Sickle-shaped crack in a round bar under complex Mode I loading

A sickle‐shaped surface crack in a round bar under complex Mode I loading is considered. First, the stress‐intensity factor (SIF) along the front of the flaw is numerically determined for five elementary Mode I stress distributions (constant, linear, quadratic, cubic and quartic) directly applied on the crack faces. The finite element method and linear elastic fracture mechanics concepts are employed. Then, a numerical procedure to calculate approximate values of SIF for a complex Mode I stress distribution on the crack faces is proposed based on both the power series expansion of the function describing such a stress distribution and the superposition principle. In order to validate the results obtained through the above procedure, a comparison with numerical data available in the literature is made.     

Stress intensity factors for cracks emanating from two-dimensional semicircular notches using the composition of SIF weight functions

This paper presents stress intensity factor (SIF) solutions for edge cracks emanating from semicircular notches using the composition of SIF weight functions. The method isolates and combines the geometrical influences defined by constitutive SIF weight functions to yield SIFs for semicircular notches in finite thickness bodies. Finite element analysis was employed to obtain the required stress distributions and to generate reference constitutive SIFs. Problems encountered with curve fitting high gradient stress distributions were addressed and a robust mathematical solution for these was formulated. The new SIF solutions were verified by comparison with published solutions showing a high degree of accuracy and reliability. The composition model was demonstrated to allow rapid generation of SIFs for mode I cracks in complex geometries where the relevant simple constitutive solutions are available. These new solutions expressed as SIF weight functions allow interpolation between the geometrical parameters for which they are valid and also to include the effect of complex stress distributions such as those due to residual stresses.     

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 analysis of three-dimensional planar embedded cracks subjected to uniform tensile stress

In this paper we describe an analytical methodology for calculating Stress Intensity Factors (SIF) on planar embedded cracks with an arbitrarily shaped front. The approach is based on a first order expansion of the celebrated integral of Oore-Burns and the actual shapes of three-dimensional planar flaws are analysed in terms of homotopy transformations of a reference disk.The solution is proposed in terms of Fourier series and the first order approximation of the coefficients is given independently from the homotopy transformations.The comparison with numerical results, taken from scientific literature, indicates that the proposed equation is very accurate when the flaw presents a small deviation from the circular shape. Finally, the closed form solution is used to predict the SIF of many types of convex and non-convex planar flaws present in engineering components such as welded structures or casting components.     

Influence of material properties of SIFs determined by frozen stress

In a prior study utilizing two materials for which thermal and mechanical properties of both materials in bimaterial specimens were matched except for modulus, it was found that modulus mismatch had a negligible effect on the stress intensity factor (SIF) level and distribution for cracks in bond lines of stress frozen photoelastic bimaterial specimens. However, bond line residual stresses increased the SIF values. Since it is almost impossible to obtain commercial stress freezing materials with matching critical temperatures (T_c) with different moduli, the present study of cracks parallel to and within bond lines utilized such materials with T_c mismatch and compared results with parallel studies with matched T_c values in order to evaluate T_c mismatch effects. Results show that T_c mismatch creates mixed mode conditions in cracks parallel to the bond line with significant increases in the mode I SIF (K₁) for cracks very near the bond line but shows little effect for cracks within or away from the bond line. The absence of a modulus mismatch effect is again confirmed as well.     

Mixed mode stress intensity distributions for part circular surface flaws

Using the frozen stress method, mixed mode stress intensity factor (SIF) distributions were obtained for a series of low aspect ratio part circular surface flaws in flat plates over a depth to plate thickness range of 0.20–0.70. Mode I results were compared with Mode I solutions in order to sense the influence of the crack surface inclination to the free boundary. It was found that maximum SIF values did not necessarily occur at maximum flaw depth. A rationale is offered to explain this observation. It was also found that the effect of the boundary inclination was to reverse the relative magnitudes of $\text{K}{}_1\text{K}\text{?}{}_1$ and $\text{K}{}_2\text{K}\text{?}{}_2$ in going from a 30° to a 60° crack surface inclination with the boundary.     

The role of flaw size and fiber distribution on tensile ductility of PVA-ECC

Polyvinyl Alcohol-Engineered Cementitious Composites (PVA-ECC) designed based on micromechanics exhibit high tensile ductility (above 1%) and limited crack widths (below 100 μm). The tensile performance of ECC is dependent on the fiber and flaw size distributions. These parameters are known to be influenced by the matrix flowability and mix processing; however, a comprehensive quantitative analysis framework linking fiber and flaw size distributions to the tensile performance of PVA-ECC is needed to supplement theoretical understanding of the relationship between micromechanical parameters and composite macro-properties. In the present work, fiber distribution (dispersion and orientation) of two different ECCs in terms of matrix flowability was investigated using fluorescence microscopy and advanced digital image analysis. The maximum flaw size distribution along the specimens was also analyzed by cross-sectional image analysis. The influences of fiber and flaw size distributions on the composite behavior of PVA-ECCs were experimentally established.     

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.     

Applicability of Weibull analysis for brittle materials

Weibull analysis for the interpretation of strengths of brittle materials was previously justified for a particular flaw size distribution. The present results show that the Weibull distribution provides a close approximation to the distribution of failure stress for all the flaw size distributions considered. However certain reservations are noted in the interpretation of the Weibull modulus.     

Contact stress distributions in a turbine disc dovetail type joint - a comparison of photoelastic and finite element results

Two dimensional photoelastic frozen stress techniques were used to investigate the stress distributions of an axially loaded dovetail joint as is found in the design of some turbine blade-disc fixings. The internal stress distributions were obtained by the shear difference method and were compared to results obtained by using the finite element method. It was found that steep principal stress gradients were present immediately below the contact surfaces in the zone adjacent to the fillet radius of the dovetail fixing, which could be an important consideration in the fatigue strength of the joint. The finite element model used gave the same trends of stress as the photoelastic model, predicted higher peak principal stresses and did not exhibit the same detailed variations of stress distribution.     

Cyclic plasticity near a cracklike elliptical flaw

An elastic-plastic analysis of a cracklike elliptical flaw under cyclic tensile loading is discussed. A highly efficient numerical approach combining aspects of the finite element and boundary collocation methods was developed to allow accurate solution detail in the root region of the flaw. Conditions of localized yielding at the flaw root is the focus of the work with applied stress levels small relative to yield stress and plastic zone dimensions comparable to the root radius of curvature. The flaw is considered isolated in an infinite sheet under plane strain constraint. Numerical results are given for the stress and strain distributions and the plastic zone changes during a constant amplitude cyclic loading. These elastic-plastic results are compared with the predictions of elastic and fully plastic analysis and also with sharp crack solutions.     

Consideration of the residual stress distributions in fatigue crack growth calculations for assessing welded steel joints

To better understand the crack closure and propagation, an analytical model is established. The residual stress effect on fatigue crack growth equations has been considered using the residual stress intensity factor (SIF) (K_res). The joint geometries, residual stress distributions (σ_res) and residual stress ratio (R_res) were considered also. K_res are calculated using the analytical weight function (WF) method and different residual stress distributions. It is to be emphasized that the current approach is little investigated. This is because the WF has already been developed to calculate SIF for an existing crack. The current approach calculates K_res for the crack that initiates and propagates until failure. Different stress distributions have been used, and R_res is defined. The validity of using the WF has been shown. SIF due to applied load (K_app) and applied stress ratio (R_app) have been considered. Fatigue crack growth rate was investigated in accordance with the current approach. The results have been verified and benchmarked.     

A notch stress intensity approach applied to fatigue life predictions of welded joints with different local toe geometry

In the Notch Stress Intensity Factor (N‐SIF) approach the weld toe region is modelled as a sharp V‐shaped corner and local stress distributions in planar problems can be expressed in closed form on the basis of the relevant mode I and mode II N‐SIFs. Initially thought of as parameters suitable for quantifying only the crack initiation life, N‐SIFs were shown able to predict also the total fatigue life, at least when a large part of the life is spent as in the propagation of small cracks in the highly stressed region close to the notch tip. While the assumption of a welded toe radius equal to zero seems to be reasonable in many cases of practical interest, it is well known that some welding procedures are able to assure the presence of a mean value of the weld toe radius substantially different from zero. Under such conditions any N‐SIF‐based prediction is expected to underestimate the fatigue life. In order to investigate the degree of conservatism, a total of 128 fillet welded specimens are re‐analysed in the present work by using an energy‐based N‐SIF approach. The local weld toe geometry, characterised by its angle and radius, has been measured with accuracy for the actual test series. The aim of the work is to determine if the N‐SIF‐based model is capable of taking into account the large variability of the toe angle, and to quantify the inaccuracy in the predictions due to the simplification of setting the toe radius equal to zero.     

Utilization of prior flaw information in ultrasonic NDE: An analysis of flaw scattering amplitude as a random variable

Probabilistic approaches to flaw detection, classification, or characterization often assume prior knowledge of the flaw distribution. It is implicit that there is a scattering amplitude distribution associated with the flaw distribution. In a number of previously published probabilistic analyses, it has been assumed that scattering amplitude is an uncorrelated, Gaussian random variable with zero mean and known variance. In the work reported here, these assumptions are evaluated for the case of a lognormal distribution of spherical flaws. The correlation, mean, variance, and nature of the scattering amplitude distribution are considered as a function of frequency and as a function of the breadth of the assumed flaw distribution. It is shown for the assumed flaw distributions that scattering amplitude is not uncorrelated and does not have zero mean. It is shown that errors in estimating the flaw distribution variance affect both the scattering amplitude mean and variance. Using both analytical and numerical procedures, the scattering amplitude distribution is shown to be lognormal at long wavelength for a lognormal distribution of spherical scatterers. At high frequency, the distribution is shown to have a bimodal character.     

Alternative equations of magnetophotoelasticity and approximate solution of the inverse problem

In magnetophotoelasticity, photoelastic models are investigated in a magnetic field in order to initiate rotation of the plane of polarization that is due to the Faraday effect. The method has been used for the measurement of stress distributions that are in equilibrium on the wave normal and therefore cannot be measured with the traditional photoelastic technique. In this category belong bending stresses in plates and shells and residual stresses in glass plates. Two new systems of equations of magnetophotoelasticity are derived. One of them describes evolution of the polarization of light in a magnetophotoelastic medium in terms of eigenvectors, the other in terms of distinctive parameters. For the latter system, an approximate closed-form solution has been found. The integral Wertheim law has been generalized for the case of stress states in equilibrium when rotation of the plane of polarization is present.     

Studies on fracture model and mechanism for compressed cast iron specimen

Based on the results of acoustic emission monitoring and electron microscope observing, the author of the paper proposes a mechanics model for compressed cast iron specimen—a column with internal inclined crack. Then numerical simulations for the model are made and the distributions of SIF K_i (i = I, II, III) along the crack front are obtained and so the fracture mechanism of suen kind of specimen is found. Finally, according to the theory of strain energy density factor, the critical fracture angle is obtained by using the known SIF. When the friction between the crack surfaces is taken into account, the fracture angle calculated agrees well with experimental results of compressed cast iron in a general laboratory.     

Probabilistic strength of {1 1 1} n-type silicon

The two-parameter Weibull strength distribution of {1 1 1} n-type silicon prismatic bars was determined in four-point bending and analyzed as a function of specimen size (width), loading rate, two different crystallographic orientations, and specimen orientation (polished or etched surface in tension). 100% fractography was performed to classify strength-limiting flaw types and to censor the strength data. All flaw types were extrinsic. Machining or cutting damage in the form of chipped edges (an edge-type flaw) was the dominant strength-limiting flaw when the polished surface was subjected to tensile stress, while a flat-bottomed etch pit (a surface-type flaw) was the dominant strength-limiting flaw when the etched surface was subjected to tensile stress. The censored Weibull strength distribution was independent of specimen width, loading rate (indicative of slow crack growth insusceptibility), and the two crystallographic orientations; however, it was dependent on specimen orientation. Pooling of the strength data was employed to tighten the confidence intervals about the censored parameters. The results from this study indicate that different extrinsic strength-limiting flaws and strength distributions will be operative depending on the manner in which a silicon component is stressed.     

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.

     

Experimental characterization of cracks at straight attachment lugs

Lugs are widely used to connect aircraft components. As damage tolerance requirements become increasingly important for design qualification, the cracked-hole problem has received sustained attention because it is the prevalent failure initiation mode of the aircraft industry and lacks an exact stress intensity factor solution. The present work deals with an experimental characterization of cracked lugs, using frozen-stress photoelasticity. Corner, transitioning and through-the-thickness cracks are considered. Experimental stress intensity distributions are presented and discussed in relation to previous studies. Various effects on SIF are assessed.