Effect Of Stress Redistribution Research Articles

Mechanics of splitting in orthotropic materials

A theoretical study is made of splitting around the boundaries of elliptical holes in an orthotropic material. The splitting is modeled as a crack with both Mode I opening and Mode II sliding. The sliding resistance on the closed portion of the splitting crack is assumed to obey a Coulomb friction law. The stress intensity factors and the critical external load for splitting propagation are calculated as functions of splitting length. The dependence of stress intensity factors and the critical external load upon the length of splitting, the root radii of the hole, elastic orthotropy, frictional coefficient and the critical energy release rate is described in terms of a universal set of nondimensional parameters. It is found that splitting is unstable in the absence of frictional resistance and stable when sufficient frictional resistance is present. Elastic orthotropy, through its interaction with frictional resistance, tends to reduce the effects of frictional sliding resistance.The stress redistribution due to splitting is also studied. It is found that the splitting is very effective in relieving the high stress concentration ahead of the tips of cracks or at the boundaries of holes. Unlike the growth of splitting itself, the stress redistribution effect is insensitive to frictional resistance. The calculated results suggest that regardless of the root radii of a flaw, a splitting crack of the length of the original flaw reduces the stress concentration factor to less than 2.

Modelling of combined high-temperature creep and cyclic plasticity in components using continuum damage mechanics

A computer-based finite-element viscoplastic damage solver has been developed for the analysis of structural components subject to combined cyclic thermal and mechanical loading. The solver, which is based on continuum damage mechanics, is able to predict the combined evolution of creep and cyclic plasticity damage by solution of the combined boundary-initial value problem. The computational difficulties which arise due to the different timescales, associated with material behaviour at the different temperatures within a thermal field, have been overcome by the use of a normalization technique. The high computer demands associated with the detailed numerical solution of combined thermo-mechanical problems, which have prevented their use in design, have been overcome by the development of a novel ‘cycle jumping’ method which avoids repetitive calculations over those cycles in which the damage fields change insignificantly. Between the ‘jumps’ in the solution technique, the damage and the strain rate fields are coupled and hence allow stress redistribution. The finite-element solver has been used to successfully predict the high temperature behaviour of a slag tap component subjected to cyclic thermal loading generated by infrared heaters and water cooling ducts. The initiation of damage and micro-cracking has been found to occur early in the lifetime at approximately 3000 cycles adjacent to the cooling duct; and the propagation of failure zones has been found to stabilize at 60 000 cycles after which no further damage evolution occurs. A further development of the technique, which requires even less computer resource, is the ‘cycle leaping’ method which neglects the effect of stress redistribution over large numbers of cycles, by leaping from the first few cycles to the final state. With this method good predictions have been made of the fields of damaged and micro-cracked material in the final state of the slag tap component. The technique has potential for use at the early or conceptual stages of design.

Creep of composite energy accumulators

Within the framework of the linear theory of anisotropic viscoelasticity a numerical analysis of the state of stress and strain of a composite inertial energy accumulator is carried out. The boundary-value problem is solved with the aid of the method of quasi-constant viscoelastic operators with finite-element realization. The article describes creep and effects of stress redistribution in lengthy rotation of flywheels.

A novel approach to stress measurements in rocksalt

A review of stress measurements performed in rocksalt indicates that, until now, no technique or calculation model can take into account the particular mechanical behaviour shown by this material. Using a modified doorstopper cell and a calculation procedure that considers the anisotropic, non-linear and heterogeneous behaviour found in rocksalt at the grain scale, it is shown through laboratory simulations, how reliable, accurate, low-cost and rapid stress measurements can be performed in this type of rock. The effect of stress redistribution at the bottom of a borehole is evaluated through numerical and physical simulations and it is demonstrated that the doorstopper technique is much less affected by this phenomena than most of the other techniques.

Analysis of plastic deformation in silicon web crystals

Numerical calculation of {111}〈110〉 slip activity in silicon web crystals generated by thermal stresses is in good agreement with etch pit patterns and X-ray topographic data. The data suggest that stress redistribution effects are small and that a model, similar to that proposed by Penning and Jordan but modified to account for dislocation annihilation and egress, can be used to describe plastic flow effects during silicon web growth.

Buckling of Shells-Pitfall for Designers

Purpose I order to produce efficient, reliable designs and to avoid unexpected catastrophic failure of structures of which thin shells are important components, the engineer must understand the physics of shell buckling. The objective of this survey is to convey to the reader a feel for shell buckling, whether it be due to nonlinear collapse, bifurcation buckling, or a combination of these modes. This intuitive understanding of instability is communicated by a large number of examples involving practical shell structures which may be stiffened, segmented, or branched and which have complex wall constructions. With such intuitive knowledge the engineer will have an improved ability to foresee situations in which buckling might occur and to modify a design to avoid it. He will be able to set up more appropriate models for tests and analytical predictions. The emphasis here is not on the development of equations for the prediction of instability. For such material the reader is referred to the book by Brush and Almroth. n Emphasis is given here to nonlinear behavior caused by a combination of large deflections and plasticity. Also illustrated are stress redistribution effects, stiffener and loadpath eccentricity effects, local vs general instability, imperfection sensitivity, and modal interaction in optimized structures. Scattered throughout the text are tips on modeling for computerized analysis. The survey is divided into nine major sections describing: 1) several examples of catastrophic failure of expensive shell structures; 2) the basics of buckling behavior; 3) classical buckling and imperfection sensitivity; 4) nonlinear collapse and the appropriateness of linear bifurcation buckling analyses for general shells; 5) bifurcation buckling with significant nonlinear prebuckling behavior; 6) effects of boundary conditions, load eccentricity, transverse shear deformation, and stable postbuckling behavior; 7) optimization of buckling-critical structures with consequent modal interaction; 8) a suggested design method for axially compressed cylinders with stiffeners, internal pressure, or other special characteristics; and 9) two examples in which sophisticated buckling analyses are required in order to derive improved designs. The paper focuses on static buckling problems.

The use of the C∗ parameter in predicting creep crack propagation rates

The applicability of the C∗ parameter for the prediction of creep crack propagation rates is considered. A new method for estimating C∗ is presented, the results from which show good agreement with those from an existing technique. Experimental results from creep crack growth tests, conducted on a 1 Cr Mo V steel using both compact tension and single edge notch bend specimens, indicate that good correlation with C∗ is obtained once the effects of stress redistribution become negligible. Finally, comparisons are drawn between C∗ and other possible correlating parameters, and the limitations of each approach are discussed.

Prediction of Torsional Strength of Tubes

A simplified analysis technique has been developed to predict torsional strength of tubes or shafts including plastic buckling limits and effects of plastic redistribution through the tube wall. Buckling predictions employ well-known formulas and concepts, but are combined in a unique procedure which provides improved accuracy over present known techniques. It was concluded that Batdorf’s equation, previously considered applicable only to relatively short tubes, is also applicable even to long slender tubes when wall stress redistribution effects are included. It was further concluded that Gerard’s recommendations for plasticity reduction factor were very accurate when obtained from compression stress-strain curves through application of the maximum shear stress theory in plasticity. Experimental verification of torsional strength prediction methods is needed for alloys other than aluminum, especially at elevated temperatures.

Tests of composite concrete beams with prestressed planks

This paper deals with tests on composite concrete beams with prestressed concrete planks. It describes the separate influences of differential shrinkage and creep as well as stress redistribution due to a great strain difference at the adjoining faces between the prestressed plank and added concrete. Existing formulas relating to differential shrinkage and creep are based on the actual strains to be expected, but in order for the designer to have this information, extensive tests are required. This paper contains qualitative data in this regard and describes means by which information can be satisfactorily obtained, including the effect of stress redistribution.

Stresses Around Wellbores in Nonlinear Rock

ABSTRACT The state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore is considered an axisymmetric body with axisymmetric loading. The initial vertical and horizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-wise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses are now reintroduced along with the changed moduli and original boundary constraints. This procedure is repeated until convergent stresses are reached. The effect of nonlinearity on stresses is examined for a 6,000-ft wellbore in a schistose gneiss and Berea sandstone using results of laboratory triaxial compression tests. The results show that the effect is restricted to one well radius from the bottom periphery of the hole. Beyond a distance of one-quarter radius, the effect of nonlinearity on stresses is almost always less than 5 percent for the cases considered. The consideration of a static pressure inside the well does not magnify the effect of nonlinearity on borehole stresses. INTRODUCTION The terms "wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding the behavior of the lined or unlined hole, hydraulic fracture response, and the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Topping1 and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (s1-s3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for the gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson's ratio (?) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of ? with deviator stress application, but the rate of increase diminishes with confinement. The ET and ? curves for the two rock types are tabulated in Tables 1A and 1B for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation.