Edge-cracked Strip Research Articles

Weight function for an edge-cracked rectangular plate

In-situ edge-cracked rectangular plates (width H, length L) comprised of first-year sea ice on McMurdo Sound were tested during recent field trips to Antarctica, and expressions applicable for a wide range of crack lengths are sought for the stress-intensity-factor (SIF), and crack-opening-displacement (COD), given that the edge-crack is subjected to arbitrary crack-face loading. A weight function able to provide the required accurate wide-ranging expressions for an edge-cracked rectangular plate (ECRP) subject to arbitrary crack-face loading is developed in this paper, given H/L=0.25,0.5,1.0,1.5,2.0, and 4.0. The accuracy of the ECRP weight function is assessed by making comparisons with the edge-cracked strip subjected to pure bending (using H/L=4.0), using the essentially identical SIF and CMOD results independently obtained by Kaya and Erdogan (1987) and Bakker (1995). Comparisons are also made with the SIF values obtained by Fett (1999) for the ECRP subjected to pure bending (for H/L=1.0,1.5, and 2.0). The double-cantilever-beam (DCB) study in Foote and Buchwald (1985) is used to assess the accuracy of the ECRP SIF for the case of concentrated loads at the crack mouth, for H/L=1/4 and H/L=1/2. For the same loading and H/L=4, the study by Kaya and Erdogan (1980) of an edge-cracked infinite strip is used to assess accuracy. For crack-face concentrated loading acting at X/L=yi, given H/L=4, the accuracy of the ECRP SIF weight function is assessed by examining associated data reported by Kaya and Erdogan (1978).

Fracture Toughness Calculation by Movable Cellular Automata Method

Fracture toughness calculation by Movable Cellular Automata (MCA) method is demonstrated in this study in order to verify the validity of application of MCA method to the fracture problems. Two different geometries: edge-cracked strip and center cracked plate tension specimen have been considered to simulate numerically, which make place in real experiments. Soda-Lime silica glass for brittle material, AISI 1040 Steel and Aluminum Alloy 2024 for ductile materials were used, respectively. Fulfillment of basic principles of fracture mechanics has been checked. In MCA method, special fracture criterion is used to describe the process of crack propagation and critical stress and displacement was obtained, which are used as input data for evaluating the fracture toughness. In comparisons with table data, the results showed the sufficient agreement, which states the facility of the MCA method in application to the fracture problems.

Intensity factors for some common piezoelectric fracture mechanics specimens with conducting cracks or electrodes

This paper provides the stress and electric field intensity factors for some common piezoelectric fracture mechanics specimens with electrically conducting cracks or electrodes. Firstly, the solution for a vertical crack with electrically conducting boundary condition on its surfaces is established for a piezoelectric strip under combining mechanical and electrical loads. Then, a surface-cracked strip, a double edge cracked strip, and a center-cracked strip, subjected to uniform stress and electric field loads simultaneously, are investigated. Also investigated is an edge-cracked strip under pure bending and uniform electric field loads. The influence of piezoelectric effect on the stress and electric field intensity factors is found to be insignificant, suggesting that the stress intensity factors of piezoelectric materials under mechanical loads can be obtained in a same way as ordinary brittle solids, and the electric field intensity factors of piezoelectric materials under electric field loads can be obtained in a same way as ordinary dielectrics. However, the results show that the mechanical loads can produce electric field intensity factors, and the electric field loads can produce stress intensity factors in piezoelectric materials, due to the fact that the medium has finite size.

A piezoelectric material strip with a crack perpendicular to its boundary surfaces

A cracked piezoelectric material strip under combining mechanical and electrical loads is considered. The crack is vertical to the top and bottom edges of the strip. The edges of the strip are parallel to the x-axis and perpendicular to the z-axis. When a piezoelectric ceramic is poled, it exhibits transversely isotropic behavior. Among many possible poled axis orientations, a particular orientation when the poling direction lies parallel to x-axis is examined in this paper. Both impermeable crack and permeable crack assumptions are considered. Numerical results are included for three kinds of fracture mechanics specimens, namely an edge-cracked strip, a double edge-cracked strip, and a center-cracked strip, subjected to uniform tensions and uniform electric displacement loads simultaneously, at the far ends. In addition, an edge-cracked strip under pure bending and uniform electric displacement loads at the far ends is also investigated in this paper.

Closed-form solution for the size of plastic zone in an edge-cracked strip

This paper is concerned with the problem of plastic zone at the tip of an edge crack in an isotropic elastoplastic strip under anti-plane deformations. By means of complex potential and Dugdale model, the stress intensity factor and the size of plastic zone are obtained in closed-form. Furthermore, the analytic solutions for an edge crack at the free boundary of a half-space and a semi-infinite crack heading towards a free surface are determined as the limiting cases of the strip geometries.

Interfacial crack propagation under various mode-mixes

Initiation and propagation of interfacial crack along bimaterial interface are considered in this study. A biaxial loading device for a single specimen is used for obtaining a wide range of mode-mixities. The specimen is an edge-cracked bimaterial strip of glass and epoxy; the biaxial loading device, being capable of controlling displacements in two perpendicular directions, is developed. A series of interfacial crack initiation and propagation experiments are conducted using the biaxial loading device for various mixed modes. Normal crack opening displacement (NCOD) is measured near crack front by a crack opening interferometry and used for extracting fracture parameters. From mixed mode interfacial crack initiation experiments, large increase in toughness with shear components is observed. The behavior of interfacial crack propagation analyzed as a function of mode-mix shows that initial crack propagation is delayed with increase of mode-mixity, and its velocity is increased with positive mode-mixity but decreased with negative case. However, it is found that crack propagation is less accelerated with positive mode-mixity than the negative mode-mixity, which may be caused by contact and/or effects of friction between far field and near-tip field along the interfacial crack.

THERMAL FRACTURE OF CERAMICS WITH TEMPERATURE-DEPENDENT PROPERTIES

Some aspects of thermal fracture mechanics of ceramics with temperature-dependent properties are studied. It is first shown that the square-root singular field still prevails in the crack tip region. However, the size of the K-dominant zone may be influenced by the effect of temperature-dependent properties. Then the steady thermal stress intensity factor in an edge-cracked strip is calculated. The results show that the stress intensity factor, which is zero when the temperature dependence of material properties is neglected, can exceed the fracture toughness of the ceramic when the temperature dependence of the material properties is considered. Finally, a temperature-dependent crack-bridging law is proposed to study the R-curve behavior of pofycrystalline ceramics subjected to elevated temperatures.

An assessment of geometry effects on plane stress fatigue crack closure using a modified strip-yield model

Using a modified strip-yield model, plane stress constant-amplitude fatigue crack growth simulations under conditions of small-scale yielding were performed for the edge-cracked strip in tension, the edge-cracked strip in bending, and the compact tension specimen with load ratios R = 0.5, 0.0, −1.0and−2.0. From these simulations, fatigue crack opening loads were predicted as a function of crack length. Geometry, loading type and crack length were observed to affect crack opening loads. The geometry-loading dependence was particularly evident for extended fatigue crack growth. Geometry-loading dependence was observed to increase for R < 0. Reductions in the crack opening loads following extended crack growth were also observed. These reductions were demonstrated to occur in the absence of large-scale plasticity in the remaining ligament. A normalized maximum applied stress intensity factor K max/σ o√W, where σ o and W represent the flow stress and specimen width respectively, was demonstrated to represent an approximate measure of small-scale yielding crack closure response similitude under plane stress conditions with R ⩾ 0. When crack opening loads were correlated in terms of this parameter, little geometry-loading dependence was observed.

STRESS INTENSITY RELAXATION AT THE TIP OF AN EDGE CRACK IN A FUNCTIONALLY GRADED MATERIAL SUBJECTED TO A THERMAL SHOCK

We analyze thermal stresses and the stress intensity factor in an edge-cracked strip of a functionally graded material (FGM) subjected to sudden cooling at the cracked surface. It is assumed that the shear modulus of the material decreases hyperbolically with the higher value at the surface exposed to the thermal shock and that the thermal conductivity varies exponentially. Volume fractions of the constituents in a ceramic-metal FGM are then determined with the assumed shear modulus gradient using a three-phase model of conventional composites. The differences between the other assumed material properties and those predicted by the three-phase model are delineated and the applicability of the assumed FGM is discussed. It is shown that the maximum tensile thermal stress in the strip without cracks is substantially reduced by the assumed thermal conductivity gradient and that the magnitude of the compressive stress is increased. A strong compressive zone just away from the thermally shocked surface is devel...

Computation of stress intensity factors for a 2-D body from displacements at an arbitrary location

An approach to stress intensity factor computation is presented which allows accurate estimation using a simple finite element program and a coarse mesh of elements. The stress intensity factor is obtained from what we term the Crack-Displacement (C-D) Factor. This involves the rate of change of displacements with crack length at the same location remote from the crack due to two loading conditions. One loading condition is merely that applied to the cracked body. The other loading condition is a virtual line force applied at the location at which the displacement rates are computed. The accuracy of the procedure is demonstrated for uniform tensile stresses applied to a center-cracked panel and an edge-cracked strip.

Asymptotic solutions for crack closure in an elastic plate under combined extension and bending

A coupled plane-bending problem is considered for an elastic Kirchhoff-Poisson plate containing a through the-thickness or (part-through) surface crack under closure. The stress intensity factors at the ends of the crack are not zero. Asymptotic solutions are derived for cases in which the ratio of the crack length to its depth is large. As is shown, the width of the contact strip decreases as the crack length increases; the limiting contact force and moment distribution may be determined by considering an edge-cracked strip with zero stress intensity factor in the thickness direction. As is also shown, the crack surface interaction in-plane force and bending moment can be derived directly from the initial force and moment distribution acting in the intact plate on the prospective crack line. The same result is valid for a collinear system of cracks; this collinear system may include alternating open and closed crack segments. In addition, the closure stress distribution is determined. For the latter, the width of the contact strip asymptote is derived as a function of the crack length coordinate, and the asymptotic stress distribution is found as a product of the thickness averaged closure stress and a function of a normalized plate thickness coordinate. The latter stress distribution is unique and universal for any slowly curving crack or crack system under closure.

Three-dimensional effects in interfacial crack propagation

The paper describes the use of crack-opening interferometry for examining the variation in normal crack-opening displacements (NCOD) along the front of an interfacial crack in an edge-cracked bimaterial strip under biaxial loading. For the glass/epoxy combination considered here, the crack front was concave in the direction of crack growth, in contrast to previous observations with a glass/polyurethane/glass sandwich specimen and cracks in homogeneous materials. The NCOD were greatest in the interior of the specimen for all mode-mixes considered and the exponents in a power-law fit of NCOD versus distance from the crack front decreased towards the free surface. The exponents varied with mode-mix, suggesting that interfacial crack-front geometries could be similarly affected.

Deformation of an edge-cracked strip subjected to an arbitrary shear surface traction on the crack faces

The displacements and strains due to a shear surface traction acting on the faces of an edge crack in a strip are obtained by using Castigliano's theorem. It is shown that the displacement at a distance larger than the thickness of the strip from the crack becomes essentially a rigid body movement. The solutions obtained provide a basis for measurement of residual shear stress from observations of displacements or strains.

Deformation of an edge-cracked strip subjected to normal surface traction on the crack faces

New solutions for stresses due to a pair of horizontal or vertical forces acting symmetrically on the surface of a strip are obtained and shown to be easier to evaluate than those that are available in the literature. The displacements and strains on the surface due to a normal stress distribution on the faces of a crack in the strip are then obtained by using Castigliano's theorem. It is shown that the displacement at a distance larger than the thickness of the strip from the crack is essentially a rigid body movement. The solutions obtained provide a basis for residual stress measurement from measurement of displacements or strains.

Formula omitted] solutions for an edge-cracked strip

Stress intensity factor solutions for very shallow and very deep cracks in an edge-cracked strip are discussed. Expressions are presented for both cases which appear to be more accurate and easier to apply than those in the literature. Based on the treatment of these two limiting cases an expression is proposed for any ratio of crack size to strip width.

On Consistency Relations in Nonlinear Fracture Mechanics

A simple form of consistency relations between generalized forces and displacements for systems exhibiting power-law behavior is presented. The later discussion focuses on certain details regarding applications of the relations to nonlinear fracture mechanics, emphasizing the finite element analysis of a single edge-cracked strip subjected to remote tension under plane strain conditions.

Significance of the load shift in single-edge notch tension tests

When single-edge-notch (SEN) specimens are tested in tension, the load is usually applied at the extremities of the specimen through single pins aligned along its center line. Upon loading the specimen, an initial positive moment which tends to assist in opening the crack is created. This moment will continue as long as there is no appreciable plastic deformation ahead of the crack and no significant change in the initial specimen geometry. As the load increases, however, the load center line considerably shifts relative to the specimen center line giving rise to a negative bending moment which tends to close the crack. Furthermore, if the specimens are to be made of highly ductile materials (e.g., line-pipe steels), the shift will be much more pronounced; thus leading to substantial discrepancies between theoretically calculated and experimentally obtained crack-opening-displacement (COD) values. The ductile fracture analysis of the edge-cracked strip problem, in general, is based on the assumption of small displacements and rotations in which case reference to the underformed geometry for equilibrium is fully justified. In this paper, it is shown that if one uses small displacement theory to solve such a problem then extreme caution should be exercised in prescribing the nature of the external loads to account for the severe geometrical changes that actually occur during the tests.

A METHOD OF ESTIMATING BIAXIAL FATIGUE GROWTH RATES

—Conventionally, fatigue growth rate data are correlated in terms of the range ΔKof the applied stress intensity factor. It is argued that a correlation involving both ΔKand the constant stress Tclose to the tip of the equivalent elastic crack should be adequate for moderate stress, biaxial fatigue data. Practical application of these ideas would involve the preparation of “T -term” compendia similar to those already available for K -calibrations. “T -term” data are presented for the case of an edge-cracked strip in tension.

Fully Plastic Solutions and Large Scale Yielding Estimates for Plane Stress Crack Problems

Fully plastic plane stress solutions are given for a center-cracked strip in tension and an edge-cracked strip in pure bending. In the fully plastic formulation the material is characterized by a pure power hardening stress-strain relation which reduces at one limit to linear elasticity and at the other to rigid/perfect plasticity. Simple formulas are given for estimating the J-integral, the load-point displacement and the crack opening displacement in terms of the applied load for strain hardening materials characterized by the Ramberg-Osgood stress-strain relation in tension. The formulas make use of the linear elastic solution and the fully plastic solution to interpolate over the entire range of small and large scale yielding. The accuracy of the formulas is assessed using finite element calculations for some specific configurations.

Matched asymptotic expansions in nonlinear fracture mechanics—I. longitudinal shear of an elastic perfectly-plastic specimen

A method of analysis based upon matched asymptotic expansions is proposed for a cracked specimen which is subjected to longitudinal shear (mode III) loading. This gives the small-scale yielding estimate of linear fracture mechanics as a first approximation, and provides systematic refinements which take account of the nonlinear interaction between the elastic and the plastic regions. Explicit solutions can be generated for any specimen which is amenable to a linear elastic analysis. Fracture parameters, such as crack opening displacement and the Jintegral, are expressed as power series in the ratio of applied stress to yield stress, and three terms are given explicitly. These are defined from linear elastic solutions alone. The edge-cracked strip and cracking from a semi-circular notch are studied as examples. Comparison with an exact solution for the former geometry suggests that the three-term expansions give useful results up to 75 % of limit load. The latter example is new and shows the effect of a notch on a crack at loads beyond the normal range of validity of linear elastic fracture mechanics.