南京地区粉土的不排水三轴压缩试验

通过全自动三轴仪进行了南京地区粉土的三轴不排水的试验,研究了围压和干密度对应力-应变曲线、孔隙水压力曲线和有效主应力比曲线的影响.试验表明:高围压状态下粉土试样呈现出弱应变软化型,而低围压状态下呈现出应变稳定型;低围压下试样在加载初期产生正孔隙水压力,随后产生负孔隙水压力,其后基本保持稳定;干密度越大,主应力差峰值越大,表现出较大的剪胀性,孔隙水压力易出现负孔隙水压力;干密度值较高时,土样处于密实状态,表现出剪胀特性,有效主应力比-应变曲线近于应变软化型;围压较低、干密度较大时,试样易表现出软化特征,试样出现剪切带破坏,强度明显下降.     

A visco-elastoplastic constitutive model for large deformation response of polycarbonate over a wide range of strain rates and temperatures

The principal purpose in this paper is to present a combined experimental and analytical study to understand the mechanical behavior of polycarbonate (PC) under a wide range of temperatures (−40 °C to 100 °C) and strain rates (0.001 up to 5000 s⁻¹). Firstly, the experiments were conducted to obtain stress-strain response from low to high rates and temperatures. Then a robust physically consistent rate and temperature-dependent constitutive model is proposed to characterize large deformation mechanical behavior of PC. According to viscoelastic theory, a nonlinear-viscoelastic model is employed to understand the elastic response. Yielding behavior is described via cooperative model. As respect to post-yield regime, it is described by the conflict and interaction between softening and hardening behavior based on the integral-form softening and kinematic hardening model. The proposed constitutive model is successfully validated by the excellent agreement between model prediction and experiment results.     

Stress softening in carbon black-reinforced vulcanizates. Strain rate and temperature effects

Stress softening of carbon black-reinforced butadiene-styrene rubber was studied as a function of the rate and temperature of the original tensile deformation. To a good approximation, stress softening depends on the product of the extension rate and a temperature function which is analytically well represented by the familiar Williams-Landel-Ferry relationship. When the elongation of the original deformation is also varied, a good correlation is obtained between stress softening and the maximum stress attained in the original extension, irrespective of the particular combination of strain, strain rate and temperature used to achieve this stress. Variables which tend to increase the stiffness of the vulcanizate, such as increased degree of crosslinking or carbon black chain structure, also increase stress softening; dilution by plasticizers decreases it. Prestressing at high strain rates and low temperatures affects the stress–strain curve of the softened vulcanizates beyond the elongation of the original extension. Connections are established between stress softening and viscoelastic and failure behavior. The evidence presented favors the contribution of several mechanisms to the general phenomenon of stress softening. These are thixotropy of transient filler structures, network chain rupture, and breakage of “permanent” filler structure. The latter appears to be most important at high strain rates, low temperatures, and with highly reticulated “structure” blacks.     

Characterization of nonideal networks by stress-strain measurements at large extensions

It is shown how a characterization of unfilled, amorphous rubber networks can be evaluated from uniaxial stress-strain measurement data. Beside the cross-linking density, the relative scission probability during the curing procedure is evaluated, which determines the amount of dangling free chain ends and the number of trapped entanglements. These values are found from the C₂ term of the Mooney-Rivlin equation by using the predictions of a tube model. A necessary requirement for applying stress-strain measurements at large extensions is the consideration of the finite extensibility component of the reduced stress. It is taken into account by using a numerical procedure, which derives from a series expansion of the inverse Langevin approximation. The experimental results found at natural rubber networks cross-linked with thiuram (TMTD) and peroxid (DCP) show that network defects cannot be neglected in the DCP networks. They are assumed to be connected to the worse tensil strength properties compared to the TMTD networks. © 1993 John Wiley & Sons, Inc.     

Modeling the rheology of gelatin gels for finite deformations. Part 1. Elastic rheological model

The rheological behavior of gelatin gels is studied through a constitutive equation derived in the literature from the classical hyperelasticity theory by using a nonlinear strain energy density. Gelatin gels are assumed to be an elastic solid here, which at a given maturation time has a degree of physical cross-links composing a permanent elastic network. It is also studied in particular: (a) the validation of the elastic rheological model proposed here in relation to the prediction of two data sets pertaining to different experimental tests (shear and simple compression) by using fixed values of rheological parameters, (b) the increase of the stress-strain nonlinearity with increasing maturation time, at a given protein concentration, (c) the evolution of the stress-strain nonlinearity with increasing gelatin concentration. It is found that gelatin gels exhibit a strong nonlinear strain energy density, which is expressed through two shear modules related to nucleation and growing of junction zones.     

An experimental investigation of the large-strain tensile behavior of neat and rubber-toughened polycarbonate

The large-strain tensile behavior of polycarbonate and polycarbonate filled with several volume fractions (f) of rubber particles is studied via an optical technique. Digital image correlation is used to determine, in two dimensions, the local displacement gradients and full-field displacements during a uniaxial tension test. Full-field strain contours, macroscopic true stress-strain behavior, and local volumetric strain are reduced from the raw test data. Full-field strain contours exhibit a decreasing degree of localization with increasing f. The true stress-strain results show a decrease in modulus, yield stress, post-yield strain softening, and subsequent strain hardening with increasing f. The volumetric strain decreases with increasing f as well. In the case of the neat polymer, comparisons are made to a three-dimensional finite element simulation.     

Stress softening of NR reinforced by in situ prepared zinc dimethacrylate

The stress softening effect of nature rubber (NR) reinforced by in situ prepared zinc dimethacrylate (ZDMA) was studied. Degree of stress softening effect (Ds) in the 4th stress–strain cycle of the NR with 10 phr (parts per hundreds of rubber) ZDMA was only 2.23 (strain = 100%), whereas it reached to 59.98 at 50 phr ZDMA (strain = 200%). The stress softening effects of carbon black filled into NR, and compared with the ZDMA effect, was also studied here. Mooney–Rivlin semiempirical equation was introduced here to analysis the stress–strain behavior of the NR vulcanize filled with in situ prepared ZDMA, and the results showed that the ZDMA/NR system has an obvious Payne effect which is in good agreement with the stress softening effect. Crosslink density analysis indicated a high ionic crosslink density in the NR filled with high content ZDMA, which contributed to the low elastic recovery of the stress softening. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Elasticity of real networks: Comparison of molecular theory with experiments

Predictions of the theory of elasticity of real networks are compared with results of experiments. The shape of the stress-strain curve for networks in the dry and swollen states and over wide ranges of strain, both in tension and compression, agrees with results of calculations based on the theory. The theory is also in close agreement with results of multiaxial stress-strain experiments and with the predictions of the degree of crosslinking obtained from measurements of the modulus. The theory may additionally be applied to the analysis of birefringence. The assumption of the linear additivity of the elastic and mixing free energies in a swollen network leads to results which are in agreement with experimental findings on different crosslinked systems.     

Stress-strain relations of steel fiber reinforced concrete under repeated compressive load

The purpose of the present paper is to examine the hysteretic stress-strain behavior of steel fiber reinforced concrete and steel fiber reinforced mortar under uniaxial compression and to propose mathematical expressions of stress-strain curves based on experimental data. The stress-strain relations are examined in terms of the volume fraction and the aspect ratio of steel fiber. It is indicated in this paper that the normalized stress - strain curves can be described by the proposed simple numerical model with a fairly good accuracy.     

Langevin-elasticity-theory-based description of the tensile properties of double network rubbers

A previously proposed and successfully tested constitutive equation denoted by the ABGIL code (a combination of the Arruda-Boyce equation based on the Langevin elasticity theory and a constraint term based on tube theories; strain-induced increase in the finite extensibility parameter is assumed) has been found to provide a good basis for quantitative interpretation of the stress-strain data recently obtained by Mott and Roland on double networks of natural rubber, prepared by introducing additional crosslinks (second network) into a first network stretched to various extents. Experimental information on properties of the first and second networks has been used to obtain their ABGIL parameters and to calculate, under the common assumption of additivity of contributions, the stress-strain properties and residual stretch of the resulting double networks. The predictive ability of the ABGIL equation has been found to be very good. Effects of the finite extensibility of network chains appear to be significant in double networks while the possible role of orientational crystallization cannot be excluded.     

Sulphonated polyisobutylene telechelic ionomers: 12. Solid-state mechanical properties

The solid-state mechanical properties of well defined sulphonated polyisobutylene telechelic ionomers are presented. Specifically, the effect of (1) molecular architecture, (2) molecular weight, (3) type of cation used for neutralization and (4) excess neutralizing agent has been investigated. In addition, the effect of moisture and ionic plasticizer on the stress-strain behaviour has also been studied.

These ionomers do not display the characteristic small-angle X-ray scattering (SAXS) peak, which is indicative of the presence of clusters, above a number-average molecular weight of about 10 000. However, below this molecular weight a weak shoulder is sometimes observed on the SAXS curve. The tri-arm species form a network structure at ambient temperatures which results in materials with good mechanical properties. The mechanical properties of the linear difunctional species are inferior to those of the three-arm star trifunctional species due to a less well developed network structure. The monofunctional species are very tacky at ambient temperatures and cannot be handled as solid materials. However, by their incorporation into the trifunctional systems they do serve as a model for ‘dangling ends’. As expected, these blends display significantly different properties than those possessed with the pure trifunctional species.

Addition of excess neutralizing agent significantly increases the high deformation properties with little effect on Young's modulus. A simple morphological model has been postulated in which it is suggested that the excess neutralizing agent resides at the ionic sites rather than being uniformly distributed throughout the matrix. Zinc-neutralized ionomers show stress-strain behaviour which is comparable to the potassium- and calcium-neutralized materials at ambient conditions, but the softening temperature is lower for the zinc neutralized material. Water absorption in these materials is relatively low. Addition of zinc stearate, an ionic plasticizer, facilitates melt processing by lowering the viscosity at high temperatures yet at ambient temperatures it crystallizes and acts as a reinforcing filler thus increasing Young's modulus.     

The tensile properties of strain‐crystallizing vulcanizates. III. The superiority of conventional over peroxide vulcanizates in terms of network microstructure

It is proposed that, when vulcanization is performed using peroxides, crosslinking leads to a simple network, whereas in conventional vulcanization crosslinking a partially interpenetrating polymer network (PIPN) is formed. Two unfilled polyisoprene networks of similar crosslink density, produced with dicumyl peroxide and 2‐bisbenzothiazole‐2,2′‐disulfide/sulfur formulations, were compared with respect to the effect of strain rate on their stress–strain and hysteresis curves at room and elevated temperatures. At high elongations, the stress–strain curves for peroxide vulcanizates show a steeper upturn than for conventional vulcanizates, but have lower tensile strength and elongation at break. On increasing the extension rate, stress–strain curves for peroxide vulcanizates rise less steeply, while conventional vulcanizates rise more steeply. For both vulcanizates the hysteresis ratio decreases on increasing the rate at which samples are extended and retracted. The effect on conventional vulcanizates is less than on peroxide vulcanizates. It is suggested that chains in peroxide networks disengage increasingly rapidly at higher strains, allowing increased strain‐induced crystallization. Rapid strain‐induced crystallization leads to low ultimate tensile strength (UTS). In more complex PIPNs, the disengagement and alignment of chains are retarded. The increased nonuniform extension of chains promotes early strain‐induced crystallization at low extensions, but overall it reduces the rate of crystallization, which occurs over a wider range of strains. This improves UTS and elongation. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 876–884, 2006     

Identification of strain-softening constitutive relation from uniaxial tests by series coupling model for localization

Recent studies of path stability in inelastic bifurcation problems have shown that, even if the specimen is stable, strain softening in uniaxial tests must localize right after the peak stress state into the smallest length permitted by the material, which is approximately equal to the characteristic length of nonlocal continuum. Without knowing this length, the uniaxial stress-strain relation cannot be identified from uniaxial test data. The post-peak stress-strain relation is analyzed on the basis of a series coupling hypotheses. Van Mier's uniaxial compression test results for specimens of different lengths show this hypothesis to be valid.     

Constitutive model and failure criterion for orthotropic ceramic matrix composites under macroscopic plane stress

To predict the nonlinear stress-strain behavior and the rupture strength of orthotropic ceramic matrix composites (CMCs) under macroscopic plane stress, a concise damage-based mechanical theory including a new constitutive model and two kinds of failure criteria was developed in the framework of continuum damage mechanics (CDM). The damage constitutive model was established using strain partitioning and damage decoupling methods. Meanwhile, the failure criteria were formulated in terms of damage energy release rate (DERR) in order to correlate the failure property of CMCs with damage driving forces, and the maximum DERR criterion and the interactive DERR criterion were suggested simultaneously. For the sake of model evaluation, the theory was applied to a typical CMC with damageable and nonlinear behavior, that is, 2D-C/SiC. The damage evolution law, strain response and rupture strength under incremental cyclic tension along both on-axis and off-axis directions were completely investigated. Comparison between theoretical predictions and experimental data illustrates that the newly developed mechanical theory is potential to give reasonable and accurate results of both stress-strain response and failure property for orthotropic CMCs.     

Tensile properties and stress relaxation of polypropylene at elevated temperatures

Samples of isotactic polypropylene(PP) were subjected to stress-relaxation experiments after simple tensile tests at four strain rates and at different levels of temperature. The relaxation moduli were determined in the range of temperature between 20 and 80°C with a relaxation period of 1200s duration. The activation energy value of the shift factor was determined using the time-temperature superposition principle. The calculated stress-strain curves and stress-relaxation curves were obtained from constitutive equations based on an overstress theory in which the temperature dependence of viscosity and the activation energy were considered. The temperature dependence of viscosity was amenable to an Arrhenius type equation. The quasi-equilibrium stress depends on both the current strain and the temperature. The calculated results were obtained by the proposed constitutive equation and compared with the data. The proposed constitutive equations based on the overstress model explain well the viscoelastic-plastic behavior of PP samples.     

Stress versus strain relationship of high strength concrete under high lateral confinement

A common application of high strength concrete (HSC) is in columns subjected to large compressive forces. However, a major problem is the insufficient ductility available in HSC columns. To determine the required lateral reinforcement to maintain sufficient ductility, a good understanding of the stress-strain behaviour of confined concrete needs to be established. This paper describes a testing program carried out to obtain experimental data of complete (ascending and descending) stress-strain relationships between axial stress, axial strain and lateral strain for HSC. Compressive strengths of concrete tested were 100 MPa and 60 MPa. The confining pressures used were 4 MPa, 8 MPa and 12 MPa. A total of 18 stress-strain curves are presented. The experimental results obtained seem to indicate that, for high confining pressures, the lateral strain at peak stress for 100 MPa concrete was 20% less than that of the 60 MPa concrete.     

A thermodynamically consistent, nonlinear viscoelastic approach for modeling glassy polymers

A thermodynamically consistent nonlinear viscoelastic constitutive theory is derived to capture the wide range of behavior observed in glassy polymers, including such phenomena as yield, stress/volume/enthalpy relaxation, nonlinear stress-strain behavior in complex loading histories, and physical aging. The Helmholtz free energy for an isotropic, thermorheologically simple, viscoelastic material is constructed, and quantities such as the stress and entropy are determined from the Helmholtz potential using Rational Mechanics. The constitutive theory employs a generalized strain measure and a material clock, where the rate of relaxation is controlled by the internal energy that is likewise determined consistently from the viscoelastic Helmholtz potential. This is perhaps the simplest model consistent with the basic requirements of continuum physics, where the rate of relaxation depends upon the thermodynamic state of the polymer. The predictions of the model are compared with extensive experimental data in the following companion paper.     

Disorder effects on the strain response of model polymer networks

Molecular dynamics simulations are used to investigate polymer networks made by either end-linking or randomly crosslinking a melt of linear precursor chains. The resulting network structures are very different, since end-linking leads to nearly ideal monodisperse networks, while random crosslinking leads to polydisperse networks, characterized by an exponential strand length distribution. Networks with average strand length 20 and 100 were generated. These networks were used to study the effects of disorder in the network connectivity on observables averaged either over the entire network or selected sub-structures. Heterogeneities in the randomly crosslinked networks cause significant differences in the localization of monomers, however, neither the localization of crosslinks nor the microscopic strain response are significantly affected. Compared to end-linked networks, randomly crosslinked networks have a slightly increased tube diameter, and as a result a slightly decreased shear modulus, but otherwise identical stress-strain behavior. For the investigated systems, we conclude that the microscopic strain response, tube diameter, and stress-strain relation are all insensitive to the heterogeneities due to the linking process by which the network were made.