Showing papers by "Lehigh University published in 1974"
TL;DR: In this paper, the authors investigated the general problem of crack extension in a combined stress field where a crack can grow in any arbitrary direction with reference to its original position, and showed that the direction of crack growth and fracture toughness for the mixed problem of Mode I and Mode II are governed by the critical value of the strain-energy-density factor.
Abstract: This paper deals with the general problem of crack extension in a combined stress field where a crack can grow in any arbitrary direction with reference to its original position. In a situation, when both of the stress-intensity factors,k
1,k
2 are present along the crack front, the crack may spread in any direction in a plane normal to the crack edge depending on the loading conditions. Preliminary results indicate that the direction of crack growth and fracture toughness for the mixed problem of Mode I and Mode II are governed by the critical value of the strain-energy-density factor,S
cr. The basic assumption is that crack initiation occurs when the interior minimum ofS reaches a critical value designatedS
cr. The strain-energy-density factorS represents the strength of the elastic energy field in the vicinity of the crack tip which is singular of the order of 1/r where the radial distancer is measured from the crack front. In the special case of Mode I crack extensionS
cr is related tok
1c alone asS
cr = (κ − 1)k
1
2
/8μ. In general,S takes the quadratic forma
1 1
k
1 + 2a
1 2
k
1
k
2 +a
2 2
k
2 whose critical value is assumed to be a material constant. The analytical predictions are in good agreement with experimental data on the problem of an inclined crack in plexiglass and aluminum alloy specimens. The result of this investigation provides a convenient procedure for determining the critical crack size that a structure will tolerate under mixed mode conditions for a given applied stress.
2,066 citations
535 citations
TL;DR: In this paper, an (oxygen)- vacancy model of the E1-center in alpha quartz, featuring an asymmetric relaxation of the two silicons adjacent to the oxygen vacancy, is presented and analyzed.
438 citations
TL;DR: In this paper, a design rationale for materials which contain flaws caused by metallurgical inclusions, fabrication and erection overloads, and fatigue cracking is outlined for materials that contain flaws.
303 citations
TL;DR: In this paper, the authors considered the plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack, using the existing solutions for the edge dislocations as Green's functions.
Abstract: The plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.
232 citations
TL;DR: In this paper, a Ti-6Al-4V titanium alloy was used to study the effect of crack closure on crack growth and showed that crack closure is not the sole cause for delay.
156 citations
TL;DR: In this paper, a singular integraL equation with the derivative of the crack surface displacement as the density function is formulated for the elastostatic plane problem of an infinite strip containing two symmetrically located internal cracks perpendicular to the boundary and a numerical technique for solving the singular integral equations with this particular type of fundamental function which is characteristic of the edge cracks is described.
Abstract: The elastostatic plane problem of an infinite strip containing two symmetrically located internal cracks perpendicular to the boundary is formulated in terms of a singular integraL equation with the derivative of the crack surface displacement as the density function. The solution of the problem is obtained for various crack geometries and for uniaxial tension applied to the strip away from the crack region. The limiting case of the edge cracks is then considered in some detail. The fundamental function of the integral equation is obtained and a numerical technique for solving the singular integral equations with this particular type of fundamental function which is characteristic of the edge cracks is described. The stress intensity factor for the complete range of net ligament-to-width ratio is calculated. The results also include the solution of the edge crack problem in an elastic half plane.
132 citations
TL;DR: In this article, a criterion for predicting the growth of three-dimensional cracks is developed on the basis of the strain energy density concept which has been used successfully for treating two-dimensional crack problems.
114 citations
TL;DR: In this paper, the fracture energies and spalling resistance of high-Al2O3 refractories were studied by measuring the work-of-fracture and the notched-beam-test methods, respectively.
Abstract: The fracture energies and spalling resistance of high-Al2O3 refractories were studied. The fracture energies, γWOF and γNBT, were measured by the work-of-fracture and the notched-beam-test methods, respectively. Spalling resistance, as measured by the relative strength retained in a water quench, correlated well with the thermal-stress resistance parameter applicable to stable crack propagation under conditions of thermal shock, (γWOF/α2E0). Many of the refractories exhibited high ratios of γWOF to γNBT; such high ratios were shown analytically to maximize the parameter (R1111=E0γWOF/S12) which describes the resistance to catastrophic spalling. The increase of crack length with increasing quenching temperature difference (ΔT) was somewhat less than that predicted theoretically; the discrepancy was attributed to an increase of crack density with ΔT. In general, the results show that fracture energy is important in establishing the spalling resistance of high-Al2O3 refractories.
101 citations
TL;DR: In this article, the effects of a broad range of loading variables on delay in fatigue crack growth at room temperature are examined for a mill annealed Ti-6Al-4V alloy.
Abstract: The importance of delay, or retardation in the rate of fatigue crack growth, produced by load interactions in variable amplitude loading on the accurate prediction of fatigue lives of engineering structures has been well recognized for some time. Heretofore, only a few simple loading combinations or spectra have been examined systematically. In this investigation the effects of a broad range of loading variables on delay in fatigue crack growth at room temperature are examined for a mill annealed Ti-6Al-4V alloy. The results are used to estimate crack growth behavior under programmed loads.
90 citations
TL;DR: In this article, the antiplane shear problem of two bonded elastic half planes containing a crack perpendicular to the interface is considered and the nature of the stress singularity for the crack terminating at and going through the interface was studied.
Abstract: The antiplane shear problem of two bonded elastic half planes containing a crack perpendicular to the interface is considered. The cases of a semi-infinite crack terminating at the interface, a finite crack away from and terminating at the interface, two cracks one on each side of the interface, and a finite crack crossing the interface are separately investigated. The nature of the stress singularity for the crack terminating at and going through the interface is studied, and it is shown that at the irregular point on the interface, for the former the power of singularity is not -1/2 and for the latter the stresses are bounded. For a material pair of aluminum-epoxy some numerical results giving the stress intensity factors, the density functions, and the crack opening displacements are presented.
01 Mar 1974-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: The arrangement, size, and boundary area of the laths that make up a packet of martensite in a coarse-grained Fe-0.2 pct C alloy were studied by replica and thin foil electron microscopy as mentioned in this paper.
Abstract: The arrangement, size, and boundary area of the laths that make up a packet of martensite in a coarse-grained Fe-0.2 pct C alloy were studied by replica and thin foil electron microscopy. Frequently laths of two habit plane variants coupled to a single {111} A plane of the parent austenite are observed in a packet. The width distribution of the laths is log normal, with the most frequently observed lath width being 0.15 microns. Larger laths between 1 and 2 microns are distributed throughout a packet. The total lath boundary area per unit volume of martensite obtained by analysis of micrographs taken from thin foils is quite high, 65,000 cm-1, and analysis of packet structure by selected area diffraction and precision dark field techniques show that there may be five times as much low angle boundary area as high angle boundary area in a packet.
TL;DR: In this article, the axisymmetric double contact problem for an elastic layer pressed against a half space by an elastic stamp is considered under the assumptions that the three materials have different elastic properties, the contact along the interfaces is frictionless and only compressive normal tractions can be transmitted across the interfaces, and, in the case of the elastic stamp, the local radius of curvature of the stamp is large compared to the stamp-layer contact radius.
TL;DR: In this article, the authors considered the problem of the pure homogeneous deformation of a unit cube of incompressible neo-Hookean elastic material by three pairs of equal and opposite forces acting normally on the faces of the cube and distributed uniformly over them.
Abstract: In a previous paper [1], the problem was considered of the pure homogeneous deformation of a unit cube of incompressible neo-Hookean elastic material by three pairs of equal and opposite forces acting normally on the faces of the cube and distributed uniformly over them. It was found that, for certain specified values of the forces, more than one equilibrium state of pure homogeneous deformation can exist. The stability of each of these states was investigated, with respect to superposed infinitesimal pure homogeneous deformations, with the same principal directions as the equilibrium state. It was found that for certain ranges of values of the applied forces, more than one equilibrium state of pure homogeneous deformation which is stable in this sense can exist. Which of these stable states is actually attained in practice will depend on the order in which the forces are applied.
TL;DR: In this paper, the tristimulus match in an opaque film using two-constant theory and four colorants can proceed in two stages: first, the computation of a rough match, and second, iteration to an exact match.
Abstract: The calculation of a tristimulus match in an opaque film using two-constant theory and four colorants can proceed in two stages: first, the computation of a rough match, and second, iteration to an exact match. The same formal matrix is used for the rough solution and for the iterative calculations, but it must be recomputed and reinverted once before the iterative stage of the program.
TL;DR: In this paper, the plane strain problem of a multi-layered composite with parallel cracks is considered and the main objective is to study the interaction between parallel and collinear cracks.
01 Jan 1974
TL;DR: In this article, the fracture initiation and fracture propagation problem is formulated as an initial-boundary value problem and all the desired field quantities may be obtained upon solving the related field equations.
Abstract: When a solid is subjected to a certain system of external loads under a given set of environmental conditions, in most cases the response is simply one of deformation in the sense that topologically the medium remains unchanged. In this case, at least conceptually, the solution of the problem presents no difficulty, that is, after the appropriate material characterization it can be formulated as an initial-boundary value problem and all the desired field quantities may be obtained upon solving the related field equations. On the other hand, in addition to deformations taking place in the body, if new surfaces are created within the medium as a result of excessive applied loads, the body is said to undergo fracture. From the viewpoint of physical applications and mathematical modeling, in this case one generally distinguishes two types of problems, namely fracture initiation and fracture propagation. For a given solid with a given defect geometry, in the former one needs to evaluate the critical level of the applied loads corresponding to the inception of the fracture process. Since no new surfaces have as yet been created, here the related mechanics problem is again a deformation type of problem complemented by an appropriate fracture criterion which relates the inherent fracture resistance of the solid to the applied loads and geometry of the medium.
TL;DR: In this paper, the Cascadia Basin sediment against the Washington continental slope, resulting from underthrusting of the Gorda-Juan de Fuca plate beneath the North American plate, progresses from passive uplift and anticlinal upwarping to thrust faulting.
Abstract: Compression of flat-lying Cascadia Basin (continental rise) sediment against the Washington continental slope, resulting from underthrusting of the Gorda–Juan de Fuca plate beneath the North American plate, progresses from passive uplift and anticlinal upwarping to thrust faulting. When folding and thrusting at the continental slope-rise boundary can no longer accommodate the rate of compression, the locus of deformation shifts offshore and a new anticline begins to form. Repetition of this deformational cycle has produced the multiple ridges of the lower continental slope and westward progradation of the continental margin. The most recent anticlinal upwarping apparently began 0.11 to 0.35 m.y. ago. Consolidation of the ridge sediment during the deformation process may be tectonically induced.
TL;DR: In this article, the authors construct a thermodynamics which is surprisingly simple and yet capable of modeling viscous fluids, viscoelastic bodies, elastic bodies, and heat conduction.
TL;DR: In this article, the authors applied self-consistent field and semi-empirical molecular-orbital calculations to compute the electronic structure of Si$(O) in the ¾-quartz structure by using various clusters of different sizes.
Abstract: The techniques developed by the authors have been applied to compute the electronic structure of Si${\mathrm{O}}_{2}$ in the $\ensuremath{\alpha}$-quartz structure by using various clusters of different sizes. The calculated valence-band structure is consistent with the results of other self-consistent-field and semiempirical molecular-orbital calculations, and with the x-ray emission and photoemission data. Among the most interesting results are the following: (i) The width of the valence band is of the order of 9 eV. (ii) The oxygen $\mathrm{sp}$ hybridization is quite small. (iii) Crossover transitions in a literal sense are negligible. (iv) A residual charge of -1.2 on oxygen indicates that the Si-O bond in Si${\mathrm{O}}_{2}$ is partly ionic and partly covalent.
TL;DR: In this article, the plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered using Mellin Transforms, and the numerical results given in the paper include the stress intensity factors, the strain energy release rates and the probable clevage angles giving the direction of crack propagation.
TL;DR: In this paper, eine Ubersicht uber Reaktionen von Phosphor-, Arsen-, Antimon- lind Wismut-Donor-Liganden gegeben.
TL;DR: In this paper, the authors investigated the effect of partially debonded infinite stringer on the stress intensity at the crack tip and solved the integral equation, obtained from the continuity of displacements along the line where the stringer and the plate are bonded.
TL;DR: In this paper, the linear Onsager theory of irreversible thermodynamics is extended to include nonlinear phenomenological relations by means of onsager fluxes, which satisfy a full system of reciprocity relations, vanish in thermodynamic equilibrium, and give a nonnegative production of entropy.
TL;DR: The effect of slow crack growth on the thermal-shock resistance of an Na2O-CaO-SiO2 glass was studied in this paper, where the critical quenching temperature difference, ΔTc, of circular rods quenched in water from known crack velocity data was calculated.
Abstract: The effect of slow crack growth on the thermal-shock resistance of an Na2O-CaO-SiO2 glass was studied. An analytic and numerical technique was developed to calculate the critical quenching temperature difference, ΔTc, of circular rods quenched in water from known crack velocity data. For rods of a specific radius and crack depth, ΔTc, was calculated to be 147°C, in favorable correspondence with experimentally observed values of 155° to 160°C. In the absence of crack growth, ΔTc was estimated to be 238°C, well in excess of the observed value and indicative of the significant effect of slow crack growth on thermal-stress resistance. It is also shown that crack growth significantly extends the time-to-failure to a value much greater than the time of maximum thermal stress. A form of subcritical crack instability is predicted at stress intensity factors well below the critical stress intensity factor, at which catastrophic failure becomes inevitable over the duration of the transient thermal stress. It is suggested that, when all other factors are equal, the effect of slow crack growth on thermal-stress resistance can be minimized by maximizing thermal diffusivity. It is also argued that surface-compression strengthening will be more effective than reduction in flaw size in increasing thermal-stress resistance. Recommendations are made for the design and selection of brittle materials subjected to thermal stress in stress-corrosive environments.
TL;DR: This is believed to be the first report of enzymes bonded to stainless steel, and inactivated catalyst can be regenerated by heating to 538°, cooling and recontacting with enzyme solution.
TL;DR: In this article, the theory of small deformations superposed on finite deformations is applied to determine the critical conditions under which bifurcation solutions (i.e. adjacent equilibrium positions) can exist.
TL;DR: In this article, the problem of fracture propagation and arrest in a cylindrical pressure vessel containing an initial surface flaw is considered, where the flaw has the most unfavorable geometry and orientation, namely, a crack lying on a meridional plane.