Showing papers on "Fracture mechanics published in 1970"
01 Jan 1970
676 citations
TL;DR: In this article, the usefulness of the finite element method for the computation of crack tip stress intensity factors is established, and the results are compared not only to the results of other analytical solutions, but additional correlation is made of two different fracture test specimen types.
608 citations
TL;DR: In this paper, it was shown that a crack front increases its length by changing its shape when it interacts with two or more inhomogeneities in a brittle material, and an expression for the fracture energy was obtained.
Abstract: Observations are presented showing that a crack front increases its length by changing its shape when it interacts with two or more inhomogeneities in a brittle material. These observations are presented for both cleavage and conchoidal types of fracture. Based on these observations and the concept that a crack front possesses a line energy, an expression for the fracture energy is obtained. This expression shows that the fracture energy should increase as the distance between the dispersed inhomogeneities is decreased. Using the Griffith fracture criterion, this result is discussed for the case of strengthening a brittle material.
501 citations
TL;DR: In this paper, a statistical theory of material strength is proposed, where the strength of the elements is assumed to be a statistic a quantity, and as the material is loaded elements fracture randomly throughout the body causing localized stress concentrations.
Abstract: A Statistical theory of material strength is proposed. Materials are considered to be imperfect heterogeneous continua composed of discrete volume elements whose characteristics are related to material structure and imperfections. The strength of the elements is assumed to be a statistic a quantity, and as the material is loaded elements fracture randomly throughout the body causing localized stress concentrations. The accumulation of these breaks results in overall failure. By relating strength to material structure this theory attempts to bridge the gap between the microscopic and continuum approaches to fracture mechanics. The theory is applied to composite materials reinforced with whiskers and continuous fibers. Comparisons with experimental data show good agreement. Results for whisker-reinforced composites appear to provide a good prediction of strength and an explanation of the disparity between the strength of individual whiskers and the strength of the composites made from them.
288 citations
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TL;DR: In this article, the authors measured the energy required to propagate a crack and observed the mechanism of fracture by microscopically observing the fracture mechanism of bone at low strain rates, showing that bone displays very high resistance to crack propagation comparable even to some metallic materials.
Abstract: Fracture of bone is investigated by measuring the energy required to propagate a crack and by observing, microscopically, the mechanism of fracture. At low strain rates bone displays very high resistance to crack propagation comparable even to some metallic materials. The type of fracture is similar to fiber‐reinforced composite materials.
227 citations
224 citations
TL;DR: Theoretical predictions of crack propagation behavior in brittle solids under conditions of thermal shock were verified by water quenching of cylindrical polycrystalline alumina rods followed by strength testing as discussed by the authors.
Abstract: Theoretical predictions of crack propagation behavior in brittle solids under conditions of thermal shock were verified by water quenching of cylindrical polycrystalline alumina rods followed by strength testing. The calculated quenching temperature difference (ΔTO) required to initiate thermal-stress fracture agreed fairly well with experiment. When fracture was initiated, strength decreased catastrophically, in agreement with theory. An expression for the strength remaining after thermal stress fracture was derived in terms of the pertinent physical parameters. Values of surface fracture energy similar to those reported in the literature agreed with experiment. Strength after thermal shock was predicted to be inversely proportional to the 1/4 power of the rod diameter; this prediction was supported by experimental data for two rod sizes. Over a range of quenching temperature differences ΔTΔT0 strength remained constant, in agreement with the theoretical expectation that the newly formed cracks were subcritical. Only at the highest quenching temperature differences could further decreases in strength be observed; the quantitative changes, however, were masked by nonlinear deformation (evidenced by permanent crack opening). It was concluded that, although thermal shock behavior of brittle ceramics can be approximated fairly well, reliable quantitative estimates require considerably more information about strength and surface fracture energies as a function of environment, stress distribution, strain rate, and temperature and specimen size effects.
210 citations
TL;DR: In this article, a comparison of the slip line flow field at the tip of a sharp crack and of a blunted crack is made, and it is shown that fatigue crack propagation is the result of repeated cyclic crack extension by alternating shear.
204 citations
TL;DR: In this paper, the authors examined the fracture and fatigue in elastic cylindrical shells with circumferential crack under axial tension and noted precracked specimens with precariness.
Abstract: Fatigue and fracture in elastic cylindrical shells with circumferential crack under axial tension, noting precracked specimens
146 citations
TL;DR: In this article, the influence of the stress ratio on the crack growth was predicted by the equation in agreement with the test results but that the effects of the environment and the load frequency could not be coped with by changes in the constants of the equation.
142 citations
01 Jun 1970
TL;DR: In this paper, both wedge force loading and remote loading techniques were employed to achieve the desired ΔK levels, and preliminary experiments were designed to test their compatibility, and the observed crack growth rates compared with those in desiccated air.
Abstract: Environmental fatigue crack propagation in 2024-T3, 7075-T6, and 7178-T6 has been studied at low levels of cyclic amplitude of stress intensity, ΔK. Both wedge force loading and remote loading techniques were employed to achieve the desired ΔK levels, and preliminary experiments were designed to test their compatibility. Testing was carried out in humid air, distilled water, and 3.5 pct sodium chloride solution, and the observed crack growth rates compared with those in desiccated air. Later studies were also conducted in an inert reference environment with a total water content of less than 2 ppm. When the data are plotted as log ΔK vs log d2a /dN, alloy 2024-T3 exhibits a marked slope transition, alloy 7075-T6 a slight slope transition, and alloy 7178-T6 a rectilinear behavior throughout the whole range of ΔK studied. The basic shape of these curves is discussed in terms of state-of-stress conditions at the crack tip, frequency effects, environmental effects, strain rate sensitivity, and metallurgical structure. An attempt is also made to correlate the rate of fatigue crack propagation in a particular environment and at a particular ΔK level with the fracture topography.
TL;DR: In this paper, the unstable growth of a crack in a large viscoelastic plate is considered, within the framework of continuum mechanics, and 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.
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.
TL;DR: In this article, 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.
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.
TL;DR: In this paper, the recovery in strength of soda-lime-silica glass cracks was determined by fracture mechanics techniques, and it was found that approximately 80% strength was recovered in cracks formed by mechanical shock, whereas only 20% were recovered after being held open to the atmosphere for several minutes.
Abstract: Cracks in soda-lime-silica glass specimens closed spontaneously; the recovery in strength was determined by fracture mechanics techniques. Approximately 80% strength was recovered in cracks formed by mechanical shock, whereas approximately 20% was recovered in cracks that closed after being held open to the atmosphere for several minutes. The high strength recovery in the mechanically shocked specimens is attributed to the very active surface formed during fracture. If the surface is allowed to adsorb O2 or H2O vapor, the activity is reduced, and healing is less complete. Crack healing can introduce surface flaws into glass that cannot be detected by current methods of nondestructive testing.
TL;DR: In this paper, a method of estimating the fracture surface energy of fiber-reinforced materials is discussed, and the surface work is shown to increase with increasing fiber content, strength and diameter, and decrease with increasing fibre modulus and matrix flow stress.
Abstract: A method of estimating the fracture surface energy of fibre-reinforced materials is discussed. The surface work is shown to increase with increasing fibre content, strength and diameter, and decrease with increasing fibre modulus and matrix flow stress (or hardness). Relatively short fibres should be used if high toughness is required, and the maximum toughness that can be achieved is limited by the amount of crack opening that can be permitted. Under certain conditions, incorporation of fibres into a material can lead to embrittlement.
TL;DR: In this paper, it was 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.
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.
TL;DR: In this paper, the first mode of failure, referred to as cyclic thermal softening, can be related to loss compliance, specimen geometry and the frequency and magnitude of the cyclic load.
Abstract: Thermoplastic components subjected to cyclic loading may distort because of localized rises in temperature and/or fracture because of incremental (fatigue) crack propagation from microscopic cracks or defects produced during the manufacturing process or by service conditions.The object of the present paper is to show quantitatively how the first mode of failure, which is referred to as cyclic thermal softening, can be related to loss compliance, specimen geometry and the frequency and magnitude of the cyclic load. The results of cyclic bending tests on polymethylmethacrylate (p.m.m.a.) and Polyvinylchloride (p.v.c.) beams of rectangular and circular cross-section are analysed. For the service conditions considered the p.m.m.a. specimens showed both failure modes whereas the p.v.c. specimens failed as a result of incremental (fatigue) crack propagation.
TL;DR: In this article, an analytical and experimental program was conducted to determine if a biaxial stress field produces a significant effect on the fatigue and fracture behavior of thin plates, and it was shown that the effect of nonsingular stresses on the behavior of a crack is examined from both a linear elastic and an elastic-plastic viewpoint.
Abstract: The results are presented of an analytical and experimental program which was conducted to determine if a biaxial stress field produces a significant effect on the fatigue and fracture behavior of thin plates. The materials tested were 6061-T4 and 6061-T6 aluminum sheets and plexiglas sheets. The experimental program included fracture tests with various magnitudes of biaxial load at fracture and fatigue tests with sinusoidal loading normal to the crack and either constant or sinusoidal stresses applied parallel to the crack. The effect of nonsingular stresses on the behavior of a crack is examined from both a linear elastic and an elastic-plastic viewpoint. The experimental study indicates that a biaxial stress field does affect the behavior of a crack in a thin sheet. An increase in the apparent fracture toughness with increasing biaxial load was observed experimentally but as yet cannot be adequately explained using linear fracture mechanics theory. Biaxial stresses were found to produce a shift in the fatigue crack growth rate data, and it is shown that this shift can be predicted using several empirical fatigue crack propagation models.
TL;DR: In this paper, the authors present theoretical analyses of the crack tip stress intensity factors for some typical basic models of sheet structures, which are based on Laurent's expansions of complex stress potentials where the expansion coefficients are determined from the boundary conditions.
TL;DR: In this paper, a model for craze formation and growth has been proposed based on a crack opening displacement approach in conjunction with a simple flow analysis to describe the movement of the liquid environment within the craze.
Abstract: Test specimens of polymethylm ethacrylate (PMMA) have been subjected to stress in the presence of methanol and the resulting craze growth behaviour has been investigated by means of the concepts of fracture mechanics. Sharp-notched tension specimens have been tested over a wide range of constant applied loads to produce craze initiation and propagation. In this way it has been found that, for tension tests under constant load, both the initiation and growth characteristics are controlled by the initial stress intensity factor, K 0 , and not by the applied stress p , as previously thought. Two distinct growth patterns have been observed, one type leading to eventual craze arrest and the other to final fracture. In the former, the craze growth rate decreased, whereas in the latter case the growth initially decreased but then eventually continued at a constant rate. Both types of growth are functions of the initial stress intensity factor. A model for craze formation and growth has been proposed based on a crack opening displacement approach in conjunction with a simple flow analysis to describe the movement of the liquid environment within the craze. The model provides equations of motion for a craze and these have successfully been used to explain the observed behaviour. The size of the void spacing within a craze has been calculated to be 2.48 x 10 -4 mm, this being in close agreement with the result obtained by Zhurkov, Kuksenko & Slutsker (1969) using direct methods. A stress equilibrium equation has enabled a craze yield stress p c to be derived as 9.06 N mm -2 for tests at 20 °C.
TL;DR: In this paper, the authors discussed the factors which determine the mean length of fiber pull-out during fracture in composites reinforced with continuous fibres having variously spaced points of weakness.
Abstract: Fibre fractures which occur near, but not at, the plane of matrix failure in a composite, lead to fibre pull-out during fracture. Energy absorbed in this process contributes directly to the work of fracture and hence to the toughness of the composite. Factors which determine the mean length of fibre pulled out during fracture are discussed for the case of composites reinforced with continuous fibres having variously spaced points of weakness. The presence of such weak points also affects the strength of the composite, but not all composites of the same strength have the same toughness. The greatest toughness for a given strength is always found in composites reinforced with discontinuous fibres.
TL;DR: In this article, a series of fatigue tests were performed on several different polymer materials representing different classes of mechanical response and a strong correlation was found between the fatigue crack propagation rate and the stress intensity factor range prevailing at the advancing crack tip.
Abstract: In order to gain a better understanding of matrix-controlled fatigue failure processes in non-metallic materials a series of fatigue tests were performed on several different polymer materials representing different classes of mechanical response Fatigue crack propagation rates between 5×10−6 in cycle−1 (127 nm cycle−1) and 4×10−4 in cycle−1 (10 300 nm cycle−1) were measured in nylon, polycarbonate, ABS resin, low-density polyethylene and polymethyl methacrylate A strong correlation was found between the fatigue crack propagation rate and the stress intensity factor range prevailing at the advancing crack tip Whereas metals exhibit comparable fatigue growth rates for a given stress intensity range when normalised with respect to their static elastic modulus, the polymer materials exhibited a 1300-fold difference in crack growth rate for a given normalised stress intensity range This observation dramatically illustrates the importance of understanding molecular motion and energy dissipation processes in polymer materials as related to their chemistry and architecture The relative behaviour of the different polymer materials could be generally correlated with their reported damping characteristics
TL;DR: In this article, the authors make a distinction between the very special extremes of plane stress and plane strain, and their relevance to the failure of complex structures and elements is emphasized, along with the need to consider bending in most shell structures.
TL;DR: The theory of the motion of a cleavage crack created by wedging open the ends of a double cantilevered crystal at a constant rate has been investigated in this article, and the results are presented for use in analysis of experimental studies of fracture dynamics in lithium fluoride reported in Part II of this series.
Abstract: The theory of the motion of a cleavage crack created by wedging open the ends of a double cantilevered crystal at a constant rate has been investigated. The results are presented for use in analysis of experimental studies of fracture dynamics in lithium fluoride reported in Part II of this series. A solution of the quasistatic equations of motion of the crack including kinetic energy effects has been found from which the dynamic fracture surface energies may be deduced for a propagating crack of this geometry by observations of either the time dependence of the crack length or the profile of the fracture opening near its tip. The detailed configurations of dislocations accompanying the tip of a moving crack in alkali halides have been calculated using dislocation dynamics and continuum elasticity theory. The plastic deformation contribution to the effective fracture surface energy has been determined and some of its consequences worked out.
TL;DR: In this article, the conditions under which crack propagation is initiated in an isotropic, brittle solid of the Griffith type when the solid is subjected to a homogeneous, uniform but otherwise arbitrary triaxial system of stresses at infinity.
Abstract: Summary
A calculation has been carried out of the conditions under which crack propagation is initiated in an isotropic, brittle solid of the Griffith type when the solid is subjected to a homogeneous, uniform but otherwise arbitrary triaxial system of stresses at infinity. The cracks have been taken to be flattened ellipsoidal cavities. The results are in broad agreement with results obtained in the two-dimensional treatment of the problem, and with experimental observations. Tensile and shear fracture is possible and the Mohr envelope is of parabolic form. Fracture initiation is shown to be independent of the intermediate principal stress.
TL;DR: In this paper, the effect of dynamic strain-ageing on the initiation and propagation of ductile fracture in mild steel was examined using scanning electron microscopy and it was shown that this crack density increases with strain.
TL;DR: Viscoelastic-plastic solid delayed fracture associated with wedge formation of crazed material at crack tip as discussed by the authors, which is a type of material that is typically unstable and unstable.
TL;DR: In this article, an infinite lateral-length elastic plate strip bonded through a Winkler elastic foundation to a rigid substrate is assumed, in which the plate is separated from the adhesive layer by internal pressure.
Abstract: Complementing an earlier paper which utilized an energy balance criterion for a continuum mechanics analysis of adhesive failure in a pressurized blister at the interface of an elastic material and a rigid substrate, the analysis is extended to include an additional elastic interlayer between them. An infinite lateral-length elastic plate strip bonded through a Winkler elastic foundation to a rigid substrate is assumed, in which the plate is separated from the adhesive layer by internal pressure. It is found that the important design parameters are the tensile modulus-to-thickness ratio of the adhesive layer and the adhesive fracture energy of separation of the respective materials. The results provide a basis for investigating changes in the chemical microstructure of the adhesive.