On the theory of the indentation test for the measurement of tensile strength of brittle materials

A theoretical solution has been obtained for the state of stress in a rectangular plate under a pair of symmetrically placed rigid indenters. The stress distributions along the two central axes have been calculated for a square plate assuming the pressure distribution under the indenters as uniform, parabolic and one resulting from 'constant displacement' on a semiinfinite boundary, for different ratios of indenter-width to side of square. The results are compared with those of photoelastic analysis of Berenbaum and Brodie and the validity of the solution is discussed. The solution has been extended to orthotropic materials and numerical results for one type of coal are given.

Digital image analysis around isotropic points for photoelastic pattern recognition

Fringe tracking and fringe order assignment have become the central topics of current research in digital photoelasticity. Isotropic points (IPs) appearing in low fringe order zones are often either overlooked or entirely missed in conventional as well as digital photoelasticity. We aim to highlight image processing for characterizing IPs in an isochromatic fringe field. By resorting to a global analytical solution of a circular disk, sensitivity of IPs to small changes in far-field loading on the disk is highlighted. A local theory supplements the global closed-form solutions of three-, four-, and six-point loading configurations of circular disk. The local theoretical concepts developed in this paper are demonstrated through digital image analysis of isochromatics in circular disks subjected to three-and four-point loads. (C) 2015 Society of Photo-Optical Instrumentation Engineers (SPIE)

Photoelastic studies on progress of separation in interference fits

Interference fits are used extensively in aircraft structural joints because of their improved fatigue performance. Recent advances in analysis of these joints have increased understanding of the nonlinear load-contact and load-interfacial slip variations in these joints. Experimental work in these problems is lacking due to difficulties in determining partial contact and partial slip along the pin-hole interface. In this paper, an experimental procedure is enumerated for determining load-contact relations in interference/clearance fits, using photoelastic models and applying a technique for detecting progress of separation/contact up to predetermined locations. The study incorporates a detailed procedure for model making, controlling interference, locating break of contact up to known locations around the interface, estimating optically the degree of interference, determining interfacial friction and evaluating stresses in the sheet. Experiments, simulating joints in large sheets, were carried out under both pin and plate loads. The present studies provide load-separation behavior in interference joint with finite interfacial friction.

A critical analysis of the shear difference method

The shear difference method which is commonly used for the separation of normal stresses using photoelastic techniques depends on the step-by-step integration of one of the differential equations of equilibrium. It is assumed that the isoclinic and the isochromatic parameters measured by the conventional methods pertain to the state of stress at the midpoint of the light path. In practice, a slice thin enough for the above assumption to be true and at the same time thick enough to give differences in the shear-stress values over the thickness is necessary. The paper discusses the errors introduced in the isoclinic and isochromatic values by the conventional methods neglecting the variation of stresses along the light path. It is shown that while the error introduced in the measurement of the isochromatic parameter may not be serious, the error caused in the isoclinic measurement may lead to serious errors. Since the shear-difference method involves step-by-step integration the error introduced will be of a cumulative nature.

A photoelastic approach to framed structure-foundation beam-soil interaction

The interaction of a framed structure with a foundation beam resting on an elastic medium, representing the soil, has been studied using the photoelastic method. The contact pressure distribution, the fibre stress in the foundation beam and frame structure, as well as the stresses in the elastic medium, have been obtained. These have been compared with theoretical results obtained by idealizing the soil as (a) elastic half plane, and (b) elastic half space. It is shown that the photoelastic method can provide an easy solution to this type of problem if the soil can be idealized as an elastic continuum.

Interaction analysis of strip footing resting on a non-homogeneous elastic medium

In this paper, a plane stress solution for the interaction analysis of strip footing resting on (i) a non-homogeneous elastic half-plane and (ii) a non-homogeneous elastic layer resting on a rigid stratum has been presented. The analysis has been done using a combined analytical and FEM method in which the discretization of the half-plane is not required and thereby minimizes the computational efforts considerably. The contact pressure distribution and the settlement profile for the selected cases of varying modulus half-plane, which has more relevance to foundation engineering, have been given. Experimental verification through a photoelastic method of stress analysis has been carried out for the case of footing on Gibson elastic half-plane, and the contact pressure distribution thus obtained has been compared with the theoretical results. Copyright (C) 1996 Elsevier Science Ltd

Design and analysis of novel compression fracture specimen with constant form factor: Edge cracked semicircular disk (ECSD)

Inspired by the Brazilian disk geometry we examine the utility of an edge cracked semicircular disk (ECSD) specimen for rapid assessment of fracture toughness of brittle materials using compressive loading. It is desirable to optimize the geometry towards a constant form factor F for evaluating K-I. In this investigation photoelastic and finite element results for K-I evaluation highlight the effect of loading modeled using a Hertzian. A Hertzian loading subtending 4 degrees at the center leads to a surprisingly constant form factor of 1.36. This special case is further analyzed by applying uniform pressure over a chord for facilitating testing.

Mixed Mode Analysis of Obliquely Oriented Edge Cracked Semicircular Disk Under Compression

A new mixed-mode compression fracture specimen, obliquely oriented edge cracked semicircular disk (OECSD) is analyzed by extending pure opening mode configuration of edge cracked semicircular disk (ECSD) under Hertzian compression. Photoelastic experiments are conducted on two different specimens of OECSD of same size and different crack lengths and inclinations. Finite element method (FEM) is used to solve a number of cases of the problem varying crack length and crack inclination. FE results show a good match with experiments. Inclination of edge crack in OECSD can be so made as to obtain any mode-mixity ratio between zero and one and beyond for any crack length. The new specimen can be used for fracture testing under compression more conveniently than the existing ones in several ways.

Characterization of friction at three contact pairs by photoelastic Isotropic point (IP)

Friction coefficient between a circular-disk periphery and V-block surface was determined by introducing the concept of isotropic point (IP) in isochromatic field of the disk under three-point symmetric loading. IP position on the symmetry axis depends on active coefficient of friction during experiment. We extend this work to asymmetric loading of circular disk in which case two frictional contact pairs out of three loading contacts, independently control the unconstrained IP location. Photoelastic experiment is conducted on particular case of asymmetric three-point loading of circular disk. Basics of digital image processing are used to extract few essential parameters from experimental image, particularly IP location. Analytical solution by Flamant for half plane with a concentrated load, is utilized to derive stress components for required loading configurations of the disk. IP is observed, in analytical simulations of three-point asymmetric normal loading, to move from vertical axis to the boundary along an ellipse-like curve. When friction is included in the analysis, IP approaches the center with increase in loading friction and it goes away with increase in support friction. With all these insights, using experimental IP information, friction angles at three contact pairs of circular disk under asymmetric loading, are determined.