Showing papers in "International Journal of Fracture in 1970"

Effect of plastic strain state on ductility and toughness

Abstract: The tensile ductility of seven structural steels was substantially reduced when the plastic strain state was changed from axisymmetric (round specimen) to plane strain. The ratio of plane-strain-tension ductility divided by axisymmetric-tension ductility declined from 72 percent for a mild steel to 17 percent for a steel with 248 ksi yield strength.

Fatigue and fracture of cylindrical shells containing a circumferential crack

Abstract: Fatigue and fracture in elastic cylindrical shells with circumferential crack under axial tension, noting precracked specimens

Delayed failure - The Griffith problem for linearly viscoelastic materials

Abstract: The unstable growth of a crack in a large viscoelastic plate is considered, within the framework of continuum mechanics. Starting from the local stress and deformation fields at the tip of the crack, a non-linear, first order differential equation is found to describe the time history of the crack size if the stress applied far from the crack is constant. The differential equation contains the creep compliance and the intrinsic surface energy of the material. The surface energy concept for viscoelastic materials is clarified. Inertial effects are not considered, but the influence of temperature is included for thermorheologically simple materials. Initial crack velocities are given as a function of applied load in closed form, as well as a comparison of calculated crack growth history with experiments. Above a certain high stress, crack propagation ensues at high speeds controlled by material inertia while at a lower limit infinite time is required to produce crack growth. Thus an upper and lower limit criterion of the Griffith type exists. For rate insensitive (elastic) materials the two limits coalesce and only the brittle fracture criterion of Griffith exists. The implications of these results for creep fracture in metals and inorganic glasses are examined.

The Calculation of Stress Intensity Factors Using the Finite Element Method with Cracked Elements

Abstract: The calculation of stress intensity factors for complicated crack configurations in finite plates usually presents substantial difficulty. A version of the finite element method solves such problems approximately by means of special cracked elements. A general procedure for evaluating the stiffness matrix of a cracked element is developed, and numerical results obtained by the simplest elements are compared with those provided by other methods.

A modified mapping-collocation technique for accurate calculation of stress intensity factors

Abstract: A technique combining the advantages of conformal mapping and boundary collocation arguments for calculating stress intensity factors for cracks in plane problems is described. The difficulty of finding the mapping function on a rigidly prescribed parameter region is avoided at the expense of using boundary collocation methods on part of the boundary. Conventional collocation arguments are modified by prescribing stress, force, and moment conditions in a least-square collocation sense. These pseudo-redundant conditions provide a reasonable basis for estimation of the effects of inaccuracy of the boundary conditions. The technique is applied to the problem of a circular disk with an internal crack under a loading of external hydrostatic tension.

An observation of crack propagation in anti- plane shear

Abstract: It is shown experimentally that in the absence of plasticity crack propagation in anti-plane shear occurs by the opening of semi-penny-shaped cracks which straddle the crack front at an angle of 45 degrees. It follows that if crack instability calculations are based on the assumption that a planar crack propagates in its own plane they are valid only if all shear stresses vanish along the crack periphery, i.e., if KIII is zero along that boundary.

The initiation of fatigue cracks from notches in mild steel plates

Abstract: Pulsating tension fatigue tests have been carried out on edge-notched specimens of a mild steel and measurements of electrical potential drop across notches have been used to determine the number of cycles to initiate cracks. The results can be described by using the range of stress intensity factor for the sharp crack situation modified to take into account the notch root radius. The models of plastic relaxation at a crack tip and analyses of the elastic stress distribution at cracks and notches are used to discuss the results. Limited evidence in the literature indicates that the stress intensity approach may provide a general description of crack initiation and propagation in notched specimens.

The stress distribution around a crack perpendicular to an interface between materials

Abstract: The plane strain problem of a crack terminating perpendicular to a planar interface between two isotropic half spaces with different elastic constants is solved to obtain the distribution of stress in the vicinity of the crack tip. The relative elastic constants are shown to strongly affect the relative magnitudes of the various stress components as well as their radial drop off with distance from the crack tip. The implications of the results with regard to failure modes in composite materials are discussed.

On the location of fracture in brittle solids-I: Due to Static Loading

Abstract: It is shown that the Weibull treatment of brittle strength may be extended to predict the distribution of the location of fracture in brittle solids. Conversely, observations of fracture location enable conclusions to be drawn about fracture loads. Illustrations are given for the three-point bending of beams and the ring-crack of plates by spherical indenters. In the latter case the problem of multiple cracking is also considered.RésuméOn montre que la procédure suggérée par Weibull pour traiter le problème de la résistance à la rupture fragile peut être étendue à la prédiction de la localisation de la rupture dans les solides fragiles. Inversément, connaissant l'emplacement de la rupture, il est possible de tirer des conclusions sur les charges qui ont engendré celle-ci. Le raisonnement est illustré par le traitement de deux exemples: la poutre fléchie sur deux appuis par une charge concentrée, et la fissuration annulaire d'une plaque de verre sous l'effet d'une bille d'indentation. Dans ce dernier cas, on considère également le problème de la polyfissuration.ZusammenfassungEs wird gezeigt, daß das Weibull-Verfahren zur Behandlung von Problemen der Sprödbruchfestigkeit auf die Vorausbestimmung der Stelle an welcher der Bruch in spröden Wertstoffen auftritt, erweitert werden kann. Umgekehrt, ist die Bruchstelle bekannt, so ist es möglich Schlüsse über die Beanspruchung zu ziehen, welche den Bruch bewirkt hat. Diese Überlegungen werden an Hand von zwei Beispielen erläutert. Das erste bezieht sich auf den Fall eines an beiden Enden aufliegenden Trägers welcher einer Punktlast unterworfen ist, das zweite, auf den Fall von Ringrißbildung einer Platte unter Einwirkung einer Kugel. Für den letzten Fall wird auch das Problem der Mehrrißbildung in Betracht gezogen.

On fracture path stability in the compact tension test

Abstract: A simple criterion based on the engineers' theory of bending is suggested for the determination of the stability of fracture path in the compact tension test.

A photoelastic evaluation of the influence of closure and other effects upon the local bending stresses in cracked plates

Abstract: Two sets of photoelastic experiments employing stress freezing were performed in order to evaluate closure and precatastrophic extension of cracks in plates under cylindrical bending. Data were compared with the Hartranft-Sih theory in order to obtain quantitative results. It was found that crack closure on the compressive side of the plate produced somewhat larger local elastic stresses on the tensile side of the plate for straight through cracks than predicted by the mathematical model. When precatastrophic extension was allowed on the tension side of the plate, accompanying stress relaxation neutralized the stress intensification effect of closure. For short, nearly square cracks, three-dimensional effects appeared to reduce the stress intensification effects due to closure.

Crack propagation at supersonic velocities: II. Theoretical Model

Abstract: A theoretical model for laser-induced supersonic cracks in crystals with weak cleavage planes is developed. The crack is pictured as being driven by a laser-induced expanding plasma. The theory predicts the crack length-time history to be expected for a given energy-time input curve. The conditions for laser-induced supersonic crack production are seen to be a large input energy relative to fracture energy, a short loading time, and a weak fracture plane. The theoretical calculations are in rough agreement with experimental observations.ZusammenfassungEs wird eine Theorie aufgestellt, nach der laserinduzierte Brüche, die mit Überschallgeschwindigkeit in Kristallebenen leichter Spaltbarkeit laufen, beschrieben werden sollen. Dabei wird angenommen, daB der Bruch durch ein sich ausdehnendes Plasma—hervorgerufen durch den Laserstrahl—vorangetrieben wird. Die Abhängigkeit der Rißlange von der Zeit wird für eine bekannte Energie-Zeit Kurve angegeben. Die Bedingungen für die Erzeugung von laserinduzierten “Überschallbrüchen” sind: eine große Anfangsenergie, eine kurze Belastungszeit und eine schwache Spaltebene. Die theoretischen Berechnungen stimmen größenordnungsmäßig mit den experimentellen Ergebnissen überein.

Brittle fracture of rocks under impulse loads

Abstract: Brittle fracture of Tennessee Marble, Charcoal Granite and sandstone was studied using the Hopkinson split bar method. The study of the actual fracture behaviour of the rock was possible as no transducers were attached to the specimens themselves. The degree of brittleness of rock was determined by using the attenuation of the first wavefront in a fracturing specimen. There existed a maximum limit to the stress amplitude which could be transmitted through a rock specimen. Fracture is initiated in rock at the same stress under both static and dynamic loads.

Twisting of an elastic plate containing a crack

Abstract: The stress distribution caused by twisting an infinite plate containing a finite crack is analyzed in terms of Reissner's theory for the bending of thin plates. The singular character and the detailed structure of the stresses near the ends of the crack are determined in closed form. Numerical results are given for the magnitudes of the stress couples and stress resultants for a range of plate thicknesses.

An atomistic study of fracture

Abstract: The atomistic relaxation method developed by the author to study the core structures of edge and screw dislocations in crystalline solids was used to investigate the configurations of atoms and crack-tip atom cohesion and stress fields in BCC (body-centered cubic) and FCC (face-centered cubic) iron. Single crystallites containing initially an atomically sharp and through crack (a vacancy sheet) of various orientations were subjected to tensile strain applied normal to the crack. It is shown that the crack tip stress fields depend importantly on the orientation of the crack with respect to the parent lattice, a result unexpected of existing linear elasticity and continuum theories.

A comparison of reaction rate models for the fracture of solids

Abstract: The application of the theory of reaction rates to the fracture of solids is reviewed. Four different models are compared and shown to exhibit three basic differences in formulation. The evidence appears to favor bond rupture, as opposed to bond slippage, as the basic mechanism leading to fracture of certain polymer systems. It is shown that other differences in the models cannot be resolved by a comparison with existing experimental data.

Dynamic fracture by spallation in metals

Abstract: Material responses and fracture criteria relevant to the description of spallation phenomena are reviewed. The state of the material at the instant of fracture is an important part of a fracture criterion. The stress state associated with plane strain is described, and the effect of the initial conditions and the time dependent conditions of the material on spallation are discussed. The important quantities in any fracture criterion are the applied stress state, the size of the critically stressed region, the critical value of stress at which fracture begins, and the critical crack velocity. Stress gradient and cumulative damage spall-criteria are discussed in relation to these more fundamental quantities. Finally, some experiments are suggested that would isolate important parameters of the spallation process.

Stress analysis of a pressurized circular hole with radial cracks in an infinite elastic plate

Abstract: The stresses are evaluated for the plane problem of radial cracks originating at the boundary surface of a pressurized, circular hole in an infinite elastic plate. The stress distribution is approximately equal to that around a pressurized and unfractured “equivalent” cavity, the radius of which is equal to that of the crack tips. The critical pressure at which brittle failure will occur is analyzed for several variations of the hole and crack geometry.

Lateral constraint in a cracked, three dimensional elastic body

Abstract: Three dimensional elastic body fracture analysis, considering lateral constraint factor contour plots

Tensile strength of butt-joined epoxy-aluminum plates

Abstract: Tensile tests conducted on butt joined epoxy-aluminum plates containing single cracks along the bond surfaces showed that there exists a characteristic crack length below which the fracture strength of the composite is mainly influenced by the stress concentrations at the bond edges. For specimens with cracks longer than the characteristic length the fracture of the composite is entirely controlled by the stress concentrations at crack tips. In the latter case the stress intensity factors defined by Sih and Rice, and Erdogan appeared to agree reasonably well with test results.

Notch root radii effects in the fatigue of polymers

Abstract: Wohler-type rotating bending fatigue tests have been performed on PVC cantilever specimens containing various sharp and blunt notches of known geometries. An attempt has been made to analyse the data obtained using linear elastic fracture mechanics concepts. Results from the sharp-notched specimens show a good correlation on a stress intensity factor basis and a fatigue limit is revealed. For blunt notches a stress intensity factor had to be calculated allowing for small flaws at the notch root, and some measure of correlation of the stress intensity factor at the fatigue limit for the various specimens is obtained.

On the sharpness of cracks compared with Wells's COD

Abstract: Crack opening displacement concept in fracture mechanics, considering crack tip radius as measure of extension potential

The effects of hydrostatic pressure on the ductility of metals and alloys

Abstract: A law governing the change in the ductility of metals and alloys under pressure is given: $$\begin{gathered} \left( {\frac{P}{{\sigma _n }}} \right) = \tfrac{1}{2}\frac{1}{{\sigma _n }}\frac{{d\sigma }}{{d\varepsilon }}\{ \varepsilon _{local} (P)^{\tfrac{3}{2}} - \varepsilon _{local} (O)^{\tfrac{3}{2}} \} + \tfrac{1}{3}\frac{1}{{\sigma _n }}\frac{{d\sigma }}{{d\varepsilon }}\{ \varepsilon _{local} (P) - \varepsilon _{local} (O)\} + \hfill \\ {\text{ }} + \tfrac{1}{2}\{ \varepsilon _{local} (P)^{\tfrac{1}{2}} - \varepsilon _{local} (O)^{\tfrac{1}{2}} \} \hfill \\ \end{gathered}$$ where P is the hydrostatic pressure, ɛlocal is the strain accumulated from the start of necking to fracture, σn necking stress and (dσ/dɛ) the coefficient of linear work hardening. This relation is derived from a newly proposed criterion of ductile fracture, viz. “constancy of hydrostatic tensile stress”, which indicates that the change of ductility with pressure obeys a three halves power law. The observed increase in ductility of widely differing metals and alloys under pressure up to 10,000 kg/cm4 has confirmed that the proposed criterion is acceptable.

An engineering analysis of ductile fractures

Abstract: A critical strain at a small distance from a crack tip is proposed as a ductile fracture criterion. Surface strain in double edge cracked specimen made of 2024-0 aluminum alloy was measured using the moire method. The strain along the crack line and near a crack tip is proportional to the cracked-section-elongation, the latter is used as a measurable quantity to characterize ductile fractures. The effect of specimen size on fracture strength and energy absorption by the specimen were analyzed. The proposed ductile fracture analysis agrees qualitatively with fracture tests on fully annealed 4340 steel and 2024-T351 aluminum.

On a plate supported by an elastic foundation and containing a finite crack

Abstract: Using an integral formulation, the equation for a plate resting on an elastic foundation, of a spring constant k and containing a crack of length 2c, is solved for the Kirchhoff bending stresses. The inverse square root singular behavior of the stresses peculiar to crack problems is obtained. Furthermore, this singularity may be related to that found in an unsupported plate by $$\frac{{\sigma _{y_{sup.} } }}{{\sigma _{y_{unsup} .} }} \approx \frac{1}{{1 + a\lambda ^2 }}$$ where a is for small values of the parameter λ is a positive constant.

On the location of fracture in brittle solids—II

Abstract: The fracture produced in a slender rod, when a compressive stress pulse reflects from a free end as tension, has often been used to measure the tensile strength of brittle solids. In the present paper it is shown that the distribution of fracture location, when many such tests are made with a rectangular pulse of fixed stress level, may be used to deduce the distribution in strength of the material. The procedure is illustrated using tests on glass rods.

The propagation law of cleavage fracture

Abstract: The equations of motion of cleavage fracture are solved and discussed for constant force, constant moment, and constant deflection. Also crack propagation in a plate is discussed. The differential equations are derived from the law of angular momentum conservation of the split parts. An energy balance, which includes the kinetic energy of the moving crack is incorporated into the law of angular momentum conservation. The static case of crack stability is a particular solution of the general propagation equation.

Adiabatic Shear Bands in Steel

Abstract: : Bands of intense shear have been reported in steels which have been subjected to a high strain rate. It was proposed that these bands were caused by unstable adiabatic shear; that the rate of thermal softening (as heat is generated locally by plastic work) is greater than the rate of work hardening of the metal. Thus shear continues preferentially in these soft bands and, if the deformation leads to fracture, then fracture usually occurs within these bands. On metallographic examination the bands appear white when etched in picral or nital, and have always been assumed to consist of martensite. Work was undertaken to check this assumption. (Author)

The study of fracture surface profiles in the electron microscope

Abstract: • A new technique is presented for the study of fracture surface topography, which may be used in addition to stereoscopic measurements. The technique essentially consists of making cross sections of carbon replicas of fracture surfaces. Figure 1 shows cross sections of a replica of a ductile fracture surface (dimpled rupture as a result of void coalescence) at various magnifications. The material is a 7079 forging; the fracture mode is flat tensile or mode I. In a, the macro-topography can be observed, whereas in b and c the shape of individual dimples can be recognized. Dimples appear to be shallow holes with a small depth to width ratio. I~ d one observes how the replica can reproduce fine details of the fracture surface, which gives some confidence in the applied method. The fracture surfaces were replicated first with a two component resin. This plastic replica had a size of about 3 x i0 mm 2 and it was made so thick as to have substantial strength and stiffness (about 2 or 3 nun thick). It could be removed from the fracture surface with a fine pair of pliers. A continuous layer of carbon was evaporated on this plastic replica; so far the method does not differ from conventional replication technique. Then the carbon film was sandwiched between the first plastic replica and a newly applied layer of two component resin poured on top of the carbon. The sandwich was placed in an empty gelatine capsule, which was further filled with the resin. When the plastic was set the gelatine was removed and the pellets so obtained were cut perpendicular to the carbon layer by means of an ultra-microtome with either a glass or a dimaond cutter (the latter giving more consistent results). Slices of 600800 ~ngstroms thick were caught on a normal 200 mesh grid and were ready for observation in the microscope. When analyzing pictures obtained by this technique one should be aware of the fact that a cut does not always pass through the middle of a dimple or a grain (in an intergranular fracture); neither is it always perpendicular to the direction of crack propagation (which may be different in various grains in case of a fatigue fracture). Hence, in the analysis one is faced with the same problems as when examining polished and etched cross sections with an optical microscope. The method for the quantitative analysis of cross sections has been elegantly treated by Ful iman [1].

Stress intensity factors for cracks emanating from rectangular cutouts

Abstract: The stress intensity factors are determined at the crack roots for a rectangular cutout with symmetric edge cracks in an infinite sheet under uniaxial tension.