Determination of the dynamic stress intensity factorsK I d andK II d,for a mixed-mode propagating crack

In this paper, the dynamic propagation problem of a mixed-mode crack was studied by means of the experimental method of caustics. The initial curve and caustic equations were derived under the mixed-mode dynamic condition. A multi-point measurement method for determining the dynamic stress intensity factors,K _I ^d , andK _II ^d , and the position of the crack tip was developed. Several other methods were adopted to check this method, and showed that it has a good precision. Finally, the dynamic propagating process of a mixed-mode crack in the three-point bending beam specimen was investigated with our method.     

Photoelastic determination of stress-intensity factors

The increasing number of analytical and numerical solutions for the crack-tip stress-intensity factor has greatly widened the scope of application of linear elastic fracture-mechanics technology. Experimental verification of a particular solution by elastic stress analysis is often a necessary supplement to provide the criteria for proper application to actual design problems. In this paper, it is shown that the photoelastic technique can be used to obtain rather good estimates of the stress-intensity factor for various specimen geometries and loading conditions. Treated are the following cases: wedge-opening load specimen, several notched rotating-disk configurations, and a notched pressure vessel. A sharp crack is simulated by a relatively narrow notch terminating in a root radius of 0.010 in or less. Stress distributions along the section of symmetry ahead of the notch tip are obtained using three-dimensional frozen-stress photoelasticity. The results are used to determine the stress-intensity factor, cK _I , by three methods. Two of these are based on Irwin's expressions for the elastic stress field at the tip cf a crack, and the other is a result of Neuber's hyperbolic-notch analysis. Agreement, with available analytical solutions is good.     

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.     

Photoelastic determination ofK I andK II : A numerical study on experimental data

The most efficient photoelastic methods to obtain stress intensity factors are those based on stress functions series expansions. The coefficients of these expansions are fitted to the experimental isochromatic pattern using an overdeterministic Newton-Raphson least squares method. In this paper, a study has been carried out to analyze the influence on the results of several numerical and experimental factors. It is shown that accurate values of the stress intensity factorsK _I andK _II can be obtained by following some recommendations given in the text and summarized in the conclusions at the end of the paper.     

Use of mixed-mode stress-intensity algorithms for photoelastic data

A generalization of irwin's method and a new algorithm, called quadratic, are proposed for the extraction of mixed-mode stress-intensity factors (SIF) in three-dimensional cracked-body problems. These new algorithms are evaluated along with the existing ones of Smith, Sanford-Dally and Theocaris-Gdoutos, and their SIF results compared.It is shown that all these algorithms deliver SIF values in good agreement and that they all can be applied reliably to near-tip photoelastic data.Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Canada on June 10–15, 1984.     

The determination of mode I stress-intensity factors by holographic interferometry

The use of linear elastic fracture mechanics generally depends upon the availability of suitable analytical or numerical solutions for the relevant crack-tip stress-intensity factor,K. Convenient experimental verification of such solutions is a valuable aid to their correct application and can provide a practical substitute in real design situations of great complexity. A convenient, new experimental technique for estimating the Mode I stress-intensity factor using holographic interferometry and test pieces cut from thin sheets of commercially available polymethylmethacrylate is described and demonstrated. The test pieces can readily be prepared to model any desired Mode I geometry and boundary conditions. In addition, a prior self-calibration procedure can be employed to enhance both convenience and accuracy. Real-time interference-fringe data from the crack-tip region are easily reduced and plotted to yield a straight line whose slope provides a one-parameter evaluation of the effect of geometry on the stress-intensity factor. This information, together with the crack length and applied stress, completely definesK.     

Determination of mixed-mode stress-intensity factors K I and K II for a subsurface crack near a concentrated force

Two-dimensional photoelastic experiments were conducted to obtain isochromatic fringe fields in the region between a crack tip and a concentrated load on the boundary of a half plane. An analysis method is developed to determine the mixed-mode stress-intensity factors due to two interacting stress singularities. The results obtained showed the dominance of the opening mode in extending a delamination crack by sliding surface loads. Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

Scattered-light determination of mode I stress-intensity factors by a fringe gradient independent technique

Integration of the scattered-light stress-optic law and established bending and singular crack-tip relationships yielded new experimental equations for calibration and for the determination of mode I stress-intensity factors which are independent of a stress-fringe gradient. Scattered-light stressoptic coefficients determined from four-point bending tests and an integrated scattered-light bending equation show good agreement with values based on stress-fringe gradients computed with polynomials. Excellent agreement was also shown between mode I stress-intensity factors predicted by the integrated stress-optic equation and analytical solutions available in the literature. Favorable comparisons were also made with predictions based on a polynomial-finite-difference method of determining a stress-fringe gradient. Analyses were limited to flaw geometries and locations where there was minimal rotation of the refraction tensor.     

Strain-gage methods for measuring the opening-mode stress-intensity factor,K I

Measurements of strain near a crak tip with electrical-resistance strain gages do not usually provide a reliable measure ofK _I because of local yielding, three-dimensional effects and limited regions for strain-gage placement. This paper develops expressions for the strains in a valid region removed from the crack tip, and indicates procedures for locating and orienting the gages to accurately determineK _I from one or more strain-gage readings.     

Experimental determination of stress-intensity factors using caustics and photoelasticity

The optical method of caustics has been used with considerable success in recent years for determining stress-intensity factors in both static and dynamic problems. However the midplane analysis explaining the formation of transmission caustics has certain approximations that need to be examined. In this paper it is demonstrated that the midplane analysis is in good agreement with the numerical solution of the exact geometrical optical equations for mapping the light-ray path in a cracked plate. Since both these analyses are obtained by imposing a two-dimensional crack-tip stress field the sensitivity of the method to the deviations from the imposed stress field is examined next. The implications of this examination on the photoelastic technique are then discussed.     

Measurement of mode I stress-intensity factors by scattered-light photoelasticity

The feasibility of using the scattered-light technique to determine Mode I stress-intensity factors is demonstrated for the case of an edge-cracked beam subjected to pure bending. Photoelastic-fringe data were utilized to obtain an expression for the fringe gradient in the singular region surrounding the crack tip. Mode I stress-intensity factors were then determined by relating the fringe gradient to the local stresses in the singular region and extrapolating these results to the crack tip. Experimental and analytical results showed good agreement and the technique is suggested for application to three-dimensional fracture-mechanics problems.     

Use of photoelasticity to determine orthotropicK I stress-intensity factor

A new experimental method of obtaining orthotropic stress-intensity factor,K _I , is presented. The orthotropic photoelasticity and orthotropic linear-elastic fracture-mechanics laws are combined. The combined set of equations is used along with half-fringe photoelasticity to determineK _I in a compact-tension specimen made of a transparent unidirectional fiberglass-epoxy material. The results are compared with finite-element-method solutions.     

Photoelastic determination of stresses in multiple-pin connectors

The design, fabrication, and testing of photoelastic models of double-lap, multiple-pin connectors are discussed. Interest is in the stresses in the inner laps. These stresses are determined by constructing models with photoelastic inner laps and transparent-acrylic outer laps. The connectors have two pins, in tandem, parallel to the load direction. A photoelastic-isotropic point is shown to permit the evaluation of load sharing between the two pins. A numerical scheme, utilizing the isochromatic- and isoclinic-photoelastic data and a finite-difference representation of the planestress equilibrium equations, is used to compute the stresses around the two pins. Representative stress distributions and stress-concentration factors are shown.     

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

A 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 Savin's 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 Poisson's ratio effect.     

Effects of mixed-mode overloading on the mixed-mode I+II fatigue crack growth

In this study, the finite element modeling of the compact tension shear specimens has been used to evaluate the effects of overloading on fatigue crack growth with mixed-mode loading I+II. Element creation and modeling is done by CASCA software. FRANC2D was used for stress analysis and the determination of crack parameters. Life estimation of samples was done by using the software ETBX. To create the mixed-mode I+II, different loading angles of 0, 15, 45 and 75 degrees (with respect to normal direction to the crack surface) were used with various overloading ratios. The effects of residual stresses due to overloading with saving and restoring capabilities were considered as a separate loading. To confirm the modeling results, models were built with ABAQUS and also compared with the results of numerical and experimental data in the literature. There are good agreements in determining the path of the crack growth and life estimation. The effects of the loading direction, overloading ratio and its load ratio, combination of overloadings and their locations on the fatigue crack growth and life are investigated.     

Experimental determination of the dynamic stress-intensity factor using caustics and photoelasticity

The methods of photoelasticity and caustics were used in conjunction with high-speed photography to determine the dynamic stress field near a moving crack. The photographs were analyzed to extract information on crack speed and the dynamic stress-intensity factor. The stress-intensity-factor histories obtained from both techniques were compared to determine the reliability of the two techniques.     

Revisit to the determination of stress-intensity factors and J-integrals using the caustics method

Applications of the optical (shadow) method of reflective caustics to measurement of the stress-intensity factor andJ integral in various specimens are investigated. The necessary experimental requirements to help determine accurate stress-intensity factor andJ integral are described. The ratios ofr _o (radius of initial curve)/r _p (plastic-zone size) andr _o/t(thickness of specimen) are found to be very important experimental parameters to obtain meaningful stress and/or strain intensities surrounding crack tips. The appropriate ranges to determine accurate values of stress-intensity factor andJ integral for polycarbonate (compact tension) and aluminum (c-shaped tension) specimens are presented. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

Photoelastic determination of dynamic crack-tip stresses in an anisotropic plate

The paper outlines a technique of determining the dynamic stress-intensity factors (SIFs) in structurally anisotropic composites from photoelastic measurement data. A composite is considered a linear elastic, homogeneous, orthotropic body. An equation is derived that relates the fringe order with the SIFs and the far-field stresses at the tip of a crack, which is parallel to the orthotropy axis __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 95–103, May 2006.