In this first part, the failure of smooth specimens in tension-compression is examined from the viewpoint of fine-crack mechanics, which has some detailed features different from those of traditional crack mechanics. An expression is given for the equivalent J integral for the stress intensity coefficient. Allowance is made for the effects of crack width on the growth rate in elastic and elastoplastic deformation.Fatigue failure is a basic cause of down time in current industrial equipment. However, in calculations on cyclic loading during design or technical diagnosis for oil and gas equipment, use has so far been made of methods and empirical coefficients introduced as long ago as the middle of the past century. Failure mechanics has been based on the growth of long cracks and has hardly been used in calculations, since in many cases one cannot assume that such cracks occur. However, in constructions there actually are small surface cracks of depth about 1 mm, which at present are not detected by nondestructive testing. The growth of such defects largely determines the residual equipment life.Here I consider the characteristic features of fatigue growth in long cracks. In calculations within the elastic limit, the basic characteristic is the stress intensity coefficient (SIC):(1) where ƒ n is a geometrical factor, ∆σ n is the range in the nominal stresses (stresses in the net cross section), and l the depth of a linear crack. Figure 1 shows long-crack fatigue-growth curves (v is crack growth rate and R = σ min /σ max is the cycle asymmetry factor). It is assumed that the nominal stress is below the elastic limit. There are two stages on each curve. In particular, on the curve R = -1, the first stage corresponds to the part AB, where there is a transition from the threshold value of the SIC ∆K th to the linear part BC, where the crack growth rate becomes a power-law function of the SIC range.Length increase (growth) occurs only if the crack is open. To describe this, we introduce the opening coefficient u = (σ max -σ op )/(σ max -σ min ), in which σ max and σ min are the maximal and minimal stresses in the cycle and σ op is the opening stress for the crack at the mouth.For a long crack in the second part of the Paris diagram, the crack opening coefficient (COC) may be approximated by (2) u R R t tc = − − 1 1 . ∆ = ∆ π K f l n n σ ,
It is shown that use in calculations of a model with two mechanisms of plastic flow, each of which is described by the Arutyunyan-Vakulenko theory, does not give rise to difficulties compared with the Ishlinskii-Prager theory, for which software packages of the ANSYS type have been developed. After small correction of these programs, it is possible to describe in more detail deformation of metals under complex loading conditions.Effects of unilateral deformation accumulation (ratcheting) in structures may be described on the basis of plastic flow theory. The greatest amount of work on plastic flow theory was carried out in the 1960-1970s in studying transient regimes of power generation equipment when a detailed description was required for features of alternating sign loading of metals. This period relates to the development of Ishlinskii-Prager plastic flow theory [1, 2] whose basic assumptions come down to the following.Stress tensor σ ij is divided into two components: active tensor s ij and supplementary stress tensor (backstress) ρ ij :The original flow surface (FS) for isotropic materials is normally prescribed by the Huber-Mises condition:where σ i = (3σ ′ ij /2) 1/2 ; σ ′ ij is stress intensity; σ ′ ij = σ ij -δ ij σ 0 is stress deviator component; σ 0 = δ ij σ ij /3 is stress spherical tensor component; δ ij is Kronecker symbol (δ ij = 1 for i = j; δ ij = 0 for i ≠ j); σ y is yield point.In nine-dimensional space of stress deviator components, Eq.(2) represents a hypersphere with radius equal to the yield point σ y . 1 The stressed state in any cross section of the structure corresponds to a point in the stress deviator space that is called "representative." With elastic deformation this point moves inwards and on reaching the FS depending on the plastic strengthening model adopted it may either move the FS as a rigid body (anisotropic or kinetic strengthening) or increase the FS radius (isotropic strengthening). 1 In this case, tensor notations are used in which Cartesian coordinates x, y, z are labeled with digits 1, 2, 3. Stress tensor component σ 11 corresponds to a stress acting parallel to axis 1 (x) on an area of orthogonal axis 1 (x). Tangential stresses in the same area are designated correspondingly σ 12 and σ 13 . We note that in order to provide the required symmetry equal stresses, for example σ 13 and σ 31 , are not substituted with one designation. Even so this substitution makes it possible to shorten the dimension of the stress space to six, although here there is a loss of specific recording symmetry and the possibility of considering the flow surface as a hypersphere.
A semi-empirical model is developed for analysis of stresses in a dent. Variation in maximum stress intensity in dents with different angular orientations relative to the shell's generatrix is demonstrated. Results of stress analysis are presented for a dent oriented along the generatrix of a pipe as a function of the dent's geometric parameters.Dents in pipelines and pressure vessels are seen as a rather widespread defect, which creates risk for continued operation of equipment as a function of the operating conditions of the structures and the mechanical properties of the material. If the load is predominately static and the material is sufficiently plastic, the existence of a dent does not exert a noticeable influence on the bearing capacity of the shell. In that case, the following basic restriction should be considered for a pipeline: the minimum diameter of the cross section should not be less than 85% of the nominal dimension.Dents with additional crack and score types of defects, and which also contain a defective welded seam, are actually dangerous. To analyze the risk associated with these defects during service, when corrosion, fatigue, or brittle (at low temperatures) failure is possible, it is necessary to evaluate concentrations of bending stresses in the wall within the zone of the dent.Considering the error generated in determining initial data, it is expedient here to utilize approximate semi-empirical models, which are based on analysis of experimental data and which make it possible to obtain simple analytical solutions. The method adopted on the basis of ASME standard B31G to evaluate the bearing capacity of pipes with corrosion damage is a typical example of this model [1].Let us examine an analytical expression, which can be used to analyze the notch-sensitivity index for technical diagnoses of pipelines and vessels.According to the exact analytical solution for flexible shells with an oval cross section [2], the maximum bending stresses
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