Maximum Shear Plane Research Articles

Low-Cycle Fatigue Under Out-of-Phase Loading Conditions

A number of tests have been conducted on a 1 percent Cr-Mo-V steel under combined cyclic axial and torsional loads with various phase relationships. It is shown that endurance and the direction of crack growth depend on the strains acting on the planes of maximum shear. Fatigue life is reduced by out-of-phase loading conditions.

Homogeneous and layered sand in triaxial compression

Samples of Ham River sand were prepared at high and low porosities by pouring through air or a liquid, the techniques being alternated for layered samples. Some samples were reinforced with horizontal sheets of various materials. To avoid edge effects near lubricated platens in triaxial compression, strains in the middle third of each sample were recorded in accurate detail. Changing the relation of the plane of deposition to the major principal stress direction revealed inherent anisotropy effects. Stress-strain and strength data show the influence of porosity, layer geometry and horizontal reinforcing sheets. In homogeneous samples the orientation of lines of zero extension in the maximum-shear plane depended on porosity but not on current strain or inherent anisotropy. Inherent anisotropy did not affect the stress-dilatancy relationship, nor did changing its axes affect the virtual coincidence of stress and strain rate axes. But pre-failure strains were largely influenced by inherent anisotropy at both porosities and the lower porosity gave appreciable strength anisotropy. Layered samples were weaker, depending on layer geometry and the loose layers sustained large strains while at maximum stress ratio. No thin ruptures formed, but at failure the strains were confined within loose layers, when these were oriented so that a line of zero extension was parallel to their plane. This orientation differed appreciably from that of maximum stress obliquity. The stress-dilatancy relationship for homogeneous samples predicted stress ratios in both layered and reinforced samples. The loose sand dilated much more when in a layer than in homogeneous samples. Des échantillons de sable provenant de Ham River ont été préparés à des porosités faibles et élevées en le versant à travers de l'aire ou un liquide, les techniques ont été alternées pour les échantillons sandwiches. Quelques échantillons ont été renfor avec des feuilles horizontales de materiaux divers. Afin d'éviter des effets de bord prés des plateaux lubrifiés dans une compression triaxiale, les déformations au tiers central de chaque échantillon ont été enrégistrées avec précision. En changeant la position du plan de sédimentation par rapport à la contrainte majeure principale, on a pu mettre en évidence des effets anisotropiques. Les mesures de contraintes-déformations et de résistance montrent l'influence de la porosité, de la géomérie des couches et des feuilles de renforcement horizontales. Dans les échantillons homogènes l'orientation des lignes à extension nulle dans le plan de cisaillement maximum dépendait de la porosité mais non pas de la déformation courante ou de l'anisotropie naturelle. L'anisotropie naturelle n'a pas affecté la relation existant entre la contrainte et la dilatance, de même que le changement de ses axes n'a pas affecté la coïncidence virtuelle des axes de vitesse de contrainte et de déformation. Mais les déformations de pré-rupture étaient largement influencées par l'anisotropie naturelle pour les deux porosités et la porosité la plus faible a donné une résistance d'anisotropie appréciable. Les échantillons feuilletés étaient plus faibles, selon de la géométrie des couches et les couches lâches ont supporté de grandes conrai-ntes pour un taux de contrainte maximum. Il n'est apparu aucune rupture mince mais à la rupture, les déformations étaient en totalité dans des couches lâches, quand celles-ci étaient orientées de telle fa¸on qu'une ligne d'extension nulle était parallèle à leur plan. Cette orientation différait notablement à partir de celle d'une obliquité de contrainte maximum. La relation contrainte-dilatance pour les échantillons homogènes a permis de prèvoir des taux de contrainte aussi bien dans les échantillons feuillétes que dans les échantillons renforcés. Le sable lâche se dilatait beaucoup plus dans une couche feuilletée que dans des échantillons homogènes.

Elastic–inelastic behavior of PET and nylon 66 monofilaments under lateral compression

AbstractResults of experiments on short lengths of nylon 66 and PET monofilament specimens, subjected to lateral compressive force between two parallel platens, are described. In the experimental procedure the change in the compressed diameter and the area of contact were determined as a function of the applied force. From these data elastic moduli in lateral compression were estimated. The load–deformation behavior beyond the elastic range exhibited a yield‐like phenomenon. SEM examination of the deformed specimen suggest the possible modes of deformation in the post‐yield behavior. It is inferred that the yield occurs due to concentration of deformation along the maximum shear planes. The deformed specimens also show specific forms of fracture initiation and growth.

A Theory for Fatigue Failure under Multiaxial Stress-Strain Conditions

A new theory for multiaxial fatigue is presented that is based on a physical interpretation of the mechanisms of fatigue crack growth. It may be represented graphically by contours of constant life, which are expressed mathematically by where ε1, ε2 and ε3 are the principal strains, •ε1 ≥ ε2 ≥ ε3. This equation underlines the importance of strain parameters in correlating fatigue data. It illustrates the effect of both the shear strain and the tensile strain normal to the plane of maximum shear. The theory is compared with several classical and recent theories, which are briefly reviewed. It is shown that classical theories of fatigue failure cannot correlate experimental data, and may be dangerous if used for design purposes.

A Theory for Fatigue Failure under Multiaxial Stress-Strain Conditions

A new theory for multiaxial fatigue is presented that is based on a physical interpretation of the mechanisms of fatigue crack growth. It may be represented graphically by contours of constant life, which are expressed mathematically by where ε1, ε2 and ε3 are the principal strains, •ε1 ≥ ε2 ≥ ε3. This equation underlines the importance of strain parameters in correlating fatigue data. It illustrates the effect of both the shear strain and the tensile strain normal to the plane of maximum shear. The theory is compared with several classical and recent theories, which are briefly reviewed. It is shown that classical theories of fatigue failure cannot correlate experimental data, and may be dangerous if used for design purposes.

Strain accumulation along the San Andreas Fault

The patterns and rates at which strain is accumulating along the San Andreas fault in California are analyzed from geodetic data. Geodimeter and triangulation data indicate displacements near the fault that are a result of homogeneous strain to an approximation within the accuracy of the data. Both sets of data indicate that nearly pure shear with a maximum shear plane nearly parallel to the fault is accumulating at a rate of about 0.7×10−6 yr−1 from San Francisco Bay to the Transverse Ranges. The nearly east-west trending segment of the fault in the Transverse Ranges is accumulating nearly uniaxial compression normal to the fault at a rate of 1.1×10−6 yr−1, indicating a ‘locking’ mechanism. At no point, with the possible exception of the Cholame Valley, do fault creep and small earthquakes substantially release the accumulating strain. A more complete set of data in the Imperial Valley suggests that the strains accumulating there are such as would be released by fault slippage at a rate of 8.5 cm yr−1 to a depth of 25 to 40 km. Slip on the Imperial fault due to small earthquakes and creep, however, occurs at a rate of only 1.3 cm yr−1, and earthquakes occur only to a depth of approximately 10 km. Strains at greater depths must be relieved by aseismic slip or inelastic deformation.

Low cycle fatigue of steels under biaxial straining

A cruciform test specimen and a loading rig are described, by which any combination of biaxial strains can be applied to a specimen. With the pressurizing equipment so far available, three states of strains have been investigated for two steels. In the mild steel used, large inclusions oriented in the roll direction aided fracture propagation when a maximum shear plane coincided with the roll direction. When not influenced by inclusions, fatigue life is related to total strain range by Coffin's law ∊ N a = C The values of α and C are different for different states of strains. Empirical formulae are given to predict results for other states of strains.

The Initiation and Propagation of Fatigue Cracks in Mild Steel Pieces of Square Section

SummaryAn investigation has been made to determine the positions and directions of initiation and the directions of propagation of fatigue cracks and to examine the correlation between these positions and directions and the planes on which maximum tensile and maximum shear stresses are generated.To afford as wide a range as possible of the ratio of maximum shear stress to maximum tensile stress, tests have been made under combinations of alternating bending and torsion; and in order to separate partially the regions of high shear stress from those of high direct stress, the tests have been made on pieces of square section with the plane of bending parallel to one diagonal of the section. Two series of tests have been made; one a preliminary series on pieces having no parallel portion and the other on pieces having a parallel portion about three times the length of the side of the square section. The positions and directions of initiation and the directions of propagation of fatigue cracks have been observed and compared with the positions and directions of the maximum tensile and shear stresses.Fatigue cracks may be initiated as a result of either high shear stress or high tensile stress and in the present series of tests on mild steel, cracking in tension has occurred in preference to cracking in shear when the ratio of the tensile stress range to the shear stress range has exceeded about 1.6; for values of this ratio less than 1.6, the cracks started in shear (and vice versa); propagation along the plane of maximum shear appears to be preferred up to a slightly greater value of the tensile/shear ratio (about 1.7 possibly). The general direction of a crack formed as a result of high tension usually follows the plane of maximum tension and that of a crack formed as a result of shear usually follows the plane of maximum shear. In detail both types of crack—in this mild steel—deviate quite widely from their general directions but this deviation bears no obvious relation to the microstructure of the material. Cracks propagating along one plane of maximum shear occasionally show a marked tendency to branch along the associated plane of maximum shear; but this tendency is not always observed and in other cases no tendency to branch has been noted.

Stresses Due to Tangential and Normal Loads on an Elastic Solid With Application to Some Contact Stress Problems

Abstract The results of two-dimensional approach using real variable method to Hertz’s problem of contact of elastic bodies are presented. Both normal and tangential loads are assumed to be distributed in Hertzian fashion over the area of contact. The magnitude of the intensity of the tangential load is assumed to be linearly proportional to that of the normal load when sliding motion of the body is impending. The stresses in the elastic body due to the application of these loads on its boundary are presented in closed form for both plane-stress and plane-strain cases. A numerical value of f = 1/3 is assumed for the linear proportionality (coefficient of friction) between the tangential and normal loads in order that the distribution of stresses may be illustrated. The significance of the stress distribution, across the contact area and in the body, is also discussed. It is shown that when the combination of loads considered in the paper are applied at the contact area of bodies in contact the maximum shearing stress may be at the surface instead of beneath the surface. For example, for plane strain, if the coefficient of friction is f = 1/3, the maximum shearing stress is at the surface and is 43 per cent larger than the maximum shearing stress, which would be below the surface, that occurs when the normal force acts alone. The effect of range of normal stress and of shearing stress on the plane of maximum shear and on the plane of maximum octahedral shear on failure by progressive fracture (fatigue) is discussed.