On the photoelastic determination of complex stress intensity factors

An improvement of the one-parameter extrapolation method of photoelastic determination of complex (mixed-mode) stress intensity factors at straight or curvilinear crack tips in a plane isotropic elastic medium due to Smith et al. [12, 13] can be achieved by measuring the absolute value of such a factor on the isochromatic fringes along properly selected polar directions and not at the maxima of the isochromatic fringes. In this way, the unknown value of the constant term of the stress field near the crack tip is taken into account. It is seen that it is always possible to find at least one appropriate polar direction to measure the absolute value of the stress intensity factor. In the case of Mode I stress intensity factors, these polar angles are = ± 120° and not = ± 90° as generally considered previously. Some numerical results are also presented in this special case and show the efficiency of the present method.     

Notch effects on photoelastic determination of mixed-mode stress intensity factors

An investigation into the notch effect on the photoelastic determination of the mixed mode stress intensity factors is presented. This accomplished by comparing the isochromatic loops generated for a crack and an ellipse in an infinite plate. The generated mathematical loops are based on the exact solutions. A method of analysis is proposed and used to correct the distorted maximum angle $\text{θ}{}_{\mathrm{m}}$ and maximum shear stress $\text{τ}{}_{\max }$ due to the notch effect. The results obtained from the photoelastic measurements based on the proposed method compare favourably with those by an earlier investigation.     

A simple method for the photoelastic determination of mode I stress intensity factors

A new simple method for the photoelastic determination of Mode I stress intensity factors from isochromatics is proposed. This method takes into account the fact that a considerable part of the error committed in the photoelastic determination of Mode I stress intensity factors K_I at crack tips, based on experimentally obtained isochromatic fringe patterns, is due to ignoring the non-singular part of the stress field near the crack tips for the evaluation of these factors. This error can, in most cases, be minimized by an appropriate selection of the polar direction from the crack tip on which the experimental measurements for the subsequent evaluation of the stress intensity factors K_I are made. The suitable polar direction for determining K_I depends in general on the distance of the point where measurements on the isochromatics are made from the crack tip. The method was applied to the problem of a simple crack inside an infinite medium under uniaxial and biaxial loading. A comparison of the present method whith the employed analogous methods shows the superiority of the proposed method.     

A simplified prediction of Kic from tensile data

A previously developed theory of fracture toughness is extended so that the plane strain fracture toughness K_IC may be calculated by a simple integration of uniaxial tensile data. K_IC values calculated by this procedure are within 3 per cent of the values obtained by the previous theory for the materials considered.     

A study of near and far field effects in photoelastic stress intensity determination

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.     

An assessment of far field effects on the photoelastic determination of mixed mode stress intensity factors

A limiting approach inquiry into far field effects on local field equations for mixed mode surface flaws is investigated by computer analysis. Curves showing the diminishing effect of the far field stress towards the cracks tip are plotted using fringe radii ratios vs fringe number. The zone used in the experimental determination of K₁ and K₂ is superimposed on these curves to investigate the extent to which K₁ and K₂ determined by the two parameter method are influenced by the far field stress.     

A vibration method for the determination of stress intensity factors

A new experimental method of determining stress intensity factors is presented. It is based upon measurements of natural frequencies of a specimen before and after the crack is introduced. Single edge notched rectangular and axisymmetrically notched cylindrical specimens were tested and the results compared with previous work. It is shown that the new test will often be sufficiently accurate and is considerably easier to carry out than other experimental procedures.     

A photoelastic determination of stress-intensity factors under thermal stresses

An experimental method for the determination of stress-intensity factors (SIF) at a crack tip under thermal loading is presented. The experimental technique used is thermophotoelasticity. Data were collected from whole-field patterns by means of a digital image analysis system. SIF values were extracted using the stress field equations obtained from Williams' stress function. The photoelastic fringe field corresponding to predicted SIFs was regenerated and superimposed onto the actual fringe field to verify the results.

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Résumé On présente une méthode expérimentale pour déterminer le facteur d'intensité de contrainte à l'extrémité d'une fissure sous une sollicitation thermique. La technique expérimentale utilisée est la thermophotoélasticité. A l'aide d'un système d'analyse digitale de l'image, on rassemble des données venant de configuration de l'ensemble du champ. Les valeurs du facteur d'intensité de contrainte en sont extraites au moyen d'équations du champs de contraintes obtenues à partir d'une fonction de contràintes de Williams. Le champs photoélastique marginal correspondant aux valeurs du facteur d'intensité de contraintes prédit est revu et superposé au champs marginal actuel en vue de vérifier les résultats.

     

Compliance and KI calibration of double cantilever beam (DCB) specimens

Stress intensity coefficients $\text{K}{}_{\mathrm{I}}\text{BH}\text{3}\text{2}\text{/Pa}$ were derived from experimental compliances for DCB specimens using the Irwin-Kies method. Specimens containing either machined slits or cracks were employed in this study. The stress intensity coefficients were determined for plane strain states of stress and compared to the analyses of Gross and Srawley and Ripling, Mostovoy and Patrick. The K_I calibration for specimens containing machined slits was found to be in excellent agreement with the earlier analyses over the range of a/H values examined. Specimens with cracks also exhibited a K_I calibration in very good agreement with those mentioned above, provided one uses the actual crack-front length Be rather than specimen width B in calculating the stress intensity coefficients.     

Numerical methods for determination of stress intensity factors of singular stress field

The asymptotic solution of the singular stress field near a singular point is generally comprised of one or more singular terms in the form of Kr^λ-1f_ij(θ). Based on the asymptotic solution of the singular stress field and the common numerical solution (stresses or displacements) obtained by an ordinary tool such as the finite element method or boundary element method, a simple and effective numerical method is developed to calculate stress intensity factors for one and two singularities. Three examples show that the stress intensity factors evaluated using the method proposed in this paper are very accurate.     

Numerical determination of a class of generalized stress intensity factors

A modification of the collocation method for the numerical solution of Cauchy-type singular integral equations appearing in plane elasticity and, especially, crack problems is proposed. This modification, based on a variable transformation, applies to the case when the unknown function of the singular integral equation behaves like A(x ? c)^α + B(x ? c)^β, where α < 0, 0 < β ? α < 1, near an endpoint c of the integration interval. In plane elasticity such a point is either a crack tip or a corner point of the boundary of the elastic medium. Thus the method seems to be quite efficient for the numerical evaluation of generalized stress intensity factors near such points. A successful application of the method to the classical plane elasticity problem of an antiplane shear crack terminating at a bimaterial interface was also made.     

A semi-theoretical and experimental approach for the determination of the stress intensity factors

The stress intensity factors for plexiglass plates containing edge cracks and subjected to either pure bending or tension are determined herein. The method of investigation was based on a semi-theoretical and experimental approach, where the stress intensity factors are expressed in terms of the measured diameter of the caustic, the crack length, and the width of the specimen. First, two basic crack arrangements (single and double edge cracks) were studied and then the method was utilized for the investigation of more complicated crack arrangements which are difficult or maybe impossible to be investigated otherwise. In particular, the stress intensity factor for plates having a sharp V-notch of various angles θ, and semi-infinite plates containing equal parallel edge cracks subjected to pure bending and tension respectively, were investigated in order to verify the validity of this method.     

Photoelastic determination of stress intensity factors in patched cracked plates

In this paper, the influence of patch parameters on stress intensity factors in edge cracked plates is studied by employing transmission photoelasticity. Edge cracked plates made of photo-elastic material are patched on one side only by $\text{E}$ glass-epoxy and carbon-epoxy unidirectional composites. The patch is located on the crack in such a way that the crack tip is not covered. Magnified isochromatic fringes are obtained by using a projection microscope of magnification 50, converted into a polariscope. Irwin's method is used to compute stress intensity factors from photoelastic data. The reduction in stress intensity factors is presented in graphical form as a function of patch parameters, namely stiffness, location and length. An empirical equation connecting reduction in stress intensity factor and these patch parameters is presented.     

Photoelastic determination of dynamic stress intensity factors in portal frames

Dynamic photoelasticity has been applied to the determination of the dynamic stress intensity factor associated with cracks in the central beam of a portal frame, next to the junction with a column. Results are presented for cracks extending over 12% of the beam depth. The value of photoelastic measurements, in conjunction with numerical analysis, for the assessment of the severity of defects in structures loaded under impact is discussed.     

Determination of the stress intensity factor by methods of photoelastic simulation

Various methods of determination of stress intensity factors from the patterns of the isochromes, the isopachs, and the absolute differences in shape at the tip of a notch are analyzed. The range of extrapolation of the values of K_I within which the theoretically obtained stress distributions coincide with the stresses measured experimentally on a model with a finite radius of the stress raiser tip is established. Determination of the parameter K_I from the patterns of absolute differences of the shape is significantly more complex than from the patterns of the isochromes and isopachs but is justified on models of a high-modulus material when increased accuracy, reliability of the results, and an analysis of the stressed and strained state of a specimen with separation of the main stresses are necessary.Translated from Problemy Prochnosti, No. 1, pp. 33–37, January, 1990.     

A stiffness derivative finite element technique for determination of crack tip stress intensity factors

A finite element technique for determination of elastic crack tip stress intensity factors is presented. The method, based on the energy release rate, requires no special crack tip elements. Further, the solution for only a single crack length is required, and the crack is advanced by moving nodal points rather than by removing nodal tractions at the crack tip and performing a second analysis. The promising straightforward extension of the method to general three-dimensional crack configurations is presented and contrasted with the practical impossibility of conventional energy methods.

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Zusammenfassung Das Verfahren der endlichen Elementen wird angewandt zur Bestimmung der elastischen Spannungsintensitäts-faktoren an einer Rißspitze. Begründet auf die Geschwindigkeit der Energiefreilassung braucht dieses Verfahren keine spezielle Rißspitzenangaben. Weiterhin braucht man nur die Lösung für eine einzige Rißlänge, und der Rill wird fortbewegt eher durch Versetzung von Knotenpunkten als durch Entziehung von Knotenzugspannung an der Rißspitze und durch Ausführung einer zweiten Analyse. Die vielversprechende direkte Ausdehnung der Methode auf allgemeine dreidimensionale Rißgestaltungen wird vorgestellt and der praktischen Unmöglichkeit der klassischen Energie-methoden entgegengestellt.

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Résumé Une technique d'analyse par éléments finis est présentée pour la détermination des facteurs d'intensité des contraintes élastiques à la pointe d'une fissure. Basée sur le taux de relaxation d'énergie la méthode ne nécessite pas d'éléments de forme particulière à la pointe de la fissure. En outre, seule est requise la solution pour une longueur déterminée de fissure simple: le processus d'extension de la fissure est obtenu en déplaçant les points nodaux du réseau plutôt qu'en ôtant les composantes de traction nodale à la pointe de la fissure et en procédant à une seconde analyse. On présente les possibilités prometteuses d'extension de la méthode à des configurations tridimensionnelles plus générales de fissures, en contraste avec les impossibilités auxquelles se heurtent les méthodes conventionnelles basées sur des considérations énergétiques.

     

A remark on the direct numerical determination of stress intensity factors at crack tips

A numerical method for the direct determination of stress intensity factors at crack tips from the numerical solution of the corresponding singular integral equations is proposed. This method is based on the Gauss-Chebyshev method for the numerical solution of singular integral equations and is shown to be equivalent to the Lobatto-Chebyshev method for the numerical solution of the same class of equations.