A photoelastic and FEM analysis of interfacial crack propagation

The linear elastic solution for the bimaterial interface crack is applied to determine the direction of crack propagation during surface-layer removal by scraping. The direction of the load which must be applied to the free end of the surface layer for continued interfacial crack propagation is determined using photoelasticity and finite elements, and results are found to be in good agreement.Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 3–6.     

Influence of late-breaking ligaments on crack propagation in compact specimens—A photoelastic study

Dynamic photoelasticity and high-speed photography were utilized to study the influence of tough ligaments on crack propagation in compact specimens. The data obtained during the fracture experiments were analyzed to obtain crack velocity, instantaneous stress-intensity factor and the energy losses away from the crack tip. The results showed that the ligaments can behave as crack arrestors or decelerators. The crack if not arrested at the ligament slowly tunnels in between the ligaments without immediately rupturing them. The ligaments also tend to increase damping losses in the specimens.     

A new photoelastic model for studying fatigue crack closure

The photoelastic analysis of crack tip stress intensity factors has been historically developed for use on sharp notches in brittle materials that idealize the cracked structure. This approach, while useful, is not applicable to cases where residual effects of fatigue crack development (e.g., plasticity, surface roughness) affect the applied stress intensity range. A photoelastic model of these fatigue processes has been developed using polycarbonate, which is sufficiently ductile to allow the growth of a fatigue crack. The resultant stress field has been modeled mathematically using the stress potential function approach of Muskhelishvili to predict the stresses near a loaded but closed crack in an elastic body. The model was fitted to full-field photoelastic data using a combination of a generic algorithm and the downhill simplex method. The technique offers a significant advance in the ability to characterize the behavior of fatigue cracks with plasticity-induced closure, and hence to gain new insights into the associated mechanisms.     

How ‘mixed’ is dynamic mixed-mode crack propagation? — A dynamic photoelastic study

Dynamic photoelastic fringe recordings associated with rapid curved crack propagation, crack division and the interaction between moving cracks and elastic waves show global dynamic mixed-mode crack-tip fringe patterns. When analysed by means of K-determination procedures an ‘apparent’ dynamic mixed-mode ratio K₂/K₁ may be denned which turns out to be a function of the particular selection of measurement data points. This paper compares experimentally recorded fringe data with numerical results in an attempt to resolve the dynamic photoelastic mixed-mode crack problem.     

A photoelastic study of friction at multipoint contacts

A new method of measuring the normal and sliding loads associated with multiple-point contact is introduced. A multiple-point contact is modeled with a steel die with a profile that simulates a rough surface. A very large scale factor is used in modeling this surface. The steel die is placed in contact with a photoelastic model of a half plane and is subjected to a normal load. This normal load is partitioned over the multiple points of contact producing an isochromatic fringe pattern that describes the stress distribution in the local neighborhood of the contact points. A sliding load is then imposed on the model which destroys the symmetry of this fringe pattern. The fringe data in this pattern are sufficient to determine the local loadsP _i andQ _i and the local coefficient of frictionf _i =Q _i /P _i at each contact point. An overdeterministic method is introduced which gives the solution forP _i ,Q _i andf _i using many data points taken from the isochromatic pattern in the local neighborhood of the contacts.Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WJ on June 9–13.     

A photoelastic study of energy loss during a fracture event

Static and dynamic photoelastic experiments were conducted to evaluate the energy lost due to damping in a thick-walled-ring specimen during a run-arrest fracture event. Short starter cracks were machined into a series of ring specimens fabricated from Homalite 100 and the specimens were loaded by a specially designed mechanical deformeter to giveK _Q/K_Imranging from 1.76 to 2.15. The crack was initiated and high-speed photographs of the isochromatic-fringe loops at the tip of the running crack were recorded. The data were analyzed to obtain the instantaneous stress-intensity factorK(t), the normalized crack positiona/w, and the crack velocity \(\dot a\) . A comparison ofK, as a function of positiona/w, was made between static and dynamic crack growth. Average values ofK were determined from these curves and estimates of initial strain energy and energy lost in forming the fracture surface were made. An energy balance was used to evaluate the energy loss due to damping in all the experiments. The energy loss during the run-arrest event was approximately 50 percent of initial strain energy.     

Two-dimensional photoelastic study of turbine-shell flanges

Results of a two-dimensional photoelastic study of turbine-shell flanges are reported. Equations of transition from model to prototype are given. A special loading jig for applying a uniform pressure to the boundary of a plane model is described. Pertinent aspects of the experimental technique are summarized.     

A dynamic photoelastic study of stress-wave propagation through an inclusion

A photoelastic study of the elastodynamic-stress fields around a circular, elastic inclusion (Solithane 113) embedded in an elastic plate (Hysol 4485) is presented. The edge of the plate was loaded by an explosive charge, which produced a plane, compressional stress wave of triangular shape. Isochromatic-fringe patterns were obtained, which give the maximum shear stresses, both inside the inclusion and in the surrounding medium. The principal stresses on the axis of symmetry were determined through the use of the oblique-incidence method. It was found that small tensile stresses are generated at the interface on the shadow side of the inclusion. The focusing effect inside the inclusion predicted by ray theory was not observed. Finally, the shape of the wavefront as the wave passes the inclusion was determined.     

A photoelastic study of contact between a cylinder and a half-space

Three-dimensional photoelasticity was employed to study a cylinder in contact with a half-space. Both bodies were modeled in epoxy resin. Three loading cases were examined, namely, the cylinder lying on its side subject to a load normal to the plane, the cylinder on its side subject to both normal and tangential loads and the cylinder standing on its end and subject to a normal compressive load, i.e., as a circular punch. The cylinders and the half-space, which was represented by a large block, were stress frozen with a known coefficient of friction and using relatively small loads so that the strain levels were low. After slicing the cylinders, which resulted in lower fringe orders than could be readily analyzed manually, an automated system based on phase stepping was used to record and process the data. Distributions of maximum shear stress and Cartesian shear stress were obtained for a large area of the slice. Stress separation was performed, using the shear difference method, to obtain the Cartesian stress components in the plane of symmetry of the half-space. These results provide confirmation, by experiment, of the theoretical and numerical models of this type of contact obtained by other investigators.     

A composite three-dimensional photoelastic method

Care must be taken in preparation and testing of three-dimensional composite photoelastic models. Some problems encountered in modeling the prototype and during model testing are: model-material failure, loss of fringe pattern in slicing, inherent shrinkage response in freezing, inadequate bonding between materials, and modular ratio difficulties. The selection of the correct plastic can eliminate the first four problems, but the correct modular ratio between the matrix and the insert has to be obtained. This investigation illustrated the behavior of commercially manufactured plastics as inserts, with a matrix material of Epon 828 epoxy. The effective moduli of elasticity of these plastics are reported for pure tension and for flexure. Since the manufactured plastics produced varying results, the use of Epon 828 epoxy as an insert was investigated. The inserts were cast in tygon tubing and their curing cycle was altered from that used for the matrix material to produce a different effective modulus of elasticity. The Epon 828 inserts gave excellent results in the beams. The use of the same material for matrix and insert eliminates many of the problems associated with composite three-dimensional photoelasticity.     

A recording photoelastic stress meter

An instrument for automatically making photoelastic measurements of stress is described. It may be used for recording transient stresses at a point or for scanning spatial stress distributions. Its use is illustrated by an application entailing the measurement of transient thermal stresses in a viscoelastic material.     

A photoelastic fiber-optic strain gage

This paper reports on the development of a photoelastic fiber-optic strain gage sensitive to transverse strain. The sensing element is made from an epoxy resin which is stress frozen to passively achieve the quadrature condition. Light, emitted from an LED operating at 820 nm, is transmitted to and from the sensing element via multi-mode fibers and the signal is detected using a dual-channel operational photodiode/amplifier.This unique combination of optics and electronics produces a fiber-optic sensor having a high signal to noise ratio and a measurement system which is lead-in/out insensitive. Results show that strains on the order of 1 microstrain can be measured over an 800 microstrain range when a dummy gage is used for compensation.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

Three-dimensional photoelastic study of stresses in rack gears

A three-dimensional photoelastic analysis using the stress-freezing and slicing techniques was employed in studying the stress distribution and concentration across the thickness of a thick rack-gear tooth. Full-size photoelastic models of about 25-mm thickness, having various teeth parameters were machined from PLM-4B plates. A special mounting fixture was designed to hold the models in the loading frame and a knife-edged line load was used in loading the models. In the analysis, the method of oblique incidence was adopted for the separation of the principal stresses. The intension was to determine the magnitude and location of the maximum stress at the tensile fillet and to establish the stress-concentration factors for various geometric tooth configurations.From this study, it was concluded that the fillet stresses depend largely upon the pressure angle, fillet radius and the position of the load. Maximum values of the tensile fillet stresses occur at the middle plane of the tooth thickness. Furthermore, the value of the stress-concentration factor increases with the increase of the tooth thickness. In general, this investigation gave values of stresses much higher than those values calculated by the simple-flexure theory.     

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.     

A photoelastic determination of mixed-mode stress-intensity factors

A new evaluation method of the isochromatic-fringe pattern for the determination of mixed-mode stress-intensity factors (SIF) was developed. The method bypasses the error-prone measurements on the isochromatic patterns near to the crack tip and uses data from the far region. Suitable extrapolation laws were given for transferring the far-from-the-crack-tip data to the near region. Then, the well-known Irwin's formulas can be used for the determination of mixed-mode SIFs. Convenient formulas facilitating the calculation of SIFs were established. Experimental evidence corroborated the results obtained by the new method.     

A dynamic photoelastic analysis of dynamic-tear-test specimen

Dynamic photoelasticity was used to analyze the transient response of dynamic-tear-test (DTT) specimens, .0889×.400m (3.5×15 in.) in size, machined from .0095m (3/8 in.)-thick Homalite-100 plates. Dynamic-stress-intensity factors, dynamic-energy release rates, and crack velocities in ten specimens were determined. Dynamic tear energies were obtained by integrating the area under the dynamic-energy release-rate curves. The average dynamic-energy release rates which were obtained by dividing the dynamic tear energies by the total length of the crack paths, were found to be approximately equal to the critical strain-energy release rate of Homalite-100. Results of the drop-weight-hammer impact vs. crack-initiation experiments showed that the crack initiated after the first buildup of impact forces in the hammer, thus indicating possible ambiguity in using a specified location on the hammer-force curve to derive a comparable static-fracture load for the DTT specimen.     

Stress separation in the photoelastic study of centrifugal stresses

This technical note refers to the problem of stress separation in the photoelastic analysis of plane models under centrifugal stresses. Two methods are described in order to determine the sum of principal stresses. These methods, which are based on the compatibility equation, reduce the determination of the sum of principal stresses to the solution of a Laplace's or Poisson's equations. As an example of application, the separation of stresses in a rotating disk with two eccentric holes is shown and comparison with the stresses obtained by using the shear-difference method is made.     

A photoelastic material with variable modulus of elasticity

Instructions are given in this paper to manufacture a photoelastic material (polyurethane rubber) exhibiting a linearly variable modulus of elasticity. In the examples given, the range ofE is of the order of 1 to 2.5. Illustrations of applications in stress analysis are included. The new material should be particularly useful in the solution of soil-mechanics problems and it can be used for its photoelastic properties, or as base for grid and moiré analysis.     

A study of effective crack length using holographic interferometry

A technique using holographic interferometry and models of thin-sheet PMMA has been adapted to study the effective crack length for slots with rounded tips of various radii. The results suggest a rational means of applying sharp-crack fracture mechanics in certain nonideal situations and are compared with earlier studies.