C. W. Smith

An Assessment of Factors Influencing Data Obtained by the Photoelastic Stress Freezing Technique for Stress Fields near Crack Tips

Abstract Factors which influence crack tip stress field data are identified as: (1) Non-linear zone near crack tip due to crack blunting. (2) Normal stress parallel to crack surface. (3) Location of region for data retrieval. The Kolosoff-Inglis solution is used in order to assess effects of crack tip blunting. A set of stress freezing photoelastic experiments are conducted on plates containing through cracks and results are compared with the Westergaard solution in order to assess the effect of Item 2 using appropriate Item 3 locations. A data conditioning computer program is employed to yield accurate values of the stress intensity factor from photoelastic data.

Determination of stress-intensity factors from photoelastic data with applications to surface-flaw problems

ATaylor-series correction to the maximum inplane shear stress was studied as a means of extending the data zone in photoelastic determination of stress-intensity factors beyond the singular region of a two-degree-of-freedom analysis. Convergence properties were obtained by comparing with several complete two-dimensional solutions. Experiments were performed on two kinds of three-dimensional problems, plates containing surface flows in both bending and extension. Results were analyzed by both a two-degree-of-freedom and aTaylor-series correction method (TSCM). Results were compared to theories of F. W. Smith and A. S. Kobayashi and R. C. Shah. It was concluded that:(1)The TSCM program converges rapidly to accurateKI values and will accommodate the scatter inherent in experimental data if the series is properly truncated.(2)The TSCM program is essentially equivalent to the two-parameter representation when only the crack-surface effects dominate.(3)When effects other than crack surfaces are important, TSCM requires more terms but still predictsKI with reasonable accuracy.

Use of three-dimensional photoelasticity in fracture mechanics

The philosophy of fracture mechanics is reviewed and utilized to formulate a simplified approach to the determination of the stress-intensity factor photoelastically for three-dimensional problems. The method involves a Taylor Series correction for the maximum in-plane shear stress (TSCM) and does not involve stress separation. The results are illustrated by applying the TSCM to surface flaws in bending fields. Other three-dimensional problems solved by the TSCM are cited.

Characterization studies of a potential photoelastoplastic material

A controlled-strain apparatus capable of performing the tests essential to establishing the yield locus of polycarbonate was designed and built. Material characterization tests were performed in the form of uniaxial strain rate, creep, isotropy, isoclinic and reloading tests. The yield locus for polycarbonate was determined and an analytical expression in the form of a hypotrochoid was developed. Yield locus results indicate that, although polycarbonate is not a Mises material, the yield locus may be approximated by a circle over a substantial range of Lode’s variable. Tests were run on large plates with holes. Good correlation with two-dimensional theory was obtained in the elastic zone and in the plastic zone where plastic strains were small.

A Study of Near and Far Field Effects in Photoelastic Stress Intensity Determination

Abstract A technique known as the Taylor Series Correction Method (TSCM) for extracting the stress intensity factor from photoelastic data is reviewed. The need for ‘artificial’ flaws is identified and an approach due to Savin is used to near field effects of various practical flaw shapes upon the apparent stress intensity factor. Using the Sneddon-Srivastav solution for a line crack in a finite width plate, the constriction of the singular zone is demonstrated as the crack tip approaches the free edge. Results indicate that care must be taken in applying TSCM to obtain photoelastic data at appropriate distances from the crack tip.

Effects of artificial cracks and poisson's ratio upon photoelastic stress-intensity determination

AbstractA series of stress-freezing photoelastic experiments were performed with multiple replications upon edge-cracked strips for three types of “cracks” in current use:(1)Rectangular slots 0.152 mm wide,(2)1.59-mm-wide slots terminating in a 30-deg vee notch of approximately 0.025-mm root radius, and(3)Natural cracks (approximately 0.0025-mm root radius). Stress-intensity results were compared with the Gross-Srawley analysis; in addition (1) was compared with Savins solution. It was concluded that (2) and (3) yield the same results but (1) was slightly higher.Both (2) and (3) were about 12 percent higher than the Gross-Srawley results. This is shown to be related to a Poissons ratio effect.

Displacement measurements around cracks in three-dimensional problems by a hybrid experimental technique

Diffraction gratings were applied to slices taken from three-dimensional stress-frozen models of bodies with cracks. The slices were then annealed to relax the reversible strains and moiré interferometry was used to determine the deformation of the slice. A virtual reference grating of 1200 ℓ/mm (30,000 ℓ/in.) was used to provide the required high sensitivity. The moiré pattern in the LEFM (linear-elastic fracture-mechanics) zone was photographed with 20 × magnification. Results were compared with those obtained photoelastically.

Influence of Precatastrophic Extension and Other Effects on Local Stresses in Cracked Plates under Bending Fields

Using the technique of stress freezing and slicing, a set of photoelastic experiments was conducted on plates, each containing a single through internal crack in a remote cylindrical bending field, where each crack suffered precatastrophic extension on the tensile side of the plate as well as closure on the compression side. Resulting stresses were compared with the Sih-Hartranft theory. Results indicate substantial stress relaxation near the tensile side of the plate due to precatastrophic extension. It is concluded that: (1) the Sih-Hartranft theory may be used to estimate local elastic stresses on the tensile side of the plate even when closure and precatastrophic extension occur; (2) complex coupling of closure and precatastrophic extension effects preclude the use of simple correction factors for existing mathematical models except for relatively small precatastrophic extension.

Stress intensities for nozzle cracks in reactor vessels

A series of six frozen stress photoelastic tests was conducted to investigate the distribution of stress-intensity factor (SIF) along a crack which occurred at the juncture of a pipe (nozzle) with a cylindrical pressure vessel. Typical photoelastic-fringe patterns are shown for slices which were taken mutually orthogonal to the flaw border and the flaw surface. A typical plot of normalized apparent SIF vs. square root of normalized distance from the crack tip is presented. The variation in SIF along the flaw border is given for all six different crack geometries and, also, the variation of SIF with varyinga/T is presented.

Mixed mode stress intensity distributions for part circular surface flaws

Abstract Using the frozen stress method, mixed mode stress intensity factor (SIF) distributions were obtained for a series of low aspect ratio part circular surface flaws in flat plates over a depth to plate thickness range of 0.20–0.70. Mode I results were compared with Mode I solutions in order to sense the influence of the crack surface inclination to the free boundary. It was found that maximum SIF values did not necessarily occur at maximum flaw depth. A rationale is offered to explain this observation. It was also found that the effect of the boundary inclination was to reverse the relative magnitudes of K 1 K 1 and K 2 K 2 in going from a 30° to a 60° crack surface inclination with the boundary.