Crack Initiation Model Research Articles

A framework toward fatigue life modeling of machining process verified in burnishing

In the present work a multiscale model was developed to predict fatigue lives of Inconel 718 after a machining process. The model captures the effects of surface integrity like residual stress, microstructure, hardness and roughness. Within this holistic predictive model, firstly burnishing process factors (viz static force, feed rate, spindle speed and pass number) are correlated to surface integrity aspects. Herein, residual stress is modeled using theory of incremental plasticity; also grain size and hardness were correlated to process factors through dislocation density evolution. In order to model the surface roughness, the Z-map approach considering the work hardening of the surface layers was utilized. The foresaid developed models of surface integrity aspects were utilized to predict the fatigue life using Navaro-Rios crack propagation together with Chen’s crack initiation models. Thus, a novel holistic model correlating machining parameters directly to fatigue life has been developed through this hybrid approach. The developed models of fatigue life and surface integrity aspects were then confirmed by series of burnishing experiments on Inconel 718. Later, the confirmed model was utilized to identify the parametric influence of burnishing process on variation of fatigue life where the results were justified using variation of surface integrity factors. Through this developed model, it was found that burnishing setting of 1000 N static force, 0.05 mm/rev feed rate, 300RPM spindle speed and 2 pass number results in improvement of HCF, MCF and LCF of 242 %, 184 % and 212 % where the obtained results from the developed framework were compatible well with experimental values.

Thermomechanical-induced cracking model for ceramic matrix composite laminates subjected to thermal gradients and transients

Regarding the potential damage and failure issues that may occur in high-temperature transient environments during the service process of ceramic matrix composite laminates, the present work proposes a multi-layer thermomechanical induced crack initiation model for ceramic matrix composite laminates subjected to thermal gradients and transients. This model can determine the history of temperature, deformation, and stress distribution within each layer of the material, as well as the steady-state energy release rate of all possible crack locations. Then the influence of bending constraints on material stress distribution and energy release rate is investigated, finding that maximum stress and energy release rate values are significantly lower without bending constraints compared to those under bending constraints. Furthermore, the study explores the impact of material structural parameters and boundary conditions on the energy release rate of ceramic matrix composite laminates, providing direct insights for designing laboratory tests and evaluating the lifespan of these materials under in-service conditions.

Machine Learning Approach for LPRE Bearings Remaining Useful Life Estimation Based on Hidden Markov Models and Fatigue Modelling

Ball bearings are one of the most critical components of rotating machines. They ensure shaft support and friction reduction, thus their malfunctioning directly affects the machine’s performance. As a consequence, it is necessary to monitor the health conditions of such a component to avoid major degradations which could permanently damage the entire machine. In this context, HMS (Health Monitoring Systems) and PHM (Prognosis and Health Monitoring) methodologies propose a wide range of algorithms for bearing diagnosis and prognosis. The present article proposes an end-to-end PHM approach for ball bearing RUL (Remaining Useful Life) estimation. The proposed methodology is composed of three main steps: HI (Health Indicator) construction, bearing diagnosis and RUL estimation. The HI is obtained by processing non-stationary vibration data with the MODWPT (Maximum Overlap Discrete Wavelet Packet Transform). After that, a degradation profile is defined and coupled with crack initiation and crack propagation fatigue models. Lastly, a MB-HMM (Hidden Markov Model) is trained to capture the bearing degradation dynamics. This latter model is used to estimate the current degradation state as well as the RUL. The obtained results show good RUL prediction capabilities. In particular, the fatigue models allowed a reduction of the ML (Machine Learning) model size, improving the algorithms training phase.

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Microstructure-Based CZE Model for Crack Initiation and Growth in CGI: Effects of Graphite-Particle Morphology and Spacing

Compacted graphite iron (CGI) is an engineering material with the potential to fill the application gap between flake- and spheroidal-graphite irons thanks to its unique microstructure and competitive price. Despite its wide use and considerable past research, its complex microstructure often leads researchers to focus on models based on representative volume elements with multiple particles, frequently overlooking the impact of individual particle shapes and interactions between the neighbouring particles on crack initiation and propagation. This study focuses on the effects of graphite morphology and spacing between inclusions on the mechanical and fracture behaviours of CGI at the microscale. In this work, 2D cohesive-zone-element-based models with different graphite morphologies and spacings were developed to investigate the mechanical behaviour as well as crack initiation and propagation. ImageJ and scanning electron microscopy were used to characterise and analyse the microstructure of CGI. In simulations, both graphite particles and metallic matrix were assumed isotropic and ductile. Cohesive zone elements (CZEs) were employed in the whole domain studied. It was found that graphite morphology had a negligible effect on interface debonding but nodular inclusions can notably enhance the stiffness of the material and effectively impede the propagation of cracks within the matrix. Besides, a small distance between graphite particles accelerates the crack growth. These results can be used to design and manufacture better metal-matrix composites.

Phase Field Fracture Modelling of Crack Initiation and Propagation in Dual-Phase Microstructures

Dual-phase (DP) steel's spread in the industry has been fueled by its highly desirable qualities, which include a unique balance of strength and ductility, making it a valuable material for applications ranging from automotive manufacturing to construction. Despite the continued progress in the research of DP steels, the complex failure mechanisms at the microscale, resulting from the coexistence of brittle martensite phases within the ductile ferrite phase, remain an area of ongoing exploration. This study aims to investigate the micro structural evolution, as well as crack initiation and propagation, in DP steels at the microscale. In this context, to accurately capture the microstructural evolution of DP steels, a rate-dependent crystal plasticity formulation is utilized for the ferrite phase alongside a phenomenological isotropic J2 plasticity model for the martensite phase. A novel ductile phase-field fracture framework has been implemented to predict crack initiation and propagation, integrating both crystal plasticity and J2 plasticity constitutive models with the phase field fracture model. Generic 3D polycrystalline Representative Volume Elements (RVEs) are created and simulated to analyze the trends influencing the failure behavior of DP steels. The numerical study includes examples with two different martensite volume fractions (15% and 37%), each characterized by varying random crystallographic orientation sets and morphologies. The obtained results suggest that despite the similarity in stress concentration regions within two different random orientation sets in a simulation with fixed volume fraction and morphology, the resulting crack paths exhibit significant differences. Additionally, it is inferred that damage appears to accumulate at the junction points of the martensite islands. Moreover, an increase in the martensite volume fraction is found to diminish the influence of crystallographic orientation on the resultant crack path. Therefore, given the aforementioned findings, it is essential to analyze the microstructural evolution, as well as crack initiation and propagation in DP steels, utilizing appropriate material and fracture modeling frameworks at the microscale.

A peridynamic model for rail crack initiation with cavity defect

Cavity defects can aggravate the rail crack initiation. To study their effect on rail fatigue crack initiation behaviour, a peridynamic model of rail crack initiation considering the characteristics of the cavity defect was proposed. First, based on the low-cycle fatigue test data, the bond failure criterion of the rail material was derived and verified to characterize the fatigue damage performance. Then, mathematical expressions for circular, triangular and rectangular defect characteristics were proposed, establishing a prefabricated method for rail cavity defects. Based on the ordinary state-based peridynamic fatigue theory, a rail crack initiation model with the cavity defect was constructed. Finally, the behaviour of rail crack initiation with the cavity defect was analysed.

The high-throughput bridge to the rapid evaluation of fatigue reliability of structural engineering materials

A high-throughput strategy using miniature specimens to evaluate the ASTM-defined fatigue endurance limits of some engineering materials through a high-throughput symmetry bending cantilever beam fatigue testing system is proposed. Employing such a high-throughput testing method for examining some typical engineering materials, we reveal that the fatigue limits obtained by the traditional testing standard can be directly determined by the high-throughput method-obtained fatigue limit multiplied by a suitable conversion factor. Such a high-throughput method was validated theoretically by the proposed crack initiation model and experimentally by the F316 stainless steel specimens subjected to different aging treatments and Gamma-ray irradiation.

FEM Simulations of Fatigue Crack Initiation in the Oligocrystalline Microstructure of Stents.

For over two decades, vascular stents have been widely used to treat clogged vessels, serving as a scaffold to enlarge the narrowed lumen and recover the arterial flow area. High-purity oligocrystalline austenitic steel is usually applied for the production of stents. Despite the popularity and benefit of stenting, it still may cause serious clinical adverse issues, such as in-stent restenosis and stent fracture. Therefore, the study of the mechanical properties of stents and in particular the prediction of their life cycles are in the focus of materials research. In our contribution, within the finite element method, a two-scale model of crack initiation in the microstructure of stents is elaborated. The approach is developed on the basis of the physically based Tanaka-Mura model (TMM), considering the evolution of shear bands during the crack initiation phase. The model allows for the analysis of the microstructure with respect to the life cycles of real materials. The effects of different loading conditions, grain orientation, and thickness of the specimen on Wöhler curves were analysed. It was found that the microstructural features of oligocrystals are very sensitive to different loading conditions with respect to their fatigue behaviour and play a major role in fatigue crack initiation. Different grain-orientation distributions result in qualitative and quantitative differences in stress distribution and in the number of cycles for crack initiation. It was found that presence of a neutral zone in the cut-out of the microstructure under three-point-bending loading conditions changes the qualitative and quantitative patterns of stress distribution and affects the number of cycles for crack initiation. It was found that under both tensile and bending loading conditions, thicker specimens require more cycles for crack initiation. The Wöhler curves for crack initiation in oligocrystalline microstructures of stents could be compared with the ones in the experiment, taking into account that for high cyclic fatigue (HCF), typically, more than 70% of the cycles refer to crack initiation. The developed numerical tools could be used for the material design of stents.

Laboratory modeling of thermal and temporal cracking in swelling clays

Crack development in a changing environment is the controlling factor for the stability and strength of expansive soils. Expansive soils exhibit large volumetric changes with changes in their moisture conditions that may occasionally lead to reduced bearing capacity and foundation failures. This study purports to model crack initiation and its spatial progression in relation to the moisture content and drying period, respectively. Volumetric soil shrinkage is determined using high-definition digital camera imaging and Vernier scale methods, while the soil settlement under vertical shrinkage deformation could be captured through a tensile stress model for soils. It was revealed that a small change in suction could trigger crack initiation, which would propagate further under different environmental conditions. Furthermore, it was observed that the crack volume increased rapidly at specific moisture content and could penetrate as deep as 1 m after nearly 1.5 months that is fully consistent with the current model predictions. A comparison between the performance of the model proposed in this study and that of two existing models shows that the former predicts the vertical shrinkage strain values in closer agreement with those observed experimentally and is less conservative than those predicted by both models. Nevertheless, the findings from this study could be used to quantify the detrimental behavior of expansive soil present in pavement subgrades and shallow foundations for lightweight structures.

The correlation of fractal dimension to fracture surface slope for fatigue crack initiation analysis under bending-torsion loading in high-strength steels

In this study, the fractal dimension of fatigue fracture surfaces is investigated in order to find an alternative failure loading indicator. Some of many metrological factors are generalized by reducing the fracture surface structure to one factor and develop an entire fracture surface procedure by analyzing the impact of surface slope and calculation resolution. Three notched geometries are studied under cyclic bending-torsion: 34CrNiMo6 high-strength steel bars with transverse blind holes; (ii) 34CrNiMo6 high-strength steel bars with lateral U-shaped notches; and (iii) 18Ni300 maraging steel hollow bars with transverse holes produced by selective laser melting. The surface topographies of fatigue fractures were measured with an optical profilometer. The bending-torsion ratio, maximum local von Mises equivalent stress and the number of cycles to crack initiation are examined using the fractal dimension. Moreover, a comparison was also made for conventional surface topography parameters such as root mean square height and void volume. A fatigue crack initiation model based on surface topography and loading conditions is proposed. The model relies on the product of the maximum local von Mises equivalent stress and the fractal dimension divided by the root mean square height to void volume ratio. The results show that the fracture plane geometry, expressed by the fractal dimension Df, can facilitate the estimation of post-failure loading history. In particular, the analysis based on the enclosing boxes method (EBM) is more accurate when it is used as an extra-fine resolution without any plane leveling.

A New Surface Node Method to Accurately Model the Mechanical Behavior of the Boundary in 3D State-Based Peridynamics

Peridynamics is a non-local continuum theory capable of modeling crack initiation and propagation in solid bodies. However, the layer near the boundary of the body exhibits a stiffness fluctuation due to the so-called surface effect and the inaccurate way of imposing the boundary conditions. Moreover, in numerical models discretized using the meshfree method with uniform grid spacing, there are no nodes on the external surface of the body where the boundary conditions should be applied. Inspired by the method of the fictitious nodes with the Taylor-based extrapolation, we propose an innovative method that introduces a new type of nodes lying on the external surface of the body, i.e., the surface nodes. These nodes represent the interactions between the nodes within the body and the fictitious nodes surrounding the body, and they are used to mitigate the surface effect and properly impose the boundary conditions via the concept of force flux. Moreover, a procedure to compute the analytical solution of peridynamic problems is developed: a manufactured displacement field is prescribed and the volume and surface forces, to obtain that displacement field, are computed. The benefits of the surface node method are shown by means of several 2D and 3D quasi-static examples by comparing the numerical results with other methods with or without boundary corrections.

CRACK INITIATION AT GRAIN BOUNDARY WITH A VARIABLE MISORIENTATION VECTOR

A model is proposed for the initiation of cracks at “knife” grain boundaries, i.e., rectilinear, broken boundaries of deformation origin, oriented along the tension axis, arising as a result of rotational incompatibility in the form of a disclination dump at the stage of pre-fracture of the material. The disorientation of the “knife” boundary decreases down to the breaking point in the body of the grain, and its decrease (rotational instability damping) occurs not continuously, but discretely through the branching of secondary low- and high-angle boundaries. In this case, along the “knife” boundary, at the points of its branching, linear mesodefects of the rotational type arise-wedge disclinations of the same sign. A model of crack initiation in an elastic field of a chain of negative disclinations that create tensile elastic stresses is proposed. When analyzing the conditions for crack initiation, a combined criterion was used, according to which the simultaneous fulfillment of force and energy conditions was required for crack initiation. Within the framework of this model, the critical values of the total value of the Frank vector of disclinations located on the “knife” boundary and the average gradient of its misorientation are calculated, upon reaching which the criterion of crack initiation is satisfied. The dependences of these quantities on the length of the “knife” boundary and the effective screening radius of the elastic field of disclinations are calculated. It is shown that the appearance of cracks is most likely at the boundaries with the largest misorientation gradient (exceeding 8–20 deg/?m, depending on the length of the boundary).

Numerical Modeling of Quasi-Brittle Materials Using a Phase-Field Regularized Cohesive Zone Model with Optimal Softening Law

In this paper, we propose an approach combining optimal softening laws and a phase-field regularized cohesive zone model (PF-CZM) for modeling the fracture and damage properties of quasi-brittle materials accurately. In this method, the optimal softening law is determined by comparing the predicted results with experimental data in the framework of the PF-CZM; three typical softening laws are considered. The PF-CZM with a length scale is used to model crack initiation and propagation without considering the mesh bias. We first investigate the mechanical responses and crack propagations of different concrete beams based on the above approach; the predicted results are compared with the data from conventional methods and experiments. The results indicate that the mechanical properties of concrete beams with the optimal softening law are better than the data reported in the literature. Further validation indicates that once the optimal softening law is determined, it is stable for the same group of materials. Moreover, we demonstrate that the PF-CZM can naturally predict and reproduce the critical notch offset and fracture transition process of three-point bending concrete beams and the fracture features of typical double-notched concrete beams, such as the interaction between two notches objectively, together with the changes of limit load capacity.

The investigation of reasonable range of initial load of low-cycle fatigue cropping for notched bars

The low-cycle fatigue cropping (LCFC) method is a new separation method that has low active load and low energy waste. A crucial challenge for the LCFC is to determine the suitable range of initial load, which impacts the crack initiation and the cross-section quality. This work proposes a novel crack initiation model which considers cumulative plastic deformation, material mechanical properties, notch stress, and material microstructure, and has a simple form. The acoustic emission technique (AET) is used to prove the validity of the model. The finite element method (FEM) and Electron backscatter diffraction (EBSD) are used to assess the effect of various initial loads. A laser confocal microscopy is used to measure the arithmetic mean deviation of the crack initiation area. The validity of the crack initiation model is proven. The critical crack initiation load (CCIL) of 316L, AISI 304, Al 6061, 1045 steel, and 16Mn bar are 2.470 mm, 2.080 mm, 1.310 mm, 2.980 mm, and 2.950 mm, respectively. The reasonable ranges of initial load for 316L, AISI 304, Al 6061, 1045 steel, and 16Mn bar are obtained.

Application of Weibull fracture strength distributions to modelling crack initiation behaviour in nuclear fuel pellets using peridynamics

The thermomechanical behaviour of uranium dioxide nuclear fuel pellets irradiated in a pressurised water reactor has been simulated using a two-dimensional application of bond-based peridynamics implemented in the Abaqus commercial finite element software. Near-surface bond failure, and hence crack initiation, were modelled assuming a probabilistic (variable) failure strain described by a Weibull distribution – with bond failure, and hence crack propagation, in the bulk of the fuel pellets modelled assuming a deterministic (fixed) failure strain. The measured dependency of the number of radial pellet cracks on heat generation rate per unit length – which we show cannot be reproduced by the common assumption in pellet modelling of a deterministic failure strain throughout the pellet volume – was accurately predicted when a size-scaled Weibull distribution with a modulus of 5 was used. However, this low modulus value was associated with the prediction of some cracks initiating away from the pellet surface, which is unphysical. Use of a Weibull modulus of 10 avoided this simulation artefact while still reproducing the experimentally observed dependency with reasonable accuracy.

Probabilistic stress and strain-life fatigue crack initiation models with mean stress effects and life-dependent scatter considering runouts

A powerful probabilistic framework is proposed to account for life-dependent data scatter in fatigue crack initiation (FCI) predictions considering mean stress effects. It is applicable to any stress, strain, or energy-based fatigue damage parameter (DP), as long as the logarithm of DP for a given FCI life Nf can be assumed to follow a three-parameter Weibull (W3P) distribution. The proposed approach, named P-DP-N, does not require the assumption of any particular statistical distribution for Nf, thus it can fit the shape of virtually any equation correlating DP and Nf. Hence, it can deal simultaneously with LCF, HCF and VHCF FCI data, considering mean stress effects and runout statistics. The approach deals with heteroscedasticity through a user-defined life-dependent scedastic function of Nf, allowing the consideration of variable data scatter in log–log scales. The P-DP-N performance is evaluated using the Walker Equivalent Strain (WES) equation proposed by the authors, which is generalized to explicitly consider fatigue limits. Procedures are proposed to calibrate both stress and strain-based versions of the deterministic WES-life FCI model, as well as to optimize the W3P parameters from the resulting P-WES-N probabilistic model, considering runout data when available. A compact computational implementation of the calibration routines is presented as well. The W3P-based P-WES-N probabilistic model is evaluated for 31 metallic alloy data sets from the literature that include non-zero mean stresses and at least twenty specimens each, totaling 1,498 uniaxial fatigue specimens, including 141 runouts. This comprehensive evaluation shows that the proposed probabilistic model is able to account for tensile and compressive mean stress effects, as well as to calibrate the usually observed increase in experimental scatter for longer FCI lives.

A novel collaborative study of abnormal roof water inrush in coal seam mining based on strata separation and wing crack initiation

Separation water inrush poses a potential threat to safe mining on the working face, whose mechanism should be investigated in order to take better prevention and control measures. In this study, aiming at the problem of separation water inrush under hydrostatic pressure, the 21805 working face of the Yushujing coal mine was chosen as the research object to establish an in-house similar simulation experiment. The experiment could reveal the evolution law of bed separation space, the process of water accumulation in bed separation space, and the breaking characteristics of separation water inrush. Meanwhile, in order to theoretically interpret the evolution of water-conducting fractured zone (WCFZ), an analytical model for wing crack initiation from compression-shear fracture and tension-shear fracture that considers T-stress was derived. The analytical model comprehensively considers the effects of overlying strata load and aquifer water pressure, fracture geometry, and rock properties. The results show that the time of separation water inrush obtained by the similar simulation experiment is consistent with the field result, and the orientation of new cracks generated due to water injection also coincides with the analytical solution. In addition, it is found that the development of bed separation space is a long-term process, which can provide a theoretical basis for the prevention and control of separation water inrush.

Experimental and modeling study on small fatigue crack initiation and propagation behavior of Inconel 617

Small fatigue crack initiation and propagation behavior of Inconel 617 was studied by in-situ SEM observation, electron back-scattered diffraction (EBSD), digital image correlation (DIC), crystal plasticity finite element method (CPFEM) and extended finite element method (XFEM) in this paper. The experimental results indicated that different surface corrosion methods used to display surface microstructure will affect the small fatigue cracking mode of Inconel 617. The local micro-scale strain field of Inconel 617 near the notch and crack tip was quantitatively measured by a new grain scale DIC method. The CPFEM-XFEM simulation model of small fatigue crack initiation and propagation characteristics of Inconel 617 was established. A new framework for small fatigue crack path and lifetime prediction at the polycrystalline scale was constructed, which includes the influences of slip system and grain boundary on small fatigue crack initiation and growth rate.

Failure probability evaluation for a weld of the heat pipe in the Mega-Power heat pipe cooled reactor

Heat pipe cooled reactor, featuring using heat pipes as passive cooling, has received renewed interest. A Monte-Carlo-based probabilistic fracture mechanics analysis code, including crack initiation and propagation model, is developed to estimate the probability of failure at a weld in the heat pipe due to stress corrosion cracking (SCC), fatigue, and high temperature creep. The application of this code is demonstrated on the heat pipe of the Mega-Power rector. The results show that SCC is more important in accelerating heat pipe failure than fatigue and high temperature creep. Failure probabilities under the condition of one or two adjacent failed heat pipes are abnormally close. Uncertainty analysis for input parameters proves initial crack size is more sensitive than temperature. This also provides a reference for heat pipe design and safety assessment of whole reactor.