Showing papers on "Stress concentration published in 1969"
TL;DR: In this article, a fracture-mechanical theory for crack propagation in brittle ceramics subjected to thermal shock is presented and the criteria of crack stability are derived for a brittle solid uniformly cooled with triaxially constrained external boundaries.
Abstract: A fracture-mechanical theory is presented for crack propagation in brittle ceramics subjected to thermal shock. The criteria of crack stability are derived for a brittle solid uniformly cooled with triaxially constrained external boundaries. Thermal stress crack instability occurs between two values of critical crack length. For short initial crack length, crack propagation occurs kinetically, with the total area of crack propagation proportional to the factor St2 (1-2v)/EG, where St is tensile strength, v is Poisson's ratio, E is Young's modulus, and G is surface fracture energy. Under these conditions the newly formed crack is subcritical and requires a finite increase in temperature difference before propagation will proceed. For long initial crack length, crack propagation occurs in a quasi-static manner and can be minimized by maximizing the thermal stress crack stability parameter Rst= [G/α2E]1/2, where α is the coefficient of thermal expansion. For heterogeneous brittle solids, such as porous refractories, the concept of an “effective flaw length” is introduced and illustrated on the basis of experimental data in the literature. The relative change in strength of a brittle solid as a function of increasing severity of thermal shock is estimated. Good qualitative agreement with literature data is found.
953 citations
TL;DR: In this article, a plane elasticity solution for the end problem in a two-layer laminated strip is derived, which is obtained as a series of non-orthogonal eigenfunctions, each of which varies exponentially along the axis of the strip.
Abstract: A plane elasticity solution is derived for the end problem in a two- layer laminated strip. The laminae may have arbitrary elastic constants and an arbitrary thickness ratio. The solution is obtained as a series of non-orthogonal eigenfunctions, each of which varies exponentially along the axis of the strip. Each exponential coefficient is a complex root of an eigenvalue equation that results from the requirement of compatible displacements at the interface.The general solution obtained in this paper may be used to find the stress field in a two-layer laminated strip subjected to specified self- equilibrating end loading. It thus permits the determination of the stress concentration near the end which is usually neglected by invok ing St. Venant's Principle.
86 citations
01 Aug 1969
76 citations
TL;DR: The solution of the two-dimensional, elastic, multiple-filament-failure stress concentration problem led to the treatment of three dimensional, elastic failure models and a two dimensional, plastic failure model as mentioned in this paper.
Abstract: The solution of the two-dimensional, elastic, multiple-filament-failure stress concentration problem led to the treatment of three-dimensional, elastic failure models and a two-dimensional, plastic...
76 citations
TL;DR: The criteria for stress corrosion crack branching in high-strength steels are shown to be (1) a constant crack velocity and (2) attainment of a critical stress intensity.
70 citations
TL;DR: The Mohr-Coulomb criterion for failure, modified in light of the concept of effective stress, is where τ c is the critical shear stress at failure, S the normal pressure, and p the pore pressure across the plane of internal slippage at failure, ϕ i the internal friction angle, and τ 0 an empirical constant, commonly referred to as the cohesive strength.
Abstract: The Mohr-Coulomb criterion for failure, modified in light of the concept of effective stress, is where τ c is the critical shear stress at failure, S the normal pressure, and p the pore pressure across the plane of internal slippage at failure , ϕ i the internal friction angle, and τ 0 an empirical constant, commonly referred to as the cohesive strength. Experiments showed that the τ 0 for sedimentary rocks is about 200 bars. Hubbert and Rubey (1959) assumed that once a fracture is started, TO is eliminated and further movement results when They proceed, however, to use this formula for the frictional sliding of cohesionless block as the criterion of failure of large thrusts, after they assumed that τ 0 could be eliminated through a concentration of stress. This assumption led to their conclusions that very long overthrust blocks are possible and that such blocks may have moved by gravitational sliding along very gentle slopes. I present arguments to show that their assumption of zero τ 0 was based upon a faulty argument and to point out that the τ 0 term should not be omitted unless it could be proved the moving block slid along an already existing fracture plane. The first part of this paper consists mainly of conclusions based on computations. Clearly, an unjustified omission of a 200-bar cohesive strength would lead to erroneous and misleading results; particularly, gravitational sliding cannot be an important mechanism if such a cohesive strength has not been eliminated during overthrust faulting. The second part presents evidence to distinguish between movements of cohesively bound blocks and cohesionless blocks. The Glarus overthrust, characterized by presence of a ductilely deformed limestone layer within the thrust zone, is considered a typical example of thrusting of cohesively bound blocks. The Heart Mountain thrust, characterized by a shattering of the “upper plate” and absence of a weak layer above the thrust contact, is interpreted as an example of thrusting of cohesionless blocks. The former is compared to slowly creeping slides moving at rates of centimeters or less per year, and the latter with catastrophic landslides (such as the Flims, Goldau, and Vaiont slides) moving at speeds of many meters per second. Third, the conclusion of Raleigh and Griggs (1963) that large thrusts can only form when a toe of the thrust is continually eroded is also traced to the assumption of zero cohesive strength along thrust plane. Otherwise, the toe effect would produce a zone of imbrication at the front of overthrust blocks, particularly those sliding downslope under their own weight.
67 citations
65 citations
TL;DR: In this article, a linear elastic fracture mechanics analysis of the conditions that produce crack instability is presented, where the authors show that if the initial crack extension causes the change in crack-tip resistance to be negative with respect to the change of cracktip loading, the crack will continue to propagate even though the loading agent remains stationary, and the crack is defined as unstable.
Abstract: A linear elastic fracture mechanics analysis of the conditions that produce crack instability is presented. If the initial crack extension causes the change in crack-tip resistance to be negative with respect to the change in crack-tip loading, the crack will continue to propagate even though the loading agent remains stationary, and the crack is defined as unstable. The value of crack-tip load when the crack becomes unstable, G
c, is not only a function of the plate material and thickness and fracture mode, but also depends on the specimen geometry and size, and on the compliance of the loading system. The crack-tip resistance, G
R, on the other hand, is essentially a property of the plate material and thickness and fracture mode if the crack-propagation is time independent. Once G
R has been experimentally determined as a function of crack-propagation distance for a particular plate material and thickness and fracture mode, the value of G
e can be calculated for the same material and thickness and fracture mode for any plate configuration for which the elastic stress analysis is known.
64 citations
TL;DR: In this article, the strength-limiting process in the fracture of semicrystalline fibers and highly oriented films is the rupture of tie molecules connecting the folded chain lamellae in the machine direction.
Abstract: The strength-limiting process in the fracture of semicrystalline fibers and highly oriented films is the rupture of tie molecules connecting the folded chain lamellae in the machine direction. This view is supported by the data on stress and temperature dependence of lifetime of fibers under load and on radical formation during the fracture experiment. The observed tensile strength, however, is about 10 times smaller and the number of fractured chains between 100 and 1000 times larger than expected on the basis of the known number of tie molecules in the fracture plane. This discrepancy is a consequence of the inhomogeneity of the micromorphology of fiber structure, which causes a much larger stress concentration on the most unfavorably located tie molecules than the average value one would expect in the case of perfectly uniform stress distribution on identical tie molecules. The fluctuation of amorphous layer thickness, of number and length of tie molecules, produces such a high stress concentration on some tie molecules throughout the sample that they rupture long before the average stress concentration is sufficient for chain fracture. By accumulation of damage caused by gradual chain rupture the weakening of the sample locally proceeds so far that at the maximum damage concentration, microcracks start to form, and the fiber breaks.
63 citations
TL;DR: A survey of existing solutions describing the stress distribution around the crack tip of an initially curved sheet is made and a method for estimating approximate stress intensity factors of other more complicated shell geometries is discussed as discussed by the authors.
Abstract: A survey of existing solutions describing the stress distribution around the crack tip of an initially curved sheet is made and a method for estimating approximate stress intensity factors of other more complicated shell geometries is discussed.
61 citations
TL;DR: In this paper, the Cottrell-Petch formulation was used to predict the probability distribution of crack orientation angles, and from these the distribution of the surface trace angles that should be observed experimentally.
TL;DR: In this paper, the effect of strain rate on the room temperature strength of soda-lime-silica glass was determined, and it was further shown that the stress concentration relationship proposed by Inglis is valid for acid-etched glass.
Abstract: The effect of strain rate on the room‐temperature strength of soda‐lime‐silica glass was determined. The strength of acid‐etched glass rods increased continuously from 190 200 to 284 800 psi on increasing the strain rate from 9×10−4 to 15×10−2 in./in./min. No difference in strengths was observed on testing in laboratory atmosphere or with the specimens wetted with distilled water. For abraded glass rods the strength in laboratory atmosphere varied from 12 555 to 16 540 psi on varying the strain rate from 3×10−3 to 9×10−2 in./in./min. Tests conducted with the abraded samples wetted with distilled water caused approximately a 10% reduction in strength, but no appreciable change in the strain‐rate sensitivity. The stress corrosion model proposed by R. J. Charles successfully predicts the room‐temperature strain‐rate sensitivity of the failure process for both acid‐etched and abraded glass samples. Using relationships derived from this model, it was further shown that the stress concentration relationship proposed by Inglis is valid for acid‐etched glass.
TL;DR: In this paper, the authors showed that fatigue crack propagation is caused by cumulative damage due to strain cycling at crack tip, relating resistance to cyclic ductility to the resistance of cyclic structures.
Abstract: Fatigue crack propagation caused by cumulative damage due to strain cycling at crack tip, relating resistance to cyclic ductility
TL;DR: In this paper, the Griffith crack in a thin plate, which is opened by a uniform all-round tension at infinity, is considered and partially closed in a symmetric manner by ties, idealized by point loads in the material, and the effect upon the stress intensity factors is discussed.
Abstract: The problem of a Griffith crack in a thin plate, which is opened by a uniform all-round tension at infinity, is considered. The crack is then partially closed in a symmetric manner by ties, idealized by point loads in the material, and the effect upon the stress intensity factors is discussed.
TL;DR: In this paper, the problem of the formation of large cracks by coalescence of separately nucleated smaller cracks is approached by statistical methods and it is assumed that nucleation of the cracks is random and independent of other cracks.
TL;DR: In this article, the authors derived an equation that describes the rate of growth of fatigue cracks under combined static and cyclic stresses, and showed that a static tensile stress has very little influence on the growth rate of the fatigue cracks, unless the maximum total applied stress is comparable to the (static) fracture stress.
Abstract: An equation is derived that describes the rate of growth of fatigue cracks under combined static and cyclic stresses. The equation predicts that a static tensile stress has very little influence on the rate of growth of fatigue cracks, even if the static stress is very much larger than the amplitude of the cyclic stress, unless the maximum total applied stress is comparable to the (static) fracture stress.
01 May 1969
TL;DR: In this article, the failure of concrete in uniaxial compression and tension is explained in terms of the energy concepts of fracture mechanics, and the difficulties associated with the measurement and evaluation of concrete “fracture toughness” are discussed.
Abstract: The failure of concrete in uniaxial compression and tension is explained in terms of the energy concepts of fracture mechanics, and the difficulties associated with the measurement and evaluation of concrete “fracture toughness” are discussed. Basic assumptions relating to slow crack growth, stress concentration because of notch and value of E to be adopted for the calculation of the fracture toughness parameters are proposed. The effect of these assumptions on the values of critical strainenergy release rate and critical stress intensity factor are reported together with the trend of values with changes in concrete properties.
TL;DR: In this paper, a linear elastic fracture mechanics is used to interpret observations of through-thickness fatigue crack growth in sheet specimens of polymethylmethacrylate, polycarbonate and an unfilled epoxy.
Abstract: Linear-elastic fracture mechanics is used to interpret observations of through-thickness fatigue crack growth in sheet specimens of polymethylmethacrylate, polycarbonate and an unfilled epoxy, and to correlate measurements of the growth of part-through and through-thickness fatigue cracks in sheet polymethylmethacrylate. It is shown that at least one of these materials may be useful for model studies of the growth of part-through thickness fatigue cracks in metallic components.
TL;DR: In this article, the stress fields around spherical elastic discontinuities in an isotropic solid subjected to externally applied hydrostatic pressure have been computed on the basis of a continuum mechanics model.
Abstract: The stress fields around spherical elastic discontinuities in an isotropic solid subjected to externally applied hydrostatic pressure have been computed on the basis of a continuum mechanics model The results have been compared with transmission electron microscopy observations of the pressure-induced development of dislocations in tungsten containing particles (thoria and hafnium carbide) or internal voids and in a model system of copper containing helium bubbles with the principal objective of elucidating the factors controlling the formation of such dislocations For the tungsten, no new dislocations were developed up to 25 kilobars, but they were observed at ThO2 and HfC particles following pressurization to some 40 kilobars The computed value of the maximum induced shear stress at that pressure is much below that required for dislocation nucleation These observations of pressure-induced dislocations are interpreted in terms of additional stress concentrations associated with surface irreg
TL;DR: In this article, Hull, Beardmore and Valintine (1965) showed that it is possible to insert cracks in specimens at 77°K and to subsequently test these specimens in tension at 77k without an intermediate rise in temperature.
Abstract: Cleavage cracks have been introduced into 〈100〉 axis single crystals of tungsten by a modification of the spark discharge technique used by Hull, Beardmore and Valintine (1965). It has been possible to insert cracks in specimens at 77°K and to subsequently test these specimens in tension at 77°K without an intermediate rise in temperature. Various other test conditions have also been used. From the values of fracture stress and crack length obtained, values of the effective surface energy, γ, have been determined. In analysing the results, account has been taken of the shape of the spark crack and specimen geometry and dimensions using theoretical analyses of the stress concentrations associated with cracks. Both the temperature of crack initiation and the temperature of crack propagation were found to affect γ. For specimens in which both initiation and propagation of the cracks took place at 77°K, a value of γ = 1700 ± 300 ergs/cm2 was obtained.
TL;DR: In this article, the stress-concentration and fatigue-strength-reduction factors were determined for grooved tensile specimens made of a fine-grained graphite, Great Lakes Carbon grade H205.
TL;DR: In this article, the growth of fatigue cracks in aluminum alloys was studied by microscopic observation of the surface of the specimen and electron fractography. And the results of analysis for the growth by Master curve method showed that there were two stages of the growth and only the 1st stage depended on ageing conditions.
Abstract: Fatigue crack propagation in aluminum alloys was studied in thin plate under plane bending the microscopic observation of the surface of specimen and electron fractography.There were two types of fatigue crack propagation according to the conditions of ageing. One was a continuous growth type; for instance, in Al-1.5%Mg2Si alloy after natural ageing, the fatigue crack was generated at the central hole of the specimen and was developed to grow up until final failure. The other was a discontinuous propagation type; for instance, the fatigue crack of the above alloy, fully age-hardened, predominantly propagated by the linking of many isolated cracks.The results of analysis for the growth of fatigue crack by Master curve method showed that there were two stages of the growth and only the 1st stage depended on ageing conditions. The rate of growth in the 2nd stage would be a function of the product of grass strain amplitude, eG and a square root of half crack length, √l. The transition from the 1st to the 2nd stage also depended on the ageing conditions.The examination of the fatigue fracture by electron fractography showed that characteristic feature of the fracture suface depended on the stage of crack growth and the ageing conditions. The 1st stage was the shear mode of crack growth and the surface was often characterized by parallel lamellae along the direction of the growth of the crack. The 2nd stage was the tensile mode of crack growth and the surface was characterized by the striations normal to the local direction of the crack growth. Each striation represented the position of the front oftranscrystalline crack at each load cycle. There were observed two types of striations; ductile and brittle. However, the latter was observed only in aluminum alloys fully age-hardened.
June1
TL;DR: In this article, an extension of the photo-elastic method to the plastic state was described, made possible by the establishment of a suitable stress-optic law, and the employment of the shear-difference method.
Abstract: Summary This paper describes an extension of the “photoelastic” method to the plastic state. Using thin models of cellulose nitrate, factors of stress concentration and stress distributions were determined for several basic cases. The extension is made possible by the establishment of a suitable stress-optic law, and the employment of the shear-difference method. The results obtained are in substantial agreement with theory and experiment. The method is at present limited to plane stress problems in the elastoplastic state without unloading.
TL;DR: In this paper, a theoretical analysis for the membrane stresses around an elliptic hole in a long, thin circular cylindrical shell with the major axis of the hole inclined at an arbitrary angle to the axis of a shell is presented.
Abstract: A theoretical analysis is presented for the membrane stresses around an elliptic hole in a long, thin circular cylindrical shell with the major axis of the hole inclined at an arbitrary angle to the axis of the shell. The analysis has been carried out for uniform normal internal pressure and axial tension. The method of solution involves a perturbation in a curvature parameter and the13; results obtained are valid, if the hole is small in size compared to the shell. A formula, from which the membrane stress concentration at the hole can be directly calculated, is presented. If one of the principal axes of the hole is parallel to the shell axis, it is found that for any state of biaxial stress in the shell, there exists a certain value of eccentricity of the ellipse for which the membrane stresses are constant all along the boundary of the hole.
TL;DR: In this article, a new model of the delay-time for yielding at constant applied stress was presented, which is consistent with the experimental observations and explains the true static upper yield point and the shape of the strain vs. time curve.
01 Jan 1969
TL;DR: In this paper, rotating bending and torsional fatigue tests of plain and notched steel specimens with electropolished surfaces were carried out, and the main results obtained are as follows.
Abstract: Rotating bending and torsional fatigue tests of plain and notched steel specimens with electropolished surfaces were carried out. The main results obtained are as follows. (1) The maximum shear stresses in the crack initiation limit of torsional fatigue are determined only by the stress gradient X independently of the notch depth as in the case of bending fatigue. (2) When the values of X are equal, the maximum shear stress in the crack initiation limit of torsional fatigue is about 1.2 times that of bending fatigue. (3) The surface states of notch roots after 107 cycles of the limit stress for crack initiation in torsional fatigue are similar to each other irrespective of the maximum stress repeated on the notch root, as in the case of bending fatigue. The fatigue damages at the crack initiation limit under torsional stresses are severer than the ones under bending stresses. (4) The mechanism of non-propagation of a crack in torsional notched specimens is different from that in bending notched specimens.
TL;DR: In this article, the effect of the size of the end gap between two aligned fibres on the yielding characteristics is examined, and it is shown that for both cylindrical and plane single fibre models, the mean applied stress at which yielding of the matrix begins increases with decreasing values of the length/diameter ratio of the fibre.