Showing papers on "Fracture mechanics published in 1987"
TL;DR: An improved description of copper and ironcylinder impact (Taylor) test results has been obtained through the use of dislocation-mechanics-based constitutive relations in the Lagrangian material dynamics computer program EPIC•2.
Abstract: An improved description of copper‐ and iron‐cylinder impact (Taylor) test results has been obtained through the use of dislocation‐mechanics‐based constitutive relations in the Lagrangian material dynamics computer program EPIC‐2. The effects of strain hardening, strain‐rate hardening, and thermal softening based on thermal activation analysis have been incorporated into a reasonably accurate constitutive relation for copper. The relation has a relatively simple expression and should be applicable to a wide range of fcc materials. The effect of grain size is included. A relation for iron is also presented. It also has a simple expression and is applicable to other bcc materials but is presently incomplete, since the important effect of deformation twinning in bcc materials is not included. A possible method of acounting for twinning is discussed and will be reported on more fully in future work. A main point made here is that each material structure type (fcc, bcc, hcp) will have its own constitutive beha...
1,718 citations
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01 Jan 1987
TL;DR: Fracture Mechanics and its Geophysical Applications as mentioned in this paper are applied to Hot, Dry Rock Geothermal Energy, with applications to Faults, Joints, Dikes and Solution Surfaces.
Abstract: Preface. Introduction to Fracture Mechanics and Its Geophysical Applications. Joints and Shear Fractures in Rock. Theory of Crack Initiation and Propogation in Rock. The Theory of Subcritical Crack Growth with Applications to Minerals and Rocks. Time-Dependant Deformation and Failure. Fracture Mechanics Approach to Hydraulic Fracturing Stress Measurements. Fracture Mechanics Applied to Hot, Dry Rock Geothermal Energy. Theoretical Displacements and Stresses Near Fractures in Rock, With Applications to Faults, Joints, Dikes and Solution Surfaces. Mechanics of Shear Rupture Applied to Earthquake Zones. Dynamic Rock Fragmentation. Experimental Fracture Mechanics Data for Rocks and Minerals.
820 citations
TL;DR: In this article, mineback experiments and laboratory tests and analyses of these data are integrated to describe this complex fracture behavior, which can occur by arresting the growth of the fracture, increasing fluid leakoff, hindering proppant transport, and enhancing the creation of multiple fractures.
Abstract: Geologic discontinuities, such as joints, faults, and bedding planes, can significantly affect the overall geometry of hydraulic fractures. This can occur by arresting the growth of the fracture, increasing fluid leakoff, hindering proppant transport, and enhancing the creation of multiple fractures. Results from mineback experiments and laboratory tests and analyses of these data are integrated to describe this complex fracture behavior.
718 citations
TL;DR: In this paper, two types of models based on a critical ratio of cavity growth or on continuum damage mechanics are presented with constant references to experimental validation studies, and conclusions can be drawn regarding the effectiveness of the methods proposed and their undeniable contribution to fracture mechanics.
687 citations
TL;DR: In this article, the authors present a methodology that relates the kinetics of material failure on the microstructural level to continuum mechanics, by introducing micro-structural descriptions of damage into the continuum constitutive relations as internal state variables.
666 citations
TL;DR: A unified derivation of crack tip flux integrals and their associated domain representations is laid out in this article using a general balance statement as the starting point, and complementary integrals which are valid for general material response and arbitrary crack tip motion are obtained.
490 citations
463 citations
TL;DR: In this article, the development of an anisotropic theory of continuum damage mechanics for ductile fracture is described, where a tensor tensor M(D) is used to characterize damage evolution and a constitutive equation of plasticity is formulated.
401 citations
TL;DR: In this paper, the influence of the nucleation and growth of micro-voids in the material near the tip of a crack is investigated, and numerical analyses of the stress and strain fields are based on finite strain theory, so that crack tip blunting is fully accounted for.
Abstract: An elastic-Viscoplastic model of a ductile, porous solid is used to study the influence of the nucleation and growth of micro-voids in the material near the tip of a crack. Conditions of small scale yielding are assumed, and the numerical analyses of the stress and strain fields are based on finite strain theory, so that crack tip blunting is fully accounted for. An array of large inclusions or inclusion colonies, with a relatively low strength, results in large voids near the crack tip at a rather early stage, whereas small second phase particles in the matrix material between the inclusions require large strains before cavities nucleate. Various distributions of the large inclusions, and various critical strains for nucleation of the small scale voids between the inclusions, are considered. Localization of plastic flow plays an important role in determining the failure path between the crack tip and the nearest larger void, and the path is strongly sensitive to the distribution of the large inclusions. Values of the J-integral and the crack opening displacement at fracture initiation are estimated, together with values of the tearing modulus during crack growth, and these values are related to experimental results.
376 citations
TL;DR: In this article, a fracture mechanics model is developed for nontransforming ceramics that show an increasing toughness with crack extension (R-curve, or T -curve) behavior, treating the increased crack resistance as the cumulative effect of grain bridging restraints operating behind the advancing tip.
Abstract: A fracture mechanics model is developed for nontransforming ceramics that show an increasing toughness with crack extension (R-curve, or T-curve, behavior). The model derives from the observations in Part I, treating the increased crack resistance as the cumulative effect of grain bridging restraints operating behind the advancing tip. An element of discreteness is incorporated into the formal distribution function for the crack-plane restraining stresses, to account for the primary discontinuities in the observed crack growth. A trial forceseparation function for the local bridge microrupture process is adopted, such that an expression for the microstructureassociated crack driving (or rather, crack closing) force may be obtained in analytical form. The description can be made to fit the main trends in the measured toughness curve for a coarse-grained alumina. Parametric evaluations from such fits conveniently quantify the degree and spatial extent of the toughening due to the bridging. These parameters could be useful in materials characterization and design. It is suggested that the mechanics formulation should be especially applicable to configurations with short cracks or flaws, as required in strength analysis.
357 citations
TL;DR: In this paper, a series of tests on the size effect due to blunt fracture is reported and analyzed, and the fracture energy is defined as the specific energy required for crack growth in an infinitely large specimen.
Abstract: A series of tests on the size effect due to blunt fracture is reported and analyzed. It is proposed to define the fracture energy as the specific energy required for crack growth in an infinitely large specimen. Theoretically, this definition eliminates the effects of specimen size, shape, and the type of loading on the fracture energy values. The problem is to identify the correct size-effect law to be used for extrapolation to infinite size. It is shown that Bazant's recently proposed simple size-effect law is applicable for this purpose as an approximation. Indeed, very different types of specimens, including three-point bent, edge-notched tension, and eccentric compression specimens, are found to yield approximately the same fracture energy values. Furthermore, the R-curves calculated from the size effect measured for various types of specimens are found to have approximately the same final asymptotic values for very long crack lengths, although they differ very much for short crack lengths. The fracture energy values found from the size effect approximately agree with the values of fracture energy for the crack band model when the rest results are fitted by finite elements. Applicability of Bazant's brittleness number, which indicates how close the behavior of specimen or structure of any geometry is to linear elastic fracture mechanics and to plastic limit analysis, is validated by test results. Comparisons with Mode II shear fracture tests are also reported.
TL;DR: In this article, an equivalent domain integral (EDI) method and the attendant numerical algorithms arc presented for the computation of a near-crack-tip field parameter, the vector Je-integral, and its variation along the front of an arbitrary three-dimensional crack in a structural component.
Abstract: SUMMARY In this paper, an equivalent domain integral (EDI) method and the attendant numerical algorithms arc presented for the computation of a near-crack-tip field parameter, the vector Je-integral, and its variation along the front of an arbitrary three-dimensional crack in a structural component. Account is taken of possible non-elastic strains present in the structure; in this case the near-tip Je-values may be significantly different from the far-field values Jf , especially under non-proportional loading.
01 Jan 1987
TL;DR: In this paper, a detailed failure criterion for ZrO2-toughened ceramics is presented, after which microstructural evolution in MgO-partially-stabilized Mg-PSZ is reviewed.
Abstract: Transformation toughening in ZrO2-containing ceramics is discussed. Specifically, microstuctures of the three distinct types of ZrO2-toughened ceramics are presented, after which microstructural evolution in MgO-partially-stabilized ZrO2 Mg-PSZ) is reviewed. The mechanical properties of such transformation-toughened ceramics are dominated by “resistance-curve” (R-curve) behavior, wherein the crack resistance increases during the course of crack propagation. Ceramics subject to R-curve behavior require a more detailed failure criterion than those subject to the usual linear elastic fracture mechanics criterion involving a critical stress intensity factor, KIC.R-curve-controlled fracture in ceramics provides a degree of very desirable flaw insensitivity, but can lead to counterintuitive relationships concerning strength, toughness, and initial flaw size. Examples of R curves of Mg-PSZ with different thermal histories are given.
TL;DR: In this paper, a steady state crack growth region has been identified wherein the cracks propagate parallel to the side surface and the general trends in cracking were found to be broadly consistent with predicted behavior governed by a zero mode II criterion and assuming that the cracks grow into a steady-state trajectory.
TL;DR: In this paper, the fracture mechanics stress intensity, K, measured for the cleavage strength of carbon steel by Professor Yokobori and colleagues, at Tohoku University and elsewhere, is shown to follow a Hall-Petch dependence on average grain diameter, l, in accordance with the model-based relationship K = c's 1 2 [σ 0 +kl −1 2 ] for which c' is a numerical factor, 5 is the effective length of the local plastic zone associated with unstable crack growth, σ 0 is a friction stress for appropriate dislocation movement within the poly
TL;DR: In this paper, a stress intensity approach is used to analyze tensile failure of brittle matrix composites that contain unidirectionally aligned fibers held in place by friction, and explicit relations are derived for the matrix cracking stress (noncatastrophic failure mode), the condition for transition to a catastrophic failure mode, and the fracture toughness in a region of catastrophic failure.
TL;DR: In this paper, Tungsten-carbide cobalt alloys in the range of technically relevant compositions were fractured under controlled conditions, and stable and unstable crack propagation were shown to be equivalent with respect to crack geometry and energy release rates.
Abstract: Tungsten-carbide cobalt alloys in the range of technically relevant compositions an microstructures were fractured under controlled conditions. Stable and unstable crack propagation are shown to be equivalent with respect to crack geometry and energy release rates. Based on microscopic observations and on measurements using SEM micrographs, the nature of the process zone, the maximum extension of plastic deformation, the types of crack paths, and the area fractions of these crack paths are determined. The results, which are in partial disagreement with earlier work, provide the basis for the qualitative understanding and the quantitative description of fracture processes in composites combining a ductile phase embedded in a brittle matrix.
TL;DR: In this paper, the authors developed a failure mode map, with axes of core relative density and the ratio of face thickness to span length, which, for a given loading configuration and set of face and solid core materials, shows the dominant failure mode for every possible beam design.
TL;DR: The FRACTURE ANalysis Code (FRANC) as mentioned in this paper is a tool that allows a practicing engineer or a researcher to perform an incremental fracture analysis at his/her desk.
TL;DR: In this paper, the Double Cantilever Beam (DCB) test geometry was utilized to investigate the rate ef fects on Mode I interlaminar fracture toughness in graphite/PEEK and graphite-epoxy composites.
Abstract: The Double Cantilever Beam (DCB) test geometry was utilized to investigate the rate ef fects on Mode I interlaminar fracture toughness in graphite/PEEK and graphite/epoxy composites. The tests were...
TL;DR: In this article, the D022-type structure of Al3Ti has been deformed under compression at 25-860°C and at temperatures above 620°C, good compression ductility is observed.
Abstract: Polycrystalline specimens of the intermetallic compound Al3Ti with the D022-type structure have been deformed under compression at 25–860°C. At temperatures below 620°C, specimens fracture with very small fracture strain since extremely localized deformation occurs and cracks are initiated in intensely deformed regions almost at yielding. At temperatures above 620°C, good compression ductility is observed. Yield stress starts decreasing rapidly with increasing temperature at around 330°C and becomes less temperature dependent above 630°C. The major mode of deformation of Al3Ti is twinning of the type (111)[112] which does not disturb the D022 symmetry of the lattice. However, at high temperatures, the four (111)[112]-type twinning systems are augmented by slip of the types [110], [100] and [010]. This would supply an explanation for the good compression ductility observed at temperatures above 620°C. Suggestions are made for further experimental work on alloying additions which may improve the du...
01 Jan 1987
TL;DR: In this article, the authors proposed a probabilistic approach to the material-related reliability of fracture-sensitive structures in the nuclear industry, such as pressure vessel, main coolant piping and steel containment.
Abstract: 1. Probabilistic approaches to the material-related reliability of fracture-sensitive structures.- 2. Probabilistic damage tolerance analysis of aircraft structures.- 3. Aircraft structural reliability and risk analysis.- 4. Stochastic crack growth models for applications to aircraft structures.- 5. Durability of aircraft structures.- 6. The reliability of pressurized water reactor vessels.- 7. Applications of PFM in the nuclear industry to reactor pressure vessel, main coolant piping and steel containment.- 8. Numerical methods in probabilistic fracture mechanics.- 9. Probabilistic fracture mechanics.- References.
TL;DR: In this article, it was shown that the phenomenon of crack growth under cyclic compressive stresses exhibits a macroscopically similar behaviour in a wide range of materials spanning the very ductile metals to extremely brittle solids, although the micromechanics of this effect are very different among the various classes of materials.
Abstract: Stable crack growth is observed in notched plates of polycrystalline alumina subject to fully compressive far-field cyclic loads at room temperature in a moist air environment andin vacuo. The fatigue cracks propagate at a progressively decreasing velocity along the plane of the notch and in a direction macroscopically normal to the compression axis. The principal failure events leading to this effect are analysed in terms of notch-tip damage under the far-field compressive stress, microcracking, frictional sliding and opening of microcracks, and crack closure. An important contribution to such Mode I crack growth arises from the residualtensile stresses induced locally at the notch-tip when the deformation within the notch-tip process zone leaves permanent strains upon unloading from the maximum nominal compressive stress. It is shown that the phenomenon of crack growth under cyclic compressive stresses exhibits a macroscopically similar behaviour in a wide range of materials spanning the very ductile metals to extremely brittle solids, although the micromechanics of this effect are very different among the various classes of materials. The mechanisms of fatigue in ceramics are compared and contrasted with the more familiar examples of crack propagation under far-field cyclic compression in metallic systems and the implications for fracture in ceramic-metal composites and transformation toughened ceramic composites are highlighted. Strategies for some important applications of this phenomenon are recommended for the study of fracture mechanisms and for the measurement of fracture toughness in brittle solids.
TL;DR: In this paper, a smeared crack model that covers tensile softening in mode I and shear softening for mode II fracture is described, and the model provides for unloading and reloading and for multiple crack formation.
Abstract: A smeared crack model that covers tensile softening in mode I and shear softening in mode II fracture is described. In addition, the model provides for unloading and reloading and for multiple crack formation. Particular forms of tension and shear softening functions and relations with more conventional models are discussed. Two examples involving mixed-mode fracture in notched, unreinforced concrete beams have been included to demonstrate the versatility of the model. The results indicate that the addition of shear softening is essential to obtain realistic results in the post-peak regime since the classical approach based on a constant shear retention factor then results in a too stiff behavior. The results furthermore demonstrate that snap-back behavior may occur in strain-softening concrete under quasistatic loading conditions. Attention is also given to the possibility of hour-glass formation when constitutive laws involving softening are deployed in a finite element model.
TL;DR: In this article, the relationship between fracture energy and compressive strength of a sphere has been theoretically studied from the viewpoint of fracture mechanics using experimental results of crushing of spheres, and the authors obtained a new equation for the change in fracture energy with size.
TL;DR: In this paper, the effect of the stress ratio on near-threshold growth of delamination fatigue cracks was investigated with unidirectional laminates made from Ciba Geigy 914C prepegs (T300/914) and from Toray P305 pre-pegs.
01 Jan 1987
TL;DR: In this paper, a solution for steady propagation of a two-dimensional fluid fracture driven by buoyancy in an elastic medium is obtained for the vertical ascent of magma through the earth's mantle and crust.
Abstract: A solution has been obtained for steady propagation of a two-dimensional fluid fracture driven by buoyancy in an elastic medium. The problem is formulated in terms of an integro-differential equation governing the elastic deformation, coupled with the differential equation of lubrication theory for viscous flow in the crack. The numerical treatment of this system is carried out in terms of an eigenfunction expansion of the cavity shape, in which the coefficients are found by use of a nonlinear constrained optimization technique. When suitably non-dimensionalized, the solution appears to be unique. It exhibits a semi-infinite crack of constant width following the propagating fracture. For each value of the stress intensity factor of the medium, the width and propagation speed are determined. The results are applied to the problem of the vertical ascent of magma through the earth's mantle and crust. Values obtained for the crack width and ascent velocity are in accord with observations. This mechanism can explain the high ascent velocities required to quench diamonds during a Kimberlite eruption. The mechanism can also explain how basaltic eruptions can carry large mantle rocks (xenoliths) to the surface.