Mode I equivalent state of crack-like defects in multiaxial stress fields

The novel concept of equivalent state randomly oriented flaws developed from the generalized fracture toughness theory [1] is presented. Based on this concept, planar defects located in multiaxial stress field regions, characterized by modes I, II, and III stress intensity factor combinations, are distinguished by a mode I equivalent state stress intensity factor % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiqadUeagaqeaa% aa!3846!\[\bar K\]₁ of identical function. Accordingly, the complex mode fracture criterion is exactly replaced by the conventional mode I criterion % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiqadUeagaqeaa% aa!3846!\[\bar K\]₁ K _1C . It is demonstrated that this criterion is mathematically equivalent to other more complex generalized fracture criteria [2,4,5], i.e., it predicts the same critical conditions.Current approximate procedures applied to crack-like defects detected in structural components, based on reorienting or orthogonally projecting the defect over a plane normal to the maximum principal tensile stress, are discussed and applied to two simple structural applications. When the results are compared with those from the proposed equivalent state flaw method, it is concluded that, to a large extent, the procedures are inconsistent and generate significant errors that may lead to incorrect decisions over the remaining service life of the structure.The equivalent state flaw concept is used to establish the equivalent state mode I threshold value % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiqadUeagaqeaa% aa!3846!\[\bar K\]₁ corresponding to complex stress state fatigue loadings.

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Résumé On présente le concept original de défauts équivalents répartis au hasard, développé à partir de la théorie généralisée sur la ténacité à la rupture [Réf. 1]. Sur base de ce concept, des défauts plans situés dans des zones à champs de contrainte multi-axiale, et caractérisés par des facteurs d'intensité de contrainte combinant les modes I, II et III, sont caractérisés par un facteur d'intensité de contrainte équivalent % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiqadUeagaqeaa% aa!3846!\[\bar K\]₁; relatif à un mode I et occupant la même fonction. Dès lors, le critère décrivant la rupture sous un mode complexe est en tous points remplacé par le critère conventionnel % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiqadUeagaqeaa% aa!3846!\[\bar K\]₁ K _1C .Ce critère est mathématiquement equivalent aux autres critères généralisés de rupture, de forme plus complexe [Réf. 2, 4, 5], en ce qu'il prédit les mêmes conditions critiques.On discute, et on applique à deux cas de structures simples, les procédures habituelles d'approximation pour des défauts assimilables à des fissures détectés dans des composants. Ces défauts sont réorientés ou projetés orthogonalement sur un plan normal à la plus grande tension principale.Lorsqu'on compare les résultats de ces procédures d'approximation à ceux que fournit la méthode proposée, on en conclut que ces procédures sont, dans une large mesure, incorrectes, et qu'elles donnent lieu à des erreurs importantes susceptibles de conduire à des décisions erronées sur la vie résiduelle d'une structure.Le concept de défaut équivalent est utilisé pour établir une valeur critique équivalente % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiqadUeagaqeaa% aa!3846!\[\bar K\]₁ en mode I, correspondant à le seuil des sollicitations de fatigue de mode complexe.

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Operated for the U.S. Department of Energy, Contract No. DE-AC12-76-N0052.     

Experimental study on critical breaking stress of float glass under elevated temperature

Cracking and subsequent fallout of glass may significantly affect fire dynamics in compartments. Moreover, the breaking tensile stress of glass, a crucial parameter for breakage occurrence, is the least well known among mechanical properties. In this work, a series of experiments were conducted, through mechanical tensile tests, to directly measure the breaking stress of float glass using Material Testing System 810 apparatus. Clear, ground and coated glass samples with a thickness of 6 mm were measured under ambient conditions, with a room temperature of 25 °C. The breaking stress of smooth glass samples was also measured at 75 °C, 100 °C, 125 °C, 150 °C, 200 °C, 300 °C and 400 °C, respectively. The results show that surface treatment may decrease the critical tensile stress of glass panes. The average breaking stress also fluctuates considerably, from 26.60 to 35.72 MPa with the temperature variations investigated here. At approximately 100 °C, critical stress reached the minimum value at which glass breakage occurs more easily. In addition, the thermal expansion coefficient was established using a thermal dilatometer, to obtain the maximum temperature difference float glass can withstand. It is intended that these results will provide some practical guidelines for fire safety engineers.     

On a certain inverse problem of temperature and thermal stress fields

Summary The paper discusses the method of solution of an inverse problem of one-dimensional temperature and stress fields for a sphere, a circular cylinder and an infinite plate. The inverse problem describes the dependance of the boundary conditions of different types on the prescribed temperature state or stress state within the body under consideration, in contrast with the direct problem which relates the temperature and stress states to known boundary conditions. To obtain a function describing the temperature of a heating medium and/or the Biot number in a simple form use has been made of the Laplace transformation. The numerical examples for both types of the inverse problems are presented.

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Über ein inverses Problem der Temperatur- und Wärmespannungsfelder

Zusammenfassung Die Arbeit Antersucht die Lösungsmethode des inversen Problems eindimensionaler Temperatur-und Spannungsfelder für eine Kugel, einen Kreiszylinder und eine unendliche Platte. uas inverse Problem beschreibt die Abhängigkeit der Randbedingungen verschiedener Drt vom vorgegebenen Temperatur- oder Spannungszustand innerhalb des betrachteten Körpers im Vergleich zum direkten Problem, welches den Temperatur- und Spannungszustand zu bekannten Randbedingungen in Beziehung setzt. Zum Erhalt einer Funktion, die die Temperatur des erwärmten Mediums und/oder die Biot-Zahl in einer einfachen Form beschreiben, wurde die Laplace-Transformation verwendet. Numerische Beispiele für beide Arten der inversen Probleme werden angegeben.

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Notation a characteristic size of the body, [m] - _t coefficient of linear thermal expansion [1/°C]; [1/°K] - parameter describing a shape of the body; - Laplace transform of the functionf, G, ... - Fourier number (dimensionless time) - Biot number - G shear modulus, [kN·cm^–2] - I (z),K (z) modified Bessel 1^st and 2^nd kind functions of the order - J (z) 1^st kind Bessel function of the order ; - thermal diffusivity, [m²·s^–1]; - , Lame constants, [kN·cm^–2] - Poisson ratio - s parameter of Laplace transformation - _°°(°,Fo), (°,Fo) radial and circumferential stresses [kN·cm^–2] - T(,Fo) absolute temperature at a point (,Fo); [°C, °K] - T _f (Fo) absolute temperature of a medium that heats a body under consideration [°C, °K] - T _m the reference temperature [°C, °K] - dimensionless temperature - u(,Fo) dimensionless displacement - dimensionless coordinate of position With 11 Figures     

Time dependent analysis of short-range monopole wake fields driven by accelerated electron beams

Combinations of integral transforms and Green's function are employed in order to obtain the distribution of the short-range monopole wake fields driven by accelerated electron beams in a cylindrical cavity. This constituted an alternative but simpler and more versatile method to the normal mode expansion which we used earlier to solve for such a distribution (Salah and Dolique, Nucl. Instr. and Meth. A 431 (1999) 27). Whereas direct comparisons of the resulting analytical expressions are found difficult to directly compare, numerical illustration of results obtained from both approaches show excellent agreements and hence confirm the fact that both approaches are equivalent.     

Size dependent interactions of nanoparticles with lung surfactant model systems and the significant impact on surface potential

The relationship between a model pulmonary surfactant system and various sized nanoparticles was investigated in this study. Diplamitoylphosphatidylcholine (DPPC) is the main lipid constituent of lung surfactant and has the ability to reach very high surface pressures (around 70 mN/m) upon compression. Due to these properties it was used as a model to simulate the lung surfactant film in vitro. The first objective of this study was to investigate the relationship between DPPC and various sized nanoparticles within the subphase through surface pressure-area isotherms. The second objective was to measure the surface potential of the different preparations (conducted on a mini-Langmuir trough) and to determine if an optimal nanoparticle size exists possessing a greater affinity for the DPPC film compared to other sizes. The results from the pressure area isotherms indicate that the interaction between DPPC and the nanoparticles is stable and that the 235 nm particles may represent an optimal size. Furthermore, the results from the surface potential experiments confirm that an interaction of the nanoparticles with the monolayer exists as indicated by surface-pressure area isotherms. Any even moderate interaction between nanoparticles and lung surfactant film might reduce or increase the surface potential of the surfactant film, and this might impact the deposition of the nanoparticles or other ligands which may be positively or negatively charged drugs within the surfactant film. Thus changes in surface potential due to nanoparticle interactions have to be taken into account for future drug targeting studies using nano-sized drug carriers.     

Ritz solutions for axisymmetric temperature and stress fields in finite elastic cylinders

Variational formulations are given for the stationary heat conduction and thermodelasticity problems of an orthotropic, non-homogeneous, finite length, cylinder. It is demonstrated that a single-element approach based upon Ritz approximations and the method of Lagrange multipliers offers and efficient means for computing the temperature and thermal stress distributions.     

Angular dependence and polarization of out-of-plane optical scattering from particulate contamination, subsurface defects, and surface microroughness

The angular dependence and the polarization of light scattered by a small particle a distance d inside and outside a reflecting surface is calculated in the Rayleigh limit. This calculation yields expressions for the polarized bidirectional reflectance distribution function matrices for in-plane and out-of-plane scattering. The results are compared with those obtained from microroughness-induced scattering. For the p-in/p-out configuration with oblique incidence, there exist out-of-plane angles for which scattering that is due to one of the mechanisms vanishes, whereas that from the others does not. By exploiting this knowledge, we can make improvements in the detection of small particles or subsurface defects. It is also shown that one must take care when differentiating subsurface-defect-induced scattering from microroughness-induced scattering using in-plane scattering and wavelength scaling laws.     

Extended bidirectional reflectance distribution function for polarized light scattering from subsurface defects under a smooth surface

By introducing the scattering probability of a subsurface defect (SSD) and statistical distribution functions of SSD radius, refractive index, and position, we derive an extended bidirectional reflectance distribution function (BRDF) from the Jones scattering matrix. This function is applicable to the calculation for comparison with measurement of polarized light-scattering resulting from a SSD. A numerical calculation of the extended BRDF for the case of p-polarized incident light was performed by means of the Monte Carlo method. Our numerical results indicate that the extended BRDF strongly depends on the light incidence angle, the light scattering angle, and the out-of-plane azimuth angle. We observe a 180 degrees symmetry with respect to the azimuth angle. We further investigate the influence of the SSD density, the substrate refractive index, and the statistical distributions of the SSD radius and refractive index on the extended BRDF. For transparent substrates, we also find the dependence of the extended BRDF on the SSD positions.     

Time and temperature dependent piezoresistance of carbon nanofiller/polymer composites under dynamic load

In this study, the behaviour of carbon nanotube/epoxy and carbon black/epoxy composites under dynamic load is studied via dynamic mechanical thermal analysis (DMTA) in combination with DC electrical resistivity measurements. DMTA measurements are carried out at fixed temperature whilst the dynamic loading frequency is varied. With this procedure, a loading frequency-dependence of the phase shift between DC electrical resistance and mechanical elongation (δ _R–ε) is observed, although the force and elongation of the sample are still in phase. Moreover, the magnitude of this phase shift, as well as the amplitude of the DC electrical resistance change shows a clear dependence on the initial electrical conductivity of the samples. In addition, temperature sweeps are carried out to investigate the temperature dependency of the piezoresistance of the samples. An abrupt change in their sensitivity is observed as soon as the glass transition of the polymer is reached. However, the trend of the resistance change beyond the glass transition is substantially different between the nanocomposites containing carbon black and carbon nanotubes, revealing a strong influence of the network characteristics on the piezoresistive behaviour of these novel materials.     

Time dependent principal stress analysis by the hybrid method of photoviscoelasticity and boundary element

In this paper the basic relations in linear isotropic photoviscoelasticity have been discussed theoretically in detail. A new routine to solve the time dependent principal stress without the measurement of isoclinics has been found. As a proof of the method, examples are illustrated at the end of this paper.     

Time dependent crack growth of type 304 stainless steel in elevated temperature sodium

The crack growth characteristics, under constant load and in elevated temperature liquid sodium, were studied for Type 304 stainless steel through using linear elastic fracture mechanics. The crack growth rates are represented by the Arrhenius equation. Furthermore the crack growth rates in sodium, at 873 K and oxygen concentrations of 0.71 and 15 ppm, were examined. The crack growth rates seem to increase in accordance with increased oxygen concentration, however the difference is slight. Scanning electron microscope observations were made of corrosion products on the fracture surface at 15 ppm oxygen. However, at 0.71 ppm the corrosion products could not be observed. So the mechanism of crack growth seems to be related to impurities in sodium.     

The effects of crack surface friction and roughness on crack tip stress fields

A model is presented which can be used to incorporate the effects of friction and tortuosity along crack surfaces through a constitutive law applied to the interface between opposing crack surfaces. The problem of a crack with a saw-tooth surface in an infinite medium subjected to a far-field shear stress is solved and the ratios of mode I stress intensity to mode II stress intensity are calculated for various coefficients of friction and material properties. The results show that tortuosity and friction lead to an increase in fracture loads and alter the direction of crack propagation.

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Résumé On présente un modèle utilisable pour tenir compte des effets de friction et de la rugosité sur les surfaces d'une fissure, en appliquant une loi constitutive à l'interface entre les surfaces opposées d'une fissure. On résoud le problème d'une fissure présentant une surface en dents de scie, dans un milieu infini soumis à un champ de contrainte de cisaillement appliqué à une certaine distance. On calcule les rapports de l'intensité de contraintes relative au mode I sur celle relative au mode II, pour divers coefficients de friction et diverses propriétés de matériau. Les résultats montrent que la rugosité et la friction conduisent à un accroissement de la charge correspondant à la rupture, et à une altération de la direction de propagation de la fissure.

     

Numerical and experimental distribution of temperature and stress fields in API round threaded connection

Thread galling is one of the main failure forms for oil tubing and casing connections, and it leads to deterioration of seal performance and connection strength of oil tubing and casing directly. A series of full-scale tests were performed on samples of API J55 steel grade non-upset tubing threaded connections. The temperature and stress field distributions of the tubing threaded connection were measured dynamically under the action of different make-up and break-out torque and velocity. Major factors, which affect the distributions of temperature and stress fields of tubing connections, were studied and their effects on thread galling failure were summarized with friction-wear theory. The FEA models of tubing threaded connections are validated by comparing the numerical results with the full-scale tests. The validated models are afterwards used to perform parametric studies on the connection behaviour.     

Measurement of temperature fields in specimens of quartz ceramic during surface ablation

The authors propose a method of mounting thermocouples and have obtained temperature fields within specimens of pure and doped quartz ceramic. The linearity of the dependence for deep isotherms has been proved experimentally.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 2, pp. 313–318, August, 1989.     

TC4薄壁件热处理过程形状尺寸变化数值预报

建立了钛合金薄壁件加热冷却过程中温度场和应力场的数学模型,利用ANSYS软件实现了对钛合金筒形件加热冷却过程中形状尺寸变化及残余应力的预报.结果表明:钛合金筒形件随炉升温至1 050℃,保温700 s后淬火至25℃,直径方向最大相对变形为 1.057%;上下边缘处单元应力状态为张应力,此处的残余应力为389 MPa;淬火过程中工件心部和外表面最大温差为150℃.     

Determination of nonstationary temperature fields and stress state in bidirectionally tapered shells of revolution

A procedure is developed for determination of the nonstationary temperature fields in shells of revolution, which are tapered in two directions and subjected to nonaxisymmetric convective heat exchange with the surrounding medium. In that case, two approaches are used: the first approach is based on use of finite differences in the meridional and circumferential directions, while in the second, the method of integral relationships is employed around the circumference, and finite differences in the meridional direction. In both approaches, power polynomials are used for the thickness variable, and an explicit difference scheme for time. The thermoelastic stress state is determined using the Kirchhoff-Love hypothesis. The method of integral relationships is used in the circumferential direction, and the method of discrete orthogonalization in the meridional direction. Results of numerical investigations are presented.Translated from Problemy Prochnosti, No. 1, pp. 63–73, January, 1996.