On the studies of residual stresses in glass plates

The theoretical foundation of the photoelastic methods being presently used for measuring and analyzing residual stresses in glass is insufficient for studying development of transient viscoelastic stress states in glass plates during tempering process and for an explanation of the actual material behavior. It is shown that the basic knowledge of photoviscoelastic effect in glass over a wide range of electromagnetic radiation and temperature is necessary for such on analysis. Some photoelastic properties of plate glass are presented.     

Study of basic patterns of light scattering in aqueous solution of milling yellow

Basic characteristics of light scattering in an aqueous solution of milling yellow are presented in a form of relations between the scattered radiant power, states of polarization of primary radiation and scattered radiation, observation angle and azimuthal angle.It is found that the state of polarization of the scattered light in milling-yellow solution can be utilized as a foundation of reliable photoelastic scattered-light techniques for flow analysis. However, Rayleight's model of scattering is nnt directly applicable.Paper contains data on major parameters of light scattering, knowledge of which is necessary to correctly design flowbirefringence experiments. In particular, these data can be used to develop a set of conditions and constraints for designing of particular scattered-light flow-birefringence experiments, and of corresponding transfer functions.     

Integrated-plane photoelastic method—Application of photoelastic isodynes

It has been shown by Pindera and Mazurkiewicz that a new type of scattered-light modulation in the plane of a two-dimensional photoelastic object can be obtained when the stationary integrated photoelastic method developed by Pindera and Straka is applied in a scanning mode and when the transfer function of the photoelastic system satisfies certain conditions. The new type of light modulation, called field of isodynes by the authors, carries information on stress components normal to the direction of propagation of primary beam, and on corresponding total-force component. The points where this stress component is equal to zero can be easily determined. The classical scattered-light modulation along a chosen line represents a cross section of a corresponding isodynes field. It is shown that these features of the method of isodynes make it possible to easily determine the distribution and values of normal stress components at any arbitrary rectilinear cross section, and to check immediately the accuracy of measurements. The experimental determination of contact stresses and contact regions using the method of isodynes is especially simple and elegant.     

Experimental/analytical characterization of composite tubes under combined loading

The paper outlines the results of an investigation to characterize the response of P75/934 graphite/epoxy tubes with a stacking sequence of [15/0/±10/0/−15] _s under pure torsion and combined axial/torsion loading. The experimentally observed nonlinear response and path-dependent failure are discussed in terms of material nonlinearities at the ply level and first-ply failure loads with the help of an analytical model. Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

Characteristic relations of flow birefringence

This is the first of two closely related papers on the flow-birefringence response to the velocity vector field of a particular liquid representing a certain class of birefringent bodies.^* The flowing material under study was the aqueous solution of the compound known under the name NGS 1828 and commonly known as “milling yellow” or “acid yellow”. This solution appears to exhibit all three major mechanisms of birefringence. The physical parameters characterizing this material depend strongly on temperature, concentration and age and, therefore, it can be considered as representing a typical class of liquids used in flow-model experiments. The paper presents the experimental evidence that the flow birefringence cannot be explained and described by the simple mathematical model of birefringence in solid continuum which relates the changes of the components of dielectric tensor to the components of stress and strain tensors, or their derivatives, and which neglects the influence of the spectral frequency (wavelength of radiation). Results are presented for transmission birefringence (and for scattered-light birefringence in the second paper) in the visible and the infrared bands of radiation. It is shown that:

- the amount of birefringence depends strongly and non-monotonically on wavelength of radiation;

- the linear range of optical response to shear-strain rate depends on wavelengths of radiation;

- the directions of optic axes strongly depend both on the shear-strain rate and on the wavelength of radiation, even in the linear range of mechanical response.

It is further shown that there exists a relation between the absorption bands, the maximum transmittance, the dispersion of birefringence, the spectral dependence of optic-axes direction, and the linear range of optical response. Within the maximum transmittance band and the linear range of mechanical response the linear range of birefringence is maximum and the dispersion of birefringence is minimum with respect to the shear-strain rate; the corresponding dispersion of optic axis is also minimum. Samples of typical recordings are given in the visible and the infrared radiation for typical flow patterns. One of the practical conclusions is that to optimize the flow-birefringence studies of engineering problems it is advisable to choose the radiation in the near-infrared range. The evidence presented shows that the common trend in engineering research toward simplification of the model of the flow-birefringence response is not necessary.     

General relations of strain-gradient stress analysis

Some particular fields of stress gradients in plates are investigated analytically and experimentally. Carriers of empirical information are light beam deflections caused by stress or strain gradients in homogeneous beams subjected to a particular case of flexure with shear. This study is based on theories and techniques of the strain-gradient method that was recently introduced by the authors. This is a generalization of prior analytical-experimental examination of strain-gradient light deflections produced in stressed plates, which had concentrated on the simplest case where information of interest is collected along a line of symmetry of the stress field and where both the information carrying light beams are deflected in the plane of symmetry only. The developed relations were tested experimentally, by using an S-beam as representative example of general plane stress field. The main purpose of the present investigation is to document the efficacy of the strain-gradient method in analysis of the general case of stress state and to test the ranges of applicability of the accepted mathematical models and of the subsequently derived relations. In this respect, the most interesting stress state is that in a beam subjected to the Saint-Venant bending, where the transversal and longitudinal axes of the beam are in pure shear. The obtained results are compared, at each step, with the predictions of the developed analytical models and with the predictions of Filon's stress function. The results of comparison are satisfactory. The procedures of evaluating the photoelastic and material coefficients using strain-gradient techniques were tested positively. The developed method can yield valuable information on the actual features of stress states in fracture mechanics. Part of the problems and first results of this investigation will be presented in the authors' paper “Strain-gradient stress analysis in Saint-Venant bending”.     

Testing theoretical bases of caustic methods in fracture mechanics and stress analysis

Determination of stress intensity factors using shadow optical method of caustics attracts increasing attention. However, the reliability and ranges of applicability of this method are seldom discussed. This paper presents such an analysis regarding the reliability and predictive power of caustic method in fracture mechanics. This analysis is performed according to the accepted methodology of testing any analytical, numerical, or experimental procedure, namely by testing its theoretical bases. The following four basic assumptions of the shadow optical method of caustics in fracture mechanics, and their consequences, are analyzed: assumption of a generalized plane stress state near crack tip; assumption that the radiant energy used to produce shadow images propagates rectilinearly inside a stressed body; assumption that the light velocity inside a stressed body depends only on stress components in planes normal to wave normals; assumption that there is no alteration in state of polarization of radiation impinging upon a stressed plate at oblique incidence.The first two basic assumptions are tested using results obtained by means of three analytical-experimental procedures, namely isodynes, gradient index method, and classical strain gages. It is known that the inaccuracies of the fourth assumption are within the noise level only when the angles of incidence are small.It is shown that the magnitudes of the effects caused by the geometric lens effect and the gradient index lens effect are comparable, and that the stress states near crack tips and bottoms of notches, which produce the geometric lens effect, are clearly three-dimensional.It is also indicated that the gradient index lens effect is caused jointly by the stress/strain-induced alteration of the optical path and by the bending of the light path caused by strain gradient.Obtained empirical evidence shows the existence of a particular relationship between the observed gradient index lens effect and the order of singularity in a particular singular solution of linear fracture mechanics, with the exception of the vicinity of the crack tip where singularities are inadmissible.     

Scattered-light optical isodynes—Basis for three-dimensional isodyne stress analysis

The paper presents the principles, theory, basic techniques, reliability and efficacy of the three-dimensional, non-destructive isodyne stress analysis. Analytical isodynes constitute the analytical component of the theoretical basis of two-dimensional and three-dimensional isodyne analysis of stresses in plates and some bulky bodies. The analytical isodynes can be obtained experimentally by means of optical isodynes which can be produced by scattered radiation under specified conditions. Theoretical bases of optical isodynes are discussed with regard to their theoretical admissibility, technical feasibility, and compatibility with the present state of knowledge. Included is discussion of the accepted mathematical models of the major physical phenomena, and discussion of the related reliability and efficacy of the isodynes. Within such a framework, isodyne stress analysis is compared with some related, typical procedures of stress analysis. Examples characterize the reliability and efficiency of the isodyne stress analysis in determination of components of actual three-dimensional stress states in plates, local effects including contact problems, fracture mechanics, and composite structures. Conclusions are based on the recognition that determination of the actual three-dimensional stresses in structures is of importance to the progress in modern design procedures, and is intellectually challenging.     

Plasticity-triggered architectural effects in periodic multilayers with wavy microstructures

Despite considerable presence of periodic multilayers with wavy architectures in nature and technology, little simulation data is available on their response. A recent investigation of wavy multilayers comprised of alternating elastic and elastic-perfectly plastic plies has revealed the important role that plasticity plays on their post-yield response relative to the corresponding flat configurations [Khatam, H., Pindera, M.-J., 2009b. Parametric finite-volume micromechanics of periodic materials with elastoplastic phases. Int. J. Plasticity 25 (7), 1386–1411]. Herein, we extend this investigation by considering the effect of elastic layer thickness on the post-yield response at several fixed elastic phase volume fractions using the parametric finite-volume direct averaging micromechanics (FVDAM) theory. The layer thickness is shown to have a substantial impact on the post-yield response whose extent depends on the loading mode and waviness amplitude, in contrast with the minimal impact on the homogenized elastic moduli. Decreasing the layer thickness at sufficiently high fixed volume fractions decreases the extent of strain hardening under transverse normal loading, as well as the maximum normal and shear stresses in the stiff layers, reducing the possibility of failure and thus potentially enhancing durability. The opposite holds under transverse shear loading for low waviness amplitudes. The presented results provide a framework for tailoring the elastoplastic response of multilayers with sinusoidally varying plies under different loading modes.