Measurement of mixed-mode fracture parameters near cracks in homogeneous and bimaterial beams

An investigation of deformation fields and evaluation of fracture parameters near mixed-mode cracks in homogeneous and bimaterial specimens under elastostatic conditions is undertaken. A modified edge notched flexural geometry is proposed for testing bimaterial interface fracture toughness. The ability of the specimen in providing a fairly wide range of mode mixities is demonstrated through direct optical measurements and a simple flexural analysis. A full field optical shearing interferometry called Coherent Gradient Sensing (CGS) is used to map crack tip deformations in real time. Experimental measurements and predictions based on beam theory are found to be in good agreement. Also, for a large stiffness mismatch bimaterial system, the interface crack initiation toughness is evaluated as a function of the crack tip mode mixity.     

Analysis of a mixed mode fracture specimen: the asymmetric double cantilever beam

An asymmetric double cantilever beam (ADCB) is a simple but effective specimen for the measurement of polymer/polymer and polymer/non-polymer bimaterial interface fracture toughness. In order to characterize fully the bimaterial interface strength, and to control the crack trajectory, the critical energy release rate, G _c, and the phase angle, , of the applied stress field as functions of loading and geometry of the specimen should be obtained. For most practical cases, has to be evaluated numerically. In this work, a boundary element analysis is carried out to obtain G and for the ADCB specimen at different material and geometry combinations. An expression for the energy release rate, G, based on Kanninen's beam on elastic foundation model is compared with the numerical results. Limitations on the use of the ADCB specimen are also discussed.     

A single leg bending test for interfacial fracture toughness determination

A single leg bending test is described and its suitability for interfacial fracture toughness testing is evaluated. The test specimen consists of a beam-type geometry comprised of two materials, one top and one bottom, with a split at one end along the bimaterial interface. A portion of the bottom material in the cracked section of the beam is removed and the geometry is loaded in three-point bending. Thus, the reaction force of the support at the cracked end is transmitted only into the material comprising the top portion of the beam. The test is analyzed by a crack tip element analysis and the resulting expressions for energy release rate and mode mixity are verified by comparison with finite element results. It is shown that, by varying the thicknesses of the two materials, the single leg bending test can be used to determine the fracture toughness of most bimaterial interfaces over a reasonably wide range of mode mixities.     

Creep crack growth in brittle materials

During steady state crack growth by diffusive cavitation at grain boundaries, crack tip fields are relaxed due to the presence of a cavitation zone. In the present analysis, analytic solutions for the actual crack tip stress fields and the crack velocity in the presence of cavitation zone consisting of continuously distributed cavities ahead of the crack tip are derived using the smeared volume concept. Results indicate that the r ^–1/2 singularity is now attenuated to r ^{–1/2 +} (0<<1/2) singularity. The singularity attenuation parameter is a function of the crack velocity and material parameters. The crack growth rate is related to the mode I stress intensity factor K by K ² at relatively high load, K ⁿ at intermediate load, and approaches zero at small load near K _th. Meanwhile, the cavitation zone extends further into the material due to the stress relaxation at the crack tip and the subsequent stress redistribution. Such relaxation effects become very distinct at low crack velocity and low applied load. Key words: Creep crack growth, brittle material, diffusive cavity growth, sintering stress, crack tip stress field.     

Analysis of beam-type fracture specimens with crack-tip deformation

A novel bi-layer beam model is developed to account for local effects at the crack tip of a bimaterial interface by modeling a bi-layer composite beam as two separate shear deformable beams. The effect of interface stresses on the deformations of sub-layers, which is referred to as the elastic foundation effect in the literature, is considered in this model by introducing two interface compliance coefficients; thus a flexible joint condition at the crack tip is considered in contrast to the rigid joint condition used in the conventional bi-layer model. An elastic crack tip deformable model is presented, and the closed-form solutions of local deformation at the crack tip are then obtained. By applying this novel crack tip deformation model, the new terms due to the local deformations at the crack tip, which are missing in the conventional composite beam solutions of compliance and energy release rate (ERR) of beam-type fracture specimens, are recovered. Several commonly used beam-type fracture specimens are examined under the new light of the present model, and the improved solutions for ERR and mode mixity are thus obtained. A remarkable agreement achieved between the present and available solutions illustrates the validity of the present study. The significance of local deformation at the crack tip is demonstrated, and the improved solutions developed in this study provide highly accurate predictions of fracture properties which can actually substitute the full continuum elasticity analysis such as the finite element analysis. The new and improved formulas derived for several specimens provide better prediction of ERR and mode mixity of beam-type fracture experiments.*Author for correspondence (E-mail address: qiao@uakron.edu)     

A new criterion for the prediction of crack development in multiaxially loaded structures

In many cases the lifetime of technical structures and components is depending on the behaviour of cracks. Due to the complex geometry and loading situation in real-world structures cracks are often subjected to a superposition of normal, in-plane and out-of-plane loading. In this paper a new criterion for 3D crack growth under multiaxial loading, that means superposition of the fracture modes Mode I, II and III, is described. The criterion allows the prediction of three-dimensional crack surfaces advancing from arbitrary 3D crack fronts with the help of the two deflection angles ₀ and ₀. The underlying theory for the development of this new criterion is described in detail.     

Dynamic crack growth along an elastoplastic bimaterial interface

Summary The near-tip stress and deformation rate fields of a crack dynamically propagating along an interface between dissimilar elastic-plastic bimaterials are presented in this paper. The elastic-plastic materials are characterised by theJ ₂-flow theory with linear plastic hardening. The solutions are assumed to be of variable-separable form with a power-law singularity in the radial direction. Two distinct solutions corresponding to the tensile and shear solutions exist with slightly different singularity strengths and very different mixities at the crack tip. The phenomenon of discrete and determinate mixities at the interfacial crack tip is confirmed in dynamic crack growth. This is not an artifact of the variable-separable solution assumption, arising from the linear-hardening material model. The dynamic crack analysis shows that the mixity of the near-tip field is mainly determined by the given material parameters and affected slightly by the crack propagation velocity. A significant variation of the mixity is observed near to the coalescing point of the tensile and shear solutions. The strength of the singularity is almost determined by the smaller strain-hardening alone, and dynamic inertia decreases the stress intensity. The asymptotic solutions reveal that the crack propagation velocity changes only the stress field of the tensile mode significantly. With increasing the crack propagation velocity, the stress singularity of the tensile solutions decreases obviously and the stress triaxiality at the tip (=0) falls considerably at the unity effective stress. These observations imply that the fracture toughness of the interface crack under tensile mode may be significantly higher than that under quasi-static conditions.     

Neutron diffraction texture study of deformed uranium plates

The texture of two depleted uranium (DU) samples, labelled DUWR and DUWR2, were studied by neutron diffraction. DUWR was prepared by warm rolling of a cast ingot, and DUWR2 was prepared by adding 20% tensile strain to the warm-rolled DUWR. Complete three-dimensional orientation distribution functions were determined using four neutron pole figures for the DUWR, and using six neutron pole figures for the DUWR2 sample, by the WIMV method of the program popLA. The textures of the two samples were essentially identical to each other. They could be described by a twisted helical density tube spiralling continuously along the -axis of the Euler space. The projection of the backbone of the density tube along the -axis cast a linear shadow running parallel to the diagonal of the - plane, which could be defined by a =+90° (and =+270°) relation. The helical tube was confined within narrow -angle limits, from 14° to 30° with the peak orientation at (103) 0 10. The diffraction patterns of the DUWR2 sample were measured from the normal direction to the rolling surface of the sample, up to the scattering angle of 108° using a 0.15 nm neutron beam. The Rietveld profile refinement using the textured diffraction pattern was quite satisfactory when the texture effect to the entire diffraction profile was corrected for by the corresponding pole density from the inverse pole figure.     

Fatigue crack growth behaviour of tungsten carbide-cobalt hardmetals

Fatigue crack propagation studies have been carried out on a range of WC-Co hardmetals of varying cobalt content and grain size using a constant-stress intensity factor double torsion test specimen geometry. Results have confirmed the marked influence of mean stress (throughK _max), which is interpreted in terms of static modes of fracture occurring in conjunction with a true fatigue process, the existence of which can be rationalized through the absence of any frequency effect. Dramatic increases in fatigue crack growth rate are found asK _max approaches that value of stress intensity factor ( 0.9K_IC) for which static crack growth under monotonic load (or static fatigue) occurs in these materials. Lower crack growth rates, however, produce fractographic features indistinguishable from those resulting from fast fracture. These observations, and the important effect of increasing mean free path of the cobalt binder in reducing fatigue crack growth rate, can reasonably be explained through a consideration of the mechanism of fatigue crack advance through ligament rupture of the cobalt binder at the tip of a propagating crack.     

The ac field around a plane crack in a metal surface when the skin depth is large

This paper considers the solution of the skin-effect or Helmholtz equation, ²=k ², for the two-dimensional flow of a uniform alternating current perturbed by a plane crack of uniform depth. Herek is the ratio of crack depthd to skin depth . When the skin depth is large compared with the crack depth andk f 0, the quasi-static approach to this problem ignores the terms on the right-hand side and constructs solutions from Laplace's equation which are essentially dc solutions and are correct to orderk. In this paper we consider behavior near the limit when the skin depth is large and give solutions which are correct to orderk ². In an example we relate the results to the interpretation of readings from an ac potential difference instrument applied to the measurement of surface-breaking cracks.     

Acoustic emission and fatigue crack growth in rigid polyurethane foam

Compact tension specimens of a rigid polyurethane foam have been tested in fatigue and crack growth has been monitored visually and by means of acoustic emission (AE). During the load cycle it has been found possible to resolve the AE activity into four regions: the crack faces un-sticking, fracture events at or close to peak load, a period of zero AE just after peak load, and AE associated with crack closure lower down the unloading part of the cycle. The fracture AE has been found to increase rapidly with crack length — consistent with a seventh power dependence on K — and to occur during every cycle at high K values, but to be absent in an increasingly greater proportion of cycles as K is decreased below about 40 kPa m^1/2. AE data obtained on samples in which crack growth occurred across the layers of foam, through the high density inter-layer skins, show that the technique is very sensitive to the crack retardation effect associated with these skins well before this retardation is detectable visually.     

A simplified approach for ductile failure analysis of semi-elliptical surface cracks

This paper presents a new simplified approach for ductile failure analysis of semi-elliptical surface cracks under uniform tension by representing the load as a multiplication of two separate functions; a crack geometry function and a material deformation function. Experimental data of specimens with wide range of crack depth, crack width, and thickness are used in the implementation of this approach. The semi-elliptical surface crack is treated as an equivalent single edge crack. An appropriate form for such a treatment is carefully selected and studied. Both the geometry and deformation functions for the studied data are developed. For the first time, an _pl value is developed for such a complex geometry. The existence of load separation, an equivalent one-dimensional crack length, and an _pl value may allow the elastic-plastic fracture parameter J to be evaluated using a single specimen for this geometry. Both the geometry function _pl and are also developed using Mattheck et al. limit load formula which is based on the Dugdale model. They agree well with those developed from the experimental data within the tested range. Finally, a key curve is developed and used in the prediction of the load-displacement records.     

On approach of crack tip energy release rate for a semi-permeable crack when electromechanical loads become very large

This paper presents an investigation on the approach of the crack tip energy release rate (ERR) for a semi-permeable crack full with air/vacuum or Silicon oil when the electromechanical loads become very large. Numerical results for a central semi-permeable crack, respectively, in seven kinds of piezoelectric ceramics are compared with those for a central impermeable crack when the mechanical loads vary from 50 to 100 MPa and the electric loads are fixed to be 1 MV/m, 0, and –1 MV/m, respectively, within the range of practical interest. It is verified that McMeekings statement (2004): as the electromechanical loads become very large, the crack tip ERR approaches the values associated with an impermeable crack is actually valid under very large mechanical and positive electric loads. However, under very large mechanical and negative electric loads, the approach is quite different showing large discrepancies between the calculated values for the semi-permeable crack and those for an impermeable crack in all seven kinds of piezoelectric ceramics. This means that his statement is not valid when the electric loads are negative even though the mechanical loads still remain very large although, mathematically, McMeekings statement is correct if McMeekings statement: very large is replaced by infinitely large. Moreover, under purely mechanical loads his statement is uncertain, depending on which kind of piezoelectric ceramic is used. It is concluded that, generally speaking, the crack tip ERR for a semi-permeable crack does not approach the values associated with an impermeable crack, depending on the direction of the electric loads with respect to the poling axis. Physically, this is because of the inherent piezoelectric effect that yields the surface charges distributed on the crack surfaces for a semi-permeable crack under the mechanical loads, whereas on the surfaces of an impermeable crack the unphysical charge-free condition leads to incorrect estimations: the applied mechanical loads do not yield any surface charges on the crack surfaces. The influence of the permittivity of medium inside the semi-permeable crack gap on McMeekings statement is discussed too. It is found that Silicon oil yields larger discrepancies than air from those for an impermeable crack.     

On the elasticT-term of a main crack induced by near tip microcracks

In the expansion form of the stress field near a crack tip, the nonsingular and constant stress acting parallel to the crack plane is called the elasticT-term, which is very important in fracture analysis. The elasticT-term of a main crack induced by near tip microcracks is analyzed. The original problem considered consists of a main crack accompanied by near tip microcracks, which are loaded remotely by the first three terms of the crack tip stress field expansion parameterized by stress intensity factorsK _I ,K _II , and the nonsingular stress, i.e., theT-term,. With the principle of superposition, the problem can be reduced to a system of Fredholm integral equations which can be solved numerically. After obtaining the solution, the induced elasticT-term is evaluated. Several typical numerical examples are given and the results are shown in Figures, from which some useful discussion and conclusions are obtained.     

Plane stress deformation zones at crack tips in polycarbonate

The plastic deformation produced crack tips in polycarbonate (PC) films stretched in tension, has been characterized by optical and transmission electron microscopy. An extensive and diffuse region of deformation is formed in unannealed specimens. Within this zone the ratio (v _f) of local film thickness to the (undeformed) thickness far away from the crack varies gradually both along and across the zone. The minimum ratio of 0.5 occurs at the crack tip. In contrast to this behaviour, films annealed for a short time just below the glass transition temperature T _g showed a highly localized response, the plastic strain being confined to a well-defined flame shaped deformation zone (DZ) ahead of the crack. Within most of this DZ, v _f is constant at 0.7, rising to 1 over a distance of 10 m at the zone tip, and falling to 0.5 over a distance of 4 m around the crack tip. Bi-refringence measurements show that a high degree of molecular orientation occurs within the zone. These experiments support the idea that an increase in the localization of the plastic strain response upon annealing below T _g is responsible for the embrittlement of PC by such heat treatment.     

A mechanical model of fatigue crack propagation. Report 2

Conclusions The proposed model of fatigue crack propagation based on the solution of the cyclic elastoplastic problem of the stress-strain state [1] makes it possible to take into account the effect of the triaxial stress state on the deformation of the material at the crack tip. The proposed algorithm of calculations of the state of damage on the basis of the principle of linear damage summation and also the agreement between the calculated and experimental data confirm the assumption on the controlling role of low-cycle damage in the mechanics of crack propagation in cyclic loading described from phenomenological positions. The main advantages of the proposed model are:The possibilities of calculating endurance in crack propagation or calculating the crack propagation rate for cases in which the variation of the range of the stress intensity factor along the crack length in structural members takes place at a variable loading asymmetry;the possibilities of describing the effect of loading asymmetry on the fatigue crack-propagation rate using only the strain criterion (Coffin's equation) since the range of the plastic strain intensity at the crack tip is, as shown in [1], a function of not only the range of the stress intensity factor K but also of its maximum value K_max;the possibilities of describing the dependence of K_th on loading asymmetry based on the assumption on the constancy of the size of the structural element for the given material;the possibilities of describing the crack propagation rate in all the three sections of the dL/dN=f(K) diagram, starting with the values K similar to K_th and ending with the value of K at which monotonic quasistatic fracture becomes the controlling process.Translated from Problemy Prochnosti, No. 8, pp. 14–18, August, 1985.     

Slow-crack propagations through bimaterial interfaces studied by scanning electron microscopy

The scanning electron microscope (SEM) is used for the study of slow crack propagation through a bimaterial interface. This work is concerned with the variation of crack velocity, the variation of crack tip opening angle (CTOA) and the stress intensity factor (K) at the crack tip, and the investigation of crack arrest phenomena at the bimaterial interface. It was observed that the crack accelerates to a maximum velocity as the crack tip approaches the interface and then decreases rapidly to a minimum value at the interface. The interface acts as a decelerator to crack propagation. The position and the value of the maximum velocity depends on the mechanical properties of two phases and specimen configuration. The crack propagates at a constant CTOA until it arrests at the interface. During the crack-arrest time the CTOA increases rapidly to a limiting value. Then the crack passes across the interface and propagates in the next phase with almost the same CTOA as the initial crack in phase I. The stress intensity factor,K, increases to a maximum value near the bimaterial interface.     

Analysis of a wavy crack in sandwich specimens

A crack in a brittle adhesive layer joining two substrates can grow in a variety of ways. The crack can grow along one of the interfaces, within the adhesive or alternate between the two interfaces. In this paper, we consider a crack that grows along an alternating path between the two interfaces. A quantitative analysis of this elastic problem is carried out using the finite element method to predict the wavelength of the alternating crack. The joint is loaded remotely by the singular stress field for a cracked homogeneous solid, parameterised by K _I and K _II , and by an in-plane tensile residual stress ₀ in the layer, parallel to the interface. The induced interfacial stress intensity factor and its phase angle are evaluated and used to predict the onset of kinking out of the interface. The wavelength of the alternating crack is found to depend on the elastic mismatch parameters, and , and on the level of residual stress in the layer, parameterised by {ie29-1}, where h is the adhesive layer thickness, {ie29-2} is a modulus quantity and {ie29-3} is the toughness of the interface.     

Effect of mode mixity on K-dominance and three dimensionality in cracked plates

The method of Coherent Gradient Sensing (CGS) in transmission, in conjunction with two and three dimensional finite element methods, is used to study the effect of mode mixity on crack tip stress fields. Using a two dimensional finite element analysis the outer bounds of the region of K-dominance were determined. A three dimensional finite analysis was utilized to study the effect of mode mixity on the three dimensional nature of the stress field in the immediate vicinity of the crack tip and to obtain an inner bound of the region of K-dominance. It was noted that increasing mode mixity leads to an increased rotation of the three dimensional zone, keeping its shape and size unchanged. In contrast, the region of K-dominance is seen to dramatically depend on mode mixity, both in shape and size. In addition, an analysis of the CGS interferograms was conducted to obtain an estimate of the regions of K-dominance experimentally. A least squares fit data analysis technique was used to extract fracture parameters, namely the stress intensity factors K _I, K _II and subsequently the crack tip phase angle, . The data points used for the least square fitting were obtained from the determined regions of K-dominance. The same fracture parameters were also evaluated from the finite element analysis, and good agreement was found between experimental measurements and finite element predictions.     

Interaction of phase-shifted fields of two single-turn coils situated above a conducting medium

An analytical solution is obtained for the problem of the interaction of two phase-shifted electromagnetic fields generated by two coaxial single-turn coils carrying alternating currents of the same frequency, but of different amplitudes and nonzero phase difference, . Two cases are considered: coils situated above a conducting half-space and above a two-layer medium. Numerical results show that is the most important parameter. If the values of and of the other parameters are chosen properly, then the curve representing the change in impedance can lie in any quadrant of the complex plane. These results can be used for developing more sensitive and more selective eddy current testing methods.