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Showing papers on "Stress field published in 1990"


Journal ArticleDOI
TL;DR: In this paper, a three-field mixed formulation in terms of displacements, stresses and an enhanced strain field is presented which encompasses, as a particular case, the classical method of incompatible modes.
Abstract: A three-field mixed formulation in terms of displacements, stresses and an enhanced strain field is presented which encompasses, as a particular case, the classical method of incompatible modes. Within this frame-work, incompatible elements arise as particular ‘compatible’ mixed approximations of the enhanced strain field. The conditions that the stress interpolation contain piece-wise constant functions and be L2-ortho-gonal to the enhanced strain interpolation, ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation. The preceding conditions are formulated in a form particularly convenient for element design. As an illustration of the methodology three new elements are developed and shown to exhibit good performance: a plane 3D elastic/plastic QUAD, an axisymmetric element and a thick plate bending QUAD. The formulation described herein is suitable for non-linear analysis.

1,559 citations


Journal ArticleDOI
TL;DR: In this article, a general definition of the driving force for threading dislocation in a nonuniform stress field is adopted to calculate the driving forces on the dislocation due to an encounter with an interface misfit dislocation on an intersecting glide plane.
Abstract: In a strained layer grown epitaxially on a substrate, the motion of a dislocation on any particular glide plane in the layer can be influenced by the presence of dislocations on other glide planes. The focus here is on the glide of a dislocation extending from the free surface of the layer to the layer‐substrate interface, the so‐called threading dislocation. A general definition of driving force for glide of a threading dislocation in a nonuniform stress field is adopted to calculate the driving force on a threading dislocation due to an encounter with an interface misfit dislocation on an intersecting glide plane. The result is examined in detail for the case of cubic materials, taking into account different combinations of Burgers vectors. The analysis makes it clear that the misfit dislocation forces the threading dislocation to glide through a channel of width less than the full layer thickness. A blocking criterion is proposed, based on the presumption that blocking will occur if the channel width is less than the critical thickness for the local reduced strain. The results indicate that this effect can be significant in blocking the glide of a threading dislocation, depending on the mismatch strain magnitude and the layer thickness.

215 citations


Journal ArticleDOI
TL;DR: In this article, a new approach for modelling the strength of notched composites has been developed based on the assumption that subcritical damage modifies the notch-tip stress field and that the state of sub-critical damage just before failure, referred to as the terminal damage state (TDS), must have a significant influence on notched strength.

141 citations


Book
30 Nov 1990
TL;DR: In this paper, the authors proposed an energy balance model for a semi-infinite crack and showed that the model can be used to detect cracks in bending plates and shells in concrete.
Abstract: 1. Introductory chapter.- 1.1. Conventional failure criteria.- 1.2. Characteristic brittle failures.- 1.3. Griffith's work.- 1.4. Fracture mechanics.- References.- 2. Linear elastic stress field in cracked bodies.- 2.1. Introduction.- 2.2. Crack deformation modes and basic concepts.- 2.3. Eigenfunction expansion method for a semi-infinite crack.- 2.4. Westergaard method.- 2.5. Singular stress and displacement fields.- 2.6. Method of complex potentials.- 2.7. Numerical methods.- 2.8. Experimental methods.- 2.9. Three-dimensional crack problems.- 2.10. Cracks in bending plates and shells.- References.- 3. Elastic-plastic stress field in cracked bodies.- 3.1. Introduction.- 3.2. Approximate determination of the crack-tip plastic zone.- 3.3. Small-scale yielding solution for antiplane mode.- 3.4. Complete solution for antiplane mode.- 3.5. Irwin's model.- 3.6. Dugdale's model.- 3.7. Singular solution for a work-hardening material.- 3.8. Numerical solutions.- References.- 4. Crack growth based on energy balance.- 4.1. Introduction.- 4.2. Energy balance during crack growth.- 4.3. Griffith theory.- 4.4. Graphical representation of the energy balance equation.- 4.5. Equivalence between strain energy release rate and stress intensity factor.- 4.6. Compliance.- 4.7. Critical stress intensity factor fracture criterion.- 4.8. Experimental determination of KIc.- 4.9. Crack stability.- 4.10. Crack growth resistance curve (R-curve) method.- 4.11. Mixed-mode crack propagation.- References.- 5. J-Integral and crack opening displacement fracture criteria.- 5.1. Introduction.- 5.2. Path-independent integrals.- 5.3. J-integral.- 5.4. Relationship between the J-integral and potential energy.- 5.5. J-integral fracture criterion.- 5.6. Experimental determination of the J-integral.- 5.7. Stable crack growth studied by the J-integral.- 5.8. Mixed-mode crack growth.- 5.9. Crack opening displacement (COD) fracture criterion.- References.- 6. Strain energy density failure criterion.- 6.1. Introduction.- 6.2. Volume strain energy density.- 6.3. Basic hypotheses.- 6.4. Two-dimensional linear elastic crack problems.- 6.5. Uniaxial extension of an inclined crack.- 6.6. Three-dimensional linear elastic crack problems.- 6.7. Bending of cracked plates.- 6.8. Ductile fracture.- 6.9. Failure initiation in bodies without pre-existing cracks.- 6.10. Other criteria based on energy density.- References.- 7. Dynamic fracture.- 7.1. Introduction.- 7.2. Mott's model.- 7.3. Stress field around a rapidly propagating crack.- 7.4. Strain energy release rate.- 7.5. Transient response of cracks to impact loads.- 7.6. Standing plane waves interacting with a crack.- 7.7. Crack branching.- 7.8. Crack arrest.- 7.9. Experimental determination of crack velocity and dynamic stress intensity factor.- References.- 8. Fatigue and environment-assisted fracture.- 8.1. Introduction.- 8.2. Fatigue crack propagation laws.- 8.3. Fatigue life calculations.- 8.4. Variable amplitude loading.- 8.5. Mixed-mode fatigue crack propagation.- 8.6. Nonlinear fatigue analysis based on the strain energy density theory.- 8.7. Environment-assisted fracture.- References.- 9. Engineering applications.- 9.1. Introduction.- 9.2. Fracture mechanics design philosophy.- 9.3. Design example problems.- 9.4. Fiber-reinforced composites.- 9.5. Concrete.- 9.6. Crack detection methods.- References.- Author Index.

134 citations


Journal ArticleDOI
TL;DR: The current results indicate that for a given system (material properties mu and nu constant), the stress distribution is a function of the ratio of contact radius to layer thickness (a/h), and while tensile stresses are seen to occur only when a/h is small, tensile strain is observed for all a/H values.
Abstract: The stress distribution in the region of contact between a layered elastic sphere and a layered elastic cavity is determined using an analytical model to stimulate contact of articulating joints. The purpose is to use the solution to analyze the effects of cartilage thickness and stiffness, bone stiffness and joint curvature on the resulting stress field, and investigate the possibility of cracking of the material due to tensile and shear stresses. Vertical cracking of cartilage as well as horizontal splitting at the cartilage-calcified cartilage interface has been observed in osteoarthritic joints. The current results indicate that for a given system (material properties mu and nu constant), the stress distribution is a function of the ratio of contact radius to layer thickness (a/h), and while tensile stresses are seen to occur only when a/h is small, tensile strain is observed for all a/h values. Significant shear stresses are observed at the cartilage-bone interface. Softening of cartilage results in an increase in a/h, and a decrease in maximum normal stress. Cartilage thinning increases a/h and the maximum contact stress, while thickening has the opposite effect. A reduction in the indenting radius reduces a/h and increases the maximum normal stress. Bone softening is seen to have negligible effect on the resulting contact parameters and stress distribution.

129 citations


Journal ArticleDOI
TL;DR: In this paper, an analytical model which represents the behavior of a reinforced rock mass near a circular underground opening in a homogeneous, uniform stress field has been developed, which adopts the concepts of elastoplasticity and considers a proper interaction mechanism between the ground and the grouted (or friction) bolts.
Abstract: An analytical model which represents the behaviour of a reinforced rock mass near a circular underground opening in a homogeneous, uniform stress field has been developed. The theory adopts the concepts of elastoplasticity and considers a proper interaction mechanism between the ground and the grouted (or friction) bolts. It highlights the influence of the bolt pattern on the extent of the yield zone and tunnel deformation. A dimensionless parameter is introduced as a design tool which relates the tunnel convergence to the bolt spacing for a given bolt length. This publication contains the derivation of the analytical model and an illustration of the effect of bolts on the stress and displacement field near an opening. Its application to tunnel design is discussed briefly. The verification of the theory by laboratory simulation and field measurements will be presented, in detail, in a future publication.

124 citations


Journal ArticleDOI
TL;DR: In this article, a microphysically based material model for the dynamic inelastic response of a brittle material is developed, which is compatible with a previously developed ductile fracture model, and can be formulated as an efficient, robust numerical algorithm for use in threedimensional computer codes.
Abstract: A microphysically based material model for the dynamic inelastic response of a brittle material is developed. The progressive loss of strength as well as the post‐failure response of a granular material with friction are included. Crack instability conditions (an inelastic surface in stress space) and inelastic strains are obtained by considering the response of individual microcracks to an applied stress field. The assumptions of material isotropy and an exponential distribution for the crack radius are invoked to provide a tractable formulation. The constitutive model requires a minimal number of physical parameters, is compatible with a previously developed ductile fracture model [J. Appl. Phys. 64, 6699 (1988)] that utilizes inelastic surfaces, and can be formulated as an efficient, robust numerical algorithm for use in three‐dimensional computer codes. The material model is implemented into a Lagrangian computer formulation for the demonstration of material response to dynamic loading conditions. Comparisons with one‐dimensional, uniaxial impact experiments are provided.

124 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the influence of mechanically induced martensitic transformation on the rate of fatigue crack growth in 304-type austenitic stainless steels and found that changing the composition of the austenite by changing composition or lowering temperature reduces the fatigue crack rate and increases the threshold stress intensity for crack growth.
Abstract: This research reports an investigation into the influence of mechanically induced martensitic transformation on the rate of fatigue crack growth in 304-type austenitic stainless steels. Two steels of different composition, 304L and 304LN, were used to test the influence of composition; two test temperatures, 298 and 77 K, were used to study the influence of test temperature; and various load ratios were used to determine the influence of the mean stress. It was found thadecreasing the mechanical stability of the austenite by changing composition or lowering temperature reduces the fatigue crack growth rate and increases the threshold stress intensity for crack growth. However, this beneficial effect diminishes as the load ratio increases, even though increasing the load ratio increases the extent of the martensite transformation. Several mechanisms that may influence this behavior are discussed, including the perturbation of the crack tip stress field, crack deflection, work hardening, and the relative brittleness of the transformed material. The perturbation of the stress field seems to be the most important; by modifying previous models, we develop a quantitative analysis of the crack growth rate that provides a reasonable fit to the experimental results.

111 citations


Journal ArticleDOI
TL;DR: In this article, the authors analyzed the 3D stress field near a crack front in a thin ductile plate and determined the existence and size of local J-dominated fields from a comparison of complete near tip stress field with the plane strain HRR solutions using a dominance parameter.
Abstract: Based on detailed finite element solutions, various aspects of the 3-D fields near a crack front in a thin ductile plate are analysed. In particular, the stress field in the immediate crack front vicinity is carefully investigated. The existence and size of local J-dominated fields are determined from a comparison of the complete near tip stress field with the plane strain HRR solutions using a dominance parameter. In conjunction with an estimated size of the finite deformation zone, the loss of HRR-dominance along the crack front is also studied. Physically, the loss of HRR-dominance at higher load occurs when the finite deformation region outgrows the (local) plane strain region, the size of which is essentially limited by the geometry of a thin plate. Alternatively, the existence (at the mid-plane) of plane strain HRR-dominance in a low hardening material under (in-plane) small scale yielding requires the thickness of a thin plate to exceed 0.5(K1/σ0)2, thus limiting the maximum in-plane extent of the plastic zone to a fractio of plate thickness. Furthermore, such a restriction on the plastic zone size precludes the coexistence of local plane strain and surrounding plane stress HRR-fields within a thin plate.

104 citations


Journal ArticleDOI
TL;DR: In this article, the authors used earthquake focal mechanisms from before and after the 1989 Loma Prieta, California earthquake to infer the coseismic stress change and found that the main shock relieved most, if not all of the shear stress acting on its fault plane.
Abstract: Earthquake focal mechanisms from before and after the 1989 Loma Prieta, California earthquake are used to infer the coseismic stress change. Before the main shock, most earthquakes correspond to right lateral slip on planes sub-parallel to the San Andreas fault, and imply a generally N-S most compressional stress axis and a vertical intermediate stress axis. Aftershocks within the main shock rupture zone, however, display almost every style and orientation of faulting, implying an extremely heterogeneous stress field. This suggests that the main shock relieved most, if not all, of the shear stress acting on its fault plane. Aftershocks that lie on the perimeter of the rupture agree with spatially uniform stress states, but only when considered in three groups: north, south, and above the main shock rupture area. In each of these areas the stress state may reflect stress transfer by the main shock.

95 citations


Journal ArticleDOI
TL;DR: In this paper, a simple model is constructed, in which a local deviatoric stress due to a density anomaly, embedded within or just below the lithosphere, and a regionally constant deviating stress field are each approximated by biaxial tensors.
Abstract: The influence of stresses arising from horizontal density contrasts on the orientation and relative magnitudes of principal stresses in an otherwise uniform lithospheric stress field is investigated. A simple model is constructed, in which a local deviatoric stress due to a density anomaly, embedded within or just below the lithosphere, and a regionally constant deviatoric stress field are each approximated by biaxial tensors. The net stress field is obtained from the sum of the two. Both the relative magnitudes of principal stresses and the magnitude of the angular difference in principal stress direction of the summed tensor compared with that obtained in the absence of buoyancy forces depend on two parameters. The first is the ratio τ/τ′, where τ is a measure of the magnitude of the regional deviatoric stress and τ′ is the magnitude of the stress arising from buoyancy forces associated with the density anomaly. The second parameter is the angle between the trend of the density anomaly and the direction of maximum compressional stress that obtains in the absence of any perturbation by the local buoyancy forces. The directions of the principal axes of the total stress field are found to differ by up to 90° from those of the reference stress field. The model is applied to the Transverse Ranges, California, where the observed 23° difference in orientation of principal horizontal compressive stress compared with the principal compressive stress direction in central California constrains the predicted value of τ/τ′ to be approximately −0.4. This is consistent with an independently calculated range of τ/τ′ in which τ′ is inferred from seismological constraints on the magnitude of density variations underneath the Transverse Ranges and τ is inferred from observations of heat flow along the San Andreas fault in central California. The agreement between the two estimates of τ/τ′ supports the hypothesis that the observed differences in horizontal principal stress orientation in California can be explained by the combined influence of a local negative buoyancy force under the Transverse Ranges and a regional stress field associated with transcurrent deformation within the Pacific-North American plate boundary zone. The observed counterclockwise angular difference in principal horizontal stress direction in the Transverse Ranges compared with central California implies that the plane of maximum right lateral shear stress is also rotated counterclockwise relative to that in central California. This supports the possibility that the “big bend” in the San Andreas fault may be a consequence of the negative buoyancy forces acting in the Transverse Ranges, and not the cause of Transverse Ranges formation, as has often been assumed.

Journal ArticleDOI
TL;DR: Stress-dependent permeability was measured in a high-porosity/high-permeability sandstone with mechanical and fluid-flow parameters similar to those found in typical North Sea reservoirs, particularly the little-investigated effect of triaxial stress configurations as mentioned in this paper.
Abstract: Stress-dependent permeability was measured in a high-porosity/high-permeability sandstone with mechanical and fluid-flow parameters similar to those found in typical North Sea reservoirs, particularly the little-investigated effect of triaxial stress configurations. Hydrostatic loading from atmospheric conditions to stress levels comparable to those found in situ causes a slight permeability reduction. When the applied stress is nonhydrostatic, the permeability decrease is more pronounced. In particular, as failure is approached in triaxial loading or unloading, the permeability may be significantly reduced (in some cases to {lt}10% of its initial value). This paper discusses the consequences of these results for interpretation of standard permeability measurements. An example quantifies the formation damage (skin) induced by the near-wellbore stress field.

Journal ArticleDOI
TL;DR: In this article, an extensional rheometer for polymer solutions is described, where the test section is a converging channel through which a test fluid is pushed at high Reynolds numbers, and several pressure drops along the channel are measured with flush mounted transducers.
Abstract: The development of an extensional rheometer for polymer solutions is described. The test section is a converging channel through which a test fluid is pushed at high Reynolds numbers, and several pressure drops along the channel are measured with flush-mounted transducers. The high Reynolds numbers ensure a core flow of purely extensional motion and the channel is shaped to produce a constant rate of extension. Analysis of the stress field shows that the pressure drop is equal to the normal stress difference τzz - τrr in the core, plus other terms which are calculated. The calculations are based on an analytical solution for inelastic power-law fluids, and the calculations were verified by finite element computations. Extensional viscosity measurements were made for a solution of a copolymer of PMMA in an organic solvent. The data show that extensional viscosity increases with extensional rate to about the 3/2 power and, at a fixed extensional rate, extensional viscosity increases roughly as the total fluid strain.

Journal ArticleDOI
TL;DR: In this article, a simple model is proposed to explain the regional stress pattern of the Indian and Eurasian plate collision, and the trajectories of the stress axes along the transcurrent faults and the Eastern Himalayan Front are approximately N-S, parallel to the relative motion of the two plates.

Journal ArticleDOI
TL;DR: An analytical solution for the three-dimensional stress field in a plate of an arbitrary thickness, 2h, and weakened by a cylindrical hole of radius a is presented in this article.
Abstract: An analytical solution for the three-dimensional stress field in a plate of an arbitrary thickness, 2h, and weakened by a cylindrical hole of radius a is presented. Far away from the hole, the plate is subjected to a uniform tensile load, σ0, in a direction parallel to the plane of the plate. The solution is shown to be derivable from a general 3D solution, which the first author constructed in a previous paper. The analysis shows the stress concentration factor to vary across the thickness and to be sensitive to the value of the radius to thickness ratio, a/h. Furthermore, it is shown that for ratios of (a/h)≧4, the results predicted by plane stress theory are more than adequate for engineering applications. Finally, the transition between plane stress and plane strain appears to occur at a/h=0.5.

Journal ArticleDOI
TL;DR: The theory and mechanics of a statistical smoothing algorithm for estimating stress fields based on observed data are described in this paper, where the user has the option of using robustness weights, or to weight the predicted stress field by assigning quality ranks to each data point.
Abstract: The theory and mechanics of a statistical smoothing algorithm for estimating stress fields based on observed data are described. Incorporated into the algorithm are tunable parameters which allow the user to adjust the smoothness and fidelity of the fitted stress field. In addition, the user has the option of using robustness weights, or to weight the predicted stress field by assigning quality ranks to each data point. Fitted stress fields can be displayed as either a gridded map (axes of maximum, or minimum, horizontal stress are shown as short bars located at each point in an evenly spaced grid), or as a stress trajectory map. Examples of predicted stress fields for southern California and western Canada, based on borehole elongation data, are displayed as stress trajectory maps. A predicted paleostress field for the Spanish Peaks intrusion complex in Colorado, based on vertical dike orientations, is displayed as a gridded map. The smoothing algorithm is not limited to the analysis of stress orientation data. Any data consisting of a set of undirected lines measured at discrete locations are appropriate for input; possible candidates include strain data, mineral or intersection lineations, and lineaments.

Journal ArticleDOI
TL;DR: In this article, a theoretical analysis of crack nucleation in isotropic polycrystalline ice due to the elastic anisotropy of the constituent crystals is presented, where the singularity of the associated stress concentrations near a grain-boundary facet junction provides the mechanism for inducing micro-crack precursors, if similar nuclei do not already exist.

Book ChapterDOI
TL;DR: In this article, the authors described the various aspects of seismic induced by mining and found that the depth of mine tremors strongly depends on the type of rocks forming the roofs and floors of ore seams.
Abstract: Publisher Summary This chapter describes the various aspects of seismicity induced by mining. An increase in seismicity in seismic areas and the generation of seismicity in aseismic areas have been observed as a result of deep underground mining and large-scale surface quarrying. Seismicity induced by mining, fluid injection, and reservoir loading are the three main types of triggered seismicity affecting the preexisting stress field in different ways. Mining operations, leading to the removal of large masses of rock, have their major impact on the elastic stress and fluid injections influence the distribution of fluid pressure in the upper layers of the crust. The orientation of the principal stress in nature is different in different tectonic environments. Regions of thrust faulting are characterized by the minimum compressive stress being vertical, in regions of normal faulting the maximum compressive stress is vertical, and in regions of strike-slip faulting the intermediate stress is vertical. It is found that the depth of mine tremors strongly depends on the type of rocks forming the roofs and floors of ore seams.

Journal ArticleDOI
TL;DR: In this article, an analysis method was developed that predicts the strain distribution in deep drawn sheet parts based on plane stress characteristic theory, which neglects both normal and shear stresses acting across the thickness of the material.

Journal ArticleDOI
TL;DR: In this paper, the results of a series of reversed direct-stress experiments performed on freshwater ice are discussed in terms of the mechanisms underlying the behavior, with particular attention to dislocation processes.

Journal ArticleDOI
X. Chen1, Timothy J. Foecke1, M. Lii1, Y. Katz1, William W Gerberich1 
TL;DR: In this paper, the authors examined the crack initiation site under various loading and hydrogen interaction conditions in precracked Fe-3wt.%Si single crystals oriented in {001} and {001}.

Journal ArticleDOI
TL;DR: In this paper, stress-based and fracture-mechanics-based concepts are introduced to show how tensile fracture are created, how shear fractures can be produced through coalescence of tensile fractures, and how they can be created simultaneously.

Book ChapterDOI
TL;DR: In this paper, the effect of a number of variables such as ambient temperature, pressure, thermal history, and molecular weight on crazing was examined in detail, and the effects of these variables on the deformation and fracture behavior of PP, PE, POM, P6, PA 6, PA 66, PBT, and PEEK were examined.
Abstract: Crazing in PP, PE, POM, PA 6, PA 66, PBT, and PEEK has been described in relation to their deformation and fracture behavior. It has been demonstrated that the nature of the damage zone ahead of a notch is governed by the type of stress field: plane stress and plane strain. Plane strain conditions favored by thick sections with notches cause a dilatational stress concentration at the tip of the local plastic zone ahead of the notch and lead to the nucleation of numerous crazes above a certain critical level of dilatational stress. The individual crazes grow along a plane normal to the major tensile stress and almost ignore the spherulitic structure. The effect of a number of variables such as ambient temperature, pressure, thermal history, and molecular weight on crazing are examined in detail.

Journal ArticleDOI
TL;DR: In this paper, a 3D structure with a dome geometry was used to locate the locations of induced earthquakes in a gas field, where the deformation of the dome is quantitatively the main process of this structural deformation.
Abstract: A 3D relocation technique permits precise locations of induced earthquakes. Geostatistical processing using the data of 87 boreholes provides the basis of a precise 3D structure, with a dome geometry. Conventional laboratory mechanical tests performed on deep rock samples (1000 m to 5000 m) define the rock properties at depths similar to those of the seismic events (1

Journal ArticleDOI
TL;DR: A theoretical analysis of the origin of residual stresses in amorphous wires and their effect on the magnetostrictive properties has been made in this article, where the residual stress distribution in the wire is attributed to the different cooling rates experienced during solidification by different regions of the wire.
Abstract: A theoretical analysis of the origin of residual stresses in amorphous wires and their effect on the magnetostrictive properties has been made. The residual stress distribution (compression in the surface and tension in the center) in the wire is attributed to the different cooling rates experienced during solidification by different regions of the wire. Theoretically calculated results agree well with reported experimental data obtained from magnetic measurements.

Book ChapterDOI
TL;DR: In this paper, the asymptotic elastic behavior of an interfacial crack occurring between two dissimilar isotropic media is reviewed, based on differing assumptions regarding crack-face boundary conditions.
Abstract: The asymptotic elastic behavior of an interfacial crack occurring between two dissimilar isotropic media is reviewed. Distinct solutions, based on differing assumptions regarding crack-face boundary conditions, can be generated. The assumption of traction-free faces generally leads to oscillatory singular asymptotic fields which mathematically cause crack-face interpenetration, an inconsistency which can be alleviated by alternatively assuming asymptotic frictionless contact. For predominant tensile loading, the elastically-calculated ratio of contact length to crack size is typically very small, but may become appreciable when shear loading is applied. In either case, the singular crack-tip stresses cannot be sustained in materials capable of limited plastic flow, and small scale yielding (SSY) should be considered. In an extension of previous work [11], we identify conditions for SSY within surrounding dominant elastic regions of both traction-free and frictionless contact types. For the latter case, approximate closed form expressions for the plastic zone size and shape are obtained as the locus of points where the elastically-calculated Mises stress equals the tensile yield strength, σ ys ,. The maximum extent of this plastic zone is approximately 3K II c2 /2σ ys 2 , where K II c , is the closed crack-tip bimaterial stress intensity factor. Precise SSY numerical calculations for an elastic/perfectly-plastic material atop a rigid substrate indicate that the asymptotic stress field in the plastically-deforming material is composed of two fan regions and two constant state regions. Within the plastic zone, the interfacial and crack-face tractions asymptotically reach constant values. Compressive crack-face tractions persist even when contained inelastic crack-tip deformation is included.

Journal ArticleDOI
TL;DR: In this article, the main features of a toughening mechanism associated with a curvilinear crack path are examined using a model consisting of a macro-crack in a brittle solid with a curved segment at the crack tip.
Abstract: The main features of a toughening mechanism associated with a curvilinear crack path are examined using a model consisting of a macrocrack in a brittle solid with a curvilinear segment at the crack tip. A numerical procedure for finite and semiinfinite cracks is formulated and evaluated using an example which has an exact solution (a finite crack in the form of a circular arc in a uniform stress field). It is shown that, for a relatively small amplitude of crack path oscillations, the toughening ratio can be taken equal to the ratio of the corresponding crack path lengths.

Book ChapterDOI
TL;DR: In this paper, the growth of initially spherical voids in periodic cubic arrays and for the initial spherical void prior to a blunting mode I plane strain crack tip were investigated.
Abstract: Three-dimensional finite element computations have been carried out for the growth of initially spherical voids in periodic cubic arrays and for initially spherical voids ahead of a blunting mode I plane strain crack tip. The numerical method is based on finite strain theory and the computations are three-dimensional. The void cubic arrays are subjected to macroscopically uniform fields of uniaxial tension, pure shear and high triaxial stress. The macroscopic stress—strain behavior and the change in void volume were obtained for two initial void volume fractions. The calculations show that void shape, void interaction and loss of load carrying capacity depend strongly on the triaxiality of the stress field. The results of the finite element computation were compared with several dilatant plasticity continuum models for porous materials. None of the models agrees completely with the finite element calculations. Agreement of the finite element results with any particular constitutive model depended on the level of macroscopic strain and the triaxiality of the remote uniform stress field. For the problem of the initial spherical voids directly ahead of a blunting mode I plane strain crack tip, conditions of small scale yielding were assumed. The near tip stress and deformation fields were obtained for different void-size-to-spacing ratios for perfectly plastic materials. The calculations show that the holes spread towards the crack tip and towards each other at a faster rate than they elongate in the tensile direction. The computed void growth rates are compared with previous models for void growth.

Journal ArticleDOI
TL;DR: In this article, the elastic interaction between an edge dislocation and a finite crack has been investigated using the dislocation-modeling approach using the applied stresses of modes I and II but also dislocations inside the crack.
Abstract: The elastic interaction between an edge dislocation and a finite crack has been investigated using the dislocation-modelling approach. We considered not only the applied stresses of modes I and II but also dislocations inside the crack. We obtained the stress field, the force and strain energy of the dislocation and the stress intensity factors at both crack tips. The unstable equilibrium positions of dislocation have been studied. Also, the criterion of dislocation emission from the crack tip has been analysed in order to understand the crack tip as a major source of dislocation.

Journal ArticleDOI
TL;DR: In this paper, the effect of the presence of soft interlayers embedded in a cross-ply laminate on transverse cracking, delamination and their interaction has been studied analytically.