Singularity of dynamic stress fields around an interface crack between viscoelastic bodies

The singular nature of the dynamic stress fields around an interface crack located between two dissimilar isotropic linearly viscoelastic bodies is studied. A harmonic load is imposed on the surfaces of the interface crack. The dynamic stress fields around the crack are obtained by solving a set of simultaneous singular integral equations in terms of the normal and tangent crack dislocation densities. The singularity of the dynamic stress fields near the crack tips is embodied in the fundamental solutions of the singular integral equations. The investigation of the fundamental solutions indicates that the singularity and oscillation indices of the stress fields are both dependent upon the material constants and the frequency of the harmonic load. This observation is different from the well-known -1/2 oscillating singularity for elastic bi-materials. The explanation for the differences between viscoelastic and elastic bi-materials can be given by the additional viscosity mismatch in the case of viscoelastic bi-materials. As an example, the standard linear solid model of a viscoelastic material is used. The effects of the frequency and the material constants (short-term modulus, long-term modulus and relaxation time) on the singularity and the oscillation indices are studied numerically.

Wave propagation and the frequency domain Green's functions in viscoelastic Biot/squirt (BISQ) media

In this paper, we examine the characteristics of elastic wave propagation in viscoelastic porous media, which contain simultaneously both the Biot-flow and the squirt-flow mechanisms (BISQ). The frequency-domain Green's functions for viscoelastic BISQ media are then derived based on the classic potential function methods. Our numerical results show that S-waves are only affected by viscoelasticity, but not by squirt-flows. However, the phase velocity and attenuation of fast P-waves are seriously influenced by both viscoelasticity and squirt-flows; and there exist two peaks in the attenuation-frequency variations of fast P-waves. In the low-frequency range, the squirt-flow characteristic length, not viscoelasticity, affects the phase velocity of slow P-waves, whereas it is opposite in the high-frequency range. As to the contribution of potential functions of two types of compressional waves to the Green's function, the squirt-flow length has a small effect, and the effects of viscoelastic parameter are mainly in the higher frequency range. Crown Copyright (C) 2006 Published by Elsevier Ltd. All rights reserved.

An asymptotic analysis for one dimensional stress wave propagation in damaged viscoelastic media

A regular perturbation technique is suggested to deal with the problem of one dimensional stress wave propagation in viscoelastic media with damage. Based upon the first order asymptotic solution obtained, the characteristics of wave attenuation are studied. In fact, there exist three different time-dependent phenomena featuring the dynamic response of the materials, the first expressing the characteristics of wave propagation, the second indicating the innate effect of visco-elastic matrix and the third coming from the time dependent damage. The comparision of first order asymptotic solution with the numerical results calculated by a finite difference procedure shows that the perturbation expansion technique may offer a useful approach to the problem concerned.

Methods of Obtaining Instantaneous Modulus of Viscoelastic Solids Using Displacement-Controlled Instrumented Indentation with Axisymmetric Indenters of Arbitrary Smooth Profiles

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic-plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a "hold" period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and "hold-at-the-maximum-indenter-displacement" for determining the instantaneous modulus using spherical indenters.

Relationships between Initial Unloading Slope, Contact Depth, and Mechanical Properties for Spherical Indentation in Linear Viscoelastic Solids

Using analytical and finite element modeling, we examine the relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in viscoelastic solids with either displacement or load as the independent variable. We then investigate whether the Oliver-Pharr method for determining the contact depth and contact radius, originally proposed for indentation in elastic and elastic-plastic solids, is applicable to spherical indentation in viscoelastic solids. Finally, the analytical and numerical results are used to answer questions raised in recent literature about measuring viscoelastic properties from instrumented spherical indentation experiments.

Size-Dependent Adhesion Strength of a Single Viscoelastic Fiber

Nano-fibrillar adhesives can adhere strongly to surfaces as a gecko does. The size of each fiber has significant effects on the adhesion enhancement, especially on rough surfaces. In the present study, we report the size effects on the normal and shear strength of adhesion for a single viscoelastic fiber. It is found that there exists a limited region of the critical sizes under which the interfacial normal or tangential tractions uniformly attain the theoretical adhesion strength. The region for a viscoelastic fiber under tension with similar material constants to a gecko's spatula is 135-255 nm and that under torque is 26.5-52 nm. This finding is significant for the development of artificial biomimetic attachment systems.

Effect of annealing on the viscoelastic and viscoplastic responses of low-density polyethylene

Two series of tensile tests with constant crosshead speeds (ranging from 5 to 200 mm/min) and tensile relaxation tests (at strains from 0.03 to 0.09) were performed on low-density polyethylene in the subyield region of deformations at room temperature. Mechanical tests were carried out on nonannealed specimens and on samples annealed for 24 h at the temperatures T = 50, 60, 70, 80, and 100 degreesC. Constitutive equations were derived for the time-dependent response of semicrystalline polymers at isothermal deformations with small strains. A polymer is treated as an equivalent heterogeneous network of chains bridged by temporary junctions (entanglements, physical crosslinks, and lamellar blocks). The network is thought of as an ensemble of mesoregions linked with each other. The viscoelastic behavior of a polymer is modeled as a thermally induced rearrangement of strands (separation of active strands from temporary junctions and merging of dangling strands with the network). The viscoplastic response reflects sliding of junctions in the network with respect to their reference positions driven by macrostrains. Stress-strain relations involve five material constants that were found by fitting the observations.

The viscoelastic and viscoplastic behavior of low-density polyethylene

Three series of tensile tests with constant cross-head speeds (ranging from 5 to 200 mm/min), tensile relaxation tests (at strains from 0.03 to 0.09) and tensile creep tests (at stresses from 2.0 to 6.0 MPa) are performed on low-density polyethylene at room temperature. Constitutive equations are derived for the time-dependent response of semicrystalline polymers at isothermal deformation with small strains. A polymer is treated as an equivalent heterogeneous network of chains bridged by temporary junctions (entanglements, physical cross-links and lamellar blocks). The network is thought of as an ensemble of meso-regions linked with each other. The viscoelastic behavior of a polymer is modelled as thermally-induced rearrangement of strands (separation of active strands from temporary junctions and merging of dangling strands with the network). The viscoplastic response reflects mutual displacement of meso-domains driven by macro-strains. Stress-strain relations for uniaxial deformation are developed by using the laws of thermodynamics. The governing equations involve five material constants that are found by fitting the observations. Fair agreement is demonstrated between the experimental data and the results of numerical simulation.

Relationship between viscoelastic transition and yield behavior of phenolphthalein poly(ether ketone)

The viscoelastic behavior of phenolphthalein poly(ether ketone) (PEK-C) and its relationship to yielding was studied. The following phenomena were observed: (1) The relaxation behavior at strain near yield closely approximated that at low strain but near the T-g; (2) the temperature and strain rate dependence of yield stress could be modeled by the one-process Eyring theory and the value of the activation volume was the same as that of the glass transition; and (3) according to the Zhurkov-Bueche equation, the cu transition was related to the yield behavior. All these results indicated that the glass transition was the main factor that controlled the yield behavior. (C) 1996 John Wiley & Sons, Inc.

VISCOELASTIC PROPERTIES OF PHENOLPHTHALEIN POLY(ETHER KETONE)

Stress relaxation and dynamic mechanical behavior of phenolphthalein poly(ether ketone) (PEK-C) have been investigated. Using Ferry's reduction method, the master curve was obtained. From the experimental results, we found that the WLF equation is not appropriate in the lower-temperature range (T < T-g). The relaxation spectrum was calculated according to the first approximation method proposed by Schwarzl and Staverman. In addition to the alpha-transition region, a second transition zone is revealed at low temperature. This transition is probably due to a restricted motion of its main chain. (C) 1995 John Wiley and Sons, Inc.

YIELD BEHAVIOR AND VISCOELASTIC INTERPRETATION BY ACTIVATION VOLUMEN OF PHENOLPHTHALEIN POLYETHER KETONE

Phenolphthalein polyether ketone (PEK-C) exhibits a marked tensile yield behaviour. The yield stress depends on strain rate and the activation volume V could be evaluated from the data of the yield stress. From the creep and stress relaxation behaviour,

EFFECT OF GAMMA-RADIATION ON DYNAMIC VISCOELASTIC PROPERTIES AND THERMAL-BEHAVIOR FOR LDPE

The effect of gamma-radiation on dynamic viscoelastic properties and thermal behavior for low density polyethylene(LDPE) have been investigated. The store energy modulus (E) of the samples increased after radiation. The beta and alpha transition temperature shifted to higher temperature with increasing irradiation dose. The results of thermal analysis show that crystal melting temperature (Tm), enthalpy(DELTAHm) and crystal disapperance temperature(Td) for irradiated samples decreases with increasing of dose.

The Displacement and Strain Field of Three-Dimensional Rheologic Model of Earthquake Preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.

Scaling, Dimensional Analysis, and Indentation Measurements

We provide an overview of the basic concepts of scaling and dimensional analysis, followed by a review of some of the recent work on applying these concepts to modeling instrumented indentation measurements. Specifically, we examine conical and pyramidal indentation in elastic-plastic solids with power-law work-hardening, in power-law creep solids, and in linear viscoelastic materials. We show that the scaling approach to indentation modeling provides new insights into several basic questions in instrumented indentation, including, what information is contained in the indentation load-displacement curves? How does hardness depend on the mechanical properties and indenter geometry? What are the factors determining piling-up and sinking-in of surface profiles around indents? Can stress-strain relationships be obtained from indentation load-displacement curves? How to measure time dependent mechanical properties from indentation? How to detect or confirm indentation size effects? The scaling approach also helps organize knowledge and provides a framework for bridging micro- and macroscales. We hope that this review will accomplish two purposes: (1) introducing the basic concepts of scaling and dimensional analysis to materials scientists and engineers, and (2) providing a better understanding of instrumented indentation measurements.

Damage of a high-energy solid propellant and its effects on combustion

In order to improve the safety of high-energy solid propellants, a study is carried out for the effects of damage on the combustion of the NEPE (Nitrate Ester Plasticized Polyether) propellant. The study includes: (1) to introduce damage into the propellants by means of a large-scale drop-weight apparatus; (2) to observe microstructural variations of the propellant with a scanning electron microscope (SEM) and then to characterize the damage with density measurements; (3) to investigate thermal decomposition; (4) to carry out closed-bomb tests. The NEPE propellant can be considered as a viscoelastic material. The matrices of damaged samples axe severely degraded, but the particles are not. The results of the thermal decomposition and closed-bomb tests show that the microstructural damage in the propellant affects its decomposition and burn rate.