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.     

Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered.     

Simulation of crack growth in composite material shell structures

This paper implements a domain integral energy method for modelling crack growth in composite material shell structures using the finite element method. Volume integral expressions to evaluate the dynamic energy release rate in a through‐thickness three‐dimensional crack are derived. Using the domain integral, the energy release rate computation is implemented in the DYNA3D explicit non‐linear dynamic finite element analysis program wherein crack propagation is modelled by releasing the constraints between initially constrained node pairs. The implementation enables the program to either determine the energy resistance response for the material (provided experimental data is available) or predict the rate of crack propagation in shell structures. The numerical implementation was verified by simulating mode I and mode III slow crack growth problems in semi‐infinite transversely isotropic media, for which analytic solutions are available. Oscillations of energy following the release of nodal constraints as the crack propagates in discrete increments were suppressed using light mass proportional damping and a moving averaging scheme. Copyright © 2004 John Wiley & Sons, Ltd.     

Fatigue crack growth simulation in heterogeneous material using s-version FEM

A fully automatic fatigue crack growth simulation system is developed using the s-version Finite Element Method (s-FEM). This system is extended to fractures in heterogeneous materials. In a heterogeneous material, the crack tip stress field has a mixed-mode condition, and the crack growth path is affected by inhomogeneous materials and mixed-mode conditions. Stress intensity factors (SIFs) in the mixed-mode condition are evaluated using the virtual crack closure method (VCCM). The criteria for the crack growth amount and crack growth path are based on these SIFs, and the growing crack configurations are obtained. At first, the basic problem is solved, and the results are compared with some results available in the literature. It is shown that this system gives an adequate accurate estimation of the SIFs. Then, two-dimensional fatigue crack growth problems are simulated using this system. The first example is a plate with an interface between hard and soft materials. The cracks tend to grow in soft materials through the interface. A second example is a plate with distributed hard inclusions. The crack takes a zig-zag path by propagating around the hard inclusions. In each case, the crack growth path changes in a complicated manner. Changes of the SIFs values are also shown and discussed.     

Fatigue crack growth resistance of ECAPed ultrafine-grained copper

This work presents the experimental results of fatigue crack growth resistance of ultrafine-grained (UFG) copper. The UFG copper has a commercial purity level (99.90%) and an average grain size of 300 nm obtained by a 8-passes route Bc ECAP process. The fatigue propagation tests are conducted in air, at load ratios R = K_min/K_max varying from 0.1 to 0.7, on small Disk Shaped CT specimens. Both stage I and stage II regime of growth rate are explored. Results are partially in contrast with the few experimental data available in the technical literature, that are by the way about high purity UFG copper. In fact, the present material shows a relatively high fatigue crack resistance with respect to the unprocessed coarse-grained alloy, especially at high values of applied stress intensity factor ΔK. At higher R-ratio a smaller threshold intensity factor is found, together with a lower stage II fatigue crack growth rate. The explanation of such crack growth retardation is based on a diffuse branching mechanism observed especially at higher average ΔK.     

Fatigue crack growth of a metastable austenitic stainless steel

The fatigue crack growth behavior of an austenitic metastable stainless steel AISI 301LN in the Paris region is investigated in this work. The fatigue crack growth rate curves are evaluated in terms of different parameters such as the range of stress intensity factor ΔK, the effective stress intensity factor ΔK_eff, and the two driving force parameter proposed by Kujawski K¹.The finite element method is used to calculate the stress intensity factor of the specimens used in this investigation. The new stress intensity factor solution has been proved to be an alternative to explain contradictory results found in the literature.Fatigue crack propagation tests have been carried out on thin sheets with two different microstructural conditions and different load ratios. The influence of microstructural and mechanical variables has been analyzed using different mechanisms proposed in the literature. The influence of the compressive residual stress induced by the martensitic transformation is determined by using a model based on the proposal of McMeeking et al. The analyses demonstrate the necessity of including K_max as a true driving force for the fatigue crack growth. A combined parameter is proposed to explain the effects of different variables on the fatigue crack growth rate curves. It is found that along with residual stresses, the microcracks and microvoids are other factor affecting the fatigue crack growth rate in the steel studied.     

Fatigue crack growth simulation in a first stage of compressor blade

A first-stage rotary compressor blade of a Model GE-F6 gas turbine failed due to vibration in early March 2008. Initial investigations showed that pitting on the pressure side of the blade caused micro cracks, leading to larger cracks due to high cycle fatigue. To assess this failure, a series of experimental, numerical, and analytical analyses were conducted. Fractography of the fractured surface of the blade indicated that two semi-elliptical cracks incorporated and formed a single crack. In this study, static and dynamic stress analyses were performed in Abaqus software. Moreover, fracture mechanics criterion was accomplished to simulate fatigue crack growth. This was carried out using a fracture analysis code for 3-dimensional problems (Franc3D) in two states. Firstly, stress intensity factors (SIFs) for one semi-elliptical surface crack and then SIFs for two semi-elliptical surface cracks were taken into account. Finally, the Paris and Forman–Newman–De Koning models were used to predict fatigue life. Since stress level and crack shape in both conditions are the same and the SIF at the crack tip reaches the fracture toughness of the blade, SIFs results indicate that insertion of a second crack has no effect on the final SIF, however, the second crack facilitates the process of reaching the critical length. So, fatigue life in two-crack condition is less than in the one-crack state.     

Fatigue crack closure determination by means of finite element analysis

Plasticity-induced crack closure is an observed phenomenon during fatigue crack growth. However, accurate determination of fatigue crack closure has been a complex task for years. It has been approached by means of experimental and numerical methods. The finite element method (FEM) has been the principal numerical tool employed. In this paper the results of a broad study of fatigue crack closure in plane stress and plane strain by means of FEM are presented. The effect of three principal factors has been analysed in depth, the maximum load, the crack length and the stress ratio. It has been found that the results are independent of maximum load and the crack length, and there exists a direct influence of the stress ratio. This relation has been numerically correlated and compared with experimental results. Differences have also been established between opening and closure points and between the different criteria employed to compute crack closure.     

Fatigue crack growth behavior of silica particulate reinforced epoxy resin composite

In the present work, fatigue crack growth tests of epoxy resin composite reinforced with silica particle under various R-ratios were carried out to investigate the effect of R-ratio on crack growth behavior and to discuss fatigue crack growth mechanism. Crack growth curves arranged by ΔK showed clear R-ratio dependence even under no crack closure, where the values of ΔK_th were 0.82 and 0.33 MPa √m for R = 0.1 and 0.7 respectively. However, crack growth curves arranged by K_max merged into almost one curve regardless of R-ratio, which indicated that crack growth behavior of the present composite was time-dependent. The value of K_max,th were in the range from 0.78 to 1.12 MPa √m. In situ crack growth observation revealed the crack growth mechanism: micro-cracking near the interface between silica particle and resin matrix occurs ahead of a main crack and then micro-cracks coalesce with a main crack to grow. The crack path was in the epoxy matrix, which was consistent with the time-dependent crack growth.     

Prediction of shape change of corner crack by fatigue crack growth circles

As a fatigue crack grows, its shape changes. Conventional method for predicting the shape change typically requires the computation of several hundred increments to get accurate results. In this paper, a new finite element simulation technique that uses fatigue crack growth circles is developed. Since the circles are perpendicular to the new crack front as well as to the current crack front, they can represent the real path of the fatigue crack well and yield more accurate results. The new technique is validated by applying it to the case of a quarter-elliptical corner crack in a plate with an open hole subjected to tension loading. The effect of the Paris–Erdogan exponent is also investigated.     

Fatigue crack initiation and growth of 16MnR steel with stress ratio effects

The effects of stress ratio on the fatigue crack initiation and growth were investigated by a newly developed unified model, which is based on the cyclic plasticity property of material and a multiaxial fatigue damage criterion in incremental form. The cyclic elastic-plastic stress-strain field was analyzed using the general-purpose finite element software (ABAQUS) with the implementation of a robust cyclic plasticity theory. The fatigue damage was determined by applying the calculated stress-strain responses to the incremental fatigue criterion. The fatigue crack growth rates were then obtained by the unified model. Six compact specimens with a thickness less than 3.8 mm were used for the fatigue crack initiation and growth testing under various stress ratios (−1.0, 0.05, 0.1, 0.2, 0.3 and 0.5). Finite element results indicated that crack closure occurred for the specimen whose stress ratio was less than 0.3. The combined effects of accumulated fatigue damage induced by cyclic plastic deformation and possible contact of cracked surfaces were responsible for the fatigue crack initiation and growth. The predicted results agreed with the benchmark mode I fatigue crack growth experiments very well.     

Fatigue crack initiation and crystallographic crack growth in an austenitic stainless steel

The lifetime of a specimen under cyclic loading is usually limited by the initiation and growth of microcracks. Experimental results for the austenitic stainless steel X6 CrNiNb 18-10 are given and a model for crack initiation and crack growth in the first grains of a polycrystalline aggregate is proposed.     

Numerical analysis of the influence of crack surface roughness on the crack path

The influence of the 3D frictional crack surface interaction on the fracture mechanical parameters as well as on the crack path is numerically investigated. For the solution of the boundary value problem the 3D dual boundary element method in terms of the discontinuous formulation is utilized. This method is especially suited for contact problems because it directly deals with the discontinuities at the crack surfaces. The contact problem is solved by the application of the penalty method. Coulomb’s frictional law is utilized for the consideration of the dissipative nature of friction. For discrete steps within one load cycle the stress intensity factors are determined by an extrapolation procedure from the stress field. Based on the analysis of a load cycle, the cyclic stress intensity factors are obtained. For the simulation of crack propagation an implicit time integration scheme of a crack propagation law implemented in terms of a predictor-corrector scheme is applied. The influence of the crack surface roughness on the crack path is shown by numerical examples.     

A multifractal analysis of fatigue crack growth and its application to concrete

As is well-known, strength of materials is influenced by the specimen or structure size. In particular, several experimental campaigns have shown a decrease of the material strength under static or fatigue loading with increasing structure size, and some theoretical arguments have been proposed to interpret such a phenomenon. As far as fatigue crack growth is concerned, limited information on size effect is available in the literature, particularly for so-called quasi-brittle materials like concrete. In the present paper, by exploiting concepts of fractal geometry, some definitions of fracture energy and stress intensity factor based on physical dimensions different from the classical ones are discussed. A multifractal size-dependent fatigue crack growth law (expressing crack growth rate against stress intensity factor range) is proposed and used to interpret relevant experimental data related to concrete.     

Variable amplitude crack growth in notched specimens

Predictions of variable amplitude fatigue crack growth in notched tensile specimens at an elevated temperature and relative high loads were conducted. The predictions were based on constant amplitude fatigue data and mean crack growth rates were calculated. Crack closure levels were calculated by comparison of crack closure free experimental data obtained with the so called constant K_I,max-method and nominal data. Also, numerical simulations of the closure level throughout the specimens were performed. Although experimental data showed rather large a scatter it was concluded that variable amplitude crack growth rates can be predicted with reasonable agreement using constant amplitude fatigue data. Also, crack growth rates cannot be predicted by LEFM in the inelastic notch affected zone, even if absence of crack closure is assumed.     

Fatigue crack growth in SiC particulates reinforced Al matrix graded composite

The SiC/Al graded composite was fabricated by powder metallurgy processing and its fatigue crack growth behavior was studied. The volume percentage of SiC particulates was distributed from 5 to 30% layer by layer on the cross section. Since the aluminium was dissolved together, there was no evident interface between the two layers with different volume fraction of SiC particulates. Fatigue crack growth was in direction of from 5 to 30% SiC layers under sinusoidal wave-form. The retardation of fatigue crack growth was found when crack propagated from low volume fraction of SiC to high volume fraction of SiC. The crack deflection and branching between two layers were observed, which decreased crack growth rates. In view of crack tip driving force, the plasticity mismatch between the layers shielded crack tip driving force, i.e. decreased the effective J-integral at the tip of the crack as the plastic zone of the crack tip spread from the weaker material into the stronger material.     

Fatigue crack growth in asphalt and asphalt-interfaces

Fatigue cracking due to traffic load is a major factor in road damage. Therefore, durability and lifetime prediction of roads plays a substantial role for road maintenance and cost planning. This paper reports a study of fatigue crack performance of solid asphalt and asphalt–asphalt interfaces by means of the wedge-splitting test. Instead of beams and the three- or four-point bending test, the wedge splitting method was used for the first time to observe crack growth on bituminous drilling cores. Samples of solid asphalt and samples with asphalt-interfaces were tested. One group of asphalt interfaces was untreated and the other was sandblasted before spreading the top layer during manufacturing. Due to the temperature dependency of material properties of asphalt, the tests were performed in a compact climate chamber at −10°, 0° and +10 °C. The challenge of determining the crack length and the crack tip were detected with an optical measurement system and picture analysis after testing. The results prove that the wedge splitting method is a highly practicable and repeatable method for crack growth testing of bituminous materials.     

Singular and non-singular approaches for predicting fatigue crack growth behavior

In this work, three classes of mechanisms that can cause load sequence effects on fatigue crack growth are discussed: mechanisms acting before, at or after the crack tip. After reviewing the crack closure idea, which is based on what happens behind the crack tip, quantitative models are proposed to predict the effects at the crack tip due to crack bifurcation. To predict the behavior ahead of the crack tip, a damage accumulation model is proposed. In this model, fatigue cracking is assumed caused by the sequential failure of volume elements or tiny εN specimens in front of the crack tip, calculated by damage accumulation concepts. The crack is treated as a sharp notch with a small, but not zero radius, avoiding the physically unrealistic singularity at its tip. The crack stress concentration factor and a strain concentration rule are used to calculate the notch root strain and to shift the origin of a modified HRR field, resulting in a non-singular model of the strain distribution ahead of the crack tip. In this way, the damage caused by each load cycle, including the effects of residual stresses, can be calculated at each element ahead of the crack tip using the correct hysteresis loops caused by the loading. The proposed approach is experimentally validated and extended to predict fatigue crack growth under variable amplitude loading, assuming that the width of the volume element broken at each cycle is equal to the region ahead of the crack tip that suffers damage beyond its critical value. The reasonable predictions of the measured fatigue crack growth behavior in steel specimens under service loads corroborate this simple and clear way to correlate da/dN and εN properties.     

Multiple random crack propagation using a boundary element formulation

This paper proposes a boundary element method (BEM) model that is used for the analysis of multiple random crack growth by considering linear elastic fracture mechanics problems and structures subjected to fatigue. The formulation presented in this paper is based on the dual boundary element method, in which singular and hyper-singular integral equations are used. This technique avoids singularities of the resulting algebraic system of equations, despite the fact that the collocation points coincide for the two opposite crack faces. In fracture mechanics analyses, the displacement correlation technique is applied to evaluate stress intensity factors. The maximum circumferential stress theory is used to evaluate the propagation angle and the effective stress intensity factor. The fatigue model uses Paris’ law to predict structural life. Examples of simple and multi-fractured structures loaded until rupture are considered. These analyses demonstrate the robustness of the proposed model. In addition, the results indicate that this formulation is accurate and can model localisation and coalescence phenomena.     

Fast multipole DBEM analysis of fatigue crack growth

A fast multipole method (FMM) based on complex Taylor series expansions is applied to the dual boundary element method (DBEM) for large-scale crack analysis in linear elastic fracture mechanics. Combining multipole expansions with local expansions, both the computational complexity and memory requirement are reduced to O(N), where N is the number of DOF. An incremental crack-extension analysis based on the maximum principal stress criterion and the Paris law is used to simulate the fatigue growth of numerous cracks in a 2D solid. Some examples are presented to validate the numerical scheme.