The interaction of mode I crack with multi-inclusions in a three-phase model

An approximately close form solution has been developed for mode I crack interacting with multi-inclusions in composite materials. The crack-tip stress intensity factor is evaluated in a three-phase model, which combines the present knowledge that the inclusions only in the immediate neighborhood of the crack-tip have strong effect on the stress intensity factor and that the far inclusions have an overall effects which can be estimated by effective properties of the composites. As validated by numerical examples, the solution has good accuracy for a wide range of the modulus ratios between the inclusion and matrix material.     

Application of an elastoplastic boundary-element method to some fracture-mechanics problems

The boundary-integral equation (BIE) method for 3D elastic fracture mechanics has been extended to the elastoplastic problem. The formulation makes use of a special elastic Green's function for the crack, thereby eliminating the need to model the crack itself. Application of the general formulation is made to problems of localized or limited plasticity. Such problems occur through the local yield of stress concentrations, together with the plastic field of the crack tip. In these problems, the elastic stress intensity factor still provides a useful characterization for cyclic-crack-growth predictions. This paper reports on an accurate and efficient calculation procedure for crack-tip stress intensity factors for cracks in welds and prestressed bolt holes, where uncracked plastic strains are important. The use of the new algorithm for crack-tip plasticity modeling is explored for small- and large-scale plasticity conditions.     

The Stress Intensity Factor of an Edge Dislocation Near an Elliptically Blunted Crack Tip

The stress field around the tip of an elliptically blunted crack induced by an edge dislocation has been obtained in closed form, from which the mode I and mode II stress intensity factors induced by the edge dislocation are obtained. The solutions apply to the edge dislocation either emitted from crack-tip surface or originated elsewhere, and for the dislocation located anywhere around the crack tip. The effects of the crack length, the crack-tip bluntness, the origination and position of the dislocation on the stress intensity factors are examined.     

A model on twinning-induced crack kinking out of a metal-ceramics interface

A continuum model is proposed to study the effects of deformation twinning on interface crack kinking in metal/ceramics layered materials. At the final stage of material failure, plastic work hardening exhausts and lattice rotation becomes main mechanism after competing with dislocation gliding. The crack-tip plasticity is established in terms of the second gradient of microrotation due to the coupling effect of the twins. The formed twinning structures not only shield the crack tip, but inhibit further dislocation emission by increasing the near-tip stress levels. A Dislocation-Free Zone (DFZ) can exist in the immediate vicinity of the tip. The model is based on the equivalence of the stresses derived from twin-based crack-tip plasticity, macroscopic plasticity and elasticity on the boundary. The two-parameter characterization of near-tip stress fields is used for the outer plastic zone to account for constraint effects. Crack kinking out of the interface follows the direction of the maximum flow stress from the crack-tip plasticity. The DFZ size and the crack-tip shielding ratio, as well as the kink angle, are obtained for various values of low hardening exponents and crack-tip constraints.     

Fracture mechanics parameters for cracks on a slightly undulating interface

Typical bimaterial interfaces are non-planar due to surface facets or roughness. Crack-tip stress fields of an interface crack must be influenced by non-planarity of the interface. Consequently, interface toughness is affected. In this paper, the crack-tip fields of a finite crack on an elastic/rigid interface with periodic undulation are studied. Particular emphasis is given to the fracture mechanics parameters, such as the stress intensity factors, crack-tip energy release rate, and crack-tip mode mixity. When the amplitude of interface undulation is very small relative to the crack length (which is the case for rough interfaces), asymptotic analysis is used to convert the non-planarity effects into distributed dislocations located on the planar interface. Then, the resulting stress fields near the crack tip are obtained by using the Fourier integral transform method. It is found that the stress fields at the crack tip are strongly influenced by non-planarity of the interface. Generally speaking, non-planarity of the interface tends to shield the crack tip by reducing the crack-tip stress concentration.     

The shielding effects of the crack-tip plastic zone

In this paper we demonstrate that a plastically deformed zone around a stressed crack tip can be, mechanically, identified with an inclusion of transformation strain by means of Eshelby equivalent inclusion method. Thus, the shielding effect of the plastic zone can be quantitatively evaluated by the present transformation toughening theory. A closed-form solution to determine the change in the stress intensity factor induced by the plastic zone is given both for plane stress and plane strain mode I cracks under small-scale yielding conditions. By using the present solution, the effects of the strain-hardening behavior of the material, the plane stress and plane strain states and the T-stress on the crack-tip shielding effects are identified.     

The Effect of a Plastically Deformed Zone Near Crack Tip on the Stress Intensity Factors

A plastically deformed particle ahead of a crack-tip is treated as an equivalent transformation inclusion by means of Eshelby equivalent inclusion theory. A general solution to determine the effect of the plastically deformed particle on the stress intensity factor of mode I crack is obtained.     

Estimating the importance of cyclic thermal loads in thermo-mechanical fatigue

A method for evaluating the effect of cyclic thermal loading on crack tip stress fields is developed. In its development, advantage is taken of the periodic nature of fatigue loading and only harmonic loadings are evaluated. Formulating the problem in this way permits the extraction of time as an explicit variable and replaces its role with a dependence on the frequency of the thermal loading. The means for evaluating the effect of periodic loadings on crack tip stress fields is the stress intensity factor which is calculated from numerically defined stress and displacement fields using a path independent integral. Results obtained indicate that stress intensity factors of cracked components exposed to thermal fatigue conditions have a significant dependence on the frequency of the thermal cycle and the crack geometry. Numerical estimates for mode I thermal stress intensity have been obtained using thermal fatigue test data for a titanium alloy and can be as high as 25 percent of the critical mode I mechanical stress intensity.     

SGBEM analysis of crack-particle(s) interactions due to elastic constants mismatch

The effects of elastic constants mismatch on the interaction between a propagating crack and single or multiple inclusions in brittle matrix materials are investigated using numerical simulations. The simulations employ a quasi-static crack-growth prediction tool based upon the symmetric-Galerkin boundary element method (SGBEM) for multiregions, a modified quarter-point crack-tip element, the displacement correlation technique for evaluating stress intensity factors (SIFs), and the maximum principal stress criterion for crack-growth direction. It is shown that, even with this simple method for calculating SIF, the crack-growth prediction tool is both highly accurate and computationally effective. This is evidenced by results for the case of a single inclusion in an infinite plate, where the SGBEM results for the SIFs show excellent agreement with known analytical solutions. The simulation results for crack growth and stress intensity behaviors in particulate media are very stable. The crack-tip shielding and amplification behaviors, as seen in similar studies using other numerical approaches, can be clearly observed.     

A mixed mode fatigue crack closure model

Fatigue crack closure conditions leading to mixed mode crack-tip stress states are discussed. A closure model based on contact between impinging fracture surface asperities is introduced. Asperity angle, magnitude of mode II interference, friction between contacting surfaces and distance of the contact surfaces from the crack-tip are features included in the model. The magnitudes of mode I and mode II stress intensity factors due to closure contact are found to vary substantially with asperity angle. Also, because of a reversal of friction force direction during cycle loading, the stress intensity factors exhibit a complex behavior. During the closure phase of the loading cycle, the mode II contribution is found to be quite significant. For loading through an entire cycle, which includes both the closure and crack open phases, nonproportional stress states are developed. Also, it is concluded that the mixed mode states developed could provide the conditions required for crack branching.     

Mode I plane stress crack-tip constraint for elastic-plastic materials with different strain hardening

Finite element analyses and simulations have been undertaken to investigate the triaxial constraint in the crack-tip regions of a stationary crack and a steady-state growing crack under mode I plane stress for elastic-plastic materials with different strain hardening. The results show that the triaxial constraint in the crack-tip region is independent of specimen geometry, and material strain hardening, both for a stationary and an extending crack quasi-statically. The triaxial constraints for the various configurations examined are in better accordance with those required by the HRR solution for a stationary crack, which defines the low and similar constraints in crack-tip regions for different material strain hardening in the plane stress case. Along the entire ligament ahead of a crack tip, the constraint level transites gradually from that defined by the HRR solution within the near tip zone to that characterized by the stress intensity factor K _I in the far field.     

Thermoelastic analysis for an opening crack in an orthotropic material

The thermoelastic analysis of an opening crack embedded in an orthotropic material is made under applied uniform heat flux and mechanical loadings. To simulate the case of an opening crack filled with a medium, a thermal-medium crack model is proposed. The thermally permeable and impermeable cracks are the limiting ones of the proposed thermal-medium one. The crack-tip thermoelastic fields induced by a crack in an orthotropic material are determined in closed forms. The elastic T-stress can be also obtained explicitly. The effects of applied mechanical loadings and the thermal conductivity of crack interior on the heat flux at the crack surfaces and the mode-II stress intensity factor are investigated through numerical computations. The obtained results reveal that an increase of the thermal conductivity of crack interior decreases the mode-II stress intensity factor. And when an applied mechanical loading is increasing, the mode-II stress intensity factor is rising.     

Effects of plastic anisotropy on crack-tip behaviour

For a crack in a homogeneous material the effect of plastic anisotropy on crack-tip blunting and on the near-tip stress and strain fields is analyzed numerically. The full finite strain analyses are carried out for plane strain under small scale yielding conditions, with purely symmetric mode I loading remote from the crack-tip. In cases where the principal axes of the anisotropy are inclined to the plane of the crack it is found that the plastic zones as well as the stress and strain fields just around the blunted tip of the crack become non-symmetric. In these cases the peak strain on the blunted tip occurs off the center line of the crack, thus indicating that the crack may want to grow in a different direction. When the anisotropic axes are parallel to the crack symmetry is retained, but the plastic zones and the near-tip fields still differ from those predicted by standard isotropic plasticity.     

Propagation of fatigue cracks from notches

Abstract

The traditional design approaches to fatigue at notches, based on stress level–endurance relationships, are briefly reviewed. It is shown, by considering crack propagation from notches and invoking a change in control mode from notch plasticity to crack-tip plasticity, that a critical stress condition can be obtained which must be exceeded if the crack is to propagate to failure. The traditional techniques are then reinterpreted and explained by this propagation method. An example is given of crack growth from a sharp defect at a weld toe. It is shown that the integration of an elastic fracture mechanics growth law can reproduce stress range–cycles to failure data for this situation. There are, however, complexities of stress analysis and crack shape. A simple treatment of residual stresses affecting the threshold and slow–growth regimes, shows some promise as a technique for accounting for residual stresses.

MST/70     

Rotation at the crack tip under uniform heat flow in an infinite medium

A complex analysis of rigid body rotation is presented. The crack-tip rotation for a line crack subjected to steady uniform heat flow is obtained in terms of thermal stress intensity factor in shear mode of the crack, the material and thermal parameters and coordinates of points close to the crack tip. The shear strip configuration is analysed on the basis of rotation and displacement at the end of the shear strip.     

Mixed-mode thermoelastic fracture analysis of orthtropic composites

This study demonstrates ability to determine the in-plane stress intensity factors, K _I and K _II, simultaneously under mixed-mode conditions in orthotropic composites by the combined use of least-squares, stress representations which are valid away from the crack and distant measured temperatures. Recognizing the stresses near a crack-tip are dominated by the stress intensity factors, it has not been uncommon to neglect the higher-order stress terms when evaluating these factors. However, and among other considerations, it is typically difficult to obtain accurate temperature information very near the crack-tip. It can therefore be advantageous to employ measured data which originate away from the crack and to retain six to eight terms in the stress functions when evaluating the stress intensity factors. On the other hand, errors in K _I and/or K _II can be appreciable if only the r^–1/2 terms are employed with distant input information.     

Boundary element analysis of fracture mechanics in anisotropic bimaterials

This paper presents a boundary element formulation for the analysis of linear elastic fracture mechanics problems involving anisotropic bimaterials. The most important feature associated with the present formulation is that it is a single domain method, and yet it is accurate, efficient and versatile. In this formulation, the displacement integral equation is collocated on the uncracked boundary only, and the traction integral equation is collocated on one side of the crack surface only. The complete Green's functions for anisotropic bimaterials are also derived and implemented into the boundary integral formulation so that discretization along the interface can be avoided except for the interfacial crack part. A special crack-tip element is introduced to capture exactly the crack-tip behavior.Numerical examples are presented for the calculations of stress intensity factors for a straight crack with various locations in infinite bimaterials. It is found that very accurate results can be obtained by the proposed method even with relatively coarse discretization. Numerical results also show that material anisotropy can greatly affect the stress intensity factor.     

A plastic flow-induced fracture theory for fatigue crack growth

A plastic flow-induced fracture theory for fatigue crack growth is presented. A new formulae for the fatigue stress intensity threshold and the fatigue crack growth rate law are derived by applying the principle of energy conservation in considering the fatigue crack growth process in the presence of local plastic flow ahead of the crack-tip. The present theory predicts not only the fatigue crack growth rate being just proportional to the rate of creation of dislocation at the crack-tip, but also the fatigue stress intensity threshold, which can be determined according to the applied fatigue stress amplitude and the characteristic size of microstructural fracture process ahead of the crack-tip, and can account for the fatigue crack growth characteristics at both low and high levels of applied fatigue stress intensity amplitude. All the results are universal and agree with the existing empirical results and experimental observations.     

Implications of interface friction for crack growth in fibre-reinforced metal matrix composites by three-dimensional finite element modelling

A three-dimensional finite element model of a compact tension specimen consisting of a Ti-6Al-4V matrix reinforced with unidirectional, continuous SiC fibres under monotonic and cyclic loading has been developed. This has enabled true Coulomb frictional interface sliding resulting from thermal residual stresses to be modelled. The results, which include the action of individual bridging fibres close to the crack-tip, are compared to results from a two-dimensional weight function method which uses fibre-induced bridging tractions on the crack face based on a constant interface strength. Reasonable agreement was found between the two methods used. An investigation of the fibre stresses showed that together with normal crack bridging tractions a strong bending component is present in the fibres which also affects crack opening and could affect the mode of fibre failure. The influence of processing induced thermal residual stresses and friction at the fibre-matrix interface on the crack growth behaviour during monotonic and cyclic loading has been assessed. It was found that the bridging fibres strongly reduce the crack-tip stress intensity factor. The thermal residual stresses produce a crack-tip opening load in the absence of an external load and have an influence on the crack-tip load ratio. The effect of the crack-tip load ratio on the fatigue threshold has a significant impact on the likelihood of crack arrest.     

Modeling of crack growth through particulate clusters in brittle matrix by symmetric-Galerkin boundary element method

The interaction of a crack with perfectly bonded rigid isolated inclusions and clusters of inclusions in a brittle matrix is investigated using numerical simulations. Of particular interest is the role inclusions play on crack paths, stress intensity factors (SIFs) and the energy release rates with potential implications to the fracture behavior of particulate composites. The effects of particle size and eccentricity relative to the initial crack orientation are examined first as a precursor to the study of particle clusters. Simulations are accomplished using a new quasi-static crack-growth prediction tool based on the symmetric-Galerkin boundary element method, a modified quarter-point crack-tip element, the displacement correlation technique for evaluating SIFs, and the maximum principal stress criterion for crack-growth direction prediction. The numerical simulations demonstrate a complex interplay of crack-tip shielding and amplification mechanisms leading to significant toughening of the material.