Crack Growth Law Research Articles

Cohesive law describing crack growth at iron/precipitate interfaces

Single dislocations and dislocation pile-ups at crystalline interfaces cause stress concentrations. This can lead to decohesion of the interfaces under tensile loading. To describe this decohesion quantitatively, a cohesive law for planar crack growth at iron/precipitate interfaces is developed. This cohesive law is based on a universal description of the adhesive energy for different interfaces. Only a single scaling factor c must be applied to convert the prediction based on this universal adhesive energy into the actual traction-separation behaviour during crack growth. This scaling factor takes into account the atomic strain and relaxations. The cohesive law derived here can be implemented in a Discrete Dislocation Plasticity framework to describe crack growth at a larger scale. The method presented in this paper for the derivation of a cohesive law can be applied to other material combinations showing brittle crack growth as well.

Modeling initiation and propagation of a hydraulic fracture under subcritical conditions

A numerical model has been developed for simulating the initiation and propagation of a plane strain or axisymmetric hydraulic fracture from an openhole wellbore in an impermeable homogeneous rock formation. The main novelty is inclusion of a subcritical growth law, thereby allowing consideration of hydraulic fracture growth when the wellbore pressure is otherwise considered insufficient to initiate fracturing. To enable tracking the moving crack front in the simulations, we develop a new tip asymptotics based on a subcritical crack growth law. The results are first validated against available analytical solutions for plane strain and axisymmetric hydraulic fractures. A comparison is presented between the solutions of the subcritical growth model and a conventional hydraulic fracture model in which fracture growth is not allowed until the stress intensity factor equals the fracture toughness of the rock. This comparison, as well as a study of the influence of the relevant parameters appearing in the subcritical growth law, indicates significant influence of subcritical growth on the evolution of the crack length and the wellbore pressure. Notably, this model provides the capability to simulate delayed growth of hydraulic fractures under pressures that are insufficient to generate instantaneous growth, which is a behavior observed in experiments but not considered by conventional hydraulic fracturing models.

Effect of Residual Stresses on Safe Life Prediction of Railway Axles

Residual stresses play an important role in fatigue crack growth in railway axles. Due to crack closure, they affect not only the stress ratio R but add directly to the effective range of the cyclic crack load in terms of stress intensity factor. In order to account for this effect in a safe life analysis, the stress intensity factor KIrs due to the residual stress is required. The cut-compliance method is a suitable means to determine KIrs. The method is described briefly, and by an example it is shown how it can be applied to railway axles. The obtained residual stresses turned out to be compressive in the vicinity of the surface, which is beneficial for the fatigue performance of the axle. If these stresses are accounted for in the crack growth law, the calculated safe life in case of a pre-existing crack-like defect is increased dramatically. Furthermore, the effect of the press-fit of the wheels is investigated. The corresponding stresses were calculated by FEM. Actually, these stresses represent another type of residual stresses and can be superimposed to the measured residual stresses in the analysis. They also affect the crack growth rate significantly.

Effects of porosities in additive manufactured Ti-6Al-4V alloy on fatigue strength

In this study, the effects of porosities in additive manufactured Ti-6Al-4V alloy on fatigue strength were invedtigated. Fatigue tests and observations of fracture surface on HIP'd (Hot isostatic pressed) and Non-HIP'd specimens were conducted. Fatigue lives of Non-HIP'd specimens were shorter than those of HIP'd. It was observed that fatigue fracture of all Non-HIP'd specimens occurred from porosities near the specimen surface. On the other hand, porosities didn't exist in fracture surface of HIP'd specimens. It was considered that existence of porosities caused shortened fatigue lives of Non-HIP'd specimens. Stress intensity factor ranges at fracture origins were examined by simulation. As a result, all of them were larger than threshold stress intensity factor range. It was considered that porosities of Non-HIP'd specimens act as initial cracks and fatigue crack grows from the initial crack. To confirm above assumption, fatigue lives of Non-HIP'd specimens were estimated by of fatigue crack growth law. It was found experimental data were plotted in the range of estimated fatigue lives based on fatigue crack growth analysis. There is a possibility that crack growth life is dominant for fatigue life of Non-HIP'd specimen with porosities.

Computational mixed mode failure analysis under fatigue loadings with constant amplitude and overload

The integrity of engineering structures can be often compromised under cyclic loading due to the propagation of the pre-existing cracks. Therefore, computationally feasible fatigue crack growth models are essential for the residual strength analysis. In the present paper, a new fatigue design model is developed for the failure assessment of mixed-mode I/II crack situations subjected to cyclic loading with either a constant amplitude or overload. A fracture mechanics-based methodology takes into account Kujawski’s crack growth law, Wheeler’s retardation model and the maximum principal stress criterion in order to estimate the residual life and crack path. Furthermore, the experimental investigation of two cracks emanating from a hole subjected to mixed mode loading is performed. Then, such a crack problem is numerically simulated applying the finite element method. The predictive capacity and accuracy of the proposed fatigue model are assessed by means of the literature-based experimental and calculated crack growth data.

A Micromechanical Method to Predict Macroscopic Behavior of Brittle Creep Failure in Rock

Brittle creep in rock has great significance for the prediction of important geohazards and stability of deep underground excavations. A major challenge in this area is to link the time-dependent cracking with macroscopic mechanical behavior. In this paper, Ashby and Sammis’ microcrack model and Charles’ crack growth law are employed to investigate the time-dependent cracking during brittle creep in rock. Based on the macroscopic and micromechanical definition of damage in rock, a new theoretical model is suggested to establish the linkage between microcrack length and macroscopic strain. In order to verify the rationality of the suggested model, comparison between theoretical and experimental results is presented. Using this new model, brittle creep of Sanxia granite is investigated and discussed in detail. It is found that evolutions of wing crack length, strain, and damage perform a similar process during brittle creep and could be divided into three phases. Effects of model parameters on creep failure behaviors also are studied.

Small internal fatigue crack growth rate measured by beach marks

Internal fatigue crack growth rates were measured using the beach marks created by repeated two-step fatigue tests on a high-strength steel. This material revealed internal fractures originating from oxide-type inclusions whose sizes ranged from 14 to 40µm. Large and small beach marks were observed depending on the conditions under which the repeated two-step fatigue tests were carried out. Small beach marks indicated small internal cracks just after crack initiation, while large beach marks indicated internal cracks in the final stages. The small internal cracks showed extremely slow growth rates that were much smaller than the lattice length: the measured growth rates were very close to those calculated using fracture mechanics. The large internal cracks showed conventional growth rates, larger than the lattice length, and the border between the large and small internal cracks was almost equal to the threshold stress intensity range ΔKth. These results show the validity of evaluating the fatigue lives by calculating the crack propagation lives of the small internal cracks as in the Tanaka-Akiniwa model. However, it has been suggested that the Tanaka-Akiniwa model overestimates the effects of inclusion sizes, meaning that the Tanaka-Akiniwa model has room for improvement. To correct this problem, we propose a new model, based on a new crack growth law, in which the crack growth rate also depends on crack size. The new model generates more realistic predictions.

Modified CCS fatigue crack growth model for the AA2019-T851 based on plasticity-induced crack-closure

Several fatigue cracks growth laws have been suggested over the past 50years. Recently, a fatigue crack propagation law was proposed by Castillo-Canteli-Siegele (CCS model) based on the assumption that fatigue crack growth takes the form of a Gumbel cumulative distribution function. Besides many physical aspects, the fatigue crack propagation laws need to account for fatigue crack opening and closure effects. Thus, in this paper a modification of the CCS fatigue crack growth law is proposed to account for the crack opening and closure effects, as well as the stress R-ratio effect, Rσ. The fatigue crack opening and closure effects are taken into account using a plasticity-induced crack-closure model. Other fatigue crack closure models can also be used in the proposed modification of the CCS crack growth model through the quantitative parameter U=ΔKeff/ΔK. This modified CCS crack propagation model using the effective stress intensity factor range, ΔKeff, is a new version of an explicit fatigue crack propagation model, supported by mathematical and physical assumptions. In this paper, the proposed model is applied using the fatigue crack growth data and mechanical properties that were collected for the 2219-T851 aluminium alloy. Based on the plasticity-induced crack-closure model, which was first formulated by Newman, and in this paper modified with a boundary correction factor, Fw, the crack opening stress intensity factor, Kop, and quantitative parameter U are determined. The results showed a good agreement between the proposed modification of the CCS fatigue crack propagation model taking into account the plasticity-induced crack-closure model with the boundary correction factor and experimental results of the fatigue crack propagation data for the 2219-T851 aluminium alloy.

Reliability-based fatigue assessment of steel bridges using LEFM – A sensitivity analysis

The lack of an established safety format prohibits a widespread use of linear elastic fracture mechanics (LEFM) for the fatigue assessment of steel bridges. The aim of this study is to facilitate a future development of a deterministic design approach. A probabilistic sensitivity analysis has been performed to study the influence of different modeling options on the resulting time variant reliability. The analyses have been performed by the first order reliability method (FORM) together with a model correction factor. The result shows the importance of modeling the crack shape in an adequate manor and, the importance of the material parameters. Other parameters as the load sequence and the option between a linear and a bi-linear crack growth law are less important. A calculation of the omission sensitivity factors shows that the uncertainties of the material parameters in the crack growth law have the most decisive influence and, thereafter, the uncertainty of the stress intensity factor.

Three-dimensional quasi-static interfacial crack growth simulations in thermo-mechanical environment by coupled FE-EFG approach

This paper presents the three-dimensional interfacial crack growth simulations using coupled finite element and element free Galerkin (FE-EFG) approach under mechanical and thermo-elastic loading. Extrinsic partition of unity (PU) enrichment technique has been employed to model a crack in the domain. Crack face and crack front have been modelled by Heaviside and asymptotic branch enrichment functions respectively whereas a material interface has been modelled by a signed distance function. Modified domain based interaction integral approach has been employed to evaluate the individual stress intensity factors. Standard Paris law of fatigue crack growth has been employed for the life prediction of interfacial cracked geometries. Several interfacial fatigue crack growth problems have been solved by the coupled EF-EFG approach.

Fatigue crack growth behavior of amorphous particulate reinforced composites

In this paper, fatigue tests were conducted on the new class of magnesium matrix composite reinforced with amorphous alloy particle. The high cycle fatigue behavior and the ability to resist crack nucleation and propagation of Ni60Nb40/Mg composites have been studied. Moreover, effects of microstructure and particle distribution on fatigue properties and crack growth mechanism are investigated. The difference of the microstructure is the cause for different crack initiation and propagation and this condition influenced fatigue life. Composites with more uniform particle distribution possess a superior fatigue resistance in fatigue limit. In situ crack growth observation revealed fatigue crack initiation occurred preferentially at particle-matrix interfaces. In addition, it was observed that the crack growth in particulate reinforced composites is highly localized phenomenon, influenced primarily by the distribution and microstructure of particles near the vicinity of the crack tip. The crack propagation through the matrix and region of well-dispersed particles is predicted by a crack growth law while crack propagation through the region of particle clusters is considerably different and unpredictable.

Modeling fatigue failure using the variational multiscale method

In this paper, we study fatigue failure using the variational multiscale method (VMM). In the VMM, displacement jumps are represented using finite elements with specially constructed discontinuous shape functions. These elements are progressively added along the crack path during fatigue failure. The stiffness of these elements changes non-linearly in response to the accumulation of damage during cyclic loading. The evolution law for stiffness is represented as a function of traction and the number of loading cycles since the initial onset of failure. Numerical examples illustrate the use of this new methodology for modeling macroscopic crack growth under Mode I loading as well as microscopic crack growth under mixed mode loading within the elastic regime. We find that the discontinuous elements can consistently predict the Mode I stress intensity factor (SIF) and the micro-structurally short crack growth paths, and that the computed Paris law for steady crack growth is controlled primarily by two parameters in the decohesion law.

Fatigue crack growth analysis of an interfacial crack in heterogeneous materials using homogenized XIGA

In this work, the fatigue life of an interfacial cracked plate is evaluated in the presence of flaws by homogenized extended isogeometric analysis (XIGA). In XIGA, the crack faces are modeled by discontinuous Heaviside jump functions, whereas the singularity in the stress field at the crack tip is modeled by crack tip enrichment functions. Holes and inclusions are modeled by Heaviside function and distance function respectively. The discontinuities are modeled in a selected region near the major crack whereas the region away from the crack is modeled by an equivalent homogeneous material. The stress intensity factors (SIFs) for the interface cracks are numerically evaluated using the domain based interaction integral approach. Paris law of fatigue crack growth is employed for computing the fatigue life of an interfacial cracked plate. The results show that the defects/ discontinuities away from the main crack barely influence the fatigue life.

Small crack growth model from low to very high cycle fatigue regime for internal fatigue failure of high strength steel

Fatigue failure of high strength steels mostly originates at nonmetallic inclusions. An optically dark area (ODA) beside the inclusion can be observed in specimens fractured at very high cycle fatigue (VHCF) regime. The present paper proposes fatigue life prediction models from low to VHCF regime. The fatigue life prediction model inside ODA has been constructed in the VHCF regime based on the master curve of the growth of ODA where fatigue failure is caused by cyclic loading assisted by hydrogen trapped by inclusion. The fatigue crack growth law is proposed for a small crack outside ODA within the framework of the area parameter model where the concept of “continuously variable fatigue limit” for small crack is introduced. The life and scatter of fatigue life originating at inclusions can be well evaluated by the proposed models.

Micro–macro modeling of brittle creep and progressive failure subjected to compressive loading in rock

A major challenge of rock mechanics is to link the time-dependent crack growth with macroscopic mechanical behavior. A new micro–macro method is presented to model the brittle creep and progressive failure of rock in compression. The Ashby’s microcrack model, Charles’ crack growth law and a new theoretical relation are incorporated into this method. This new relation is suggested to establish the linkage between microcrack growth and macroscopic strain based on the macroscopic and micromechanical definition of rock damage in this paper. The long-term strength of rock could also be calculated using this suggested micro–macro method. Rationality of the suggested method is verified through the theoretical and experimental results. Furthermore, effects of confining pressure on brittle creep and progressive failure of Sanxia granite is investigated. Theoretical corresponding relation between crack growth, damage and strain is investigated. And theoretical foundation of deep-buried construction design is also discussed in this paper.

Delayed Fracture of Glass Bulbs Used in Fire Sprinklers

Very rarely, glass bulb sprinkler heads activate when there is no fire or elevated temperatures. In such cases, the bulb fragments are never recovered. Speculation may arise that there was a defect in the bulb from manufacturing or installation, which led to its eventual failure. We investigated the growth of such defects using the principles of fracture mechanics and the well-known laws of slow crack growth in glass. These laws include the existence of a threshold, below which cracks do not grow at all, and above which cracks grow at a velocity that is greater than a minimum value. As a result, bulbs either never fail, or fail within a relatively short time after the crack or defect is created. Finite element and fracture mechanics analyses for a typical bulb indicates that the maximum delay is of the order of hours or weeks, not years. Experiments confirm this phenomenon. Over 100 bulbs were intentionally damaged, then placed under a constant load. A total of 44 bulbs, for which the combination of damage and load happened to be above the threshold for crack growth, failed within days (up to 36 days), while all other 58 bulbs survived over 2 years without failure. The theoretical analysis and the experiments demonstrate that fracture of sprinkler bulbs occurs relatively quickly after the introduction of a defect: if a bulb fractures in service without apparent cause, there must have been some event to damage the bulb or the sprinkler head in the days or weeks before the activation.

Influence of superimposed vibrational load on dwell time crack growth in a Ni-based superalloy

Sustained loads have for some Ni-based superalloys been shown to give rise to increased crack growth rate at elevated temperature. Such loads generate a history dependent fatigue problem due to weakening and cracking of grain boundaries during dwell times, later broken apart during subsequent load cycles. So far most studies have focused on the interaction of load cycles, overloads, and temperature. However, vibrations of different kinds are to some extent always present in engine components, and an investigation of how such loads affect the dwell time cracking, and how to incorporate them in a modelling context, is therefore of importance. In this paper a study of the most frequently used gas turbine material, Inconel 718, has been carried out. Mechanical crack propagation testing has been conducted at 550°C for surface cracks with and without the interaction of superimposed vibrational loads. Subsequent investigation of the fracture behaviour was performed by scanning electron microscopy and the modelling work has been conducted by incorporating the vibration load description within a history dependent crack growth law. The obtained results show reasonable accuracy with respect to the mechanical test results.

XFEM for fatigue and fracture analysis of cracked stiffened panels

This paper presents the development of methodologies using Extended Finite Element Method (XFEM) for cracked unstiffened and concentric stiffened panels subjected to constant amplitude tensile fatigue loading. XFEM formulations such as level set representation of crack, element stiffness matrix formulation and numerical integration are presented and implemented in MATLAB software. Stiffeners of the stiffened panels are modelled using truss elements such that nodes of the panel and nodes of the stiffener coincide. Stress Intensity Factor (SIF) is computed from the solutions of XFEM using domain form of interaction integral. Paris's crack growth law is used to compute the number of fatigue cycles up to failure. Numerical investigations are carried out to model the crack growth, estimate the remaining life and generate damage tolerant curves. From the studies, it is observed that (i) there is a considerable increase in fatigue life of stiffened panels compared to unstiffened panels and (ii) as the external applied stress is decreasing number of fatigue life cycles taken by the component is increasing.

DBEM crack propagation in friction stir welded aluminum joints

This paper deals with the simulation of multiple crack propagation in friction stir welded butt joints and the aim is to assess the influence of process induced residual stresses on the fatigue behavior of the assembly. The distribution of the process induced residual stresses is mapped by means of the contour method; then, the computed residual stress field is superimposed, in the DBEM environment, to the stress field due to a remote fatigue traction load and the crack growth is simulated.A two-parameters crack growth law is used for the crack propagation rate assessment. The Stress Intensity Factors are evaluated by the J-integral technique. Computational results have been compared with experimental data, provided by constant amplitude crack propagation tests on welded samples, showing the subdivision of the overall fatigue life in the two periods of crack initiation and crack propagation.

Effect of Mean Stress on Small Fatigue Crack Growth Rate on Low Carbon Steel with Several Simulated HAZ Heat Treatment

In this study, to clarify the effect of microstructure of Heat Affected Zone (HAZ) and residual stress of weld on small fatigue crack growth behavior, uniaxial fatigue testing with surface small fatigue crack growth observation were carried out for low carbon steel with three simulated HAZ heat treatment under several mean stress conditions. As a results, εna type small crack growth law was also effective to HAZ microstructure under zero mean stress. Under tensile mean stress condition, fatigue fracture life and small fatigue crack growth life were decreased. In addition, it is clarified that small fatigue crack growth rate acceleration under tensile mean stress was able to be evaluated by using Smith-Watson-Topper equivalent strain εeq which is obtained from mean stress dependency of fatigue fracture life for smooth specimen and εeqna type modified small crack growth law was proposed. Furthermore, it is clarified that εeq was proportional to εeff which was evaluated by crack opening point measured with Digital Image Correlation technique. It is considered that equivalent strain εeq implicitly includes small crack growth life and effect of crack closure.