Showing papers in "International Journal of Fracture in 1978"

Review and extension of compliance information for common crack growth specimens

Abstract: Elastic compliance expressions for compact type (CT) and WOL specimens have been formulated for a wide range of crack lengths (0.2 ⩽a/W ⩽ 0.975) using results from Newman's modified boundary collection techniques and Wilson's deep crack analysis. The location of the axis of rotation of the specimen arms at various crack lengths has been calculated and subsequently used in a proposed extrapolation technique to predict compliance at any location of the specimen convenient for measuring deflection during a crack growth test. The predicted compliances were found to be in excellent agreement with expreimental values for the two specimen types considered. Compliance expressions are also included for the center crack tension specimen.

Conditions for shear localization in the ductile fracture of void-containing materials

Abstract: This paper investigates the possibility that ductile fracture occurs by the McClintock-Berg mechanism of localization of deformation within a narrow shear band, owing to the progressive softening of the material by increasing porosity due to void growth. The ductility predicted for a macroscopically homogeneous sample of a voided material is shown to be unrealistically large and hence an initial inhomogeneity of properties is considered, in the sense of an analysis by Marciniak and Kuczynski in the related problem of local necking in sheet metals. General conditions for a localization bifurcation with an initial inhomogeneity (imperfection), concentrating deformation to allow localization within it, are derived. The initial imperfection is taken in the form of a void-containing, thin slice of a material and is assumed to have a void volume fraction slightly larger than the outside of the imperfection. Elastic-plastic constitutive rate relations for void-containing materials proposed by Gurson are adopted to the conditions for the localization bifurcation. The critical conditions are analyzed numerically to discuss the sensitivity of localization conditions to an initial imperfection, in consideration of the implications for the theory of ductile fracture. The results suggest that the existence of an initial imperfection makes it possible for localization to occur at a reasonable strain, and the predictions from this analysis seem broadly consistent with reported experimental observations.

Line Crack Subject to Shear.

Abstract: Field equations of nonlocal elasticity are solved to determine the state of stress in the neighborhood of a line crack in an elastic plate subject to a uniform shear at the surface of the crack tip. A fracture criterion based on the maximum shear stress gives the critical value of the applied shear for which the crack becomes unstable. Cohesive stress necessary to break the atomic bonds is calculated for brittle materials.

An analysis of the crack tip stress field in DCB adhesive fracture specimens

Abstract: The problem of a cracked adhesive bonded DCB-type fracture specimen has been analyzed using a hybrid stress model finite element analysis which incorporates an advanced crack tip element. Stresses in the near and far fields have been studied as a function of adherend/adhesive modulus ratio and adhesive thickness. The results are compared to monolithic systems with regard to the stress intensity factor and the localization of the singular stress domain associated with the crack tip.

Stochastic strength and fatigue of fiber bundles

Abstract: Stochastic models for the failure of single fibers and fiber bundles are considered with a historical perspective. All surviving fibers in the bundle at any time t are assumed to share the load equally. Of particular interest is the tensile strength and time to failure in fatigue of such fibers and bundles. The stochastic model for the failure of single fibers is shown to have realistic features and a very favorable evaluation of the model is carried out using recently reported experimental data. Using asymptotic results for bundles which were recently obtained by the author, bundle failure is compared with single fiber failure. Many behavioral features carry over from fiber to bundle. But bundle lifetime is typically far less under fatigue loadings, though a moderate reduction in bundle load restores the lost lifetime. Most important, the variability in bundle lifetime and strength is inversely proportional to the square root of the number of fibers in the bundle. The results have implications in the design of cable structures.

Measurement of rubber cutting resistance in the absence of friction

Abstract: A method for assessing the resistance of rubbers to cutting by sharp objects is described. It involves the application of the cutting implement -a razor blade-to the tip of a crack in a stretched tear test piece. The method enables effects of friction on the cutting process to be substantially eliminated. Under these conditions two distinct forms of cutting are observed: one is a slow time-dependent process, while the other involves rapid, “catastropic” failure. Effects of test piece shape and deformation on the cutting behaviour can be taken into account by use of fracture mechanics. The relative cutting resistance of different rubbers is found to vary according to the test conditions. At low deformations the onset of catastrophic cutting can be defined by a simple relationship which is applicable to all rubbers examined.

Influence of transverse shear on an axial crack in a cylindrical shell

Abstract: An axial crack in a cylindrical shell is investigated by use of a 10th order shell theory, which accounts for transverse shear deformations as well as a special kind of orthotropy. The symmetric problem is formulated in terms of two coupled singular integral equations, which are solved numerically. The asymptotic membrane and bending stress fields ahead of the crack are found to be self similar. Stress intensity factors are given as a function of the shell parameter for various values of the ratio shell radius to shell thickness. Considerable differences from 8th order shell theory results are found for the bending stresses, while the membrane stresses of the 8th order theory seems to be a lower limit reached for very thin shells.

Elastodynamic analysis of crack by finite element method using singular element

Abstract: The finite element method using a singular element near the crack tip is extended to the elastodynamic problems of cracks where the displacement function of the singular element is taken from the solution of a propagating crack. The dynamic stress intensity factor for cracks of mode III or mode I deformations in a finite plate is determined. The results of computation for stationary cracks or propagating cracks under dynamic loadings are compared with the analytical solutions of other authors. It is shown that the present method satisfactorily describes the time variation of the stress intensity factor in dynamic crack problems.

Fatigue crack closure over the range of stress ratios from −1 to 0.8 down to stress intensity threshold level in HT80 steel and SUS304 stainless steel

Abstract: The closure phenomena of fatigue cracks were investigated with a 1 mm gage length extensometer over the range of stress ratio, R, from −1 to 0.8. Plate specimens with a center slot of HT80 steel and SUS304 stainless steel were fatigued under push-pull loading, and the crack propagation rate, da/dn, was measured. The stress ratio, R, was found to influence da/dn in both materials. The crack opening stress intensity factor, K op, was determined from the relationship between the crack tip extensometer displacement and the load. The effective stress intensity range ratio, U(=ΔKeff/ΔK), decreases with the decrease of the stress intensity amplitude, ΔK/2. As for the data which show the crack closure phenomena (R≦0.4), the relationship between log(da/dn) and log(ΔK eff/2) falls on a straight line near the stress intensity threshold level. For R=0.8 where the crack tip is fully open over the whole range of loading, the data show a discrepancy from the same line. The strain at the crack tip was also measured with the Moire fringe multiplication method. A large amount of plastic strain at the crack tip was observed even below the crack opening load for R=−1 in HT80 steel. These phenomena show that fatigue damage still exists when the crack is closed. These also show that the crack closure cannot fully account for the effect of R on da/dn.

Non-linear fracture mechanics

Abstract: The fracture of solids is analyzed using the formalism of equilibrium mechanics. A partially cracked, mechanically loaded reversible system is considered. A stability criteria is formulated. The equilibrium theory is valid for non-linear load deflection relationships and is applied to linear elastic fracture mechanics, the Hertz test and J IC tests.

A method for predicting crack growth in nonhomogeneous viscoelastic media

Abstract: Equations are developed for predicting crack growth in the opening mode for quite general situations, including many quasi-static and dynamic problems involving moisture and temperature gradients in monolithic and composite materials. Except for the small zone of failing material at the crack tip, the body is assumed to be linearly viscoelastic. A method for obtaining viscoelastic stresses and displacements from elastic solutions is first described. The traction boundary condition for the crack faces is not in general satisfied by these results. However, it is shown by modifying the failure zone in the elastic problem this condition can be met, and an integral equation for the stress in the modified failure zone is derived. Approximate analysis similar to that used previously by the author in stress analysis is then employed to solve the integral equation and develop relatively simple equations for predicting crack speed; these equations relate crack speed in the viscoelastic material to stress intensity factors in a suitably defined elastic body.

The numerical evaluation of a class of generalized stress intensity factors by use of the Lobatto-Jacobi numerical integration rule

Abstract: The Lobatto-Jacobi method of numerical solution of Cauchy type singular integral equations and determination of stress intensity factors, based on the use of the corresponding numerical integration rule, was modified so as to become applicable to the evaluation of a special class of generalized stress intensity factors associated with a real singularity. The same technique can also be used for the evaluation of generalized stress intensity factors associated with a pair of complex conjugate singularities. An application of the method to a plane elasticity problem is also made. Finally, the modification of the method valid for a pair of complex conjugate singularities is illustrated in detail in a numerical example.

The effect of rate on the impact fracture toughness of polymers

Abstract: The determination ofG cfor a polyethylene and PTFE from a conventional energy measuring impact test is described, together with the use of plastic zone and slow crack growth corrections. The rate of the test is changed by two decades by varying the specimen dimensions andG cas a function of loading time is determined. A remarkably strong time dependence (t −0.42) is observed and this is discussed in terms of loss processes in the craze region at the crack tip.

The deformation and fracture kinetics of stress corrosion cracking

Abstract: The concepts of deformation and fracture kinetics theory are extended for the analysis of stress corrosion cracking. A single, coherent system is developed that provides the full kinetics description of the typical SCC behavior. The kinetics approach shows that Regions I and II are associated with two consecutive energy barriers, parallel with the single barrier associated with Regon III. The kinetics analysis of two consecutive barriers leads to a four-term expression, rather than to the generally considered two-term form. The effect of the threshold stress intensity is predicted by the complete desxription of the consecutive barrier system.

A compendium of sources of fracture toughness and fatigue-crack growth data for metallic alloys

Abstract: This Technical Memorandum presents sources of fracture toughness and fatigue crack growth data for metallic alloys. This is Part 3 of a three volume report.

Stress intensity factors for three-dimensional cracks

Abstract: The method of superposition of analytical and finite-element solutions is proposed for determining three-dimensional distributions of the stress intensity factor; the singular part of the solution is expressed by a linear combination of analytical solutions, and the rest by a finite-element solution. The method is applied to a round bar with a circumferential crack and plates with penetrating cracks. Detailed distributions of the stress intensity factor near the plate surfaces are investigated with the aid of Benthem's theory, which shows that less than 0.5% of the plate thickness is severely influenced by the plate surfaces in the case of a compact tension specimen. Computations for the present method can be performed with a general purpose program for finite element analysis without using special elements.

Summary of SIF design graphs for cracks emanating from circular holes

Abstract: A summary is given of existing solutions for stress intensity factors for through-the-thickness cracks emanating from circular holes. New solutions are given for some cases of cracks at circular holes in finite plates. The results were obtained by the finite element method with isoparametric eight-noded quarter point elements and the J-integral. Computational problems arising at short cracks are discussed and an approximate method evaluated. The accuracy of the given data is in general within a couple of percent.

Debond dynamics of an elastic strip, I: Timoshenko-beam properties and steady motion

Abstract: The paper considers debond of a Timoshenko-beam from a substrate which is rigid during the event. Essential relations expressing support conditions, continuity conditions, conservation of momentum and energy balance are discussed. Details relating to steady motion are exemplified.

Crack propagation in linear viscoelastic solids: some new results

Abstract: An extension of a theory of linear viscoelastic fracture is derived which removes a former restriction that Poisson's ratio is a constant. The new formulation thus includes both material property characteristics, i.e. the bulk (dilatation) and shear (distortion) linear viscoelastic compliances. Characteristic crack growth laws, assuming a Dugdale region ahead of the crack, are developed for creep laws which depend linearly upon time but are thought to be representative of more general materials. Examples include a single crack, a linear array of cracks, and a specialized cyclic load application.

Interaction of elastic waves in two bonded dissimilar elastic half-planes having Griffith crack at interface—I

Abstract: The paper deals with the problem of finding the stress distribution near a Griffith crack located at the interface of two bonded dissimilar elastic half-spaces. The crack is opened by the interaction of a plane harmonic elastic wave, incident normally on the crack. The problem is first reduced to a set of simultaneous dual integral equations which are further transformed to a set of simultaneous singular integral equations. These are solved numerically by reducing them to a set of algebraic equations. The solution is used to calculate the stress intensity factors.

Stress intensity factors for cracked holes and rings loaded with polynomial crack face pressure distributions

Abstract: The purpose of this report is to present some recent stress intensity factor solutions for cracked rings and holes which may be of general interest to other investigators. The present results are based on mode I solutions reported previously for radially cracked holes in large plates [I] and for radially cracked rings [2] loaded with an arbitrary crack face pressure. These through-thickness flaw geometries, showing the crack face pressure p(x), are presented in Fig. i. In addition to the single crack configurations shown, symmetric double flaws are also considered. Note that the ring geometry is limited to an aspect ratio Ri/R o = 0.5. As described in [I] and [2], stress intensity factor solutions for these two problems were obtained by weight function techniques and are given by K I = (H/K*) p(x) ~n/~a dx (1) o Here H is a constant which is defined by the modulus of elasticity and Poisson's ratio, K* is the known stress intensity factor for a given loading applied to the flaw geometry of interest, a is the crack length, x is the distance from the edge of the hole or bore of the ring, and is the crack opening profile corresponding to the known stress intensity factor solution K*. The solution for uniaxial tension described by Bowie [3] and reported in [4] was used for K* for the cracked hole problems, while the result obtained by Jones [5] for a point compressive load along the crack plane served as K* for the ring geometry. A convenient numerical technique for approximating the crack surface profile n and for computing the partial derivative ~n/~a is described in [I]. If the crack face pressure p(x) is defined as the unflawed hoop stress distribution next to the hole or ring when subjected to the loading of interest, (I) yields K I for the corresponding crack problem. This procedure was shown in [i] and [2] to give stress intensity factors which agree well with independent solutions for a variety of problems, as was recently used to obtain stress intensity factors for coldworked holes in aluminum plates and for autofrettaged cylinders [6]. The coldworking and autofrettaging processes involve introduction of residual stresses into the component by a radial expansion into the plastic range. The coldworked hole results agree well with corresponding experimental measurements and enabled accurate prediction of specimen fatigue lives, while the autofrettaged cylinder calculations agree favorably with previous solutions in the literature [7]. Thus, it is felt that these crack face pressure solutions are of practical use for analyzing fastener holes and thickwalled cylinders.

Strip yield models of creep crack incubation and growth

Abstract: The strip yield model of Dugdale and Bilby, Cottrell and Swinden is applied to analyse the incubation and growth of creep cracks. This extends previous work by Vitek (on incubation) and by Heaton and Chan (following To) on growth. Following both Vitek and Heaton and Chan, the main criterion of crack growth used is a COD-based one. The crack is assumed to grow at constant crack opening displacement (COD) φ=φc and the creep strain ∈t at the crack tip is assumed to be φ/h, where the gauge length is a material constant. The COD-based theory indicates that the incubation and failure timest i,t fare controlled by the stress intensity factorK at large stresses, but by the net stress at very low stresses. A weakness of the theory is that it neglects primary-creep effects: these have to be absorbed by modifying the secondary-creep index. If this is done, then comparison with two independent experiments shows moderately good agreement with the COD-based theory for botht iandt f.

An investigation into the effect of thickness on the fracture behaviour of compact tension specimens

Abstract: An experimental investigation into the fracture behaviour of 1 Cr Mo V compact tension specimens is described. The plane strain fracture toughness of 64.2 MN/m3/2 is compared with the fracture toughness determined from compact tension specimens of thickness 50 mm, 25 mm, 13 mm, 6 mm, and 3 mm.

Material scale length as a measure of fracture toughness in fracture mechanics of plastic materials

Abstract: An approach is suggested for describing the fracture toughness of relatively tough materials, in particular, low-strength steels It is shown that the fracture toughness of such materials is characterized by a material scale length {ie185-1} or {ie185-2} (K-cohesion modulus, KIC-critical stress intensity factor) not only within the framework of LEFM, but also in the case of large-scale yielding of materials

A finite element investigation of stable crack growth in anti-plane shear

Abstract: Although the anti-plane strain case is of minor practical value in engineering applications, such an idealization facilitates mathematical investigations of strain and displacement fields accompanying extending cracks. This paper presents finite element solutions to anti-plane strain crack propagation problems and contrasts the numerical results with available analytic solutions in an effort to assess the accuracy of the numerical procedures. The nature of dominant strain singularities for stationary and moving cracks, the question of stableversus unstable or catastrophic crack growth and the implications of various proposed fracture criteria are discussed.