Micromechanics analysis on evolution of crack in viscoelastic materials

A preliminary analysis on crack evolution in viscoelastic materials was presented. Based on the equivalent inclusion concept of micro-mechanics theory, the explicit expressions of crack opening displacement delta and energy release rate G were derived, indicating that both delta and G are increasing with time. The equivalent modulus of the viscoelastic solid comprising cracks was evaluated. It is proved that the decrease of the modulus comes from two mechanisms: one is the viscoelasticity of the material; the other is the crack opening which is getting larger with time.

Analytical techniques for indentation of viscoelastic materials

Indentation of linearly viscoelastic materials is explored using elastic-viscoelastic correspondence analysis for both conical-pyramidal and spherical indentation. Boltzmann hereditary integrals are used to generate displacement-time solutions for loading at constant rate and creep following ramp loading. Experimental data for triangle- and trapezoidal-loading are examined for commercially-available polymers and compared with analytical solutions. Emphasis is given to the use of multiple experiments to test the fidelity and predictive capability of the obtained material creep function. Plastic deformation occurs in sharp indentation of glassy polymers and is found to complicate the viscoelastic analysis. A new method is proposed for estimating a material time-constant from peak displacement or hardness data obtained in pyramidal indentation tests performed at different loading rates.

NUMERICAL AND ANALYTICAL VERIFICATION OF A MULTISCALE COMPUTATIONAL MODEL FOR IMPACT PROBLEMS IN HETEROGENEOUS VISCOELASTIC MATERIALS WITH EVOLVING DAMAGE

Composites are engineered materials that take advantage of the particular properties of each of its two or more constituents. They are designed to be stronger, lighter and to last longer which can lead to the creation of safer protection gear, more fuel efficient transportation methods and more affordable materials, among other examples. This thesis proposes a numerical and analytical verification of an in-house developed multiscale model for predicting the mechanical behavior of composite materials with various configurations subjected to impact loading. This verification is done by comparing the results obtained with analytical and numerical solutions with the results found when using the model. The model takes into account the heterogeneity of the materials that can only be noticed at smaller length scales, based on the fundamental structural properties of each of the composite’s constituents. This model can potentially reduce or eliminate the need of costly and time consuming experiments that are necessary for material characterization since it relies strictly upon the fundamental structural properties of each of the composite’s constituents. The results from simulations using the multiscale model were compared against results from direct simulations using over-killed meshes, which considered all heterogeneities explicitly in the global scale, indicating that the model is an accurate and fast tool to model composites under impact loads. Advisor: David H. Allen

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

Hybrid Materials Combining Photoactive 2,3-Didecyloxy Anthracene Physical Gels and Gold Nanoparticles

Organic/inorganic hybrid gels have been developed in order to control the three-dimensional structure of photoactive nanofibers and metallic nanoparticles (NPs). These materials are prepared by simultaneous self-assembly of the 2,3-didecyloxyanthracene (DDOA) gelator and of thiol-capped gold nanoparticles (AuNPs). TEM and fluorescence measurements show that alkane-thiol capped AuNPs are homogeneously dispersed and tightly attached to the thermoreversible fibrillar network formed by the organogelator in n-butanol or n-decanol. Rheology and thermal stability measurements reveal moreover that the mechanical and thermal stabilities of the DDOA organogels are not significantly altered and that they remain strong, viscoelastic materials. The hybrid materials display a variable absorbance in the visible range because of the AuNPs, whereas the strong luminescence of the DDOA nanofibers is efficiently quenched by micromolar amounts of AuNPs. Besides, we obtained hybrid aerogels using supercritical CO2. These arc very low-density porous materials showing fibrillar networks oil which fluorinated gold NPs arc dispersed. These hybrid materials are of high interest because of their tunable optical properties and are under investigation for efficient light scattering.

The effect of nucleation time on the growth of a microvoid in a viscoelastic material

In this paper, discussions are focused on the growth of a nucleated void in a viscoelastic material. The in situ tensile tests of specimens made of high-density polyethylene, filled with spherical glass beads (HDPE/GB) are carried out under SEM. The experimental result indicates that the microvoid nucleation is induced by the partially interfacial debonding of particles. By means of the Laplace transform and the Eshelby's equivalent inclusion method, a new analytical expression of the void strain at different nucleation times is derived. It can be seen that the strain of the nucleated void depends not only on the remote strain history, but also on the nucleation time. This expression is also illustrated by numerical examples, and is found to be of great usefulness in the study of damage evolution in viscoelastic materials.

Crack propagation in the power-law nonlinear viscoelastic material

An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented. The creep incompressilility assumption is used. To simulate fracture behavior of craze region, it is assumed that in the fracture process zone near the crack tip, the cohesive stress sigma(f) acts upon the crack surfaces and resists crack opening. Through a perturbation method, i. e., by superposing the Mode-I applied force onto a referential uniform stress state, which has a trivial solution and gives no effect on the solution of the original problem, the nonlinear viscoelastic problem is reduced to linear problem. For weak nonlinear materials, for which the power-law index n similar or equal to 1, the expressions of stress and crack surface displacement are derived. Then, the fracture process zone local energy criterion is proposed and based on which the formulas of cracking incubation time t

Viscoelastic properties of high pressure and heat induced tofu gels

Tofu gels were rheologically examined to determine their storage or elastic (G′) and loss or viscous (G″) moduli as a function of frequency within their linear viscoelastic limits. The tofu gels were made using either glucono-δ-lactone (GDL) or calcium sulphate (CaSO4·2H2O), followed by either heat treatment (heated soymilk at 97 °C prior to coagulation and subsequently held at 70 °C for 60 min, HT) or high pressure treatment (400 MPa at 20 °C for 10 min, HP). The overall moduli values of the GDL gels and CaSO4·2H2O gels of both physical treatments were similar, each gave frequency profiles expected for weak viscoelastic materials. However, although both temperature and high pressure treatments could be used to produce tofu gels, the final products were not the same. Pressure formed gels, despite having a higher overall “consistency” (increasing values of their moduli), had a proportionately higher contribution from the loss modulus (increased tan δ). Differences could also be observed using confocal scanning laser microscopy. While such treatment may give rise to differing systems/structures, with new or modified organoleptic properties, the more “open” structures obtained by pressure treatment may well cause processing difficulties if subsequent reworking or moulding is required.

Viscoelastic properties of high pressure and heat induced tofu gels

Tofu gels were rheologically examined to determine their storage or elastic (G') and loss or viscous (G '') moduli as a function of frequency within their linear viscoelastic limits. The tofu gels were made using either glucono-delta-lactone (GDL) or calcium sulphate (CaSO4 center dot 2H(2)O), followed by either heat treatment (heated soymilk at >= 97 degrees C prior to coagulation and subsequently held at 70 degrees C for 60 min, HT) or high pressure treatment (400 MPa at 20 degrees C for 10 min, HP). The overall moduli values of the GDL gels and CaSO4 center dot 2H(2)O gels of both physical treatments were similar, each gave frequency profiles expected for weak viscoelastic materials. However, although both temperature and high pressure treatments could be used to produce tofu gels, the final products were not the same. Pressure formed gels, despite having a higher overall "consistency" (increasing values of their moduli), had a proportionately higher contribution from the loss modulus (increased tan delta). Differences could also be observed using confocal scanning laser microscopy. While such treatment may give rise to differing systems/structures, with new or modified organoleptic properties, the more "open" structures obtained by pressure treatment may well cause processing difficulties if subsequent reworking or moulding is required. (c) 2007 Elsevier Ltd. All rights reserved.

A stress relaxation model for the viscoelastic solids based on the steady-state creep equation

Creep and stress relaxation are inherent mechanical behaviors of viscoelastic materials. It is considered that both are different performances of one identical physical phenomenon. The relationship between the decay stress and time during stress relaxation has been derived from the power law equation of the steady-state creep. The model was used to analyse the stress relaxation curves of various different viscoelastic materials (such as pure polycrystalline ice, polymers, foods, bones, metal, animal tissues, etc.). The calculated results using the theoretical model agree with the experimental data very well. Here we show that the new mathematical formula is not only simple but its parameters have the clear physical meanings. It is suitable to materials with a very broad scope and has a strong predictive ability.

Dynamic analysis for different finite element models of beams with viscoelastic damping layer

Many new viscoelastic materials have been developed recently to help improve noise and vibration levels in mechanical structures for applications in automobile and aeronautical industry. The viscoelastic layer treatment applied to solid metal structures modifies two main properties which are related to the mass distribution and the damping mechanism. The other property controlling the dynamics of a mechanical system is the stiffness that does not change much with the viscoelastic material. The model of such system is usually complex, because the viscoelastic material can exhibit nonlinear behavior, in contrast with the many available tools for linear dynamics. In this work, the dynamic behavior of sandwich beam is modeled by finite element method using different element types which are then compared with experimental results developed in the laboratory for various beams with different viscoelastic layer materials. The finite element model is them updated to help understand the effects in the damping for various natural frequencies and the trade-off between attenuation and the mass add to the structure.

Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders

Mathematics Subject Classification: 74D05, 26A33

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.