Some stress intensity factors for self-similar cracks,derived from path-independent integrals

Summary A new method of computing stress intensity factors for self-similar cracks in the plane is discussed. It is based on some known path-independent integrals whose forms make them suited for use in elastic fields showing expansional invariance. General integral formulas for the various segments of a chosen integration contour are presented and also applied. The integrals generally express the total energy release rate at self-similar growth, but for the expansion loaded star crack and the symmetrically cracked wedge opened by concentrated forces the stress intensity factors are obtained in closed form.

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Zusammenfassung Ein neues Verfahren der Berechnung von Spannungsintensitätsfaktoren zugehörig selbstähnlichen Riss-systemen in der Ebene wird diskutiert. Es beruht auf einigen bekannten wegunabhängigen Integralen, deren Formen sie in expansionsinvariablen elastischen Feldern anwendbar machen. Die allgemeinen Integralformeln der verschiedenen Abschnitte eines speziell gewählten Integrationsweges werden sowohl vorgezeigt als angewandt. Gewöhnlicherweise drücken die Integrale die totale Energiefreisetzung eines Rissystems bei selbstähnlichem Zuwachs aus. Für den expansionsbelasteten Sternriss und für den symmetrisch gespaltenen Keil, der von Punktkräften geöffnet wird, werden aber die Spannungsintensitätsfaktoren in abgeschlossener Form erhalten.

     

Cusp catastrophe model for binge drinking in a college population

A cusp catastrophe model for binge drinking behavior was developed and tested with attitude toward alcohol consumption and peer influence as the two control parameters. Similar models were also developed for frequency and quantity of alcohol use. Participants were 1,247 students who completed the Long Form of the Core Alcohol and Drug Survey. The results were strongest for the binge drinking criterion (R(2) = .90), compared to a linear model (R(2) = .34) that is usually associated with the Theory of Planned Behavior or Theory of Reasoned Action. The results have numerous implications for the development of interventions and for future research.     

Determining the intensity factors for stresses,electric-flux density,and electric-field strength in multiply connected electroelastic anisotropic media

Formulas are derived to evaluate the intensity factors of stresses, electric-flux density, and electric-field strength in two-dimensional problems of elasticity, thermoelasticity, electroelasticity, magnetoelasticity, thermoelectroelasticity, and thermomagnetoelasticity for anisotropic bodies with holes and plane (rectilinear) cracks __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 56–62, June 2007.     

Stability analysis for two kinds of equations in two-species population dynamics

In this paper we study the stability for equilibrium points of equations in two-population dynamics.We discuss two predator-prey-patch models.Model1 is described by a differential equation.Model2 is described by an integral differential equation.We obtain the conditions for the stability of their equilibrium points.The results show that the overall population stability despite local extinction is realizable.     

Stress intensity factors for cracks in grooved rolls used for hot-rolling

A procedure is described for the calculation of stress intensity factors for surface cracks in a section roll. Results are given in terms of the load acting on the roll and the average pressure acting on the roll/workpiece interface. It is noted that the load acting on the roll can be determined for individual cases by experimentally measuring the deformation of the roll stands: this obviates the necessity of relying on theoretical estimates of the roll/workpiece pressure. The stresses in the uncracked roll are determined using an axisymmetric finite element model. However, for the subsequent calculation of stress intensity factors the analysis is reduced to a plane strain model. It is shown that it may not be necessary to carry out finite element stress analyses on cracked rolls to determine stress intensity factors.     

Correlation equations for friction factors and convective coefficients in tubes containing bundles of internal, longitudinal fins

Finned tubes are commonly employed in tubular heat exchangers to augment the heat transfer rates between two dissimilar fluid streams. The goal of this study is two-fold: a) to determine the laminar, fully developed velocity and temperature fields for long, internal, longitudinal finned tubes; and b) to construct empirical correlation equations applicable for the asymptotic friction factor and the asymptotic Nusselt numbers as a function of the number of fins and the relative fin height in the bundle. Neither the fluid dynamics nor the heat transfer literature provides information for the second goal, which can be extremely useful to thermal engineers for the implementation of Computer-Aided Design (CAD) of internal, longitudinal finned tubes in heat exchange devices. Moreover, for the validity of the correlation equations, a seldom adopted criterion for the critical Reynolds number has also been introduced as an indispensable guideline to warrant laminar regimes. Received on 24 January 1997     

Critical factors for frequency-dependent fatigue processes in composite materials

Several fatigue-test parameters, including cyclic frequency, prefatigue material conditioning (preloading and step loading) and test-control modes (strain control and load control) are investigated and their effect on the fatigue response of composite materials is discussed. A conceptual model based on the test results is offered to aid in the understanding of fatigue processes in composite materials and the effect of frequency on fatigue response.     

Determination of mixed-mode stress intensity factors, fracture toughness, and crack turning angle for anisotropic foam material

A numerical and experimental investigation for determining mixed-mode stress intensity factors, fracture toughness, and crack turning angle for BX-265 foam insulation material, used by NASA to insulate the external tank (ET) for the space shuttle, is presented. BX-265 foam is a type of spray-on foam insulation (SOFI), similar to the material used to insulate attics in residential construction. This cellular material is a good insulator and is very lightweight. Breakup of segments of this foam insulation on the shuttle ET impacting the shuttle thermal protection tiles during liftoff is believed to have caused the space shuttle Columbia failure during re-entry. NASA engineers are interested in understanding the processes that govern the breakup/fracture of this material from the shuttle ET. The foam is anisotropic in nature and the required stress and fracture mechanics analysis must include the effects of the direction dependence on material properties. Material testing at NASA Marshall Space Flight Center (MSFC) has indicated that the foam can be modeled as a transversely isotropic material. As a first step toward understanding the fracture mechanics of this material, we present a general theoretical and numerical framework for computing stress intensity factors (SIFs), under mixed-mode loading conditions, taking into account the material anisotropy. We present SIFs for middle tension – M(T) – test specimens, using 3D finite element stress analysis (ANSYS) and FRANC3D fracture analysis software. SIF values are presented for a range of foam material orientations. Mode I fracture toughness of the material is determined based on the SIF value at failure load. We also present crack turning angles for anisotropic foam material under mixed-mode loading. The results represent a quantitative basis for evaluating the strength and fracture properties of anisotropic foam insulation material.     

Screening for C283Y gamma-sarcoglycan mutation in a high-risk group of Bulgarian Gypsies: evidence for a geographical localization and a non-random distribution among Gypsy subgroups

Limb-girdle muscular dystrophy type 2C (LGMD2C) is an autosomal recessive disorder caused by mutations in the gamma-sarcoglycan gene. A 'private' Gypsy C283Y mutation was detected in this gene. Recently, a number of LGMD2C-affected families belonging to a Xoroxane Gypsy group have been detected in eastern Bulgaria and all of these cases were due to the same mutation. We have screened 300 unrelated individuals of reproductive age from this high-risk Xoroxane Gypsy group, settled in Sliven. The genetic test by PCR-SSCP analysis for the C283Y mutation revealed a carrier frequency of 7.7%. The screened sample was ethnically not homogeneous. It was divided in ethnonym groups on the basis of social and economic status, language characteristics and trades. We found that the C283Y was not randomly distributed among the Gypsy subgroups. The disease seemed to be limited to the Xoroxane Gypsy group and geographically localized in eastern Bulgaria.     

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.     

Intensity factors for subinterface cracks in dissimilar anisotropic piezoelectric media

Summary A subinterface crack paralleling an interface between two dissimilar piezoelectric solids is considered. When the distance between the interface and the crack is small compared to all other in-plane lengths, the problem can be analyzed as an asymptotic problem for a semi-infinite crack lying at some distance away from the interface. An integral equation for the asymptotic subinterface crack is derived, and a solution of the integral equation for small-generalized Dundurs parameters is obtained. Relations between the intensity factors for the subinterface crack and interface intensity factors of the corresponding interface crack are obtained for a conducting crack as well as for an insulating one.This work was supported by the Brain Korea 21 Project in 2000.     

WEIGHT FUNCTION FOR STRESS INTENSITY FACTORS IN ROTATING THICK-WALLED CYLINDER

The equation of stress intensity factors(SIF) of internally pressurized thick- walled cylinder was used as the reference case.SIF equation of rotating thick-walled cylinder containing a radial crack along the internal bore was presented in weight function method.The weight fumction formulas were worked out and can be used for all kinds of depth of cracks,rotating speed,material,size of thick-walled cylinder to calculate the stress intensity factors.The results indicated the validity and effectiveness of these formulas.Meanwhile,the rules of the stress intensity factors in rotating thick-walled cylinder with the change of crack depths and the ratio of outer radius to inner radius were studied.The studies are valuable to engineering application.     

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.     

压电界面裂纹裂尖强度因子的显式计算公式

对常见横观各向同性压电材料(TIP)中界面裂纹的裂纹面与压电材料的极化方向成任意夹角的一般情况进行了研究,通过推导得到了计算裂尖强度因子的显式外推公式,同时给出了裂纹面与极化方向垂直的典型情况下的外推公式.这些显式计算公式为常见数值方法如有限元法及边界元法在压电材料断裂力学中的应用提供了便利.     

Dynamics of a discrete population model for extinction and sustainability in ancient civilizations

We analyze a discrete version of a recently developed ratio dependent population-resource model. This model has been used to study the decline of the human and resource populations on Easter Island and the chaotic dynamics of moose and wolf populations in Canada. The dynamical system exhibits a rich behavior of fractal basins of attraction and a Neimark-Sacker bifurcation route to chaos. The model consists of a coupled pair of logistic equations, with the carrying capacity for the predators proportional to the number of prey.     

Stress intensity factors for curved and kinked cracks in plane extension

A singular integral equation containing the crack opening displacement (COD) is developed for solving plane elasticity problems. The crack may contain any number of kinks at different intervals and orientations, such as a saw-tooth shape. Cracks in the form of a sine wave can also be treated. The crack tip stress intensity factors are evaluated for a variety of crack shapes and the results are displayed graphically. The distance between the crack tips is found to be a dominant factor on the crack tip stress intensity while the angle between the tangent to the crack tip and load direction determines the proportion of Mode I and II stress intensity factors.     

Explorative study of costs, effects and savings of screening for female fragile X premutation and full mutation carriers in the general population

OBJECTIVE: Evaluation of the costs, effects and savings of three strategies for female fragile X premutation and full mutation carrier screening in the general population. METHODS: We calculated the costs, effects and savings by using a general model for prenatal, preconceptional, and school carrier screening. Assumptions were based on literature data, expert opinions, prices and tariffs. RESULTS: Prenatal screening will detect most carriers and will lead to the highest number of avoided fragile X syndrome patients. The costs per detected carrier are quite similar for all screening programmes (around USD 45,000). All screening strategies have a favourable cost-savings balance (USD 14 million for prenatal screening, USD 9 million for preconceptional screening and USD 2 million for school screening). CONCLUSIONS: From an economic point of view, there is no obstacle to fragile X screening. The decision to screen or not can (and should) therefore concentrate on discussion of medical, social, psychological and ethical considerations.     

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.     

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.     

Computational micromechanics model for the convection of a cracks population in a brittle material

We stated in Sánchez et al. (Proc. 15th IMACS World Congress, Vol. 5, 1997, p. 513), the objective rate law governing the general evolution, nucleation, growth and convection, of a diluted 3D population of arbitrarily oriented, penny-shaped, non-interacting stable microcracks that is dragged along the flow of a regular motion of a simple continuous body of brittle material.This requires the prior analysis of the convection process in the hypothesis of ignoring crack nucleation. It follows that the evolution of the microcrack population is here due only to the rotation of the crack planes as a consequence of the deformation processes of the microcracked brittle solid.The determinant role of this case in the general evolution problem, is also so in its numerical treatment.In this paper, use is made of the Bubnov–Galerkin spectral method with respect to the angular variable defining the orientation of a crack to numerically solve the mathematical model of the pure convection of microcracks in the no-nucleation hypothesis.The paper is completed with three applications. The corresponding microcracks evolutions have been graphically displayed showing a behaviour that agrees with the expected.Indications about the computer codes implementing the numerical algorithm are included in an appendix.