Mixed Loading Research Articles

Propagation of fatigue cracks in mixed loading

A model is proposed of propagation of a fatigue crack which makes it possible to determine its growth rate at different ratios of KI and KII as well as during the variation of the stress ratio. The model can be used to determine the ratio of the stress intensity factors of the first and second kind corresponding to the threshold growth rate of the fatigue crack. The results of the calculations are compared with experimental data.

Performance measurement of interconnected CSMA/CD LANs

A performance measurement study of two Carrier Sense Multiple Access with Collision Detection local area networks interconnected by bridges and fibre optic links is considered. The network is subjected to memory-to-memory read tests with varying loads using artificially generated traffic from personal computer workstations. The tests span a number of configurations with varying loadings on intranetwork and internetwork traffic. The throughput-delay performance of the network is quantified and analysed. The bridge penalty is found to be load dependent. The penalty is high initially, but decreases as the load increases. The decrease can be attributed to the interleaving effect in the bridge processing. It levels off eventually and yields a 10% overhead at the steady state. With mixed loading of intranetwork and internetwork traffic, the bridged network shows a significant improvement in throughput and delay in comparison with an equivalent single network connected by repeaters.

Localized asymmetric crack closure with stick-slip in the contact

An idealized problem is solved revealing several new contact and stick-slip configurations in partially closed cracks subjected to mixed mode in-plane loading. An initially open crack under remote tension is closed locally by two concentrated line loads whichpinch the crack shut. The reverse situation with localized separation due to line loads which pry the crack open is also investigated. The line loads may be placed such that isolated closure (or separation) removed from either one or the other, or both crack tips may be obtained. Examples of results for all of the possible contact configurations are presented. Remote shear stress is also considered, the various stick-slip patterns are delineated, and frictional history effects are discussed. Results for the actual contact and stick-slip status, contact tractions, mode I and II crack opening displacements and stress intensity factors are presented in parameter studies of the variation of the magnitude and position of the line loads. The mode I results are based on a new exact solution of the normal stress integral equations, while the mode II results are derived numerically from the shear stress integral equations with frictional shear tractions calculated from the mode I solution for the contact stress. Applications of this type of problem include reinforcement to arrest slow crack growth and mixed-mode fatigue crack closure due to either cyclic stationary loading or traveling loads.

A finite element study of the near crack tip deformation of a ductile material under mixed mode loading

In ductile fracture, voids near a crack tip play an important role. From this point of view, a large deformation finite element analysis has been made to study the deformation, stress and strain, and void ratio near the crack tip under mixed mode plane strain loading conditions, employing Gurson's constitutive equation which has taken into account the effects of void nucleation and growth. The results show that: (i) one corner of the crack tip sharpens while the other corner blunts, (ii) the stress and strain distributions except for the near crack tip region, can be superimposed by normalizing distance from the crack tip by a crack tip deformation length, i.e., a steady-state solution under a mixed mode condition has been obtained, (iii) the field near a crack tip can be divided into four characteristic fields ( K field, HRR field, blunted crack tip field, and damaged region), and (iv) the strain and void volume fraction become concentrated in the sharpened part of a crack tip with increasing Mode II component.

Permanent Strains from Cyclic Variable‐Amplitude Loadings

Cyclic triaxial tests were performed on a well‐graded railroad ballast with a maximum particle size of 38 mm (1.5 in.). Samples were compacted in a split mold to reproduceable density states and subjected to repeated applications of compressive axial stresses. The cumulative permanent axial strains that developed, for constant‐amplitude loadings, were found to be dependent upon the permanent strain after one cycle of loading, the loading magnitude, and the number of applied loading cycles. Staged tests were conducted in which a sequence of variable loads was applied to the same sample. For these variableamplitude tests, the final permanent strains were independent of the order of the applied loadings. A superposition method is presented to characterize the mixed loading conditions. The results for the variable‐amplitude tests indicated that the maximum load controlled the permanent strain development, with negligible additional strains developing after returning to a lower repeated stress level. Partial u...

Cleavage, dislocation emission, and shielding for cracks under general loading

The purpose of this paper is to consider the conditions for the existence of a cleavage crack in a lattice and its response to all types of external loads when shielded by neighboring dislocations. The theory will be constrained to cleavage on one plane and crack branching is not permitted. In the first part of the paper, general relations are derived for the elastic interactions between a cleavage crack and a dislocation and between pairs of dislocations in the presence of the crack. These results are expressed in terms of the local k-field of the crack tip, the shielding contributions from the dislocations, and the complete specification of the forces on the two types of defects. In the second part, criteria for crack cleavage and emission under static conditions are developed for general loading. It is found that for reasons having to do with the basic nature of a crack on the atomic level, that the condition for equilibrium of a cleavage crack involves primarily only the mode I part of the local k-field, and that smaller contributions from modes II and III depend on subtle details of the atomic bonding in the crack core. On the other hand, dislocation emission depends on the full specification of all three components of the local k-field. The complete description of the crack tip conditions is then found to be possible in terms of a simple crack stability diagram in the three dimensional local k-space. The primary result is that combined cleavage and emission states are possible under mixed loading wherein a cleavage crack can generate significant plasticity in mode II and III dislocation configurations. In the third part, the overall static equilibrium configuration of the shielded core crack and its dislocation cloud is considered. General theorems developed show that for symmetric dislocation configurations, mode I configurations only shield the k 1 loading at the crack tip etc, and that the slip force mutually exerted on two symmetrically placed dislocations is exactly zero. Simplified fracture toughness relations are also derived. Finally, the overall picture developed for a shielded cleavage crack under general loading is summarized.

OPTIMAL DISTRIBUTION OF MULTIFUNCTIONAL CATALYSTS IN A PACKED BED REACTOR

The problem of the optimal distribution of two multifunctional catalysts is analyzed. Two methods for obtaining optimal catalyst profiles, an analytic-numeric method and the method of steepest ascent, are compared. Though the analytic-numeric method yields a more accurate solution, the method of steepest ascent is usually easier to apply. Optimal catalyst loading profiles are determined for two cases of commercial interest: selective oxidation of butene and naphtha reforming with bimetallic catalysts- A sequential loading of the bismuth molybdate and the vanadium phosphate catalysis is recommended for low butene concentration levels, while at higher butene levels a mixed loading of the two catalysts may be desirable. For commonly encountered naphtha feedstocks a sequential loading of the Pt-Re and the Pt-Ir catalysts tends to be optimal. These compare well with experimental evidence in the literature.

高力Ａｌ合金の動ＳＣＣき裂進展に及ぼす材料異方性の影響

The influences of anisotropy of material on static and dynamic SCC crack growth rates including the case of part-through one have been investigated using high-strength aluminum alloy ZK 141 (JIS 7N01) sensitive to active path corrosion type SCC. As for through crack growth, the crack plane orientation had a great influence not only on the crack growth rate but also on the threshold value; when the crack growth direction was longitudinal, i.e., in S-L and T-L specimens, anodic dissolution at grain boundaries was easily brought about, resulting in an enhancement of crack growth rate and a decrease in threshold value with respect to L-T specimens, where the crack growth direction was long transverse. This crack growth enhancement and the decrease in threshold value were especially marked on S-L specimens. Moreover, superimposed vibratory stresses had a great influence on the crack growth rate for T-L and L-T specimens. However, the dynamic SCC crack growth rate was smaller than that of static SCC for S-L specimens, with a slightly higher KDSCC value than that of KISCC, which results from crack branching. In a corrosive environment, part-through static and dynamic SCC cracks grew in the longitudinal direction as well as in the surface and the depth directions. The longitudinal cracks grew under a mixed loading of Mode I and Mode II.

Application of the critical load assessment method for stable crack growth analysis

A new systematic procedure has been developed for analyzing stable crack growth. In this method, the crack instability point can be predicted from a single J-l record, which is developed from a given material J r- curve and the J- integral-related solutions resulting from stress analysis of a flawed structure. Here l represents the physical load applied to the structure. The development of the J-l relation that satisfies the equilibrium state of crack growth is so simple that hand calculator analysis is possible for complex structural geometries with available j- related stress analysis results. The advantage of the new method over existing ones, such as the failure assessment diagram approach or the tearing instability theory, is that it can predict the critical physical load level and the crack instability point at the same time without resorting to the use of a fixed diagram or evaluating tearing modulus. The validity of the procedure has been demonstrated by solving a center-cracked tensioned panel with various loading mechanisms (displacement-controlled, load-controlled and mixed loading systems) and a pressure vessel geometry under internal pressure.

Core-Management Analysis of the Fugen Heavy-Water-Moderated Plutonium-Uranium Mixed Oxide Reactor

A core management analysis of a 165-MW(electric) plutonium-uranium mixed-oxide-fueled heavy water reactor, Fugen, has been carried out and compared with some of the operational data through the initial cycle and three reload cycles. During these burnup cycles, the Fugen reactor has experienced refueling of 72 plutonium-uranium fuel bundles and 76 UO/sub 2/ fuel bundles, including four special bundles for irradiating test samples. The core burnup, thermal flux distribution, power distribution, coolant flow distribution, etc., were calculated and compared with measurements. The rootmean-square (rms) error of the calculated thermal flux over the three-dimensional spatial nodes was found to be about3% for various core conditions, and the rms error of the calculated core flow distribution was within 2%. The reload patterns have been chosen in such a way that mixed oxide and UO/sub 2/ fuel bundles can exist in a mixed bed loading with no attendant reactor control problems.

Phosphorus loadings to lakes and some of their responses. Part 2. Regression models of summer phytoplankton standing crops, winter total P, and transparency of New York lakes with known phosphorus loadings 1

An interrelated series of regression equations is derived to define the response of lake ecosystems to mixed zone phosphorus loadings in terms of simple and readily determinable parameters. Data used were collected over 1–4 yr for 16 lakes in central New York State characterized by a wide variety of morphometries, hydrologies, and phosphorus loadings.The regressions describing the dependence of summer phytoplankton standing crop and winter total P concentration on loading and of standing crop on total P were linear. Those characterizing water transparency as a function of standing crop and winter total P were parabolic. All regressions showed high correlation coefficients.The overall model composed of these regressions establishes a quantitative basis for the concept that phosphorus supplied to lakes exerts a uniquely controlling role on phytoplankton standing crop. The regressions may he used for trophic state description and in the development of management strategies for lakes.

A nonsymmetric compliance matrix approach to nonlinear multimodulus orthotropic materials

Multimodulus materials have moduli or stiffnesses under tension loading which are different from those under compression loading. Several approaches to their analysis have been suggested recently. Most of these approaches are based on the hypothesis that the compliance matrix in the strain-stress relations must be symmetric. Jones makes the matrix symmetric by weighting the tension compliances and the compression compliances on the basis of the proportion of tensile and compressive stresses. Isabekyan and Khachatryan determine very severe restrictions under which a multimodulus material has a symmetric compliance matrix in all coordinate systems. However, the Jones weighted compliance matrix approach cannot be derived from basic principles. Moreover, the Isabekyan and Khachatryan restricted compliance matrix approach is not realistic because the properties of known multimodulus materials do not satisfy their restrictions. The purpose of this paper is to relax the previously held requirement of compliance matrix symmetry to see whether suitable agreement can be obtained between predicted and measured strain response of ATJ-S graphite to mixed tension and compression loading under plane stress conditions.

Influence of Flank Wear on the Stresses in a Cutting Tool

The present paper is devoted to the study of the influence of flank wear upon the contact and internal stresses in a single-point tool. A comprehensive model for the distribution of contact stresses along the wear land is proposed and compared with experimental results obtained from photoelastic investigations. For this purpose orthogonal machining of lead was carried out at low speed and constant depth of cut, making use of a transparent epoxy tool provided with a pre-honed wear flat along the flank surface. Wear level and rake angle seem to have influence on both the tool-chip and tool-work contact stresses in differing degrees. The elastic stress field in the tool wedge is evaluated analytically for given mixed boundary loading conditions. These results, on comparison with the experimental data obtained from photoelastic investigation and actual cutting test, indicate noticeable influence of wear level upon contact stress redistribution and stress field reorientation. Based on this, the role of flank wear upon the brittle strength of the tool is clarified.