Creep behavior of crack near bi-material interface characterized by integral parameters

Creep behavior of crack in dissimilar materials is studied using steady-state C^* path independent integral and ABAQUS finite element code. The specific geometry involves an edge crack parallel to the interface of a bi-material tensile specimen at high temperature. Under extensive creep, the C^* value for the bi-material specimen can be significantly higher than that for the homogeneous specimen. For small-scale creep material mismatch has little influence on the transient integral designated by C_t. The integral parameters C^* or C_t are shown to depend on the inhomogeneity of the system and cannot characterize the creep behavior of cracks.The approach is extended to creep crack growth in a welded compact tension specimen. Modification factors are introduced for different crack and weld interface geometries.     

Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally, the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method (FEM). Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.     

Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally, the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method (FEM). Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.     

Stress intensity factors for anisotropic layered composites: Part II—isolated double periodic cracks

The formulation in Part I (Theoret. Appl. Fracture Mech. 17, 205–219 (1992)) of this work for collinear cracks in alternate layers of an anisotropic laminate is extended to a system where each of the cracked layer contains a periodic array of parallel cracks. These cracks are also collinear such that they are periodic in two mutually perpendicular directions. Finite Fourier transform is applied at discrete points for one of the space variables reducing the problem to a singular integral equation. The unknown is expressible in terms of the crack opening displacement as in Part I. Displayed graphically are the normalized stress intensity factor, effective stiffness of the laminate, and the interlayer stresses. The local stress intensity factor for the double array crack system is always less than that for a single isolated crack depending on the periodicity ratio. The interlayer stresses directly ahead of the crack are elevated, the intensity of which increases with decreasing distance between the crack tip and interface. Increase in the thickness of the adjoining layer tends to decrease the interlayer stresses nearest to the crack tip, a result that is to be expected.     

Stress intensification in cracked shank of tightened bolt

Defects or cracks in the shank of bolts can degrade their load carrying capacity. The ways with which loading and residual stress intensify the crack border stress field can be reflected through the stress intensity factor quantity as defined in the linear elastic fracture mechanics theory. Use is made of the stiffness derivative method where quarter-point singular finite elements are used in the numerical calculation. Improved accuracy is achieved by considering the displacements not only of the main nodes but also of those quarter-point nodes in plane normal and adjacent to the crack.Numerical results are obtained for a semi-elliptical shaped crack in the bolt shank owing to tension, bending, residual stress and stress caused by tightening of the bolt. Maximum value of the Mode I stress intensity factor K_a due to tension or bending could prevail either at the deepest point on the crack border or at the root of the shank where the crack border terminates depending on the aspect ratio of the ellipse. In general, K₁ at the deepest point of crack penetration is larger than that at the free surface for tension and bending for a fixed crack depth with reference to the bolt diameter. Tightening of the bolt tends to increase K₁ at the free surface if the crack depth is small. The opposite is obtained for deeper cracks. Assumed residual stress effect obtained from experimental data is found to have negligible influence on the stress intensity factor when compared with that arising from tensile load.     

Stress intensity factors for interface crack in finite size specimen using a generalized variational approach

A generalized variational approach together with eigenfunction expansion is applied to determine the stress intensity factors for interface crack in finite size specimen. Application is also made of the complex potentials such that a complex stress intensity factor with components corresponding to the Mode I and II stress intensity factors can be identified with one of the leading coefficients in the eigenfunction expansion. Obtained are the numerical values of the stress intensity factors for an interface edge crack in a bimaterial rectangular specimen. The outside boundary is subjected to uniform stress normal and parallel to the crack. Solutions are also obtained for the same crack aand specimen geoinetry is subjected to a pair of equal and opposite concentrated forces along the open end away from the edge crack. The third example pertains to the case of three-point bending where the centre concentrated load is directed along the interface dividing the two materials. Numerical results are obtained for four different combinations of the bimaterial specimen with an interface edge crack.     

Measurement of the Residual Stress Tensor in a Compact Tension Weld Specimen

Neutron diffraction measurements have been performed to determine the full residual stress tensor along the expected crack path in an austenitic stainless steel (Esshete 1250) compact tension weld specimen. A destructive slitting method was then implemented on the same specimen to measure the stress intensity factor profile associated with the residual stress field as a function of crack length. Finally deformations of the cut surfaces were measured to determine a contour map of the residual stresses in the specimen prior to the cut. The distributions of transverse residual stress measured by the three techniques are in close agreement. A peak tensile stress in excess of 600 MPa was found to be associated with an electron beam weld used to attach an extension piece to the test sample, which had been extracted from a pipe manual metal arc butt weld. The neutron diffraction measurements show that exceptionally high residual stress triaxiality is present at crack depths likely to be used for creep crack growth testing and where a peak stress intensity factor of 35 MPa√m was measured (crack depth of 21 mm). The neutron diffraction measurements identified maximum values of shear stress in the order of 50 MPa and showed that the principal stress directions were aligned to within ~20° of the specimen orthogonal axes. Furthermore it was confirmed that measurement of strains by neutron diffraction in just the three specimen orthogonal directions would have been sufficient to provide a reasonably accurate characterisation of the stress state in welded CT specimens.     

A crack perpendicular to and terminating at a bimaterial interface

Using dislocation simulation approach, the basic equation for a finite crack perpendicular to and terminating at a bimaterial interface is formulated. A novel expansion method is proposed for solving the problem. The complete solution to the problem, including the explicit formulae for theT stresses ahead of the crack tip and the stress intensity factors are presented. The stress field characteristics are analysed in detail. It is found that normal stresses {ie27-1} and {ie27-2} ahead of the crack tip, are characterised byQ fields if the crack is within a stiff material and the parameters |p _T | and |q _T | are very small, whereQ is a generalised stress intensity factor for a crack normal to and terminating at the interface. If the crack is within a weak material, the normal stresses {ie27-3} and {ie27-4} are dominated by theQ field plusT stress. This work was supported by the Swedish Research Council for Engineering Sciences.     

Kinking of a crack emanating from the free surface of a beam under pure bending

A perturbation technique developed by Karihaloo et al. is employed to obtain the stress intensity factors at the tip of a kinking crack that emanates from the free surface of a beam under pure bending. Under the condition that the kink extends in the direction of vanishing K₁₁ the crack path is obtained as well as a path stability condition. From conditions on K₁ a material parameter r^* akin to that of Ramulu and Kobayashi's r_c is obtained. By analysis of the slope of the kinking crack a stability condition is obtained corroborating the stability condition from consideration of vanishing K₁₁. It is shown that for a beam in pure bending the nonsingular remote stress term T must be greater than some positive critical value for kinking to occur confirming the results of Sayir and Schindler.     

Comparison of energy release rate and minimum strain energy density for potential failure of composite with bi-material interface

An analytical method is developed to describe the fields of stress and displacement in a bi-material strip specimen with an edge interfacial crack. All of the basic governing equations, boundary conditions on crack surfaces and conditions of continuity along the interface are satisfied by the eigenfunction expansion method. The other boundary conditions are satisfied by the generalized variational principle. The stress intensity factors are calculated for determining the energy release rate and minimum strain energy density factor S_min that is used the strain energy density criterion. Problems with oscillatory singularity and contact zone are discussed. Not only the effects of bi-material modulus ratio, thickness ratio, Poisson's ratio and crack length to S_min, but also the influences of bi-material modulus ratio, thickness ratio to phase angle are presented. Among these parameters, particular situations where S_min become jeopardously high and lead to failure are discussed.     

Residual stresses near a rail end

Stress fields near a cut end of a rail containing longitudinal residual stress typical of roller-straightened rail were studied using analysis and a finite element model. For a self-equilibrating residual stress distribution with equal maximum and minimum stresses, the distance to reach 95% of the mid-rail residual stress field is from 0.7 to 1.8 times the rail height, with the finite element model predicting a length of 1.1 times the rail height. This gives a measure of the accuracy of the simpler analytical models. At the rail end, the longitudinal residual stress goes to zero, and the vertical residual stress near mid-web reaches a maximum of approximately 27 ksi (186 MPa) (1.35 times the maximum mid-rail longitudinal residual stress of 20 ksi, or 138 MPa). The maximum shear stresses are 6 ksi (41 MPa) and −8 ksi (−55 MPa) near the head-web and web-base intersections, respectively, approximately 2 in. (51 mm) from the end of a 7.3 in. (185 mm) high rail. The shear stress is zero at the cut end and in mid-rail. The worst possible end-crack is a horizontal web crack in the vertical residual stress field at the rail end. The stress intensity K_I on such a crack is estimated to reach 20 ksi√in. (22 MPa√m) for cracks 0.5 in. (13mm) long. This is already 0.4 to 0.8 times K_I for carbon and alloy rails, and about 0.5 times K_Ic for a long crack.     

Crack deflection at an interface between dissimilar elastic materials: Role of residual stresses

A crack intersecting an interface between two dissimilar materials may advance by either penetrating through the interface or deflecting into the interface. The competition between deflection and penetration can be assessed by comparison of two ratios: (i) the ratio of the energy release rates for interface cracking and crack penetration; and (ii) the ratio of interface to material fracture energies. Residual stresses caused by thermal expansion misfit can influence the energy release rates of both the deflected and penetrating crack. This paper analyses the role of residual stresses. The results reveal that expansion misfit can be profoundly important in systems with planar interfaces (such as layered materials, thin film structures, etc.), but generally can be expected to be of little significance in fiber composites. This paper corrects an earlier result for the ratio of the energy release rate for the doubly deflected crack to that for the penetrating crack in the absence of residual stress.     

Rail web fracture in the presence of residual stresses

A recent accident involving roller-straighened alloy rail has raised the question of the safety of such rails. This work shows that the residual stresses in roller-straightened rail can indeed self-drive a long web crack. Specifically, the stress intensity K_I due to release of the key component, longitudinal stress, if of the order of the critical stress intensity for initiation K_Ic for both plain carbon and alloy rail. At cut ends, the resulting vertical residual stresses can give rise to K_Ic if there are 0.1–1 in (3–25 mm) cracks. In this work, checks of the existing residual stress data for self-consistency suggest that the data are only accurate within a factor of two. Therefore, a more direct method is proposed for measuring K_I on a web crack by saw-cutting the web.     

An Experimental Study of Mixed Mode Crack Initiation and Growth in Functionally Graded Materials

Quasi-static mixed mode crack initiation and growth in functionally graded materials (FGMs) was studied through fracture experiments on polymer-based FGMs manufactured by selective ultraviolet irradiation poly(ethylene carbon monoxide)—a photo-sensitive copolymer that becomes more brittle and stiffer under ultraviolet irradiation. The objective of the study was to determine whether crack kinking criteria for homogeneous materials, e.g., maximum hoop stress criterion, also hold for FGMs. Single edge notched tension specimens with different spatial variations of Young's modulus, failure stress and failure strain, were tested. Near tip mode mixity was introduced either by inclining the crack to the remote loading direction, as in the case of homogeneous materials, or to the direction of material gradient, or both. A full-field digital image correlation technique was used to measure in real-time the displacement field around the crack tip while it propagated through the graded material, and to extract the fracture parameters of stress intensity factor K _I and K _II , and the T-stress. It was found that the nonsingular T-stress term in the asymptotic expansion for stresses plays a very important role in accurately measuring fracture parameters. It was also found that the maximum tangential stress criterion can be applied to the case of FGMs to predict crack kinking provided that the effect of the T-stress is accounted for and the process zone size is small compared to the intrinsic material gradient length scale. However, for accurate crack path prediction at a length scale comparable to the material gradient, detailed material property information is required. In general, the crack will propagate towards a region that exhibits less fracture toughness, but, unlike the case of homogeneous materials, along a path where K _II is not necessarily equal to zero.     

CONSTRAINTS ON THE CRACK TIP PLASTIC FIELDS UNDER LARGE SCALE YIELD

Plane strain elastic-plastic finite element analyses are used to study the stress, strain fields around a straight crack in power hardening plastic material. Center crack panel (CCP), single edge crack panel (SECP) and double edge crack panel (DECP) tension specimens are analyzed with various crack lengths. Two local constraint parameters, i.e. in-plane stress ratioT _x and out-of-plane constraintT are analyzed, which are defined as tangential stress dividing normal (open) stress and out-of-plane stress dividing the sum of tangential stress and normal stress respectively. Numerical analyses indicate that the two local constraint parameters are nearly independent of the specimen geometry and the loading level in the plastic zone. Methods of estimating two constraint parameters and ways to define the boundary of the blunt zone are given. By using these parameters, the stress distributions in the plastic zone, especially in the blunt zone can be accurately predicted. Project supported by the National Foundation of Distinguished Young Scientists of China (No. 59625510).     

An improved experimental method for the determination of the critical stress intensity factor KIc of brittle materials

The critical stress intensity factor K_Ic is determined by a simple and accurate method, using small test specimens and a simple procedure in this paper.Single edge V-notched tension specimens made of PMMA are subjected to a load which is slowly increased until the crack begins to move from the notch tip. During the crack propagation event shadow patterns at the tip of the crack are recorded in a video recorder. Under these loading conditions, the creating real crack propagate slowly until the crack propagation velocity take an abrupt increase and the entire fracture of the specimen takes place. The stress intensity factor which correspond to the transition from the slow to fast crack speed, is the critical stress intensity factor K_Ic and it can be the fracture toughness of the material.The results are accurate and in good agreement with those values of K_Ic which are calculated by approximate theoretical expressions.The purpose of this paper is to introduce an improved, simple and accurate experimental method for the determination of fracture toughness of brittle materials.     

Singular stress field near the edge of interface of bonded dissimilar materials with an interlayer

For bonded dissimilar materials, the free-edge stress singularity usually prevails near the intersection of the free-surface and the interface. When two materials are bonded by using an adhesive, an interlayer develops between the two bonded materials. When a ceramic and a metal are bonded, the residual stress develops because of difference in the coefficient of thermal expansion. An interlayer may be inserted between the two materials to defuse the residual stress. Stress field near the intersection of the interface and free-surface in the presence of the interlayer is then very important for evaluating the strength of bonded dissimilar materials.In this study, stress distributions on the interface of bonded dissimilar materials with an interlayer were calculated by using the boundary element method to investigate the effect of the interlayer on the stress distribution. The relation between the free-edge singular stress fields of bonded dissimilar materials with and without an interlayer was investigated numerically. It was found that the influence of the interlayer on the stress distributions was confined within a small area of the order of interlayer thickness around the intersection of the interface and the free-surface when the interlayer was very thin. The stress distribution near the intersection of the interface and the free-surface was controlled by the free-edge stress singularity of the bonded dissimilar materials without the interlayer. In this case, the interlayer can be called free-edge singularity-controlled interlayer. If a stress distribution on the interface is known for one thickness of an interlayer h, stress distributions on the interface for other values of h can be estimated.     

Fatigue crack opening stress based on the strip-yield model

The modified strip-yield model based on the Dugdale model and two-dimensional approximate weight function method were utilized to evaluate the effect of in-plane constraint, transverse stress, on the fatigue crack closure. The plastic zone sizes and the crack opening stresses considering transverse stress were calculated for four specimens: single edge-notched tension (SENT) specimen, single edge-notched bend (SENB) specimen, center-cracked tension (CCT) specimen, double edge-notched tension (DENT) specimen under uniaxial loading. And the crack opening behavior of the center-cracked specimen under biaxial loading was also evaluated. Normalized crack opening stresses σ_op/σ_max for four specimens were successfully described by the normalized plastic zone parameter Δω^′_rev/ω^′ considering transverse stress, where Δω^′_rev and ω^′ are the size of the reversed plastic zone at the moment of first crack tip closure and the size of the forward plastic zone for maximum stress, respectively. The normalized plastic zone parameter with transverse stress also was satisfactorily correlated with the behavior of crack closure for CCT specimen under biaxial loading.