Sharp Inclusions Research Articles

Two dimensional displacement and stress fields for tri-material V-notches and sharp inclusions in anisotropic plates

The singular behavior for multi-material V-notch notched plates is studied in this paper, considering both isotropic and anisotropic materials. Firstly, by introducing the asymptotic expansions of displacements near the apex of the sharp notch, the elastic governing equations are transformed into eigen ordinary differential equations. The stress singularity orders and eigen angular functions are then obtained solving the established equations by using the interpolating matrix method. Secondly, using in combination the results from proper finite element analyses and the asymptotic analytical solution derived, an over-deterministic method is employed to calculate the amplitudes of the coefficients in the asymptotic expansions of displacements and stresses near the V-notch tip. The efficiency of the proposed method is assessed analyzing several notched specimens made of different materials. The accuracy of the notch stress intensity factors and the displacement and stress fields are evaluated by comparison with results available in the literature, as well as the results obtained from a number of finite element analyses.

Crack onset assessment near the sharp material inclusion tip by means of modified maximum tangential stress criterion

In the case of particle reinforced composites, where the particles are in a form of sharp material inclusions, singular stress concentration exists on each tip of each inclusion. This is due to the geometric and material discontinuities between matrix and particle. These points of stress concentration are susceptible of crack initiation and thus often responsible for failure of the whole structure. The modified maximum tangential stress criterion is employed in order to predict crack onset conditions.

Crack onset assessment near the sharp material inclusion tip by means of modified maximum tangential stress criterion

In the case of particle reinforced composites, where the particles are in a form of sharp material inclusions, singular stress concentration exists on each tip of each inclusion. This is due to the geometric and material discontinuities between matrix and particle. These points of stress concentration are susceptible of crack initiation and thus often responsible for failure of the whole structure. The modified maximum tangential stress criterion is employed in order to predict crack onset conditions.

Multi-Parameter Based Stress Distribution in Vicinity of Sharp Material Inclusion Tip

General Singular Stress Concentrators (GSSCs) which exhibit singular stress concentration are often responsible for crack initiation and thus failure of the component. The GSSC of the type of bonded bi-material junction occurs in a variety of technical applications including but not limited to sharp material inclusions, silicate based composites and electronic components. The GSSC cannot be assessed by means of standard fracture mechanics. Approaches of generalized fracture mechanics require precise description of stress distribution near the stress concentration points. In order to determine the stress field accurately, the paper incorporates the multi-parameter based description.

Duality for $A_\infty$ weights on the real line

Under the same bounds on G_q -constants and A_p -constants, the optimal exponents for sharp inclusions between Gehring G_q -class of weights and Muckenhoupt A_p -class ( 1 < p, q < \infty ) are Hölder conjugate, if p and q are conjugate. This is a consequence of a representation theorem of A_\infty weights in terms of W^{1,r} -biSobolev maps and a duality result between G_q and A_p classes in dimension one. We prove also that sharp a priori bounds on constants correspond under the Hölder conjugate mapping \phi(t)= \frac{t}{t-1} .

An inverse geometric problem: Position and shape identification of inclusions in a conductor domain

Abstract This work presents a methodology for identifying inclusions in a conductor domain. The methodology is based on electrical potential measurements on the external boundary of a conductor body subjected to a prescribed set of electrical current injections. The boundary of each inclusion is approximated by a special kind of spline, whose control points have an extra parameter related to the distance between the control point and the curve. Such special feature allows identification of smooth or sharp inclusions with the same initial guess. The identification is an inverse problem that, in this work, is solved by the Levenberg–Marquardt Method. This iterative method tries to locate the minimum of an objective function, the square of the norm of a residual vector function, given by the differences between electrical potential measurements and the computed ones. The computation of the electrical potential is called forward problem and it is solved by an implementation of the direct formulation of the Boundary Element Method (BEM). The present paper addresses two approaches for computing the derivatives of the residual function with respect to the minimization parameters, required by the Levenberg–Marquardt Method. The first one is based on finite differences and the second one is based on the direct differentiation of the integral equation of the BEM for potential problems. Performance comparisons of these two approaches are presented, based on numerical experiments of identification of inclusions with noisy datasets computationally obtained.

Sharp inclusions and lacunary series in mixed-norm spaces on the polydisc

We establish the sharpness and strictness of continuous inclusions in mixed-norm spaces of n-harmonic functions on the unit polydisc of ℂ n . To this end, we modify a wellknown counterexample of Hardy and Littlewood and give a characterization of lacunary series with Hadamard gaps in mixed-norm and weighted Hardy spaces.

Quantifying Democracy of Wavelet Bases in Lorentz Spaces

We study the efficiency of the greedy algorithm for wavelet bases in Lorentz spaces in order to give the near best approximation. The result is used to give sharp inclusions for the approximation spaces in terms of discrete Lorentz sequence spaces.

Brittle intergranular fracture at elevated temperatures in low–alloy steel

AbstractRecent studies of stress-relief cracking in low-alloy steels have focused attention on a novel mode of brittle intergranular fracture which occurs at elevated temperatures (300–650°C) in hard, coarse–grained heat–affected–zone microstructures. Fracture initiates at stress concentrators such as sharp cracks or inclusions, and can propagate under static loading at rates of 10−11−10−5 ms−1 to produce intergranular facets with very little associated plastic deformation. The stress-intensity parameter K has been used to characterize crack growth, and three regimes of behaviour have been observed: (i) a threshold region at growth rates of 10−11−10−10 m S−1, (ii)a plateau region, in which growth rates are independent of K between 10−10 and 10−8 m S−1, and (iii) a region of highly K-sensitive crack growth between 10−8 and −5 m S−1. Independent Auger electron spectroscopy analyses have demonstrated that sulphur segregates locally to the high-temperature crack tip, giving rise to the embrittlement of a limi...

The Creighton pluton, Ontario: an unusual example of a forcefully emplaced intrusion: Discussion

Dutch (1979) states that pre-Sudbury breccia tectonic structures are confined to the immediate vicinity of the Creighton pluton and are not present in the country rocks in areas removed from this body. His contention that this early deformation is 1 attributable to forceful (diapiric) emplacement of the pluton is based in large part on the assumptions that: (1) the pluton was emplaced as a diapir capable of generating and transmitting the necessary stress; and (2) there was no deformation of regional significance prior to the formation of the Sudbury I breccia (and, by inference, the associated Sudbury : Nickel Irruptive and Whitewater Group). The Creighton pluton was forcefully emplaced into its host rocks, but this probably occurred in connection with a tectono-metamorphic event of regional significance. The pluton does not display many of the features characteristic of diapirs, such as outward-plunging lineations, a rim syncline, or development of contact shear and mylonite zones (Stephannson 1977). It does contain abundant, rotated country-rock inclusions. The contacts between the granite and the inclusions are generally sharp and unsheared and many inclusions display metamorphic reaction rims indicating lack of postsolidification movement (see Card 1968, photo 7, page 15). Numerous granite dykes and apophyses cut the inclusions and extend into the country rocks. Agmatitic contact zones of foliated countryrock inclusions in foliated granite are present (Card 1978a). These features, along with its porphyritic texture and restricted composition indicate that the Creighton pluton was emplaced as a magma, primarily by a block-stoping mechanism, rather than as a diapir. The structural patterns observed by Dutch (closed foliation loop in an inclusion, parallelism of foliation to contacts, etc.) are probably ascribable to the combined effects of preintrusion deformation of the country rocks, magi matic (crystal mush) Row, and later, superimposed deformation that has affected the pluton, its inclusions, and the country rocks (Card 1978~). In stating that there was no deformation of regional significance prior to the formation of the Sudbury breccia (and hence no pre-breccia tectonic structures in areas removed from the Creighton pluton), Dutch follows Brocoum and Dalziel's (1974) contention that the Sudbury Structure and the adjacent Southern and Grenville Provinces were affected by a single, post-Nickel Irruptive tectonometamorphic event. Brocoum and Dalziel's hypothesis is untenable for a number of reasons, including the following: (1) There is geological, geochronological, and paleomagnetic evidence for a regional event involving deformation, metamorphism, and plutonism prior to emplacement of the Nipissing Diabase some 2150 Ma ago (Card 1968; Church and Young 1972; Van Schmus 1976; Morris 1977). Indeed, emplacement of the Creighton pluton some 2200 Ma ago is part of this event. (2) The available geochronological data indicate that major metamorphism of the Huronian occurred about 1900 Ma ago (Fairbairn et al. 1969; Van Schmus 1976) prior to the formation of the Sudbury breccia and emplacement of the Nickel Irruptive some 1840 Ma ago (Krogh and Davis 1974). Huronian rocks, both regionally and adjacent to the Nickel Irruptive, have metamorphic mineral assemblages and structural elements that are not present in the Nickel Irruptive or the Whitewater Group. Huronian rocks adjacent to the Nickel Irruptive have mineral assemblages diagnostic of the amphibolite facies. The Nickel Irruptive and the Whitewater Group, in contrast, display low greenschist facies assemblages (Card 1978b). Regionally, the Huronian rocks display several generations of major and minor tectonic struc-