Experimentally determined stress-intensity factors for single-edge-crack round bars loaded in bending

Dimensionless stress-intensity factors were determined for single-edge-crack solid and hollow round bars loaded in bending. These factors were calculated from experimental compliance (inverse slope of load-displacement curve) measurements made on round bars loaded in three-point bending. The compliance specimens had span to diameter ratios of 6.67 and 3.33, and measurements were made over a range of dimensionless crack lengths from 0.002 to 0.70. The tests were made using 3-in. (76-mm) and 6-in. (152-mm) solid and hollow round bars notched on one side; the hollow bars had an inner to outer diameter ratio of 0.33. A comparison was made with data in the literature for rectangular bars; for ana/D of 0.0001, the dimensionless stress-intensity factor for a solid round bar is 1.3 vs. 2.0 for a rectangular bar.     

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.     

Dispersive bending waves in uniform bars

The traveling bending waves in a long beam of rectangular cross section were measured and calculated. The bending waves were induced by impacting with a steel sphere and measured with strain gages at several distances from the point of impact. The impact force was calculated as a function of time by integrating the dynamic equations of the sphere and the beam. The force spectrum was then found using a fast-Fourier-transform (FFT) calculation and multiplied by the moment-frequency response of the beam to determine the moment spectrum. The moment-time function was calculated by an inverse FFT. The traveling wave is dispersive; its spectrum was found from that at the point of impact by phase shifting each component by an angle proportional to the distance and to the square root of the frequency. Again the time curve was determined by an inverse FFT. The indentation stiffness of the beam was found to be very much less than that of the elastic half space because of transverse bending. After the impact force was recalculated with this correction, the calculated moment-time traces agreed very well with the measured ones.     

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.     

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.     

An analytical approach for the calculation of stress-intensity factors in transformation-toughened ceramics

Stress-induced transformation toughening in Zirconia-containing ceramics is described analytically by means of a quantitative model: A Griffith crack which interacts with a transformed, circular Zirconia inclusion. Due to its volume expansion, a ZrO₂-particle compresses its flanks, whereas a particle in front of the crack opens the flanks such that the crack will be attracted and finally absorbed. Erdogan's integral equation technique is applied to calculate the dislocation functions and the stress-intensity-factors which correspond to these situations. In order to derive analytical expressions, the elastic constants of the inclusion and the matrix are assumed to be equal.     

A critical review of methods for determining stress-intensity factors from isochromatic fringes

Two-parameter methods of fracture analysis for determining the stress-intensity factor from photoelastic isochromatic-fringe data were critically reviewed. The methods of Irwin, Bradley and Kobayashi, and Smith were developed in detail and differences in the three approaches were noted. Theoretical fringe loops were generated for a crack of length 2a in a semi-infinite plate with biaxial loading. These fringe loops were used to compare the three analysis methods and to determine the accuracy of each method. All three methods give a close estimate of the stress-intensity factor, with the Bradley-Kobayashi differencing procedure providing the most precise estimate ofK. However, if measurement errors become excessive (larger than 2 percent) the differencing procedure magnifies these errors and the original method proposed by Irwin is the recommended approach. The two-parameter methods can be employed to determineK to within ±5 percent, provided the angle of tilt of the isochromatic-fringe loop is 73 ≤θ _m < 139 deg. Ifθ _m is outside this range, the two-parameter methods should not be employed.     

Effects of superimposed hydrostatic pressure on fracture in round bars under tension

The effect of superimposed hydrostatic pressure on fracture in round bars under tension is studied numerically using the finite element method based on the Gurson damage model. It is demonstrated that while the superimposed hydrostatic pressure has no noticeable effect on necking, it increases the fracture strain due to the fact that a superimposed pressure delays or completely eliminates the nucleation, growth and coalescence of microvoids or microcracks. The experimentally observed transition of the fracture surface, from the cup-cone mode under atmospheric pressure to a slant structure under high pressure, is numerically reproduced. It is numerically proved that the superimposed hydrostatic pressure has no effect on necking for a damage-free round bar under tension.     

Fatigue crack closure of surface flaws loaded in pure bending

The objective of this paper is to report fatigue crack growth and closure behavior for surface flaws subjected to pure bending. An optical interference technique is employed with PMMA, a transparent polymer, to determine the three-dimensional crack-surface displacement field. The point-wise measure of crack closure along the crack front obtained from optical interference is compared with an average (bulk) crack-opening load determined via crack-mouth-displacement gage measurements. In addition, the effect of crack-closure loads on the subsequent growth of the surface flaw is examined. Dr. Ray is currently associated with The Boeing Company, Seattle, WA.     

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.     

Photoelastic investigation of stresses in bars with reinforced semicircular notches under bending

The object of the work described was to obtain information about the stresses in reinforced plastic bars. Tests were carried out under bending on a bar with a composite reinforced semicircular notch. The bars were of epoxy resin reinforced with duralumin. The reinforcements are the concentric, crescent and arch types. The relations between the maximum shear stress and breadth of bars are obtained. The most suitable reinforcements are discussed.     

Numerical computation and analytical estimation of stress-intensity factors for strips with multiple edge cracks

In this paper, stress-intensity factors for a two-dimensional problem are determined. Strips with multiple symmetrical edge cracks in tension are investigated. A simple analytical estimation is compared to numerical results. The influence of penetration of the crack faces and mixed-mode loading on the numerical results is investigated. A simple method to estimate stress-intensity factors for strips with multiple edge cracks is proposed.     

Experimentally determined properties of softening functions in pseudo-elastic models of the Mullins effect

This paper aims to identify the true source of limitations of pseudo-elastic models for describing the stress-softening phenomenon in elastomers which were recently proposed in the literature [Ogden, R.W., Roxburgh, D.G., 1999. A pseudo-elastic model for the Mullins effect in filled rubber. Proceedings of the Royal Society of London A 455 (1988), 2861–2877; Elías-Zúñiga, A., Beatty, M.F., 2002. A new phenomenological model for stress-softening in elastomers. Zeitschrift für angewandte Mathematik und Physik (ZAMP) 53 (5), 794–814]. These models as well as their modified versions [Mars, W.V., 2004. Evaluation of pseudo-elastic model for the Mullins effect. Tire Science and Technology, TSTCA 32 (3), 120–145; Elías-Zúñiga, A., 2005. A phenomenological energy-based model to characterize stress-softening effect in elastomers. Polymer 46 (10), 3496–3506] fail to give fully satisfactory coincidence of experimental data and theoretical predictions. In this paper a suitable analysis of experimental data published in the open literature is presented. This analysis shows several interesting features regarding the nature of the stress-softening phenomenon (widely known as the Mullins effect). In particular, it is shown that the magnitude of stress softening varies with strain in a non-monotonous manner and this non-monotonous character of the stress-softening phenomenon strongly depends on magnitude of the pre-strain. This experimental fact is in contradiction with the basic assumption used in pseudo-elastic models that the stress softening is described by a monotonously increasing function of strain. The common theoretical basis of pseudo-elastic models of stress softening and the source of this conflict are clarified.     

On plastic localization and failure in plane strain and round void containing tensile bars

Gurson's constitutive model describing effects of void nucleation and growth in ductile metals is adopted for numerical analysis of plastic localization and failure modes in axisymmetric and plane strain tensile tests. A simple numerically oriented treatment of void coalescence is utilized. The analysis is performed in the framework of the bifurcation approach and no initial imperfections are needed to trigger localizations. The unsymmetric eigenvalue problem is solved by using a perturbation scheme which essentially reduces the problem to a symmetric eigenvalue formulation for a recently proposed “symmetrized comparison solid” of nonassociated plasticity plus the easily computable perturbation correction. The results obtained are shown to qualitatively reproduce the essential features observed experimentally in uniaxial tests.     

Stress-concentration factors for semielliptical notches in beams under pure bending

Elliptical notches in rectangular beams under pure bending are examined photoelastically. Stress-concentration factors due to a single elliptical notch are obtained for wide ranges of 2a/h andd/h, where 2a, d, andh are the width of notch, depth of notch, and depth of beam, respectively. In particular, the geometries of the optimum elliptical notches producing the least stress concentrations are obtained. Almost the whole elliptical boundary of these notches are stressed to the same peak, which indicates that these notches will probably produce the least stress concentrations among all notches, elliptical or nonelliptical. The graphs herein will enable the designers to find the stress-concentration factors of elliptical notches and to pick out the geometry of the optimum notch which will give the least stress concentration for any given values of 2a/h andd/h. Stresses and the stress-concentration factors at the bottom of the beam opposite the notch are also obtained. These stresses, though smaller in magnitude, are of an opposite sign to the peak stress at the notch. For brittle materials, a smaller tensile stress may be more critical than a large compressive stress; therefore, these stress-concentration factors are also given.     

Variation in stress-intensity factor and back-surface displacement for surface cracks

Knowledge of the magnitude and variation in the stress-intensity factor (SIF) around the perimeter of a surface crack is essential for an accurate analysis of a flawed component. SIFs for surface flaws of various semi-elliptical geometries were analytically determined. Three-dimensional linear-elastic finite-element analysis was performed to determine the maximum SIF for bending and tension for each of 12 crack geometries which represent deep surface flaws in finite-thickness plates. Experimental verification of one of the crack geometries was performed. Interferometry techniques were used to determine the actual variation in SIF along the curve crack front due to bending. In addition to the SIF calculations, physical characteristics are noted as observed in the analytical and experimental evaluations.     

Stress-concentration factors for multiple semielliptical notches in beams under pure bending

Uniformly spaced semielliptical notches in rectangular beams under pure bending are examined photoelastically. Minimum stress-concentration factors, produced by multiple elliptical notching of beams, are obtained for wide ranges of notch width, semiminor elliptical axis, notch depth, notch pitch and depth of beam. In particular, the geometries of the optimum elliptical notch producing the least stress concentration are obtained for a practical range of parameters. Stress-concentration factors for beams with multiple semi-elliptical notches are compared to those for beams with single semielliptical notches and to those for beams with semicircular notches. The maximum reduction of stress-concentration factor for beams with multiple semielliptical notches is to approximately 37 percent of the stress-concentration factor for beams with single semielliptical notches. Within the range of parameters investigated, the stress-concentration factor for beams with multiple semielliptical notches was 15 to 37 percent less than that for multiple semicircular notches.