mechanics based approach, using the reference stress concept, has been provided to allow the effects of volume ratio, fibre aspect ratio, and fibre spacing on the creep behaviour of uniaxial metal matrix composites to be quickly assessed. It is shown that fibres are much more effective than particles in reducing creep deformations. In addition, volume ratio and fibre aspect ratio have a large effect on creep properties, while fibre spacing has a relatively small effect. The existence of cracks at the ends of fibres is shown to reduce seriously the effectiveness of the reinforcement. The creep properties for loading in transverse directions are much lower than for loading in longitudinal directions.

MST/2059     

Equipment for creep testing under tensile stress and hydrostatic pressure

The design and operation of equipment is described that permits creep tests to be made under independently controlled tensile stresses and superimposed hydrostatic pressures at elevated temperatures. The range of usefulness and applications of the equipment are briefly indicated.     

Piezoresistivity in continuous carbon fiber polymer-matrix and cement-matrix composites

Piezoresistivity was observed in continuous unidirectional carbonfiber cement-matrix and polymer-matrix composites. The fiber volumefraction was 2.6–7.4% and 58% for cement-matrix andpolymer-matrix composites respectively. The DC electrical resistancein the fiber direction increased upon tension in the fiber directionfor the cement-matrix composite, due to fiber-matrix interfacedegradation, but decreased upon tension for the polymer-matrixcomposite due to increase in the degree of fiber alignment.     

A comparison of constant strain rate and creep testing procedures in superplasticity

Tests were conducted on the Zn-22 wt% Al eutectoid alloy to compare experimental conditions of true constant strain rate and true constant stress when there is relatively minor grain growth. The stress-strain curves show the presence of significant strain hardening which precedes steady-state flow. In the steady-state condition, similar stresses are obtained when the strain rate is incrementally cycled on a single specimen. There is an extensive primary stage of creep in both Regions I and II, although in Region II the time involved is often very short. It is re-affirmed that, in the absence of significant grain growth, steady-state flow data may be obtained using either constant strain rate or creep testing procedures.     

Fundamentals, processes and applications of high-permittivity polymer-matrix composites

There is an increasing need for high-permittivity (high-k) materials due to rapid development of electrical/electronic industry. It is well-known that single composition materials cannot meet the high-k need. The combination of dissimilar materials is expected to be an effective way to fabricate composites with high-k, especial for high-k polymer-matrix composites (PMC). This review paper focuses on the important role and challenges of high-k PMC in new technologies. The use of different materials in the PMC creates interfaces which have a crucial effect on final dielectric properties. Therefore it is necessary to understand dielectric properties and processing need before the high-k PMC can be made and applied commercially. Theoretical models for increasing dielectric permittivity are summarized and are used to explain the behavior of dielectric properties. The effects of fillers, fabrication processes and the nature of the interfaces between fillers and polymers are discussed. Potential applications of high-k PMC are also discussed.     

The constant stress tensile creep behaviour of a superplastic zirconia-alumina composite

A detailed study was conducted to evaluate the constant stress tensile creep behaviour of a superplastic 3 mol% yttria-stabilized zirconia-20 wt% alumina composite. The comprehensive experimental results indicate that creep deformation may be expressed in the form exp(–585 000/8.3T), where is the steady-state creep rate, is the imposed stress, is the linear intercept grain size andT is the absolute temperature. Microstructural observations revealed that there is very little dislocation activity, or change in grain size or shape. A detailed analysis was conducted to evaluate the possible rate-controlling mechanisms in terms of the experimentally determined mechanical properties and the microstructural observations. Based on the maintenance of an equiaxed microstructure and the strong grain size and stress dependence, it is concluded that creep occurs by a grain-boundary sliding/grain rearrangement process.     

Deformation and failure of ice under constant stress or constant strain-rate

Fine-grained isotropic ice was tested in uniaxial compression at ?5°C. Tests were made under: (1) constant strain rate, and (2) constant stress, with total axial strains up to about 7%. Constant rate tests for the range 10^?7 to 10^?3 s^?1 gave stress/strain curves which exhibited two distinct yield points for rates up to about 10^?4 s^?1. The “initial yield point”, at which internal cracks begin to form at a high rate, occurred at strains in the range 0.03–0.6%, the strain for initial yielding increasing with strain rate. A secondary yield point occurred at axial strains close to 1%. However, above 10^?4 s^?1 the initial yield point became dominant and the secondary yield point disappeared. At the lowest rates (10^?7–10^?6 s^?1), the secondary yield point was distinct, but the initial yield occurred at a stress level equal to, or greater than, that for secondary yield. Constant stress tests for the range 0.8–3.8 MPa gave creep curves which had a minimum strain rate at strains close to 1%. For strains less than 0.2% the resolution and data sampling were inadequate for accurate determination of strain rate as a function of time or strain, but there were fairly clear indications of another strain rate minimum in the range of 0.01%–0.1% axial strain.Direct comparison of the results for constant stress and constant strain rate suggests that the two tests give much the same information when interpreted suitably. Detailed comparisons and interpretations of the data will be given in a subsequent paper.     

Experimental characterization of thermo-oxidation-induced shrinkage and damage in polymer-matrix composites

This paper focuses on the experimental characterization of thermo-oxidation in carbon-fiber-reinforced polymers (CFRPs) exposed to “high” temperatures (up to 150 °C) and “high” oxygen pressures (up to 5 bars), at the microscopic scale. Unidirectional IM7/977-2 composite specimens were aged at 150 °C under atmospheric air and under oxygen pressure (1.7 bars and 5 bars): periodic tests were carried out to characterize degradation phenomena after different aging times. The thermo-oxidation-induced resin shrinkage and fiber/matrix debonding were measured on the CFRP sample surface by confocal interferometric microscopy (CIM) and scanning electron microscopy (SEM). The results show that thermo-oxidation-induced degradation strongly depends on aging time, distance between fibers and partial oxygen pressure.     

树脂基稀土-铁系超磁致伸缩复合材料的磁致伸缩及其高频磁性能

以粉末粘结、模压成型方法,研制了0-3型的E-44环氧树脂基稀土-铁系超磁致伸缩复合材料。采用电阻应变片技术与Agilent 4294A型动态阻抗分析仪,研究了超磁致伸缩合金/环氧树脂复合材料的磁致伸缩性能及高频磁性能,并对所制备的磁致伸缩复合材料的磁导率、截止使用频率等随频率和树脂体积分数的变化规律进行了系统研究。结果表明:树脂的添加,不仅可以提高复合材料的截止频率和高频磁性能,使其具有良好的高频响应特性,其截止频率达30 MHz以上;而且通过适当选择树脂的体积分数,复合材料仍能保持良好的磁致伸缩性能,当树脂体积分数分别为20%、30%时,磁致伸缩系数分别达808×10-6、821×10-6,而当复合材料中树脂的体积分数为50%时,其磁致伸缩系数仍高达592×10-6。探讨了树脂/磁致伸缩复合材料的磁电耦合机制。      

Modelling the viscoelastic stress relaxation of glass fibre reinforcements under constant compaction strain during composites manufacturing

Viscoelastic stress relaxation of glass fibre reinforcements is commonly encountered in the manufacture of glass fibre reinforced polymer composites. A better understanding of the phenomenon, coupled with an ability to predict this behaviour, will aid improved manufacturing process control and tooling design. Finished product quality may also be bettered by virtue of increased knowledge of stresses acting within the composite product. This paper presents a simple Maxwell element-based model to both simulate and help explain the viscoelastic stress relaxation of glass fibre reinforcements under compressive strain compaction of layers during composites manufacturing. The model was validated against experimental data for reinforcement materials of different architecture, and good-to-reasonable predictions of the stress relaxation response were obtained.