Terms Of Stress Intensity Factor Research Articles

Evaluation of stress intensity factors by multiple reference state weight function approach

The advantages of expressing stress intensity factors in terms of weight functions are widely appreciated. However, the main obstacle in the determination of weight functions has been the definition of the crack opening displacement (COD) field. There are several approaches currently used, the most common is assuming an expression to define COD in terms of the crack dimensions and stress state. A recent development in weight function application simplifies the tranditional stress intensity factor calculation. This development uses more than one reference stress intensity factor and associated stress field to eliminate the need to assume a COD field. This paper describes current application of COD for weight functions and explains the full advantage of adopting a multiple reference state (MRS) weight function approach.

EDGE-CRACKED PLATE WITH ONE FREE AND ONE CONSTRAINED BOUNDARY SUBJECTED TO SUDDEN CONVECTIVE COOLING

The transient thermal stress edge crack problem for an elastic strip with free and fully constrained boundaries is considered. The plate is suddenly subjected to convective cooling on the face containing the edge crack while the other face is insulated. The solution of the problem is obtained by using the superposition technique results in a singular integral equation that is solved numerically. The results of the transient temperature and thermal stress distributions in the uncracked strip are presented. Also, numerical results are obtained for the stress-intensity factor in terms of the Fourier number, crack length, and different values of the Biot number.

Fracture of CFRP containing impregnated fibre bundles

The fracture behaviour of carbon-fibre-reinforced plastic composites (CFRP) has been studied by using specimens containing fibre bundles which were impregnated with polymer before being incorporated in an epoxy matrix. The results on CFRP with impregnated bundles show that the impact fracture toughness, the crack growth resistance in terms of stress intensity factor, and the specific work of fracture are enhanced by more than 100%, depending on the impregnant material and fibre volume fraction, as compared to the control composites without bundle impregnation. These beneficial effects are attributed to the increased stability of cracking associated with the bridging of fracture surfaces by the impregnated bundles which act as single fibres of huge diameter effectively increasing the fibre pull-out length. Statistical analysis also demonstrates that bundle impregnation can improve the tensile strength of the bundle as well as the uniformity of strength distribution.

Multiple void-crack interaction

This paper presents a method for fracture analysis of a general two-dimensional system containing multiple holes, or voids, and cracks. The superposition technique is used to break the problem into a number of single-hole and single-crack problems. Each hole problem is modeled using the method of pseudo-tractions, and each crack problem is modeled by a distribution of dislocations. An integral equation approach is developed, based on two types of fundamental solutions, one due to point loads in a solid with a hole and the other due to point dislocations in an infinite elastic body. The resulting integral equations present Cauchy-type singularities only on the crack part of the multiple hole-crack problem. The results in terms of stress intensity factors (SIFs) are presented for a variety of hole-and-crack arrangements, relative sizes of cracks and holes, spacings and crack orientations. The amplification and retardation effects on SIFs are investigated. It is found that the hole-crack arrangements have significant effects on the nature of the amplification or retardation. In the fractured porous elastic medium (modeled as a crack surrounded by holes), amplification or retardation can occur, depending on the relative size of the holes and cracks and the spacing between them. Very strong retardation exists as the spacing becomes small. Some optimal retardations (void toughening) are achieved by adjusting the geometry parameters. An array of periodical crack-hole structure is examined as a numerical example.

Energy release rate of symmetric adhesive joints

A formula is derived for the mixed mode energy release rate of adhesive joints in terms of local stress concentrations σ max and τ max determined by beam theory. The formula G= 1 2 t E′ a σ 2 max 1 2 t G a τ 2 max is equivalent to a similar expression from two-dimensional elasticity theory in terms of the stress intensity factors K I and K II . The equivalence permits explicit determination of the two stress intensity factors K I and K II in terms of the finite stress concentrations σ max and τ max determined by technical beam theory. The reinterpretation of the stress concentration from beam theory in terms of stress intensity factors enables the use of simple beam-type calculations for fracture predictions without the need for a detailed three-dimensional analysis. While the stress concentrations (σ max and τ max increase with decreasing thickness t of the adhesive layer, the energy release rate ℷ is nearly independent of t. The centrally loaded symmetric lap joint is analysed in detail and explicit results for the mixed mode energy release rate ℷ and the corresponding load phase angle Ψ = tan −1(K II/K I) are given. For long joints Ψ = 49°, independent of adhesive properties, increasing for shorter joints.

コンクリート面ＦＲＰライニングの接着強度

Recently, it has been reported that the corrosive damage of concrete structures occurs at many waste water treatment facilities. In order to prevent this problem, FRP lining is being applied on the concrete surface. In this application, the lined FRP should show a fairly high adhesive strength to the concrete surface.Generally a Kenken-type adhesive strength tester is used to evaluate the adhesive strength between them. But it was revealed that this method could not evaluate such an adhesive strength precisely. Therefore, in this report, it has been studied to develop a new practical way to evaluate this adhesive strength.In this new method, the real adhesive strength between lined FRP and cement mortar was measured in such a way that only a vertical peeling force was loaded to the end of the FRP. The results obtained were discussed in terms of stress intensity factor K as a fracture mechanical parameter.

Boundary element analysis of plane anisotropic bodies with stress concentrations and cracks

The quadratic isoparametric element formulation of the boundary element method (BEM) for full anisotropy in two-dimensions is developed in this paper. It may be used for the analysis of composite structures. Quarter-point traction-singular crack-tip elements are introduced for treating fracture problems and analytical expressions for the stress intensity factors in terms of the BEM computed tractions or displacements on these elements are derived for cracked anisotropic bodies. This enables the fracture parameters to be accurately obtained in a quick and direct manner. A set of stress concentration problems and two other crack problems are considered to demonstrate the versatility and the modelling efficiency of this numerical method. Excellent agreement between the BEM results and those in the literature is obtained even with relatively coarse mesh discretisations. Some new results are also presented for the problem of an inclined crack near the free surface of a semi-infinite graphite epoxy sheet.

The mechanics of matrix cracking in fiber reinforced ceramic composites containing a viscous interface

A detailed fracture mechanics analysis of matrix cracking in a fiber reinforced ceramic composite is presented for the case where the fiber—matrix interface exhibits viscous flow as can be the case when ceramic composites containing amorphous interfacial layers are subjected to loads at elevated temperatures. The analysis considers the case where matrix cracks are fully bridged by fibers, and the role of the viscous interface is to introduce a time dependence into the stress-intensity formulations. Such time-dependence arises because the bridging fibers are able to pull out of the matrix by viscous interfacial flow, with the result that the crack opening, as well as the actual (or shielded) matrix crack-tip stress-intensity factor, increase with time under the action of a constant externally applied load to the composite. The differential equation governing the mechanics of the fiber pull-out is derived. This is then applied to obtain expressions for the time-dependence of the crack opening and the effective crack-tip stress-intensity factor in terms of material and microstructural factors. These expressions predict that the matrix crack will exhibit stable crack growth, with the crack growth rate being essentially crack length (and time) independent and a function only of the applied stress and of material and microstructural factors. It is also shown that the composite lifetime is independent of the sizes of pre-existing cracks and is dependent only on a critical microstructure dependent flaw size, applied stress and microstructural factors.

Stress Intensity Factor and Energy Release Rate for Interfacial Cracks Between Dissimilar Anisotropic Materials

The framework of fracture mechanics analysis for interface cracks as outlined by Willis (1971) is recast into a form resembling the customary framework for cracks in homogeneous materials. Based on the complex-valued “stress concentration vector” introduced by Willis, a new definition of real-valued stress intensity factors is introduced. The definition is an extension to that for cracks in homogeneous materials and reduces to the one given recently by Rice for isotropic interface cracks. In terms of the new stress intensity factors, tractions ahead of the crack and the relative crack face displacements given by Willis are rewritten into real-form expressions. The energy release rate obtained by Willis is also expressed into a real form in terms of the stress intensity factors. The validity of using the stress intensity factors as parameters controlling fracture is discussed along the line advanced by Rice (1988).

Rigid body rotation at the tip of a slant crack in an infinite plate

Using Kolosov-Muskhelishvili relations of stresses the rigid body rotation is obtained in the form of complex potentials. The rotation at a point near the tip of a slant crack is expressed in terms of stress intensity factors and the coordinates (r, ι) of the point. The relation of rigid body rotation near the crack tip are used to describe some features of mode I and mode II crack tip plastic zone. The rotation field surrounding the tip of a slant crack in infinite plate is obtained and its properties are discussed.

Application of a Singular Integral Equation Method to a Crack Branching at an Interface

The plane elastostatic problem of a crack branching at a fiber/matrix interface in carbon fiber reinforced composites is considered using a micromechanical model. The model is a crack which originates in one half-plane and branches at a bimaterial interface of a bonded plane consisting of an isotropic and an orthotropic half-planes. The method of continuous distribution of dislocations reduces the problem to a system of a simultaneous singular integral equations of the second kind, which is solved nemerically by use of the Lobatto-Jacobi integration rule. The singular stress field at the crack tips is investigated in terms of stress intensity factors and crack opening displacements.

Finite element method simulation of crack propagation in a brittle microcracking solid

A finite element method simulation of crack propagation was used to study the effects of microcracking at facets as a damage process in brittle composites and the consequence for material toughness. A continuum model for microcracking at grain boundary facets was used in conjunction with the elasticity law. The model accounts for modulus reduction only and neglects residual strain effects. The nonlinear finite element equations were solved incrementally. The solution for each load increment was obtained using a Newton iteration method. Crack propagation was achieved by successive tip node relaxation upon satisfaction of a critical energy release rate criterion. The crack was allowed to propagate by approximately ten times the height of the initial microcrack zone. A substantial increase of the height of the damage zone prior to steady state propagation was observed. The applied stress intensity factor was increased to sustain crack growth, and crack tip shielding occurs as a result of the wake. The amount of toughening was up to 40% in terms of stress intensity factor and was influenced by the parameters of the constitutive law. Stress, strain, and microcrack density distributions near the tip of the steadily growing crack are discussed.

Numerical estimation of stress intensity factors in patched cracked plates

The fatigue and fracture performance of a cracked plate can be substantially improved by providing patches as reinforcements. The effectiveness of the patches is related to the reduction they cause in the stress intensity factor (SIF) of the crack. So, for reliable design, one needs an accurate evaluation of the SIF in terms of crack, patch and adhesive parameters. In this investigation a finite element technique to compute the SIF through the J- integral for patched cracked plates is presented. TRIM6 and TRUMPL elements of ASKA are employed to model cracked sheet and cracked sheet-adhesives-patch regions, respectively. Path independency of J- integral for unpatched plates is shown by considering many contours. For patched plates, the contours chosen do not enclose the patch-cracked sheet region. The values of SIF's are obtained for unpatched edge-cracked unpatched centre-cracked and patched centre-cracked plates. These values are compared with the analytical and numerical results existing in the literature. This study shows that conventional finite elements can be used to model patched cracks and reasonable estimate of SIF can be made via the J- integral .

Nondestructive evaluation of crack length and stress intensity factor by means of J and M integrals.

For a two-dimensional body with a crack, J integral is described as a function of stress intensity factor, while M integral is expressed in terms of stress intensity factor and crack length. By combining these characteristics with the path-independence of these two integrals, a method was proposed of evaluating crack length and stress intensity factor simultaneously from strain-gage measurements along a given integral path. Engineering applicability of the proposed method was examined by experiments and FEM simulation analysis with a center-cracked panel and a double-edge-cracked panel. Good accuracy was obtained for the stress intensity factor determined form J integral, irrespective of crack length. The crack length evaluation was also satisfactory for long cracks, but relatively poor for short cracks; this resulted form the accuracy of M integral evaluation. Gauss quadrature was found useful for reducing number of measuring points of strain without sacrificing the accuracies of the two quantities.

High strain-rate crack growth in rate-dependent plastic solids

At high crack velocities in metallic materials nearly all plastic strain accumulates at very high strain-rates, typically in the range 10 3 s −1 to 10 5 s −1. At these rates, dislocation motion is limited by dynamic lattice effects and the plastic strain-rate increases approximately linearly with stress. The problem for a crack growing at high velocity is posed for steady-state, small scale yielding in elastic/rate-dependent plastic solids. A general expression is derived for the near-tip stress intensity factor in terms of the remote intensity factor, or equivalently for the near-tip energy release-rate in terms of the overall release-rate. An approximate calculation of the plastic strain-rates provides this relation in analytical form. Imposition of the condition that the near-tip energy release-rate be maintained at a critical value provides a propagation equation for the growing crack. A single, nondimensional combination of material constants emerges as the controlling parameter. Implications for dynamic crack propagation are discussed.

Analytical estimation of stress intensity factors in patched cracked plates

The fatigue and fracture performance of a cracked plate can be substantially improved by providing patches as reinforcements. The effectiveness of the patches is related to the reduction they cause in the stress intensity factor (SIF) of the crack. So, for reliable design, one needs an accurate evaluation of the SIF in terms of the crack, patch and adhesive parameters. In this investigation, a centrally cracked large plate with a pair of symmetric bonded narrow patches, oriented normally to the crack line, is analysed by a continuum approach. The narrow patches are treated as transversely flexible line members. The formulation leads to an integral equation which is solved numerically using point collocation. The convergence is rapid. It is found that substantial reductions in SIF are possible with practicable patch dimensions and locations. The patch is more effective when placed on the crack than ahead of the crack. The present analysis indicates that a little distance inwards of the crack tip, not the crack tip itself, is the ideal location, for the patch.

Extension of Crack Energy Density Concept to Arbitrary Direction and Energy Release Rate to Non-self-similar Crack Growth

Crack energy density is a parameter which was proposed as one of the most important fracture parameters by one of the authors and enables us to make a unified smooth description of fracture mechanics from linear to non-linear problems. In this paper, the crack energy density concept is extended to an arbitrary direction except self-similar direction, the relations between the newly defined parameter eφ and well-known fracture parameters ( Jφ -integral, stress intensity factor) are obtained, and the availability of eφ as fracture criterion to mixed mode crack problems is demonstrated. It is also shown that crack energy density becomes equal to energy release rate in case of elastic problems, therefore, it can be said that the energy release rate to non-self-similar crack growth which has not been solved yet is given by the expression of eφ in terms of stress intensity factors obtained.

Section method for the calculation of stress intensity factors

The section method is proposed for the approximate calculation of stress intensity factors in terms of the mean stress at crack sites and the net section nominal stress. A large number of solutions are shown to be in good agreement with available analytical and numerical solutions. The section method is easy to use for engineers.

Studies on crack growth rate under high temperature creep, fatigue and creep-fatigue interaction—II: On the role of fracture mechanics parameter [formula omitted

For high temperature creep, fatigue and creep-fatigue interaction, several authors have recently attempted to express crack growth rate in terms of stress intensity factor K I = α aσ g , where a is the equivalent crack length as the sum of the initial notch length a 0 and the actual crack length a ∗ , that is, a = a 0 + a ∗ . On the other hand, it has been shown by Yokobori and Konosu that under the large scale yielding condition, the local stress distribution near the notch tip is given by the fracture mechanics parameter of aσ gƒ(σ g ), where a is the cycloidal notch length, σ g is the gross section stress and ƒ(σ g ) is a function of σ g . Furthermore, when the crack growth from the initial notch is concerned, it is more reasonable to use the effective crack length a eff taking into account of the effect of the initial notch instead of the equivalent crack length a. Thus we believe mathematical formula for the crack growth rate under high temperature creep, fatigue and creep-fatigue interaction conditions may be expressed at least in principle as function of a effσ g , σ g and temperature. In the present paper, the geometrical change of notch shape from the instant of load application was continuously observed during the tests without interruption under high temperature creep, fatigue and creep-fatigue interaction conditions. Also, the effective crack length a eff was calculated by the finite element method for the accurate estimation of local stress distribution near the tip of the crack initiated from the initial notch root. Furthermore, experimental data on crack growth rates previously obtained are analysed in terms of the parameter of a eff σ g with gross section stresses and temperatures as parameters, respectively.

Studies on crack growth rate under high temperature creep, fatigue and creep-fatigue interaction—I: On the experimental studies on crack growth rate as affected by [formula omitted] and temperature

Many experimental studies have been reported on the measurements of crack growth rate and the observation of crack growth behaviour under high temperature creep, fatigue and creep-fatigue interaction in literatures. However, many of them have been done in air atmosphere. Furthermore, in many of them the measurements of the crack growth rate have been carried out by interrupting intermittently the running of the testing machine. In such experiments the complex effects due to the atmosphere, the interruption period and the corresponding unloading operation for the crack length measurement might have been involved. In the present paper in order to eliminate such effects, series of experimental studies on the crack growth behaviour under creep, fatigue and creep-fatigue interaction conditions on 304 stainless steel have been carried out by using high temperature microscope and observing the crack length continuously during running the test without interruption in vacuum of 10 −5mm Hg. Among the results, it was found that crack growth rates on a time basis, da/dt, under high temperature creep and creep-fatigue interaction conditions can not be described in terms of solely elastic stress intensity factor k i or only net section stress σ net, both independent of gross section stress σ g. The relation between crack growth rate and stress intensity factor under high temperature fatigue condition changes with some trend according to gross section stress at lower K I level and it can be approximately described in terms of stress intensity factor K I only, at higher K I level. The threshold stress intensity factor and the threshold net section stress under high temperature creep, fatigue and creep-fatigue interaction conditions appears to be almost independent of temperature.