Photoelastic investigation on the Crack-arrest capability of a pretensioned stiffened plate

Dynamic photoelasticity, employing a 16-spark-gap Cranz-Schardin camera system, was used for dynamic analysis of propagating cracks in stiffened panels. The method of finite elements was used for a corresponding static analysis. Photoelastic models included 0.009525×0.25×0.25 m Homalite-100 plates with 10- and 25-percent pin-joined and bonded stringers. Static and dynamic strain-energy release rates, kinetic-energy release rates and stringer-load concentration factors were determined in stiffened panels that were pretensioned and then impacted by a projectile. It was found that the arrest capability of a stiffened panel could be assessed through the kinetic-energyrate concept. Also bonded stiffeners were found to be more effective in arresting a propagating crack than a corresponding pin-joined stiffened panel.     

Dynamic crack curving and branching under biaxial loading

A 16-spark-gap camera was used to record the dynamic photoelastic patterns of ten centrally cracked, Homalite-100 specimens which fractured under ten initial biaxial-stress ratios ranging from 3.7 to 0, some of which do not exist in normal fracture specimens. The dynamic photoelastic patterns of curved cracks were used to verify the previously developed dynamic-crack-curving criterion. Cracks which immediately curved upon propagation in three specimens under abnormally high inital biaxial loading were used to verify the static counterpart of the dynamic-crack-curving criterion under these extreme loading conditions. A previously developed dynamic-crack-branching criterion was also verified by four dynamic photoelastic results involving cracks which eventually branched under the lower initial biaxial loading.     

Dynamic-finite-element and dynamic-photoelastic analyses of two fracturing homalite-100 plates

A dynamic-finite-element code, HONDO, was used to analyze two single-edged-notch fracturing Homalite-100 plates which had been previously studied by dynamic photoelasticity. A single-edged crack in the finite-element model was advanced in incremental jumps such that the time-averaged crack velocity matched the measured crack velocity in the Homalite-100 plate. Dynamic-energy-release rates were computed for a constant-velocity crack and a crack which arrested after a somewhat constant deceleration. These results were compared with the corresponding dynamic-energy-release rates, which were computed from the dynamic-stress-intensity factors determined by dynamic photoelasticity, and with static-strain energyrelease rates. Despite the crude modeling of the running crack, the coarseness of the finite-element-grid breakdown and the differences in the modeled and actual grip conditions, the computed and measured dynamic-energy-release rates, except for occasional large differences, generally agreed within 10 percent of each other.     

Photoelastic investigation on the crack-arrest capability of a hole

Dynamic photoelasticity employing a 16-spark gap Cranz-Schardin camera system was used to determine certain conditions leading to fracture arrest by a circular hole ahead of a propagating crack. Photoelastic models of 3/8×10×10-in. Homalite-100 plates with a 1/2-in. edge crack were loaded in a fixed-grip configuration and crack arrest was made possible by central holes of 1/2, 1/4, and 0.15-in. diameters. In one test of a uniformly loaded plate with a central hole of 0.15-in. diameter, the propagating crack continued through this hole. Changes in dynamic-stress-intensity factors, as the crack tip approaches the hole, as well as changes in the dynamic-stress-concentration factors at the far side of the hole were studied, and these results were compared with the corresponding static results determined by finite-element analysis. This comparison shows that the static analysis can be used to qualitatively assess the arrest capability of the hole using the maximum static-stress concept or the proposed concept of strain energy released as the crack penetrates the hole.     

Dynamic fracture analysis by moiré interferometry

Dynamic moiré interferometry was used to measure separately theu- andv-displacement fields surrouding a rapidly propagating crack tip in Homalite-100 and 7075-T6 aluminum-alloy plates. These transient crack-tip-displacement data were then used to compute the dynamic stress-intensity factor and the remote stress component.J-integral values were also estimated using the static approximate procedure of Kanget al. This static analysis provided the correctJ when the contour integral was taken within 3 mm of the crack tip.Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–13.     

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 wave fields in plates weakened by curvilinear holes with edge cracks

The dynamic fracture of plates weakened by holes with edge cracks and subjected to impulsive loading is studied using the dynamic photoelastic method. The time dependences of the stress intensity factors and the crack growth rate are examined for three models of plates with circular holes and edge cracks __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 79–84, February 2006.     

A system of modified epoxies for dynamic photoelastic studies of fracture

In order to develop a moderately tough transparent polymer, a three-component modified epoxy was investigated. The polymer system included an epichlorohydrin/bisphenol A epoxy, a polyoxypropyleneamine curing agent and a curing accelerator. Twelve different compositions were prepared and evaluated in a series of static and dynamic tests to determine the material properties important in photoelastic studies of fracture. Static tests showed that the critical strain-energy release rate could be varied from 1.4 to 4.1 lb/in. by changing the constituents in the blending of the epoxy. These results forG _Ic indicate that the modified epoxies are considerably tougher than Homalite 100 (G _Ic =0.33 lb/in.) which is commonly employed as a model material in dynamic photoelastic studies. Dynamic photoelastic tests were conducted with half-plane models in order to determine the dilatational- and distortional-wave velocities,c ₁ andc ₂, as well as dynamic values of the modulus of elasticityE and Poisson's ratio ν at loading times of the order of 10^?5 s. These results indicated that the dynamic modulus of some of the modified epoxies was significantly higher than the static modulus indicating that these polymers are rate sensitive. One of the epoxy materials, Blend No. 3 withG _Ic =2.65 lb/in. (464J/m²), was calibrated dynamically. The material fringe value changed nearly linearly as a logarithmic function of time with an increase of about 100 percent as the loading time decreased from 10⁴ to 10^?4 s. This large variation inf _σ implies that the calibration constant must be adjusted when interpreting dynamic fringe patterns. Two of the epoxy compositions were also characterized in a number of fracture experiments involving crack propagation at velocities ranging from arrest conditions to terminal velocity where branching initiates. Dynamic isochromatic-fringe loops were photographed with a Cranz-Schardin multiple-spark camera. The fringe loops were analyzed to give the instantaneous stress-intensity factorK as a function of crack velocity å. The å vs.K curves appear to be invertedL shapes; however, there appears to be a double branch on the vertical part of theL. Also a slightly higherK is required for accelerating cracks and a lowerK for decelerating cracks. Further investigation is required to identify the basic mechanism involved in this fracture behavior.     

Dynamic photoelastic and dynamic finite-element analyses of dynamic-tear-test specimens

The transient response of the dynamic-tear-test specimen of a brittle material, Homalite-100, was investigated by dynamic photoelasticity and dynamic finite-element method. The dynamic stress-intensity factors obtained from dynamic photoelasticity and dynamic finite-element analyses were in reasonable agreement with each other. The dynamic finite-element analysis also showed that the dynamic-fracture-initiation toughness could be determined from the dynamicstrain response of a strain gage located near the crack tip in conjunction with a simple static analysis. Dynamic-fracture-toughness vs. crack-velocity relation was also obtained.     

Simultaneous Observation of Phase-Stepped Images for Photoelasticity Using Diffraction Gratings

Phase-stepped photoelasticity is a powerful method for full-field stress analysis, but sequential collection of the multiple required images limits the technique to static loading applications. We have developed a system that utilizes diffraction gratings to collect four phase-stepped images simultaneously with a single camera for transient loading applications. Two adjacent, perpendicularly oriented, 1D Ronchi rulings are placed after a transparent sample to split the light into equal intensity beams for each diffraction order. The four beams that are diffracted once in the x direction and once in the y direction transmit through arrays of analyzing polariscope elements, with different combinations of fast-axis orientations for four phase-stepped images. The mirrors and imaging lenses in the system work in concert to focus each beam onto separate quadrants of the same CCD. We demonstrate the system for stress analysis of compressive loading of a Homalite-100 disk and of a Homalite-100 plate with a central hole. This system has the potential for photoelastic analysis of time-dependent materials and of dynamic events, when equipped with a high-speed camera.     

An analytical and experimental stress analysis of a practical mode II fracture test specimen

A boundary-collocation method has been employed to determine the Mode II stress-intensity factors for a pair of through-the-thickness edge cracks in a finite isotropic plate. An elastostatic analysis has been carried out in terms of the complete Williams stress function employing both even and old components. The results of the numerical analysis were verified by a two-step procedure whereby the symmetric (Mode I) and antisymmetric (Mode II) portions of the solution were independently compared with existing solutions. Since no previous analytical solutions existed for the asymmetric loading of an edge-cracked plate, the complete solution was verified by comparison with a photoelastic analysis. A compact shear (CS) specimen of Hysol epoxy resin was loaded in a photoelastic experiment designed to study the isochromatic-fringe patterns resulting from the Mode II crack-tip stress distribution. The experiment verified that a pure mode II stress distribution existed in the neighborhood of the crack tips, and confirmed the accuracy of the boundary-collocation solution for the Mode II stress-intensity factors. Specimen center-line stress-distribution data were obtained photoelastically and employed to refine the boundary-collocation analysis. Agreement between the analytically and experimentally determined Mode II stress-intensity factors was excellent.     

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.     

Transient thermal fracture of cracked plates

The effects of a transient thermal load on a cracked plate are studied experimentally using photothermoelasticity. The three crack configurations of an edge crack, an interior vertical crack and an interior crack inclined at 45 deg are analyzed. In each case, the initially heated plates are subjected to cooling along the edge, while the faces of the plate are either completely insulated, or noninsulated, or in a third case, they are covered with heated transparent Plexiglas plates. It is shown that among the three cracks, the largest transient maximum stress-intensity factor occurs for the edge crack. The inclined crack is subjected to a mixed-mode loading. Among the three cooling conditions, the most severe is the insulated faces case while the noninsulated is the least severe. The relative effect of the cooling conditions on the stress-intensity factors for the three crack types is different enough that the results with one cooling condition would not represent those of another one. A comparison of the experimental transient stress-intensity factors for the vertical crack cases to the finite-element results shows good agreement.     

Dynamic stress-intensity factors for unsymmetric dynamic isochromatics

The mixed mode, near-field state of stresses sourrounding a crack propagating at constant velocity is used to derive a relation between the dynamic stress-intensity factorsK _I,K _II, the remote stress component σ _ox and the dynamic isochromatics. This relation, together with an over-deterministic least-square method, form the basis of a datareduction procedure for extracting dynamic,K _I,K _II and σ _ox from the recorded dynamic photoelastic pattern surrounding a running crack. The overdeterministic least-square method is also used to fit static isochromatics to the numerically generated dynamic isochromatics. The resultant staticK _I,K _II and σ _ox are compared with the corresponding dynamic values and estimats of errors involved in using static analysis to process dynamic isochromatic data are obtained. The data-reduction procedure is then used to evaluate the branching stress-intensity factor associated with crack branching and the mixed-mode stress-intensity factors associated with crack curving.     

A Study on the Evaluation of the Fracture Process Zone in CCNBD Rock Samples

The safety of many civil and mining concrete and rock structures including pre-existing crack networks is fundamentally affected by the mechanical behaviour of the material under static and cyclic loading. In cyclic loading case, cracks can grow at a lower load level compared to the monotonic case. This phenomenon is called fatigue due to subcritical crack propagation and depends on the behaviour of the fracture process zone (FPZ). This study presents the results of laboratory diametrical compression tests performed on Brisbane tuff disc specimens to investigate their mode-I (tensile) fracture toughness response to static and cyclic loading and relevant FPZ. The FPZ and fracture toughness response to cyclic loading was found to be different from that under static loading in terms of the ultimate load and the damage mechanisms in front of the chevron crack. A maximum reduction of the static fracture toughness (K _IC ) of 42 % was obtained for the highest amplitude increasing cyclic loading test. Detailed scanning electron microscope (SEM) examinations were performed on the surfaces of the tips of the chevron notch cracks, revealing that both loading methods cause FPZ development in the CCNBD specimens. When compared with monotonic FPZ development, the main difference with the cyclically loaded specimens was that intergranular cracks were formed due to particle breakage under cyclic loading, while smooth and bright cracks along cleavage planes were formed under static loading. Further, the SEM images showed that fatigue damage in Brisbane tuff is strongly influenced by the failure of the matrix because of both intergranular and transgranular subcritical fracturing.     

Stress-intensity factors for surface cracks in functionally graded materials under mode-I thermomechanical loading

This paper describes the development and application of a general domain integral method to obtain J-values along crack fronts in three-dimensional configurations of isotropic, functionally graded materials (FGMs). The present work considers mode-I, linear-elastic response of cracked specimens subjected to thermomechanical loading, although the domain integral formulation accommodates elastic–plastic behavior in FGMs. Finite element solutions and domain integral J-values for a two-dimensional edge crack show good agreement with available analytical solutions for both tension loading and temperature gradients. A displacement correlation technique provides pointwise stress-intensity values along semi-elliptical surface cracks in FGMs for comparison with values derived from the proposed domain integral. Numerical implementation and mesh refinement issues to maintain path independent J-values are explored. The paper concludes with a parametric study that provides a set of stress-intensity factors for semi-elliptical surface cracks covering a practical range of crack sizes, aspect ratios and material property gradations under tension, bending and spatially-varying temperature loads.     

Dynamic fracture toughness of Homalite-100

Dynamic fracture toughness of Homalite-100 determined by T. Kobayashi and Dally are compared with those previously obtained by the authors where similarities in the two results for single-edged-notch specimens of various configurations are noted. Dynamic fracture toughness of Araldite B obtained by Kalthoff, Beinert and Winkler and those of Homalite-100 obtained by the authors are then compared and, again, similarities in the two results and, in particular, the scatters in experimental data for wedge-loaded DCB specimens of different sizes are found. All three teams of investigators used static near-field solution to compute the dynamic stress-intensity factors from recored dynamic isochromatics or dynamic caustics. Errors generated through this use of static near-field solutions, as well as through the use of larger isochromatic lobes, are thus discussed.     

Comparison of the techniques of transmitted caustics and photoelasticity as applied to fracture

A comparison of the optical techniques of photoelasticity and caustics as applied to fracture mechanics is presented. Static as well as dynamic experiments were conducted using the two methods with the same specimen geometry and under the same loading conditions. The results for the crack-tip stress-intensity factor as a function of crack length were obtained from both techniques in three different specimen geometries. A comparison of the results shows good agreement under static conditions but large differences for running cracks.     

Stress-intensity factor for plain concrete in bending—Prenotched versus precracked beams

A series of experiments conducted to compare the behavior of beams with notches to those with natural cracks has recently been completed. A total of 42 beams with notches formed by casting teflon strips into the concrete were tested to failure. A companion series of 42 beams were statically precracked following the procedure described in Ref. 5. The ranges of crack depth to beam depth varied from 0.3 to 0.7 (nominally). Two strengths of concrete were used and the 3-in.×4-in.×15-in. (span) beams were tested on three-point or four-point bending. Comparisons are made on the basis of computed stress intensity using a finite-element program developed by the writers. Results of this study show the following: (1) in all cases the naturally cracked beams yielded higher failure loads and stress-intensity values than notched beams with the same crack length; (2) the averageK ₁ values for precracked beams were approximately 38 percent, 77 percent and 96 percent greater than for notched beams for crack-depth ratios of 0.3, 0.5 and 0.7 respectively.     

Static fracture testing of PMMA plates having flawed fastener holes

Results of static fracture tests on PMMA plates with part-elliptical cracks at fastener holes are presented. Experimental configurations include three crack locations with respect to both open and loaded holes. During static testing, slow growth prior to specimen separation allows for calculation of the maximum stress-intensity factor and identification of the location on the crack border at which it occurs. The testing techniques developed produce a simple, economical means of experimentally validating theoretical analyses of crack problems.