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.     

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.     

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.     

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.     

Photoelastic determination of mixed-mode stress-intensity factorsK I,KII andK III

On the basis of existing photoelastic methods for the determination ofK _I andK _II, this paper presents an experimental method for determiningK _III with photoelastic data, and a photoelastic method for comprehensively determiningK _I,K _II andK _III under the complex stress condition. A frozen three-dimensional photoelastic model is first used to determineK _I andK _II from the slice perpendicular to the flaw edge. Then, from that slice, a sub-slice is taken to determine the factorK _III. This method is examined by comparison with two test models.     

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.     

Measurement of stress-intensity factor by means of a-c potential drop technique

A loading effect on a-c potential difference measured for two-dimensional stationary surface crack is examined under opening load without shear. An increment of potential difference caused by a load change is revealed to have a proportional relationship with an increment of the stress-intensity factor,K _I. Also, the constant of proportionality of the relationship is found to be independent of the crack length. Based on this relationship, a procedure is developed for measurement ofK _Iby means of the a-c potential drop technique.     

Determination of stress-intensity factors of fillet-welded T-joints by computer-assisted photoelasticity

Fillet-welded T-joints with crack-like discontinuities are analyzed using the photoelasticity method. Stress-intensity factors of opening modes are determined for undercut, overlap and center-line crack of fillet joints with respect to the various loading conditions and the weld dimensions. The photoelastic analysis uses a 20-point overdeterministic approach. The accuracy of fringe measurement is obtained by iteration of the measured results on a pattern-recognition software.Paper was presented at 1983 SESA Spring Meeting held in Cleveland, OH on May 15–20, 1983.     

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.     

Classification of stress-intensity factors from isochromatic-fringe patterns

The stresses in the local neighborhood of a crack tip have been used to develop a relation between the isochromatic-fringe orderN, its position parametersr and θ and the stress field expressed in terms of stress intensities,K _I ,K _II , and a far-field stress σ _ox . This relation was programmed and a plotting routine was developed to map isochromatic (σ₁ ? σ₂) fields in the neighborhood of the crack tip. The stress intensitiesK _I andK _II and the far-field stress σ _ox were varied and isochromatic fields were constructed for each combination. As bothK _II and σ _ox influence the size, shape and orientation of the isochromatics loops in a systematic manner, the pictorial representation of the isochromatic fields can be used to classify the state of stress (K _I ,K _II and σ _ox ) at the crack tip. Isochromatics which classify six different states of stress have been illustrated and methods used to determineK _I ,K _II , andσ _ox in five of the six states are given.     

Determination of stress-intensity factors by the method of caustics in anisotropic materials

This paper studied the applicability of the method of caustics to anisotropic materials under Mode I and mixed-mode static-loading conditions and introduced the procedure to obtain stress-intensity factors (SIF) in anisotropic materials by the method of caustics.The mapping equations for initial and caustic curves in anisotropic materials were introduced and their computer graphical images were compared to the experimental ones to check the validity of the mapping equations proposed in this paper. The agreement between them was found to be satisfactory.Two kinds of equations to determine SIF in anisotropic materials by the method of caustics are proposed in this paper. Corroborative experiments carried out by using the orthotropic materials under various loading conditions are presented. In the case of Mode I loading condition, the SIF's obtained by this paper's methods were found to be close to the results by another method, i.e., boundary-element method (BEM). And in the case of mixed-loading condition, the SIF's by this paper and BEM show little differences, (2.2–24.4 percent) with respect to the slanted angle of crack.     

Numerical evaluation of generalized stress-intensity factors in multi-layered composites

The problem of the evaluation of the generalized stress-intensity factors for re-entrant corners in multi-layered structural components is addressed. An approximate analytical model based on the theory of multi-layered beams is presented. This approach provides a simple closed-form solution for the direct computation of the Mode I stress-intensity factor for the general problem of a re-entrant corner symmetrically meeting a bi-material interface. For the self-consistency of the theory, re-entrant corners in homogeneous materials and cracks perpendicular to bi-material interfaces can also be gained as limit cases of this formulation. According to this approach, the effects of the elastic mismatch parameters, the value of the notch angle and the thicknesses of the layers on the stress-intensity factor are carefully quantified and the results are compared with FE solutions. FE results are obtained by applying a combination of analytical and numerical techniques based on the knowledge a priori of the asymptotic stress field for re-entrant corners perpendicular to a bi-material interface and on the use of generalized isoparametric singular finite elements at the notch tip. A good agreement between approximate and analytical/numerical predictions is achieved, showing the effectiveness of this approach.     

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.     

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.     

Determination of stress-intensity factors for cracks in tubes under torsion

An experimental investigation by two-dimensional photoelastic technique is carried out to study the stress distribution and to determine the stress-intensity factors for arbitrarily oriented cracks in thin cylindrical shells subjected to torsion. A new method is employed to evaluate the pure and mixed-mode SIF's.