Phase transformations in materials studied by micro-Raman spectroscopy of indentations

 Phase transformations occurring in materials under high pressures are important for a wide range of problems in materials science and solid-state physics. Most of the results in this area have been obtained using various sophisticated high-pressure cells. We studied solid-state phase transformations and amorphisation under high non-hydrostatic pressures in very simple experiments using a combination of hardness indentation tests with micro-Raman spectroscopy. Amorphisation of diamond, that did not occur under hydrostatic loading, has been observed. Shearing and distortion of cubic diamond structure above 100 GPa resulted not only in its amorphisation, but also in the formation of threefold coordinated carbon. A carbon film that was squeezed between a SiC substrate and diamond indenter lost its graphitic structure and produced a Raman band typical of diamond-like carbon (DLC). Even for such a well-studied material as Si, principally new data have been obtained. High spatial resolution of the method allowed us to show that the Raman spectrum that was previously ascribed to a metastable Si-III phase originates from two different high-pressure phases of Si. Up to five different phases of Si were found within a single impression. Studies of reversible transformations that occur upon unloading or heating of samples by the laser beam have also been carried out. Amorphisation and/or phase transformations have been observed for some other materials, such as SiC, quartz, Ge, GaAs and other. The combination of indentation tests with micro-Raman spectroscopy provides a powerful and fast tool for in-situ and ex-situ monitoring of pressure-induced phase transformations in materials. Received: 2 January 1997 / Accepted: March 1997     

Torsion of viscoelastic spheres in contact

The theory of elastic contact between two spherical bodies is used as a basis for an extension to include the contribution of the viscous effects to the total stress for viscoelastic spheres subjected to twisting moments. Expressions relating twisting moment to penetration of slip and penetration of slip to twist angle are derived. Two term power series truncations of the relations are then used to derive approximate expressions for torsional compliance of the bodies. Validation experiments for the extended model were performed by use of a rheometer device. Applications for the model in post-harvest agriculture include extraction of material properties for use in Discrete Element Modelling of mechanical interactions of fruits and other regular shaped produce during machine handling. A specific application is performed involving the use of a rheometer to measure the coefficient of friction for fruit-fruit contact.     

Damage zone interaction due to non-oriented Vickers indentations on brittle materials

Induced damage in brittle materials due to two interacting Vickers indentations at various orientations was investigated using a three-dimensional finite element model. The model considers tensile cracking and compressive yielding behavior of ceramics. Damage evolution due to both the simultaneous and sequential double indentations was studied. The simulation results indicated that the induced damage zone patterns are strongly a function of the relative orientation of the two indenters. The existence of another nearby indentation reduces the crack size on the side closer to the first indentation but increases the overall median damage zone size. These results were validated by sequential Vickers indentation experiments on borosilicate glass. The evolved damage patterns were further rationalized based on Bousinesq and blister field stress fields. Finally, the implication of these results on material removal mechanisms due to simultaneous interaction of several grits in a ceramic grinding process is discussed.     

The normal aging viscoelastic contact problem

The problem of a mechanically smooth rigid indentor of arbitrary asymmetric curved profile being pressed against the surface of a linear viscoelastic half-space is reconsidered. A mechanical argument is used to remove restrictions and extend the range of validity of the solution given in [2] which is simplified and given for an aging material. Still, the shape of the contact area is always the same as that of some member of the one parameter family of contact areas associated with the corresponding elastic problem and the viscoelastic solution is expressed in terms of the allied elastic solutions.     

Dynamic behaviour of two-phase viscoelastic materials

Cylindrical two-phase epoxy resin specimens have been tested under oscillating loading over a wide range of temperatures and frequencies, taking into consideration the role of the interfaces between the main constituent elements of the composites. New bounds for the loss moduli, which were about 10% higher than those predicted by the law of mixtures, have been established for the case of specimens of good interfacial adhesion, a result which supports the assumption of the importance of the role of the interface region.     

微观非均匀粘弹性材料吸声性能研究

橡胶类粘弹性材料作为吸声覆盖层时,可在内部加入空腔或掺杂其它材料改善其吸声特性.当大量分布的空腔尺度远小于波长时,这种微观非均匀的材料在宏观上看是均匀的,可以用一种均匀材料来等效.本文对含小球形空腔的橡胶材料,数值计算了等效介质参数及吸声系数.研究了腔大小、含量及橡胶材料参数对吸声的影响.     

The steady-state plane normal viscoelastic contact problem

The steady-state problem is considered for a viscoelastic half-space subjected to periodic normal loading, under plane strain conditions. The case of a standard linear solid is discussed in detail and numerical results are presented.     

Relaxation in elastic and viscoelastic materials

The mechanical compliance and modulus retardation/relaxation functions are examined in terms of a general behaviour which contains more than one process. An analytical approach to the transformation in the anelastic response between the compliance and the modulus is derived and applied to a cooperative model of relaxation behaviour. In particular it is shown that mechanical viscoelasticity is equivalent to the anomalous low frequency dispersion process that has been observed in dielectrics containing quasifree charges. Comparison with published experimental data over a wide range of solid materials shows the validity of the cooperative model to mechanical relaxation.     

The constitutive equation of a complete nonlinear viscoelastic material

Summary The present paper is concerned with a more general form of the constitutive equation for viscoelastic materials as given by the authors in [1] and [2]. The generalization consists in assuming the instantaneous part of deformation to be a nonlinear function of the time-dependent stress state. The constitutive equation is obtained on the basis of the generalized superposition principle formulated in [1] the sense of which is presently completed and analyzed from the mathematical point of view. It is shown that the present theory includes as a particular case the theory of creep for metals given byOdqvist [3].

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Zusammenfassung Die vorliegende Arbeit beschäftigt sich mit einer allgemeineren Form der Materialgleichung für viskoelastische Stoffe, als sie von den Autoren in [1] und [2] angegeben wurde. Die Verallgemeinerung besteht darin, daß der augenblickliche Anteil der Deformationen als nichtlineare Funktion des zeitabhängigen Spannungszustandes angenommen wird. Die Materialgleichung wird aufgrund des verallgemeinerten Superpositionsprinzips, wie es in [1] formuliert wurde, erhalten; dieses wird nun vervollständigt und einer mathematischen Analyse unterzogen. Es wird gezeigt, daß die vorliegende Theorie die Kriechtheorie der Metalle, wie sie vonOdqvist [3] angegeben wurde, als Spezialfall enthält.

     

Nonlinear compressive deformation of viscoelastic porous materials

Two nonlinear viscoelastic solutions are presented for a porous, foam type material. The first is for the hydrostatic compression of the foam, while the second is for the one-dimensional compression of an infinite slab of the material. Relative to the particular viscoelastic constitutive equation employed, the first solution is exact, whereas the second, obtained through the use of a physical hypothesis, is approximate. Both solutions predict the macroscopic, average stress in the foam, required by the corresponding deformation processes. The theoretical results are compared with experimental measurements on a foam material at a porosity of 48.5%. The effect of material hysteresis is revealed and discussed.     

Phenomenological model of slowly aging viscoelastic materials

The article deals with the model of slowly aging viscoelastic material which makes it possible to take the effect of the load on the aging process into account. From the overall reaction the component is isolated which does not depend on the aging process, and to describe it, known dependences for material, invariant in time, are used.Translated from Problemy Prochnosti, No. 7, pp. 3–5, July, 1990.     

The viscoelastic behavior of short-fiber composite materials

This article examines the viscoelastic behavior of unidirectional short-fiber composites. Each fiber is approximated by an ellipsoidal elastic inclusion embedded in a viscoelastic matrix. The static correspondence principle which relates the viscoelastic problem to the elastic problem is applied to the modified expression of the effective elastic moduli of short-fiber composites originally derived by the authors. Numerical examples for various fiber aspect ratios are shown based upon the collocation approximation method. Comparisons of the result with the self-consistent method are also presented.     

A review of fracture in viscoelastic materials

This review is written in honor of Max L. Williams who not only started this International Journal of Fracture (the author’s Ph.D. advisor. Originally the Journal was called International Journal of Fracture Mechanics) but who had a seminally fundamental influence on the course of fracture mechanics in general, and specifically as applied to the time dependent failure of elastomers/polymers. In view of that background this article reviews developments over more than 50 years, as colored by my own experiences in regard to this topic. It seems appropriate to include a historical perspective that starts during pre-journal times and addresses the need for understanding time dependent processes governing fracture in rate sensitive materials. To the largest extent, the rate dependence is important where polymers are involved, though under more limited conditions metals and igneous solids as well as ligneous ones exhibit time dependent fracture characteristics. Such facts notwithstanding, the major discussion in this contribution is devoted here to the time dependent fracture of polymeric materials, and elastomeric ones in particular. The emphasis will be thus on time dependent issues governed primarily by the fracture processes in elastomeric solids, which have evolved largely in parallel to problems devoted to the more rigid polymers. Because consideration of fracture of the rigid polymers has often, if not usually, minimized the time dependence, only cursory attention is paid to these, in spite of the fact that they constitute a very important class of materials in the modern engineering community. From an engineering perspective this review is motivated also by an exposition of a persistent lack of knowledge concerning time dependent fracture issues. Most of the work attached to the notion of viscoelastic fracture is—intentionally or by omission—associated with the phenomenon of crack growth under steady state conditions with the expectation that this understanding leads implicitly to resolution of problems governed by transient loadings. Besides reviewing the historical evolution of the knowledge in this field over the past half century, it is a main purpose of this paper to offer information that has either been ignored or has not been explored (this includes the work of the author), but which contradicts this “popular” perception. It is thus an intentionally large part of this presentation which documents compelling motivation for addressing fracture aspects, that are generally important from an engineering design and analysis point-of-view: specifically, it is intended to illustrate the remarkable degree by which the steady state solution to crack propagation deviates from experimental information when transient conditions prevail, and the large range of time scales over which this failure behavior is observed.     

Analysis of viscoelastic behaviour of transversely isotropic materials

In this paper a constitutive equation to describe the mechanical behaviour of materials, reinforced with unidirectional fibres, is presented. The material behaviour of both matrix and fibres may be viscoelastic. The constitutive equation is a linear relation between the second Piola–Kirchhoff stress tensor and the Green–Lagrange strain tensor. The effective relaxation functions in the constitutive equation are composed of component relaxation functions employing the structural model of Hashin and Rosen. A two-dimensional membrane element incorporating this constitutive equation is implemented in a finite element program. The results of several calculations are presented in order to demonstrate the possibilities of the numerical tool. One calculation concerns a square membrane with a circular hole in its centre. The effect of fibre orientation on deformation and stresses will be displayed for this structure as well as for another membrane structure.