Application and power of criteria for testing the homogeneity of variances. Part II. Nonparametric criteria

The distributions and power of nonparametric tests of the homogeneity of dispersion characteristics (Ansari–Bradley, Mood, Siegel–Tukey, Capon, and Klotz) are studied. A comparative analysis is made of their power relative to the classical tests for the homogeneity of variance (Fisher, Bartlett, Cochran, Hartley, Levene). Tables of percentage points for the Cochran test are given for non-normal distributions.     

Application and power of criteria for testing the homogeneity of variances. Part I. Parametric criteria

A comparative analysis is made of the power of classical (Fisher, Bartlett, Cochran, Hartley, and Levene) tests of variance homogeneity. The distributions of the statistics of the tests are studied when the assumption that the sample obeys a normal law breaks down.     

Anisotropy and failure criteria for concrete

Summary The migration of water within fresh concrete to produce the phenomenon known as “water gain” appears to have received far too little attention, particularly as regards failure theories which assume that concrete exhibits isotropic behaviour. It is shown that concrete is anisotropic when subjected to either tensile or compressive stresses. Reliable comparisons of tension and compression test results must therefore relate the direction of testing the specimens to the vertical direction at casting. The design of cast in-situ columns, for example, based on normal cube test results can be particularly unsafe. The effects of anisotropic behaviour upon failure envelopes for biaxial states of stress are also considered.

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Résumé La migration d'eau à travers le béton frais, qui produit le phénomène du ressuage, ne parait pas avoir suscité une attention suffisante, particulièrement en ce qui concerne les théories de la rupture qui dépendent de l'hypothèse d'un comportement isotropique du béton. On montre ici que le béton est anisotropique lorsqu'il est soumis à une contrainte en traction ou en compression. Une étude comparative sérieuse des résultats d'essais en traction et en compression doit par conséquent relier la direction de l'essai des éprouvettes à la direction verticale au moment du coulage. Le calcul de poteaux coulés in-situ d'après les résultats de l'essai normal sur cube peut, par exemple, être particulièrement inadéquat. On considère aussi les effets du comportement anisotropique sur les enveloppes de rupture pour la condition de contrainte biaxiale.

     

Strain-rate-dependent failure criteria for composites

The objective of this study was to characterize the quasi-static and dynamic behavior of composite materials and develop/expand failure theories to describe static and dynamic failure under multi-axial states of stress. A unidirectional carbon/epoxy material was investigated. Multi-axial experiments were conducted at three strain rates, quasi-static, intermediate and high, 10⁻⁴, 1 and 180-400 s⁻¹, respectively, using off-axis specimens to produce stress states combining transverse normal and in-plane shear stresses. A Hopkinson bar apparatus and off-axis specimens loaded in this system were used for multi-axial characterization of the material at high strain rates. Stress-strain curves were obtained at the three strain rates mentioned. The measured strengths were evaluated based on classical failure criteria, (maximum stress, maximum strain, Tsai-Hill, Tsai-Wu, and failure mode based and partially interactive criteria (Hashin-Rotem, Sun, and Daniel). The latter (NU theory) is primarily applicable to interfiber/interlaminar failure for stress states including transverse normal and in-plane shear stresses. The NU theory was expressed in terms of three subcriteria and presented as a single normalized (master) failure envelope including strain rate effects. The NU theory was shown to be in excellent agreement with experimental results.     

Growth criteria for solvent crazes

Single methanol crazes are grown from sharp cracks in polymethylmethacrylate. Double exposure holographic interferometry is used to determine the sequential strain energy release rates G and opening displacement profile of the craze from the initiation of growth to its cessation. The craze stress profile is determined at various points in its growth from the opening displacement profiles using a Fourier transform method. The rapid increase in G observed just before the craze ceases to grow demonstrates that craze growth criteria based on the concept of a constant critical total strain energy release rate cannot be correct. Similarly, the large stress concentration which develops just behind the craze tip at growth cessation is incompatible with the assumption that the craze grows to a length that just eliminates a stress singularity at its tip (Dugdale model). This feature, however, would be expected if sufficient methanol cannot reach the fibrils just behind the tip of the craze to plasticize them fully.     

Pyramidal yield criteria for epoxides

The tensile, compressive and shear yield strengths of two epoxides were measured under superposed hydrostatic pressure extending to 300 MN m^–2. For both materials, the ratio of the moduli of the tensile, _T, to compressive, _C, yield stress at atmospheric pressure was approximately 34, as has been reported previously for a number of thermoplastics. The ₂= ₃ envelope in stress space was plotted according to these two-parameter ( _C and _T) yield criteria: conical, paraboloidal and pyramidal; the best correlation was with the last. The experimental tensile and compressive data for tests under pressure, however, fit slightly better two straight lines which are consistent with a three-parameter single hexagonal pyramidal yield surface. For plane stress and shear under pressure yield envelopes of these surfaces, the correlation with experimental data is again best for the pyramidal criteria, except for biaxial or triaxial tension when these resins are brittle. The third independent parameter employed in the pyramidal criterion was the equi-biaxial compressive yield stress, determined by tensile experiments under appropriate superposed hydrostatic pressure; alternatively plane strain compressive yield stress, _PC, may be used.     

Local criteria for ductile fracture

Strain distributions in specimens suitable for studying the initiation of fracture are reviewed, and distributions are developed for the steady-state propagation of cracks in plane strain lension of fully plastic materials. The functional forms of local fracture criteria are discussed for different metallurgical mechanisms. It is concluded that:

1. pure Mode I (normal) fracture is unlikely to exist except in cleavage.
2. there is both theoretical and experimental evidence for the development of both: sharp and flat-bottomed cracks.
3. simultaneous diffuse and concentrated (Dugdale-Muskhelishvili) flow fields can occur in torsion of longitudinally grooved bars if the stress-strain curve has a maximum which causes band formation, so that a displacement criterion becomes appropriate for final fracture.

     

Stability criteria for column stacks

Today, column stacks in the warehouse usually consists of unit loads and are regarded generally as being sufficiently stable. But the stability of such stacks may vary according to the compression resistance of an individual unit or by the toppling stability of the complete column. To evaluate the stability of a given column, or to calculate the critical stack dimensions, different methods are described and compared on the basis of the elastic modulus in compression, the inclination angle of an individual unit under a central test load, or the natural frequency of a freely oscillating complete stack after a previous lateral deviation. This results in a variety of useful procedures to give an approximate estimate of the toppling stability of stacked unit loads and packages.     

Asymptotic criteria for model selection

Summary A general frame is given in which model selection criteria can be derived. At first conditions are stated under which the asymptotic distribution of minimum discrepancy estimators can be given. The results are used to derive an approximation to the expected discrepancy. Estimators of this expectation, i.e. model selection criteria, are proposed.

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Zusammenfassung Ein allgemeiner Rahmen wird gegeben, in dem man Kriterien zur Modellauswahl herleiten kann. Zuerst werden Bedingungen angeführt, unter denen man die asymptotische Verteilung von Minimum-Diskrepanz-Schätzern angeben kann. Mit den Resultaten wird dann eine Annäherung an die erwartete Gesamtdiskrepanz berechnet. Schätzer dieser Erwartung, also Kriterien zur Modellauswahl, werden vorgeschlagen.

     

Release criteria for patients having undergone radionuclide therapy and criteria for their crossing the state border of the Russian Federation

By means of a conservative dosimetry model, the values of operational radiological criteria for patients released from hospital--residual activity in a body and dose rate near the patient's body--are substantiated based on the effective dose limit of 5 mSv for persons helping the patient or living with him and 1 mSv for other adults and children. Two sets of operative criteria for radionuclides (125)I, (131)I, (153)Sm and (188)Re used in Russia for radionuclide therapy were derived. Release criteria for (125)I well differ from such values in other countries because in this work absorption of (125)I low-energy photon radiation in the patient was taken into account. When a patient having undergone radionuclide therapy crosses the frontier of Russia, high-sensitivity devices for radiation control at the custom can detect the patient. A simplified radiological assessment of the patient was suggested aimed at provision of radiation safety for patient companions in transport.     

Droplet breakup regimes and criteria for their existence

An analysis of experimental and theoretical studies of droplet breakup by a gas flow in shock tubes and nozzles is presented. A system of criteria defining droplet breakup regimes is developed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 1, pp. 64–70, January, 1981.     

Nonlocalized fatigue damage of metals and alloys. Part 3. Strain and energy criteria

The paper considers methods of accelerated determination of endurance limits of metals and alloys based on the analysis of regularities in their inelastic deformation, strain and energy criteria of fatigue fracture, and methods for life prediction with the use of those criteria. __________ Translated from Problemy Prochnosti, No. 1, pp. 5–31, January–February, 2006.     

Relationship of fracture mechanics criteria. Report 1. Force loading

Fracture mechanics critria, used in calculations in practice, are presented in the form in which they can be compared on the plane of loading parameters. Equations are derived for determining the critical stress intensity factors in relation to the fracture toughness of the material, mechanical properties and temperature. The temerature dependences of the critical stress intensity factors calculated from different criteria, are compared.Translated from Problemy Prochnosti, No. 4, pp. 3–7, April, 1990.