R. Prabhakaran

Photo-orthotropic-elasticity

A method of producing transparent model materials for photo-orthotropic-elastic studies is presented. This material fabricated from glass fibers and a modified polyester matrix exhibits continuous relatively smooth fringe patterns which are linearly related to the state of stress. As such, the heterogenous material can be treated as a homogenous medium with orthotropic properties.Three photoelastic constantsfL,fT andfLT are necessary to describe the photoelastic response of the orthotropic materials to a general state of stress. Methods are established for predicting these photoelastic constants from the properties of the constituents. These methods are based on stress proportioning between the fibers and the matrix and upon the linear summation of the retardation from each constituent. The relations derived forfL,fT andfLT were verified experimentally and found to be in close agreement with measured values.A stress-optic law is derived on the basis of stress partitioning between the two constituents in a unidirectionally fiber-reinforced laminate. The adequacy of this stress-optic relation is confirmed by experimental verification. Comparison of this stress-optic relation with the expression advanced by Pih and Knight shows the validity of their initial concepts but the inadequacy of their partitioning functions. Detailed comparison of the stress-optic law with the analog relation proposed by Sampson shows excellent agreement. Indeed, the use of Sampsons stress-optic law is recommended and the law based on stress partitioning is to be considered as a fundamental theoretical proof of the Sampson relation. Finally, the applicability of Sampsons stress-optic law to bidirectionally reinforced materials was confirmed with a thorough experimental verification.

Load and resistance factor design (LRFD) approach for bolted joints in pultruded composites

The application of glass fiber-reinforced polymeric matrix composites in civil engineering structures has been increasing rapidly in recent years. Pultruded composites are attractive for structural applications because of their continuous production and excellent mechanical properties. The present study is intended to be a step in understanding bolted joints in pultruded composites. Specifically, bolted connections in pultruded plates are investigated for their block shear and net tension failure modes. Configurations and dimensions have been selected to highlight the block shear and net tension failure phenomena and to compare the behavior of composites to the standard practice in the case of steel connections. Specimens with single and multiple holes have been tested in tension under bolt-loading conditions. Some of the specimens were instrumented with strain gages and the load-strain responses were monitored. The failed specimens were examined for the cracks and fracture patterns. The results have been analyzed using the strength calculations similar to those used in the load and resistance factor design (LRFD) procedures for steel structures. Two LRFD-type formulae for block shear and net tension failure for pultruded composites are proposed in the present paper. It was found that the failures in the bolt-loaded pultruded specimens could be predicted reasonably well with the proposed formulae. The use of these formulae is also demonstrated by means of examples. The proposed resistance factors are checked with additional test results.

Strain-Optic Law for Orthotropic Model Materials

A strain-optic law for orthotropic birefringent model materials, based on the concept of Mohr circle of birefringence, is developed. The strain-fringe value, like the stress-fringe value, is influenced by the fiber orientation angle and the ratio of the principal strains. The strain-optic law is experimentall y verified by testing a unidirectional ly glass fiber reinforced circular disk under diametral compression. It is shown that an average strain-fringe value can be used in strain analysis of orthotropic models and the resultant error is less than 20% in most cases. A similar attempt to use an average stress-fringe value leads to much larger errors. The measured isoclinic parameters are found to give the principal strain directions to a very good approximation. It is proposed that orthotropic photoelastic models can be treated as isotropic models to obtain an approximate strain analysis by employing the strain-optic law and an average strain-fringe value.

Response of composite plates to blast loading

The transient response of composite plates, with and without central circular holes, to blast loading is studied. The modal-analysis approach has been used in the computation of numerical results, which have been obtained for isotropic and orthotropic plates, with and without holes. In order to verify the theoretical results, experiments have been conducted on aluminum and unidirectionally reinforced E-glassepoxy plates, using a shock tube as the loading device. The experimental peak dynamic strains (normalized with respect to the pressure) are compared with the theoretical values. The strain-time history is also shown for a particular gage location in the composite plate. Finally, a comparison of dynamic-amplification factors, defined as the ratio of the peak dynamic strains to the static strains, has been made between the isotropic and the composite plates.

Tensile fracture of composites with circular holes

Abstract The tensile fracture of a bidirectionally reinforced glass fiber/epoxy laminate was studied. The “hole size effect”, i.e. the reduction in strength with an increase in hole size at constant stress concentration factor, was investigated. It is shown in this paper that a size effect is exhibited by unnotched specimens for one of the principal material directions. This size effect should be taken into account in assessing the hole size effect. The inherent flaw size according to linear elastic fracture mechanics as well as the characteristics dimension according to the point-stress failure criterion of two-parameter models are determined and compared. On the basis of the results of this investigation it is suggested that the inherent flaw size as well as the characteristic dimension depend on the hole size.

An investigation of the losipescu and asymmetrical four-point bend tests

The Iosipescu shear test, utilizing a notched specimen in bending and a modification—the asymmetrical four-point bend (AFPB) test—were evaluated as shear tests for composites. This paper summarizes the results of an extensive numerical and experimental investigation of the Iosipescu and AFPB test methods. Finite-element analyses were conducted to assess the influence of notch parameters and load locations on the stress state in the specimen. The shear moduli and the shear strengths were experimentally measured for a quasiisotropic graphite/epoxy laminate using both the Iosipescu and the AFPB test methods. The tests were conducted for various combinations of notch parameters and load locations. The test results indicate that changes in the notch geometry and load locations aimed at improving the stress distribution in the test section resulted in unexpected changes in the failure mode.

Application of the least-squares method to elastic and photoelastic calibration of orthotropic composites

New experimental methods continue to be proposed for determining the in-plane elastic constants of orthotropic composite materials, as no single method has been found completely satisfactory. In particular, the in-plane shear modulus is difficult to measure. In this paper, an orthotropic half-plane subjected to a concentrated edge load is proposed as a calibration specimen. Photoelastic calibration of orthotropic-birefringent composites is also difficult due to the need to conserve the commercially unavailable, difficult-to-make model materials and the absence of many closed-form solutions. In this paper, the orthotropic half-plane specimen is proposed for photoelastic calibration of birefringent-orthotropic model materials also. For elastic and photoelastic calibration of orthotropic materials, the least-squares procedure is used for processing the experimental data.

The interpretation of isoclinics in photo-orthotropic-elasticity

Significant progress has been made in the interpretation of isochromatic fringes in photo-orthotropic-elasticity. However, the isoclinic fringes have not yet been satisfactorily interpreted. While it has been recognized that the isoclinics do not give the principal-stress directions in the composite model, there has been speculation that the isoclinics may give the principal-strain directions.An experimental study of the isoclinic fringes in orthotropic models was undertaken. The model material employed consisted of a transparent, unidirectionally reinforced, E-glass-polyester composite. First, the optical isoclinic parameters were measured in uniaxial stress fields for compression specimens as a function of the fiber-orientation angle. It was observed that, while the optical isoclinic parameter was different from the composite principal-stress angle, it was also different from the composite principal-strain angle. The optical isoclinic parameter was predicted very well by the Mohr circle of birefringence postulated by Sampson.In the second set of experiments, the optical isoclinic parameter was measured in biaxial stress fields by testing a circular disk in diametral compression. The actual state of strain and stress at the center of the disk was measured by means of a rectangular strain-gage rosette. Again it was observed that the optical isoclinic parameter was predicted very well by Sampsons relation. Thus, the isoclinic fringes in orthotropic models can be satisfactorily interpreted and Sampsons scheme can be utilized to obtain the individual principal stresses in orthotropic models.

Holographically determined isopachics and isochromatics in the neighborhood of a crack in a glass composite - The application of photo-orthotropic-elasticity to fracture studies of composite materials in evaluated and discussed

The isochromatic and isopachic fringes are obtained holographically in the neighborhood of a central crack in a tensile, orthotropic glass-composite plate. The general inability to separate the principal stresses or strains from such information alone under anisotropic conditions is discussed, as are the results relative to fracture-mechanics implications.

On the stress-optic law for orthotropic-model materials in biaxial-stress fields

The stress-optic law for othotropic-model materials, proposed by Sampson on the basis of a simple analogy to the isotropic-model materials, is examined for biaxial-stress fields. The stress-optic law is reduced to a simple form for special cases. It is also shown that the zero-order isochromatic fringe corresponds to an isotropic state of stress only in the case of balanced laminates. A glass-fiber-reinforced plastic disk with the glass fibers in only one direction is examined under diametral compression photoelastically and by means of strain-gage rosettes, with the loading direction perpendicular and at 45 deg to the reinforcement direction. The fringe order along the horizontal diameter is computed from the simplified stress-optic law making use of stress values from strain-gage readings and compared with the observed fringe order. Based on a fairly good agreement of the fringe orders, it is shown that a circular-disk specimen can be used to calibrate an orthotropic-model material. The three independent material-fringe values,fL,fT,fLT, can be found from measurements of the fringe order and the strains at the center of the disk for the three cases of loading perpendicular, parallel and at 45 deg to the reinforcement direction.