Showing papers on "Stress field published in 1985"
PARC1
TL;DR: In this article, the stress theorem presented previously by the present authors is derived in detail and is related to the virial and force theorems, and explicit forms of the stress field within the local density approximation are given, together with a generalization of the approximate Liberman form for pressure.
Abstract: The stress theorem presented previously by the present authors is derived in detail and is related to the virial and force theorems. Stress fields are considered in two alternative forms, both of which give the same macroscopic stress and forces on nuclei when integrated over appropriate surfaces. A crucial concept is interactions that ``cross'' surfaces. Explicit forms of the stress field within the local-density approximation are given, together with a generalization of the approximate Liberman form for pressure. Reciprocal-space expressions and ab initio calculations are considered in detail in an accompanying paper.
560 citations
TL;DR: In this paper, a technique for the measurement of the residual stress tensor averaged over a specified volume within a component is described, which involves measurement of small changes in lattice spacing using high resolution neutron diffraction.
Abstract: A technique is described for the measurement of the residual stress tensor averaged over a specified volume within a component. The method involves measurement of small changes in lattice spacing using high resolution neutron diffraction. The stress is inferred from these measurements of the strain, and the theory of the relationship between the two quantities is described, including the effects of crystalline anisotropy. The various types of high resolution neutron diffractometer suitable for the work are described. Experimental results validating the method are given for a simple bent bar of mild steel of known strain, a plastically strained mild steel bar, and a mild steel tube of known torsional strain. Examples of the method in practical use are given by a cracked fatigue test specimen, a double-V test weld and a weld joining a tube to a plate. A more detailed example is the anisotropic response of a polycrystalline sample under elastic and plastic strain; this is illustrated by measurements...
348 citations
TL;DR: In this paper, the stress field in a coated continuous fiber composite subjected to thermo- mechanical loadings is calculated by use of four concentric circular cylinders model and the target material is Ni- or SiC-...
Abstract: The stress field in a coated continuous fiber composite subjected to thermo- mechanical loadings is calculated by use of four concentric circular cylinders model. The target material is Ni- or SiC-...
229 citations
TL;DR: In this paper, the authors compared the sintering behavior of a rigid substrate and a free film, and found that the shear rate of the film is more important than its densification rate when the film was constrained by a substrate.
Abstract: A model is presented in which the sintering behavior of a ceramic film which is constrained by a rigid substrate is contrasted with the sintering behavior of a free film. The problem is made simple by the assumption that the stress field developed in the film is uniform. This simplification allows several closed form solutions to be obtained. The solutions give new insights into the sintering behavior of films supported on a substrate. It is found (1) that the shear rate of the film is more important in the sintering process than its densification rate when the film is constrained by a substrate, (2) that the incompatibility stress is time dependent and reaches its maximum value during the initial stages of sintering, (3) that the magnitude of that maximum stress may be tensile or it may be compressive depending on the shear response of the material, and (4) that if the incompatibility stress is tensile it can lead to the formation of cracks or defects in the ceramic film.
224 citations
TL;DR: In this paper, the singularity of the crack tip stress field in a nonhomogeneous medium having a shear modulus with a discontinuous derivative was investigated and the problem was solved for a finite crack and extensive results were given for the stress intensity factors.
Abstract: The singular nature of the crack tip stress field in a nonhomogeneous medium having a shear modulus with a discontinuous derivative was investigated. The problem is considered for the simplest possible loading and geometry, namely the antiplane shear loading of two bonded half spaces in which the crack is perpendicular to the interface. It is shown that the square-root singularity of the crack tip stress field is unaffected by the discontinuity in the derivative of the shear modulus. The problem is solved for a finite crack and extensive results are given for the stress intensity factors.
199 citations
TL;DR: In this paper, the analysis of stress intensity factors KI, KII and KIII by the body force method is developed for an arbitrarily shaped surface crack, and the maximum value Kθmax of Kgq, along the crack front can be expressed by the approximate formula: K θ max ≅ 0.650 σ0√π√areap; Poisson's ratio v = 0.3, where areapis the crack area projected in the direction of the maximum principal stress σ 0.
165 citations
TL;DR: In this article, the authors have calculated the regional stress field in the Indian plate, implementing dependence of slab pull and ridge push on the age of the oceanic lithosphere in the finite element procedure.
Abstract: We have calculated the regional stress field in the Indian plate, implementing dependence of slab pull and ridge push on the age of the oceanic lithosphere in the finite element procedure. The high level of the calculated stress field (order of a few kbar) and the dominance of compression in the plate are consequences of the unique dynamic situation of the present-day Indian plate. The calculated stress field explains the concentration of intraplate deformation in the region of the Ninetyeast Ridge and yields insight into the variations in stress directions in the Australian continent.
161 citations
TL;DR: In this article, the Coulomb criterion for frictional sliding was used to evaluate the possibility of slip on preexisting faults at the Yucca mountain tuffs. But, the results showed that for coefficients of friction close to 0.6, movement on favorably oriented faults of all orientations should be stable.
Abstract: Hydraulic fracturing stress measurements and acoustic borehole televiewer logs were run in holes USW G-1 and USW G-2 at Yucca Mountain as part of the Nevada Nuclear Waste Storage Investigations for the U.S. Department of Energy. Eight tests in the saturated zone, at depths from 646 to 1288 m, yielded values of the least horizontal stress S_h that are considerably lower than the vertical principal stress S_v. In tests for which the greatest horizontal principal stress S_H could be determined, it was found to be less than S_v, indicating a normal faulting stress regime. The borehole televiewer logs showed the presence of long (in excess of 10 m), vertical, drilling-induced fractures in the first 300 m below the water table. These are believed to form by the propagation of small preexisting cracks under the excess downhole fluid pressures (up to 5.2 MPa) applied during drilling. The presence of these drilling-induced hydrofractures provides further confirmation of the low value of the least horizontal stresses. A least horizontal principal stress direction of N60°W–N65°W is indicated by the orientation of the drilling-induced hydrofractures (N25°E–N30°E), and the orientation of stress-induced well bore breakouts in the lower part of USW G-2 (N65°W). This direction is in good agreement with indicators of stress direction from elsewhere at the Nevada Test Site. The observed stress magnitudes and directions were examined for the possibility of slip on preexisting faults. Using these data, the Coulomb criterion for frictional sliding suggests that for coefficients of friction close to 0.6, movement on favorably oriented faults could be expected. For coefficients of friction of 1.0, preexisting faults of all orientations should be stable. Laboratory studies on the Yucca Mountain tuffs, reported elsewhere, yield coefficients of friction ranging from 0.6 to 0.9.
116 citations
TL;DR: In this article, an in situ TEM experiment on martensitic nucleation was performed using sub-micron ZrO2 particles which were initially defect free Extrinsic, spontaneous and heterogeneous nucleation is induced by introducing dislocation loops with a strong shear component and Hertzian contact stresses into selected particles.
110 citations
TL;DR: In this paper, the authors used a tensor tensor model to resolve two distinct stress fields with directions of extension that differ by ∼60° and showed that these mixed-mode movements probably represent stress oscillations in time and space rather than discrete stress reorganizations.
Abstract: At Hoover Dam, 40 km southeast of Las Vegas, Nevada, well-exposed, highly faulted Miocene rocks provide an excellent opportunity to study the paleostress history of a very small area within a region where previous geologic studies indicate clockwise rotation of paleostress and a nearness to a major strike-slip fault-zone boundary. Within <0.5 km3 of rock, the sense of slip was determined on almost 500 separate faults. The fault-slip data show internal consistency with respect to lithology, size of faults, and location within the small area. With respect to fault slip, however, the data represent an in-homogeneous mixture of primarily strike-slip and dip-slip motions. From this mixture, it is possible to resolve two distinct stress fields with directions of extension that differ by ∼60°. Each stress field corresponds to a mixture of strike-slip and dip-slip faults, and thus the orientations of σ 1 and σ 2 are not tightly constrained. If, however, the data are first separated into strike-slip and dip-slip faulting modes and subsequently searched for sub-populations that correspond to contrasting paleostress orientations, the computations yield tightly constrained tensors that illustrate two distinct stress fields with subhorizontal σ 3 axes that trend N50°E and N75°W. The σ 1 and σ 2 axes permutate in two vertical planes that strike N40°W and N15°E, because σ 1 and σ 2 are close in value, relative to σ 3. These relationships suggest that strike-slip and dip-slip faulting belong to the same tectonic regime.
Qualitative observations of polyphase slip, fault-fault offsets, and fault-bedding geometric relationships, when evaluated in the context of changes in σ 3 orientation and permutations of σ 1 and σ 2, provide a basis for a two-stage, late Cenozoic structural evolution at Hoover Dam. These stages are (1) strike-slip faulting (partly pre-tilt) and dip-slip faulting and associated stratal tilting and (2) mostly post-tilt, complexly interrelated strike-slip, oblique-slip, and dip-slip faulting. The qualitative evaluations indicate that strike-slip and dip-slip faulting alternated in time during the second stage of deformation and may have done so during the first. These mixed-mode movements probably represent stress oscillations in time and space rather than discrete stress reorganizations. In contrast, the two different orientations of σ 3 either represent a major clockwise rotation of the stress field or a major counterclockwise rotation of the rocks during the faulting history. Each alternative is consistent with regional geologic relationships, and the choice of which is correct cannot be made within the small area that was studied.
106 citations
TL;DR: In this paper, hydraulic fracturing stress measurements and a tele-viewer survey were conducted in a 1.6 km-deep well at Auburn, New York, which was drilled at the outer margin of the Appalachian Fold and Thrust Belt in the Appalachian Plateau, penetrates approximately 1540 m of lower Paleozoic sedimentary rocks and terminates 60 m into the Precambrian marble basement.
Abstract: Hydraulic fracturing stress measurements and a borehole televiewer survey were conducted in a 1.6-km-deep well at Auburn, New York. This well, which was drilled at the outer margin of the Appalachian Fold and Thrust Belt in the Appalachian Plateau, penetrates approximately 1540 m of lower Paleozoic sedimentary rocks and terminates 60 m into the Precambrian marble basement. Analysis of the hydraulic fracturing tests indicates that the minimum horizontal principal stress increases in a nearly linear fashion from 9.9±0.2 MPa at 593 m to 30.6±0.4 MPa at 1482 m. The magnitude of the maximum horizontal principal stress increases in a less regular fashion from 13.8±1.2 MPa to 49.0±2.0 MPa over the same depth range. The magnitudes of the horizontal principal stresses relative to the calculated overburden stress are somewhat lower than is the norm for this region and are indicative of a strike-slip faulting regime that, at some depths, is transitional to normal faulting. As expected from the relative aseismicity of central New York State, however, analysis of the magnitudes of the horizontal principal stresses indicates, at least to a depth of 1.5 km, that frictional failure on favorably oriented preexisting fault planes is unlikely. Orientations of the hydraulic fractures at 593 and 919 m indicate that the azimuth of the maximum horizontal principal stress at Auburn is N83°E±15°, in agreement with other stress field indicators for this region. The borehole televiewer log revealed a considerable number of planar features in the Auburn well, the great majority of which are subhorizontal (dips < 5°) and are thought to be bedding plane washouts or drill bit scour marks. In addition, a smaller number of distinct natural fractures were observed on the borehole televiewer log. Of these, the distinct steeply dipping natural fractures in the lower half of the sedimentary section at Auburn tend to strike approximately east-west, while those in the upper part of the well and in the Precambrian basement exhibit no strong preferred orientation. The origin of this east-west striking fracture set is uncertain, as it is parallel both to the contemporary direction of maximum horizontal compression and to a late Paleozoic fracture set that has been mapped to the south of Auburn. In addition to these planar features the borehole televiewer log indicates paired dark bands on diametrically opposite sides of the borehole throughout the Auburn well. Processing of the borehole televiewer data in the time domain revealed these features to be irregular depressions in the borehole wall. As these depressions were consistently oriented in a direction at right angles to the direction of maximum horizontal compression, we interpret them to be the result of stress-induced spalling of the borehole wall (breakouts).
TL;DR: In this paper, the authors provided several simple models for the state of thermoelastic stress in a young oceanic lithosphere, taking into account a comparison of the predictions of these models with the characteristics of near-ridge earthquakes.
Abstract: Thermoelastic or thermal stress is a potentially important contributor to the state of stress in the oceanic lithosphere. The present paper provides several simple models for the state of thermoelastic stress in a young oceanic lithosphere, taking into account a comparison of the predictions of these models with the characteristics of near-ridge earthquakes. Attention is given to the characteristics of near-ridge earthquakes, sources of stress in an oceanic lithosphere, previous models of thermal stress, the calculation of thermal stress, and thermal stress models. A test is conducted of the hypothesis that thermoelastic stress is a significant component of the stress field in a young oceanic lithosphere. The considered models support the hypothesis that thermoelastic stress is a significant component of the stress field in a young oceanic lithosphere.
TL;DR: In this paper, the authors discuss the stress fields when a spheroidal inclusion, free to slip along its interface, is subjected to a constant nonshear eigenstrain, and when an elastic body containing the inhomogeneity is under all-around tension or uniaxial tension at infinity.
TL;DR: In this article, three-dimensional elastic interactions between a half-plane crack and sources of internal stress such as transformation strains and dislocations are analyzed, including the stress intensity factors induced along the crack front by the source and the overall energy change and stress field induced in the source region owing to the presence of the crack.
TL;DR: In this paper, three crustal sections, located in key zones of the Calabrian Arc and Southern Apennines, have been drawn on the basis of the available geological, geophysical, seismological and volcanological data.
01 Jan 1985
TL;DR: In this paper, the authors present a model of a system ice lobe - substratum, which is to a large degree controlled by gravitational forces, where the energy to move and imbicate glacial thrust sheets around the margins of an ice lobe, is supplied by the continuous flow of ice into the ice lobe.
Abstract: Cj derse Vallei (centre of the Netherlands) several questions arose about the origin of these landforms. The Gelderse Vallei is a Saalian glacial basin filled with younger sediments, 40 km long and up to 20 km wide, running NNW-SSE. Thrust sheets which build up the ice-pushed ridges on either side of the valley were transported away from the centre of the basin. They are up to 25 m thick and are pushed to a level about 100 m above the decollement. The thrust sheets, mainly consisting of coarse sand layers, moved as rigid masses, while only the finegrained basal layers deformed by heterogeneous simple shear. Pore water pressure plays an important role by greatly reducing the sliding friction in the decollement layer. Once a glacial thrust sheet is formed, the weight of the upward moving frontal part (the toe) offers a resistance to movement, which can not be overcome by the basal shear stress of the glacier alone. Basal shear stresses in most glaciers are in the order of 0.1 MPa (1 bar) and appear to be incapable of lifting a toe of the size found in most ice-pushed ridges in the Netherlands. The article presents a model of a system ice lobe - substratum, which is to a large degree controlled by gravitational forces. The dilemma may be solved by the concept of the gradient stress field under the marginal area of an ice lobe. This concept was first formulated by Rotnicki (1976). Because ice thickness decreases towards the margin, the substratum is subjected to a decreasing load in the same direction. If the increments of stress difference under a slab of ice in the marginal zone are summed, a gradient stress is arrived at which is di rected towards the ice edge. An estimate of the forces involved in the static equilibrium around the glacier margin indicates that the contribution by the gradient stress field is sufficient to move the toe. In the model proposed in the article, the energy to move and imbicate glacial thrust sheets around the margins of an ice lobe, is supplied by the continuous flow of ice into the ice lobe. The dimensions of icepushed ridges are thus to a high degree functions of the thickness of the ice lobe or icecap. The Gelderse Vallei ice lobe will have been at least 250 m thick to be able to form the ridges. The basal shear stress contributes less to the tectonic transport, the larger the thrust sheets and the high er the ice-pushed ridges.
TL;DR: In this article, a complete statically admissible stress field is derived for the problem of the stability of the unsupported span of a tunnel and the solution is based on the lower bound theorem of plasticity.
Abstract: Complete statically admissible stress fields are evaluated for the problem of tunnel stability. The tunnels are supported by uniform internal pressure due to a lining or rock bolts. In both cases plane deformations are assumed. Additionally, a complete stress field is derived for the problem of the stability of the unsupported span of a tunnel. The latter problem is formulated three dimensionally. In all cases the Mohr Coulomb yield criterion is used. The solution is based on the lower bound theorem of plasticity, which states that the stability of a statical system is proved if at least one admissible stress field exists.
TL;DR: In this paper, the elastic field of a semi-infinite wedge crack and its interaction with a screw dislocation under mode III loading conditions are examined and the stress field around the wedge crack is expressed in terms of a wedge stress intensity factor.
Abstract: The elastic field of a semi‐infinite wedge crack and its interaction with a screw dislocation under mode III loading conditions are examined. The stress field around the wedge crack is expressed in terms of a wedge stress intensity factor. The rate of falloff of the stress field with distance from the crack tip is found to be a function of the wedge angle. The relationship between the stress intensity factors for the wedge and sharp cracks is derived and used to estimate the magnitude of stress relaxation occurring at the crack tip due to crack blunting. The crack extension force for the wedge crack is calculated and is shown to be zero. The modifications in the stress field and the local wedge stress intensity factor due to the presence of the dislocation are calculated. From the image stress on the dislocation, the condition for the emission of dislocations from the wedge crack is obtained in terms of the critical wedge stress intensity factor for dislocation generation. It is found that the emission of dislocations from the crack tip is more difficult when the crack is blunting.
TL;DR: In this article, the authors investigated the contribution of spreading (mid-Atlantic) ridge stress in the upper crust of the Eastern Canada plate tectonic system to the development of crustal stresses.
Abstract: Diversified phenomena are contributing to our knowledge of various aspects of the stress field and the origin of the crustal stresses in eastern Canada. Both in situ stress measurements (to 2100 m) and earthquake fault plane solutions in the upper crust (∼5–20 km) indicate that the maximum horizontal stress is greater than the vertical. Absence of earthquakes in the lower crust (>20 km) implies a comparatively lower deviatoric horizontal stress in this layer. Stress directions as determined from both in situ measurements and earthquake fault plane solutions indicate an overprint confined to the ENE octant, which correlates with the direction predicted by modeling of plate tectonic stresses. Thus spreading (Mid-Atlantic) ridge stress is considered to be one of the important contributors to the stress field in eastern Canada. Viscoelastic relaxation of this stress is considered to enhance the deviatoric stress level in the upper crust, while simultaneously reducing that in the lower crust. The crust acts as a stress guide within which stresses in the upper crust that are lost through brittle failure (i.e., earthquake stress drop) can be replenished from the lower crust; moreover, the directionality predicted by modeling of spreading (Mid-Atlantic) ridge stress is maintained. Incomplete postglacial rebound also contributes to deviatoric compression. Other possible contributors to the upper crustal stress field are basal drag and membrane stress, but the relative contributions from these sources are not properly understood.
TL;DR: In this paper, a numerical study of stress within descending slabs beneath island arcs provides a general interpretation for the occurrence of deep and intermediate-focus earthquakes, and the computation of stress due to several factors, which have been proposed for the interpretation of the double-planed seismicity of intermediate-depth events, shows that thermal expansion and olivine-spinel phase change play an important role in earthquake generation.
TL;DR: In this paper, a new method for calculating the stress field in bounded ice shelves is used to compare strain rate and deviatoric stress on the Ross Ice Shelf, Antarctica.
Abstract: A new method for calculating the stress field in bounded ice shelves is used to compare strain rate and deviatoric stress on the Ross Ice Shelf, Antarctica. The analysis shows that strain rate (per second) increases as the third power of deviatoric stress (in newtons/sq meter), with a constant of proportionality equal to 2.3 x 10 to the -25th.
TL;DR: In this paper, the KImax formula is used to define the area of area:き裂面積, where the area is bounded by the number of pixels.
Abstract: 体積力法によってポアソン比ν≠0の場合の任意形状表面き裂の問題を解析する方法を示した. き裂が物体の自由表面と交差する点の近傍におけるK1の挙動を正方形表面き裂を例にとって検討し, Benthemの理論と比較するととも表面効果が存在する層がき裂の代表寸法の10-3のオーダであることを示した. 表面き裂の形状が極端に凹凸を有しない限り, また極端に細長くない限り, KImaxは, [numerical formula] で近似できる. area:き裂面積.
TL;DR: In this paper, the authors consider the mechanical behavior of an elastic body containing small cavities or holes periodically distributed in the vicinity of a surface interior to the body, and they use homogenization with respect to the variables tangent to E and matched asymptotic expansions for the normal variable.
Abstract: We consider the mechanical behavior of an elastic body containing small cavities or holes periodically distributed in the vicinity of a surface ∑ interior to the body. It constitutes a model of two pieces imperfectly stiked together. The method of analysis is some sort of homogenization with respect to the variables tangent to E and matched asymptotic expansions for the normal variable. This furnishes the local problem to be solved numerically in actual situations to obtain the local stress field. Of course the very stress concentration depends on the shape of the hole or crack. The particular problem of two pieces sticked together with a narrow uniform layer of another medium is completely worked out.
TL;DR: In this article, the authors determined fault plane solutions of four recent events in central and northern Brazil and compared these solutions with previously determined solutions of other events in Central and southeast Brazil.
TL;DR: More than a thousand acoustic-emission (AE) hypocenters were determined in a cylindrical andesite specimen under two-stage uniaxial creep at stresses of 204 and 214 MPa as discussed by the authors.
Abstract: More than a thousand acoustic-emission (AE) hypocenters were determined in a cylindrical andesite specimen under two-stage uniaxial creep at stresses of 204 and 214 MPa. Strains were monitored for 6 peripheral points at the middle part of the cylindrical specimen's wall. The strain data indicate gradual increase of nonuniform deformation during steady creep and strong intensification of the nonuniformity during acceleration creep and, therefore, biased stress distribution within the specimen. The correlation between dilatant strain and AE hypocenters was investigated for whether or not tensile cracks emit AE. The region with high AE activity shows only a small dilatant strain. This negative correlation between AE and the dilatant region may eliminate tensile cracks as possible AE sources. A composite focal-mechanism solution of local AE events, covering a wide solid angle of the focal hemisphere, indicates that shear fractures emit AE waves. The direction of the compressional axis in this solution shows a significant deviation from that inferred from the applied external force, suggesting that the local stress field is governed by preexisting weak zones that are, presumably, produced by tensile cracks within the specimen. AE hypocenters tended to form clusters during steady creep under the constant compressional stress. During acceleration creep caused by a small step increase of the external stress, the preceding clusters disappeared while a new cluster appeared in an incipient fault plane. This suggests that changes in seismicity pattern such as migrations or quiescences of swarm—important clues for earthquake predictions—may be caused by an instantaneous change in the tectonic-stress levels.
TL;DR: In this paper, the authors investigated the physical basis for these variations by studying the stress field in the Nazca plate with emphasis on the region near the trench, and inferred that the regional stress field may have a significant effect on the topography of the seaward trench slope.
TL;DR: In this paper, a study of the combined use of laser-speckle and finite-element methods for stress analysis is described, where displacement data can be used as boundary conditions for the examination of a subregion of the structural component to be analyzed.
Abstract: A study of the combined use of laser-speckle and finite-element methods for stress analysis is described. The speckle technique provides displacement data which can be directly input to a finite-element computer program for the determination of stresses. The displacement data can be used as boundary conditions for the examination of a subregion of the structural component to be analyzed. A substantial reduction in computational effort can be realized over conventional finite-element analysis of the entire structure. Also, a sizeable reduction in the required amount of experimental data may occur since direct numerical differentiation of the data is not required for strain evaluation. Acceptable accuracy may be obtained even when experimental displacement data may be too scarce for traditional numerical differentiation. Random error in experimental displacement is illustrated to have localized effects on the calculated stress field.
TL;DR: In this article, an analytical solution for the description of the stress and strain fields appearing under the inhomogeneous temperature distribution and boundary conditions characteristic to the Czochralski growth of single crystals was derived.
TL;DR: In this paper, two-dimensional crack problems in elastic homogeneous isotropic media are considered which describe rupture over a fault surface characterized by non-uniform stress drop Solutions can be found in which the stress field is finite at the crack tips and the rupture surface is not assigned a priori, but is part of the solution These crack models are consistent with the frictional stress threshold criterion for slip arrest over pre-existing fault surfaces.
Abstract: Summary Two-dimensional crack problems in elastic homogeneous isotropic media are considered which describe rupture over a fault surface characterized by non-uniform stress drop Solutions can be found in which the stress field is finite at the crack tips and the rupture surface is not assigned a priori, but is part of the solution These crack models are found to be consistent with the frictional stress threshold criterion for slip arrest over pre-existing fault surfaces A crack is found to stop when its contribution to the stress field is opposite to the stress drop at the crack tips The quasi-static propagation of a crack up to the arrest configuration is studied in terms of the minimum energy principle The crack spontaneously propagates in such a way as to make the value of the stress intensity factor at one tip equal to the value at the other tip Furthermore a tip propagating in a region with higher friction is found to move more slowly than the other tip propagating in a region with lower friction Simple criteria for fracture arrest are derived, in terms of a properly averaged stress drop Piecewise constant stress drop profiles are explicitly considered yielding a variety of solutions which can be applied to modelling asperities or barriers over a fault plane The evaluation of the amount of the energy released during the quasi-static crack propagation shows that stopping phases cannot be efficiently radiated if the crack comes to rest in a low friction region