A new method of determining the stress intensity factor K from isochromatic fringe loops

This paper describes the four parameter method of analysis for determining the stress intensity factor K. Dynamic photoelastic isochromatic fringe patterns associated with cracks propagating in centerpin loaded, eccentric-pin-loaded and crack-line-loaded SEN specimens of Homalite 100 were recorded. Data was obtained for tests over a range of crack velocities from arrest to the terminal velocity of 14,900 in. sec (378 m sec).Six measurements describing the size and shape of the experimental isochromatic loops were used to determine the stress intensity factor K by employing a comparison function to match analytical and experimental results. The analytical isochromatic loops were generated with a Westergaard stress function of the form $\text{Z(z) =}\text{K}\text{√2πz}\text{{1 + β(}\text{z}\text{a})}$ and a superimposed normal stress σ_Ox=αK|√2πz which acts parallel to the direction of crack extension. Results were obtained by the computer program (FRACTURE) for different values of the four parameters to give 8925 analytical fringe loops. Another computer program (SEARCH) was used to find a small group of solution which given very low values of the comparison function f_c. The final solution which contains the value of K was obtained from the small group by selecting the most consistent solution.The results obtained for Homalite 100 show that K_min and K_k are nearly the same and that ? increases abruptly from 0 to about 10,000 in./sec (254 msec) for modest increases in K above 400 psi √in. (4.4 × 10⁵$\text{Nm}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$). Further increases in crack velocity require significant increases in K until terminal velocity is     

Error analysis for determination of stress intensity factors from isochromatic crack tip fringe patterns

A statistical error analysis for the stress intensity factor as determined by the classical apogee point method is represented. Random errors in the measurements of apogee distance, tilt angle and crack tip position are considered the most typical sources for inaccuracies in the determination of the stress intensity factor.     

Analysis of mixed-mode isochromatic crack-tip fringe patterns

Summary Westergaard stress function representations of the stress field around the tip of a stationary crack subjected to mixed-mode loading are employed to develop a general relationship between the isochromatic fringe orderN, its position parametersr and and the general stress field expressed in terms of several parameters, the stress intensitiesK ₁,K ₂, a far field stress parameter , and higher order term parameters ₁ and ₂. These parameters are varied and isochromatic crack tip fringe patterns are constructed for a set of classified combinations. Since the size, shape, orientation, and other particular features of the fringe patterns depend strongly on the combination of parameters chosen they can be used to classify crack tip fringe patterns. The introduction of fringe loop diagrams not only facilitates the classification procedure and enables a classification without plotting fringe patterns, but it also permits qualitative and quantitative evaluation of the isochromatic patterns. Isochromatics which classify fourtyeight different states of stress are investigated and the majority of them have been illustrated.

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Analyse von Isochromatenfeldern um Rißspitzen unter gemischter Beanpruchungsart

Zusammenfassung Isochromatenbilder, welche den Spannungszustand um eine im gemischten Spannungsfeld ruhende Rißspitze repräsentieren, werden untersucht. Eine allgemeine Beziehung wird hergeleitet zwischen der Ordnung der IsochromatenN, deren Lageparameterr und und dem allgemeinen Spannungsfeld um die Rißspitze, welches im Rahmen einer mehrparametrigen Bruchmechanik durch die SpannungsintensitätsfaktorenK ₁ undK ₂, einem Fernspannungsfeldparameter und zweier weiterer Parameter ₁ und ₂ definiert ist. Die beiden letzteren Parameter sind mit den Gliedern höherer Ordnung in der Entwicklung der Westergaardschen Spannungsfunktionen verwandt. Die Parameterm=K ₂/K ₁, , ₁, und ₂ werden variiert und Isochromatenbilder für eine Reihe von Parameterkombinationen dargestellt.Die Tatsache, daß die verschiedenen Parameter Größe, Gestalt, Orientierung und weitere wesentliche Charakteristika des Isochromatenbildes parameterspezifisch verändern, gestattet eine vollständige Klassifizierung der Isochromatenbilder. Die Einführung von Isochromatendiagrammen erleichtert nicht nur das Kalssifizieren der Isochromatenfelder sondern erübrigt aufwendige numerische Zeichenprogramme zu deren Darstellung und dem Studium derer Charakteristika. Darüber hinaus ist eine qualitative wie auch quantitative auswertung in einfacher Form möglich. Zwillingsbildung von Isochromaten sowie lokale Minima von Isochromatenfeldern sind durch diese Diagramme quantitativ erfaßbar. Das Klassifikationsschema umfaßt 48 Grundfälle. Die Mehrheit der damit verbundenen Isochromatenfeldern ist abgebildet.

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With 21 Figures     

A theoretical-experimental method of determining stress intensity factors

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 4, pp. 97–101, July–August, 1989.     

Stress intensity factor determination from isochromatic fringe patterns—A review

It is the aim of this paper to present an overview of the major publications and persons that have contributed to the development in the area of determining stress intensity factors (SIF) from photoelastic isochromatic fringe patterns. The authors task concludes with a reference list at the end of the paper, which contains a total number of 147 publications and 129 authors, starting with the well known papers by Post, Wells and Post from the fifties, and terminating with papers published in 1986. For convenience a separate, alphabetic listing of authors is also provided. Although most of the papers compiled deal with applications of the techniques, a good deal of the papers are devoted to development of the methods. Static loading conditions are studied in the majority of the papers, but dynamic cases are also covered. Almost all other aspects of the problems are covered in the papers listed, e.g. mode I, mixed-mode conditions, two- and three-dimensional problems, near- and far-field effects, and plate bending problems, to mention a few.     

A contour integral computation of mixed-mode stress intensity factors

A path independent contour integral formula for the distinct calculation of combined mode stress intensity factors in linear plane elasticity problems is presented. The method is based on a Somigliana type singular integral representation and is easily appended to existing finite element computer codes. Numerical results to three problems with known perturbation solutions are given and demonstrate the accuracy and stability of the method.

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Résumé On présente une intégrale de contour indépendante du chemin de parcours pour le calcul sélectif des facteurs d'intensité des contraintes correspondant à une combinaison de modes, dans le cas de problèmes d'élasticité plane et linéaire. La méthode se base sur une représentation de l'intégrale singulière du type Somigliana, et peut être aisément adaptée aux codes existant pour le calcul des éléments finis par computer. Des résultats numériques sont fournis dans le cas de trois problèmes comportant des solutions de perturbation connues; ils démontrent l'exactitude et la stabilité de la méthode proposée.

     

A method of determining stress intensity factors in reinforced panels

N. E. Zhukovskii Aviation Institute, Khar'kov. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 29, No. 2, pp. 72–77, March–June, 1993.     

Extrapolation techniques for determining stress intensity factors

A theoretical basis is developed for the extrapolation technique of Chan, Tuba and Wilson and Ayres and Siddall for determining stress intensities from finite element results. The conditions for which the technique is valid is presented for the Mode I only, Mode II only, and mixed mode condition.     

Characterization of isochromatic fringe patterns for a dynamically propagating interface crack

The isochromatic fringes surrounding a crack propagating along a bimaterial interface have been developed and characterized. A parametric investigation has also been conducted to study the influence of various fracture parameters on this isochromatic fringe pattern. The relevant fracture parameters of interest were the crack-tip velocity, the mode mixity of loading and the non-singular stress field component. In all the cases the fringe pattern was compared with the more familiar patterns that are generated for the case of crack propagation in homogeneous media. It was found that both the crack tip velocity and the mode mixity of loading have a significant effect on the size and shape of the isochromatic fringe pattern surrounding a crack tip propagating along a bimaterial interface. However, the non-singular stress field component was found not to have a substantial effect on the fringe pattern. This is in contrast with the case of crack propagation in homogeneous media, where the non-singular stress field component determines the tilt of the fringe contours. The paper also presents an appropriate scheme to analyze experimental fringe contours to extract the various fracture parameters of interest. Finally, this scheme is employed to analyze actual experimental data from a typical bimaterial interface fracture experiment.     

Experimental calculation of mixed-mode notch stress intensity factors for anisotropic materials

This study developed a least-squares method to find the notch stress intensity factors (SIFs) of anisotropic materials using image-correlation experiments without the requirement of smooth procedures. Complex displacement functions are deduced into a least-squares form, and then displacements from the image-correlation experiments are substituted into the least-squares equation to evaluate the notch SIFs for anisotropic materials. Experimental results compared with the H-integral and finite element analyses show that the SIFs evaluated from the current method are acceptably accurate if more than five displacement terms are included. Moreover, the least-squares SIFs are not sensitive to the maximum or minimum radius of the area from which data is included, so experimental data very near the notch tip is not necessary.     

Evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods

A method for evaluating mode I, mode II and mixed-mode stress intensity factors from in-plane displacement fields using the method of nonlinear least-squares is proposed in this paper. Along with stress intensity factors, crack tip location and rigid body displacement components are determined simultaneously from both displacement components obtained using full-field optical methods or numerical methods. The effectiveness is validated by applying the proposed method to mixed-mode displacement fields obtained through digital image correlation, displacement fields obtained by analysis using elasto-plastic finite element method, and displacement fields around a fatigue crack obtained by electronic speckle pattern interferometry. Results show that the proposed method can extract stress intensity factors from the displacement fields both accurately and easily. Furthermore, they can be determined even if the material at a crack tip exhibits small-scale yielding. It is expected that the proposed method is applicable to various fracture problems during experimental and numerical evaluation of structural components.     

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 method for determining dynamic stress intensity factors from cod measurement at the notch mouth in dynamic tear testing

A formula is derived for determining dynamic stress intensity factors directly from crack mouth opening displacements in dynamic tear test specimen. The results obtained by the present estimation method for stationary as well as propagating cracks agree excellently with those directly obtained through a highly accurate moving-singularity finite element method. The present method can also be applied for other types of specimen which have a relatively short edge crack without any loading on the crack surface. The present simple estimation method should be of great value in the experimental measurement of dynamic stress-intensity factors for propagating cracks in (opaque) structural steel dynamic tear test specimens.     

A method of determining stress intensity factors in reinforced panels (report 1)

Conclusions 1. We proposed a theoretical-experimental method of determining the SIF in the panels.2. The numerical experiments make it possible to substantiate the measurement base of the relative displacements of the crack edges.3. Approximation of Eq. (1) ensures a high accuracy at m = 1 in the panel A and m = 2 in the panel B.4. In the case of short cracks, calculations can be carried out using Eq. (4) and (5).5. In practice in determining the SIF it is sufficient to measure displacements at 1–3 points.6. A special feature of the method is the possibility of restoring the loads acting on the panel, and contract forces.N. E. Zhukovskii Aviation Institute, Khar'kov. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 1, pp. 84–89, January–February, 1993.     

Two measurement techniques for determining effective stress intensity factors

Two methods were studied for determining crack closure and locking effects under combinations of mixed mode I and II loading, namely the strain gauge and the surface replica methods. They demonstrated that strain gauges are able to detect the mode I crack closure but not mode II crack locking. As an alternative, the surface replica method is suggested as a practical technique for measuring mode II crack locking effects. The effective mode II stress intensity factor range can be estimated by comparison of the actual measured sliding range between a pair of crack faces and the theoretical sliding range.     

Simple methods of determining stress intensity factors

A prerequisite for any fracture mechanics analysis of a cracked structure, is a knowledge of the stress intensity factor at the tip of the crack. Many methods are available for evaluating stress intensity factors, but if the structural configuration is complex, they are usually costly in time and money. This paper describes some simpler approximate methods which are both quick and cheap. Their use is illustrated by examples typical of aerospace applications, e.g. cracks at holes and cracks in stiffened sheets. The errors introduced into calculations of residual static strength and fatique lifetimes by the use of such approximations are acceptable for many practical cases: They are usually no greater and often smaller than those due to uncertainties in other parameters such as service loads, material toughness, etc.