Crack Advances Research Articles

Single and Double Cantilever Beam Large Displacement Mixed Mode Fracture Toughness Test Methods and J-Integral Analyses

Abstract The J-integral is applied to the single cantilever beam (SCB) and double cantilever beam (DCB) test specimens subjected to both mixed-mode I and II loading and large displacements. The methods proposed and resulting closed-form theoretical equations allow for the instantaneous evaluation of J during laboratory tests, requiring only the applied load and angular rotation of the specimen loading link, loading points, and remaining ligament. These measurands can be acquired using a common load cell and markers, a digital video camera, and image analysis software. In general, the equations do require knowledge of the specimen elastic moduli and shear moduli, as well as the specimen linear dimensions. Since the test data can be analyzed and J determined throughout the test instantaneously, and since, due to geometric nonlinearities, the ratio of mode I and mode II loading will likely vary significantly throughout the test, each specimen can be used to generate multiple data points. If crack length is determined throughout the test, presumably by directly measuring the crack length optically, or if the load drops abruptly due to crack growth, then when the crack advances, critical values of J for mixed-mode loading can be determined using the methods and results presented. It is noted that moderate to large translational and rotational displacements may improve the accuracy of the results using these methods. The results are applicable to standard pure mode I or pure mode II SCB and DCB tests as well and reduce to known equations in those special cases.

Single fluid-driven crack propagation in analogue rock assisted by chemical environment

During the operation of hydraulic fracturing as used in many geo-energy and geo-environment applications, chemical stimulation is often incorporated for cracking enhancement in low-permeability geological formations for the purpose of an optimization of energy recovery. The mechanism of subcritical crack propagation in a chemically reactive environment is essential for understanding of the involved coupled chemo-mechanical process and a better control of acid-assisted hydraulic fracturing. It has been postulated that the rate of crack propagation under environmental loads is inherited from the chemical processes involved including the reaction and the diffusive transport. However, laboratory explorations focusing on the evolving interplay between the propagation of a fluid-pressurizing individual crack and the environment it is subject to via a variable chemical intensity imposed have been rare. Here we present an experimental investigation on a single tensile crack propagation in alginate hydrogel as an analogue material for brittle rocks, driven by the injection of a chemically reactive fluid kept at constant pressure using a Hele-Shaw cell setup. We show that an intensified chemical environment can accelerate tensile crack propagation in both subcritical crack growth and fracturing regimes, while leading to the Region III fracturing of less brittle characteristics. During the experiment, crack-tip blunting upon injection of reactive solutions was observed, suggesting a competing mechanism between the crack-tip geometry induced toughening and the chemically induced softening within the process zone as the crack advances. Our results provide quantitative insights into how a chemically reactive environment facilitates the growth of a single macroscopic crack of mode I opening in a low-permeability matrix through coupled chemo-mechanical feedback. The imposed chemical environment promotes crack propagation while alleviating the stress concentration at the advancing crack tip, suggesting a more energy-efficient method compared to pure water fracturing. We anticipate our experimental investigation presented here to be a starting point of sound laboratory support for future studies towards a more controllable technique of chemical stimulation in geomaterials as well as complementing the ongoing modeling efforts in reactive chemo-mechanics.

Crack-Length Estimation for Structural Health Monitoring Using the High-Frequency Resonances Excited by the Energy Release during Fatigue-Crack Growth.

Acoustic waves are widely used in structural health monitoring (SHM) for detecting fatigue cracking. The strain energy released when a fatigue crack advances has the effect of exciting acoustic waves, which travel through the structures and are picked up by the sensors. Piezoelectric wafer active sensors (PWAS) can effectively sense acoustic waves due to fatigue-crack growth. Conventional acoustic-wave passive SHM, which relies on counting the number of acoustic events, cannot precisely estimate the crack length. In the present research, a novel method for estimating the crack length was proposed based on the high-frequency resonances excited in the crack by the energy released when a crack advances. In this method, a PWAS sensor was used to sense the acoustic wave signal and predict the length of the crack that generated the acoustic event. First, FEM analysis was undertaken of acoustic waves generated due to a fatigue-crack growth event on an aluminum-2024 plate. The FEM analysis was used to predict the wave propagation pattern and the acoustic signal received by the PWAS mounted at a distance of 25 mm from the crack. The analysis was carried out for crack lengths of 4 and 8 mm. The presence of the crack produced scattering of the waves generated at the crack tip; this phenomenon was observable in the wave propagation pattern and in the acoustic signals recorded at the PWAS. A study of the signal frequency spectrum revealed peaks and valleys in the spectrum that changed in frequency and amplitude as the crack length was changed from 4 to 8 mm. The number of peaks and valleys was observed to increase as the crack length increased. We suggest this peak–valley pattern in the signal frequency spectrum can be used to determine the crack length from the acoustic signal alone. An experimental investigation was performed to record the acoustic signals in crack lengths of 4 and 8 mm, and the results were found to match well with the FEM predictions.

FEA based fatigue crack growth analysis

The AA6061-T6 aluminium alloys are hugely applicable, where strength of material is predominant. Majority of the failure of such type of structure is due to fatigue. The observation of fatigue crack enhancement is very useful to predict the remaining existence of the shape and therefore, to understand the fatigue failure. By knowing the plastic zone, crack growth rate can be approximated on the basis of plastic zone size. It helps to save time and material that is required in experimentation to evaluate crack growth rate. Many researchers investigated the dependency of fatigue crack enhancement on plastic area size; however there may be restricted literature to be had on plastic area dedication of AA6061-T6 aluminium alloys. In this research article the fatigue crack enhancement rate of AA6061-T6 aluminium alloys experimentally and plastic zone is determined at crack tip when crack advances using ANSYS. Fatigue crack growth tests were performed to record the ‘No. of cycles’ and ‘Stress intensity factor’ as crack advances. The crack growth rate in steady state regime was determined and analyzed. The crack advancement was also analyzed in ANSYS and ‘No. of cycles’ and ‘Stress intensity factor’ were determined analytically. A comparison of experimental data and ANSYS data was made to check the suitability of application of ANSYS in fatigue crack increase evaluation of AA6061-T6 aluminium alloys. Finally plastic region at crack tip changed into decided the use of ANSYS.

Elemental Crack Advance assessment and verification for its use in LBB analysis

The leak before break (LBB) concept is today widely employed at the nuclear industry to preclude catastrophic rupture, mainly on pipes. This paper presents two complimentary procedures. Both of them are applied via the Finite Element Method, for demonstrating LBB on austenitic stainless steel vessels. Those procedures are submodeling and the Elemental Crack Advance method. One procedure verifies the results obtained using the other, making them robust and trustworthy. Those practices are illustrated on the ALFRED reactor using the software ANSYS. They are applicable to geometrical shapes for which simplified expressions of the J-integral are not available. This illustration, proves as well, that by means of small design modifications such as thickening the bottom head, LBB can be demonstrated in the ALFRED reactor. The submodeling technique stands as the main vehicle in the LBB demonstration exposed at this work. The Elemental Crack Advance method lies as a tool for verifying a wide variety of Fracture Mechanics assessment, including non-LBB related ones.

Fatigue-Resistant elastomers

The resistance of a material to the growth of a crack is characterized by fracture toughness under monotonic load, and by fatigue threshold under cyclic load. The fatigue threshold of engineering elastomers is commonly limited to ∼50 J/m2, much below their toughness (103∼105 J/m2). Here we report fatigue-resistant elastomers with threshold beyond 500 J/m2. Such an elastomer is a composite of two elastomers: a lattice of a hard elastomer embedded in a matrix of soft elastomer. Both the hard and soft elastomers are elastically stretchable, with small hysteresis. At a crack front in the composite, the soft matrix shears greatly, which de-concentrates stress in the hard lattice. When the crack advances in the composite, the energy dissipated scales with the feature size of the lattice. By contrast, when a crack advances in a homogeneous elastomer, the energy dissipated scales with the mesh size of the polymer network. The fatigue-resistant elastomers open new opportunities for applications requiring stretchable materials.

Hydrolytic crack in a rubbery network

We report an experimental finding that a crack advances in a polydimethylsiloxane (PDMS), under a small stress, in a moist environment. PDMS chains consist of siloxane bonds with methyl side groups. The methyl groups make PDMS hydrophobic, and PDMS hydrolyzes extremely slowly under no stress. Nonetheless, we find that a crack advances under the combined attack of water and stress. Our experimental data support the hypothesis that PDMS is susceptible to stress-assisted hydrolysis, but show that the activation area for PDMS is smaller than that for silica by two orders of magnitude. We attribute this large difference to the molecular structures of the two materials: a glassy network and a rubbery network, respectively. This finding suggests that stress-assisted reaction should concern many elastomers and gels in engineering and medicine.

Atomistic simulation of crack propagation along γ-TiAl lamellar interface

Due to start-up and shut-down operations of engine, TiAl structural components usually undergo not only static but also cyclic mechanical loading. The crack propagation mechanisms of γ-TiAl under two types of loading are studied in this work to reveal the differences of the mechanisms under constant strain rate and cyclic loading. Since the crack prefers to nucleate at the interface, two types of loadings are applied to a γ-TiAl interface system with a pre-existing micro-crack at the interface by the means of classical molecular dynamics simulation, the loading direction is along [111] perpendicular to the interface. The evolution of crack tip and dislocation is observed in atomistic scale. The results show that, under both loading types, the crack propagates asymmetrically, Shockley dislocations emit on the (-1-11) slip plane from the right crack tip and slip along [-1-1-2] direction. The dislocations blunt the extension of crack while the left crack tip propagates in a brittle way. During the cyclic loading, different with constant strain rate condition, the crack advances and dislocations slip with increasing loads and retreat during unloading. In addition, the stress decreases and the crack length increases with the increase of the cyclic loading number.

Fracture Toughness and Fatigue Threshold of Tough Hydrogels.

Hydrogels of numerous chemical compositions have achieved high fracture toughness on the basis of one physical principle. As a crack advances in such a hydrogel, a polymer network of strong bonds ruptures at the front of the crack and elicits energy dissipation in the bulk of the hydrogel. The constituent that dissipates energy in the bulk of the hydrogel is called a toughener. A hypothesis has emerged recently that tougheners increase fracture toughness greatly but contribute little to fatigue threshold. Here we ascertain this hypothesis by studying hydrogels of two kinds, identical in all aspects except for tougheners. A Ca-alginate/polyacrylamide hydrogel has ionic bonds, which act as tougheners, resulting in a toughness of 3375 J/m2 and a threshold of 35 J/m2. A Na-alginate/polyacrylamide hydrogel has no ionic bonds, resulting in a toughness of 169 J/m2 and a threshold of 17 J/m2. These results motivate a discussion on the development of fatigue-resistant hydrogels.

Pipeline girth friction welding of the UNS S32205 duplex stainless steel

In most cases, welding is a critical issue and one that motivates a constant search for alternative solutions that can both reduce costs and increase efficiency. Supported by numerical simulation data, the present work evaluated the microstructure across the weld cross-section and the respective Charpy impact toughness at 0 °C for the different regions formed for the pipeline girth friction welding of the UNS S32205 alloy. The results indicated that the most important microstructural modifications occurred at the weld interface as a consequence of the combination of very high temperature and a great deal of plastic deformation. The considerable drop in impact toughness for this region is related to substantial changes in austenite morphology and an excessive ferrite grain growth. Moreover, pronounced austenite reorientation and increased ferrite fraction surrounded the weld interface, which in turn took its proportional toll on toughness. Finally, the analyses of the crack profiles revealed that as the crack advances to regions of either reformed or reoriented austenite crystals, cleavage facets appear on fracture surfaces in varying intensity, producing the corresponding reduction in impact toughness.

Crack Growth Driving Force at Tip of Stress Corrosion Cracking in Nuclear Structural Materials at Initial Stage

The mechanical state at the crack tip is one of the major factors affecting the stress corrosion cracking (SCC) growth rate in structural materials of the nuclear power plant. To understand the crack growth driving force and its effect on SCC growth rate in the whole process of SCC, a finite element model of the SCC growth process was built using a commercial software ABAQUS. Sequentially the working load, residual stress, and the film induced stress (FIS) produced by the oxide film formation in front of the crack tip during SCC initial stage were discussed in this paper. The results indicate that the FIS produced by the formation of oxide film is the main crack growth driving force during the initial stage of SCC. While the working load and residual stress gradually become the main crack growth driving force as SCC crack advances.

Crack Growth Resistance in Metallic Alloys: The Role of Isotropic Versus Kinematic Hardening

The sensitivity of crack growth resistance to the choice of isotropic or kinematic hardening is investigated. Monotonic mode I crack advance under small scale yielding conditions is modeled via a cohesive zone formulation endowed with a traction–separation law. R-curves are computed for materials that exhibit linear or power law hardening. Kinematic hardening leads to an enhanced crack growth resistance relative to isotropic hardening. Moreover, kinematic hardening requires greater crack extension to achieve the steady-state. These differences are traced to the nonproportional loading of material elements near the crack tip as the crack advances. The sensitivity of the R-curve to the cohesive zone properties and to the level of material strain hardening is explored for both isotropic and kinematic hardening.

A novel procedure to determine the cohesive law in DCB tests

A novel method is presented for the determination of mode I cohesive law for the characterization of delamination in unidirectional carbon fiber reinforced polymer laminates. The energy release rate as a function of the crack advance is determined based on an analytical approach where the compliance variation of the specimen as crack advances is used in order to obtain the crack length for every pair of load and displacement data. Based on the same analytic approach, the crack tip opening displacement is determined as a function of the equivalent crack advance assuming that the Fracture Process Zone development is analogous to an equivalent crack advance Δa. These measurements are used to compute the Energy Release Rate and crack opening displacement from which a cohesive law is determined by numerical differentiation. This new method provides a simple way to obtain the mode I cohesive law using only the load and displacement data obtained from the testing machine, without any external displacement measurement technique and without any assumption of the form of the cohesive law.

Stationary and propagating cracks in a strain gradient visco-plastic solid

A first order visco-plastic strain gradient constitutive model and a cohesive zone formulation are embedded within a modified boundary layer (MBL) model for the analysis of crack tip fields and crack growth. The MBL model is loaded using a mode I asymptotic crack tip solution, with the boundary displacement calculated from the stress intensity factor. The influence of the rate-dependent constitutive parameters and the intrinsic material length on fracture relevant quantities are investigated in parametric study. Two scenarios are considered: (1) a stationary crack under constant loading and (2) a crack advance under monotonic loading. Finite element model analyzes are performed. For stationary cracks it was found that the effects of the intrinsic lengthscale of the strain gradient plasticity model are more prominent for large visco-plastic power exponents, and increase with hold time. The results of computations of crack advances under monotonic loading suggest that plastic strain gradients reduce crack growth resistance and crack initiation toughness, especially for a large visco-plastic power exponent. For small values of intrinsic material length the dependence of the initiation toughness and tearing modulus on the intrinsic length is strong, but then saturates for large values of intrinsic material length. Loading rate effects are found to be more pronounced for cases with a small value of the intrinsic lengthscale.

Avalanches in dry and saturated disordered media at fracture.

This paper analyzes fracturing in inhomogeneous media under dry and fully saturated conditions. We adopt a central force model with continuous damage to study avalanche behavior in a two-dimensional truss lattice undergoing dilation. Multiple fractures can develop at once and a power-law distribution of the avalanche size is observed. The values for the power-law exponent are compared with the ones found in the literature and scale-free behavior is suggested. The fracture evolves intermittently in time because only some avalanches correspond to fracture advancement. A fully saturated model with continuous damage based on the extended Biot's theory is developed and avalanche behavior is studied in the presence of fluid, varying the fluid boundary conditions. We show that power-law behavior is destroyed when the fluid flux governs the problem. Fluid pressure behavior during intermittent crack tip advancement is studied for the continuous-damage fully saturated model. It is found that when mechanical loading prevails, the pressure rises when the crack advances, while when fluid loading prevails, the pressure drops when the crack advances.

A novel mixed-mode cohesive formulation for crack growth analysis

Modeling fracture with a cohesive zone model requires an appropriate cohesive law for correlating interfacial tractions and crack face separation, especially in mixed-mode loading scenarios. Various approaches have been employed in order to develop such a law which can be characterized into potential-based and non-potential-based formulations. A critical re-examination of these methods is presented here, followed by a novel mixed-mode formulation which satisfies a physical criterion for crack propagation. Specifically, as the crack propagates, the trailing current crack tip is defined through the vanishing of normal and tangential components of the interfacial tractions simultaneously. A general formulation for mixed-mode conditions is proposed in this paper. In particular, given normal and tangential traction separation laws for pure normal and tangential modes as being material properties, the normal and tangential traction separation laws in mixed-mode loading are formulated so that all traction components disappear at the same effective separation when the crack advances. The new mixed-mode law is used to analyze three standard fracture problems in laminated composites, including double cantilever beam (DCB), end-notch flexure (ENF), and mixed-mode bending (MMB). A comparison with predictions from some selected mixed-mode cohesive laws and experimental data available in the literature is also included to further validate the proposed mixed-mode law.

Modeling of steady-state crack growth in shape memory alloys using a stationary method

Shape memory alloys experience phase transformation from austenite to martensite around crack tip. When the crack advances, martensitic transformation occurs at the tip and the energy that goes into this transformation results in stable crack growth like in the case of plastic deformation. In literature, steady-state crack growth in elasto-plastic materials with small scale yielding at the crack tip has been successfully modeled using stationary methods. In this work, Mode I steady-state crack growth in an edge-cracked Nitinol plate is modeled using a non-local stationary method (Moumni, 1995). The Zaki–Moumni (ZM) constitutive model is utilized for this purpose. The model is implemented in ABAQUS by means of a user-defined material subroutine (UMAT) to determine transformation zones around the crack tip. Steady-state crack growth is first simulated without considering reverse transformation to calculate the effect of transformation on stress distribution in the wake region, then reverse transformation is taken into account. The effect of reorientation of martensite near the crack tip as a result of non-proportional loading is also studied. The stress distribution and the phase transformation region are compared to results obtained for the case of a static crack.

A continuum damage failure model for hydraulic fracturing of porous rocks

A continuum damage mechanics (CDM) based constitutive model has been developed to describe elastic, plastic and damage behavior of porous rocks. The pressure sensitive inelastic deformation of porous rocks together with their damage mechanisms are studied for drained and undrained conditions. Fracture mechanics of microcrack and micro-void nucleation and their coalescence are incorporated into the formulation of the CDM models to accurately capture different failure modes of rocks. A fracture mechanics based failure criterion is also incorporated to accurately capture the post fracture crack advances in the case of progressive failures. The performance of the developed elastoplastic and CDM models are compared with the available experimental data and then the models are introduced into a commercial software package through user-defined subroutines. The hydraulic fractures growth in a reservoir rock is then investigated; in which the effect of injection pressure is studied and the simulations are compared with the available solutions in the literature. The developed CDM model outperforms the traditional fracture mechanics approaches by removing stress singularities at the fracture tips and simulation of progressive fractures without any essential need for remeshing. This model would provide a robust tool for modeling hydraulic fracture growth using conventional elements of FEA with a computational cost less than similar computational techniques like cohesive element methods.

Overview of interfacial fracture energy predictions for stacked thin films using a four-point bending framework

Developing a robust predicting methodology on the interfacial fracture energy of dissimilar materials is urgently needed to meet the mechanical strength requirements for investigating novel materials and subsequent device structures with the bonded types of multi thin films. Thus, this paper provides an overview of useful approaches according to linear-elastic interfacial fracture mechanics, such as J-integral method, modified virtual crack closure technique (MVCCT), and analytical solutions derived from the relationship between the stress field of delaminated tip and crack tip opening displacements to compare their estimated capability of cracking energy. A popular technique for determining the interface adhesion of thin coatings is the four-point bending test (4-PBT). The testing vehicles of 4-PBT allow a more thorough validation of the foregoing predicted approaches based on finite element analysis compared with the simulated results with related experimental data. The critical energies of 18J/m2, 78.53J/m2, 52.01J/m2, and 71.02J/m2 for the bonded interfaces of SiO2/SiLK, Ta/SiLK, TaN/SiLK, and Si3N4/SiLK stacked nano-scaled thin films are precisely judged, respectively. The predicted results of the J-integral method match well with the MVCCT estimation. The results reveal that the opening fractured mode is dominant at the beginning of the crack advances along the bonded interface of Ta/SiLK, TaN/SiLK, and Si3N4/SiLK stacked films as the interfacial crack length increases. Moreover, the essential trends of dependences for the modulus ratio and thickness ratio of stacked thin films on interfacial energy release rate are logically identified and investigated. Therefore, this paper could be regarded as a design guideline of interfacial fracture behavior for stacked films utilized in the development of advanced device technologies.

Fatigue crack growth of arbitrary planar cracks in welded components

Engineering components that are subjected to cyclic loads frequently contain imperfections which can rationally be assessed using linear elastic fracture mechanics. Fatigue crack growth models make use of the stress intensity factor (SIF) range and the maximum SIF or R-ratio to describe the driving force for crack propagation. Determining the stress intensity factor in welded components is difficult because the stress field is complex due to the structural geometry of the component, the local geometry of the weld and the residual stresses caused by the welding process. In many cases, the crack geometry will also be complex. Weight function (WF) solutions for numerous crack geometries have been published, e.g. for through cracks, edge cracks, surface cracks and corner cracks. However, the use of the WF for cracks of arbitrary shape is less developed. The point-load WF method for arbitrary planar cracks gives sufficiently accurate estimates of stress intensity factors for embedded cracks, but the results for the surface and edge cracks are less accurate. A new form of the general point-load WF more suitable for surface breaking cracks is proposed and is combined with a crack tip plasticity-based crack growth model. During numerical simulations, cracks are normally modelled using a discrete number of linear segments. A new method for shifting these segments as a crack advances is also proposed. The method is verified based on comparison with published experimental results for welded rectangular hollow section joint subjected to bending and torsion.