Fatigue Crack Initiation Model Research Articles

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

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.

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.

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.

A peridynamic frictional contact model for contact fatigue crack initiation and propagation

Cyclic contact between components can cause cracks in the contact area. Peridynamics can overcome the difficulty of solving cracks and other discontinuities in classical continuum mechanics. A new peridynamic sliding frictional contact model is proposed and verified by a two-dimensional point contact sliding simulation. Then, a two-dimensional plane strain elastoplastic peridynamic model of a single micro-contact asperity is established, and the fatigue crack initiation and propagation in the micro-contact area during fretting wear is analyzed. The results show that in fretting wear, crack initiation originates from the area of maximum shear stress below the surface. The subsurface crack initially propagates in the direction parallel to the surface, and then gradually propagates to the surface. Finally, the crack grows to the free surface and forms wear debris. The contact pressure and the coefficient of friction in the contact surface can affect the crack initiation depth and crack propagation path, thereby affecting the size of wear debris. The crack propagation path is not sensitive to the change of the coefficient of friction of the crack surface. This study helps to understand the mechanism of fretting wear and provides a reference for predicting fretting wear.

A probabilistic model for low-cycle fatigue crack initiation under variable load cycles

A probabilistic low-cycle fatigue (LCF) model, ProbLCF-VA, is proposed in this work to describe the scatter of the LCF crack initiation life for homogeneous materials subjected to variable or random load cycles. This model can be implemented either to estimate the probabilistic cumulative damage for a given load history consisting of variable cyclic loads, or to predict the probabilistic LCF crack initiation if distributional estimates of a random load spectrum are available. More importantly, the proposed model is capable of describing certain prevailing effects such as load interaction and small cycle contributions, which are very commonly observed in fatigue tests with variable amplitude cyclic loads but can hardly be described by other models with physical and mathematical foundations. Model predictions are illustrated with multiple examples and compared to those from classical cumulative damage rules. The result shows a good qualitative match between the model prediction and test data in the literature on load interaction effects.

Thermomechanical fatigue life due to scatter in constitutive parameters

For critical component application, such as aerospace turbine rotors, it is imperative to be able to make accurate in-service material behaviour and component life predictions for both design and monitoring of component life. The development of such predictive capability is dependent on the quality of the experimental data from which the material parameters are derived. This paper shows the effect that scatter which may be present within experimental data, manifesting itself within the constitutive parameters derived from this data, has on the resulting fatigue crack initiation life of the nickel-based superalloy RR1000. Industrial relevance was added to this investigation by the use of flight representative thermomechanical fatigue loading cycles and state of the art material behaviour and fatigue crack initiation models used within the finite element simulations conducted. The effect of the ‘scatter in’ to the modelling approach on the outcoming predictions is made via a Monte-Carlo analysis. This analysis consisted of running the same simulation several times, but with the experimentally determined and validated ‘baseline’ constitutive parameters varied via correction factors built into the model, for each run via a singular value decomposition procedure. It was found that small ‘scatter in’ has only a very localised ‘scatter out’ effect on the crack initiation predictions under the flight representative loading.

Crack Propagation in the Tibia Bone within Total Knee Replacement Using the eXtended Finite Element Method

Understanding of fracture mechanics of the human knee structures within total knee replacement (TKR) allows a better decision support for bone fracture prevention. Numerous studies addressed these complex injuries involving the femur bones but the full macro-crack propagation from crack initiation to final failure and age-related effects on the tibia bone were not extensively studied. The present study aimed to develop a patient-specific model of the human tibia bone and the associated TKR implant, to study fatigue and fracture behaviors under physiological and pathological (i.e., age-related effect) conditions. Computed tomography (CT) data were used to develop a patient-specific computational model of the human tibia bone (cortical and cancellous) and associated implants. First, segmentation and 3D-reconstruction of the geometrical models of the tibia and implant were performed. Then, meshes were generated. The locations of crack initiation were identified using the clinical observation and the fatigue crack initiation model. Then, the propagation of the crack in the bone until final failure was investigated using the eXtended finite element method (X-FEM). Finally, the obtained outcomes were analyzed and evaluated to investigate the age-effects on the crack propagation behaviors of the bone. For fatigue crack initiation analysis, the stress amplitude–life S–N curve witnessed a decrease with increasing age. The maximal stress concentration caused by cyclic loading resulted in the weakening of the tibia bone under TKR. For fatigue crack propagation analysis, regarding simulation with the implant, the stress intensity factorand the energy release rate tended to decrease, as compared to the tibia model without the implant, from 0.152.5 to 0.111.9 (MPa) and from 10240 to 5133 (J), respectively. This led to the drop in crack propagation speed. This study provided, for the first time, a detailed view on the full crack path from crack initiation to final failure of the tibia bone within the TKR implant. The obtained outcomes also suggested that age (i.e., bone strength) also plays an important role in tibia crack and bone fracture. In perspective, patient-specific bone properties and dynamic loadings (e.g., during walking or running) are incorporated to provide objective and quantitative indicators for crack and fracture prevention, during daily activities.

Microstructural analysis and fatigue crack initiation modelling of additively manufactured 316L after different heat treatments

This study investigates the fatigue behaviour of 316L stainless steel manufactured by laser powder bed fusion. More specifically, the influence of the microstructure on fatigue is analysed for four different material conditions: as-built, stress relieved, fully annealed and hot isostatic pressed. Fully reversed tension-compression fatigue results on miniaturised vertically built and machined samples indicate that as-built and stress relieved specimens exhibit superior fatigue behaviour compared to fully annealed and hot isostatic pressed ones. Fine sub-grained cellular microstructure in as-built and stress relieved samples resulted in high fatigue performance, which was decreased with microstructure coarsening from the high temperature heat treatments. Secondly, a microstructure-based fatigue crack initiation model is adapted for additively manufactured 316L and verified for different material states. The results show that the analytical model depicts a conservative prediction for crack initiation life when compared with experimental results for full fracture. This validation offers the potential to expand the model for other material and process conditions.

Low cycle fatigue damage model and sensitivity analysis of fatigue crack initiation by finite element approach

To meet the design requirements, different types of defects are often machined on the surface of fatigue components. Local stress concentration formed at the notch accelerate the initiation of fatigue crack, therefore greatly shorten the service lives of such components. Based on the theory of continuous damage mechanics and the principle of irreversible thermodynamics, the damage evolution model of low cycle fatigue is investigated. By programming the damage evolution model as UMAT subroutine and coupling it to ABAQUS, the fatigue damage and crack initiation life of notched P92 steel samples under specific loads are simulated, and the crack initiation location is determined. Furthermore, the damage evolution and crack initiation sensitivity of notch morphology are considered. The results show that the crack initiation occurs easily in the notch root where the damage is greatest and the plastic strain accumulates fastest under cyclic loading. The fatigue damage accumulates slowly at the initial stage, but the damage accumulates rapidly after the cumulative damage reaches a critical value. The fatigue damage evolution and fatigue initiation life are very sensitive to the notch morphology parameters. The notch morphology need to be carefully analyzed, to improve the fatigue life of the notched samples.

A Methodology for Incorporating the Effect of Grain Size on the Energy Efficiency Coefficient for Fatigue Crack Initiation Estimation in Polycrystalline Metal

Estimating fatigue crack initiation of applied loading is challenging due to the large number of individual entities within a microstructure that could affect the accumulation of dislocations. In order to improve the prediction accuracy of fatigue crack initiation models, it is essential to accurately compute the energy dissipated into the microstructure per fatigue loading cycle. The extent of the energy dissipated within the microstructure as a fraction of the overall energy imparted by loading has previously been defined as the ‘energy efficiency coefficient’. This work studied the energy efficiency coefficient as a factor in the measurement of accumulated plastic strain energy stored at the crack initiation site during cyclic loading. In particular, the crystal plasticity constitutive formulation was known as ’length scale independent’ previously. As a result, a semi-empirical approach was presented whereby the potential effect of grain size can be accounted for without the use of a strain gradient plasticity approach. The randomized representative volume elements were created based on the experimental analysis of grain size distribution. The work was aimed at capturing some of the effects of grain size and utilizing them to complete a semi-empirical estimation of crack initiation in polycrystalline materials. The computational methodology ensured the representative of microstructural properties, including the elastic constant and critical resolved shear stress via appreciable fit achieved with the empirical tensile test results. Crystal plasticity finite element modeling was incorporated into a finite element code to estimate the potential for crack initiation. The energy efficiency coefficient was computed for a class of material with grain size to C11000 electrolytic tough pitch (ETP) copper. This methodology can improve fatigue crack initiation life estimation and advance the fundamental study of energy efficiency coefficient during fatigue crack initiation.

A 2D peridynamic model for fatigue crack initiation of railheads

Due to the use of PDEs (Partial Differential Equations), classical continuum mechanics is difficult to solve the problems of discontinuous deformation. Using integral equations, peridynamic theory can overcome this difficulty. A 2D method for predicting fatigue crack initiation of railheads was presented based on the peridynamic theory. First, the reasonable values of the model parameters were analyzed. Second, the accuracy of the method was verified through comparisons with the results of classical continuum mechanics and existing conclusions in the literature. Finally, the effects of wheel-rail rolling-sliding status, friction coefficient, and wheel load on fatigue crack initiation were analyzed and discussed.

Fatigue design challenges: Recent linear and nonlinear models

Reliable fatigue design rules affect the proactive identification of safety parameters in engineering structures. Numerous fatigue crack initiation and propagation models, linear and nonlinear, have been developed for designing purposes or estimation of the remaining life of aging structures. Depending on the adopted assumptions, the accuracy varies for different loading histories, loading types, and materials. Semi empirical models are simple but yield significant inaccuracies. Models with better theoretical basis provide better accuracy, but implementation in real conditions is problematic. In the present work, a review of author’s recent fatigue crack initiation and propagation models based on physical mechanisms is presented and improvements are proposed. Verification of the models on test results is provided and discussed.

Isothermal fatigue damage mechanisms at ambient and elevated temperature of a cast Al-Si-Cu aluminium alloy

Cast aluminium alloys have a key position as structural materials for the automotive industry combining good mechanical performance, excellent castability and thermal conductivity, making them a suitable choice for engine parts such as cylinder heads. In this paper, the low-cycle fatigue behaviour of a cast aluminium alloys is investigated at ambient and elevated temperatures by the use of in situ optical surface crack monitoring, secondary electron microscopy and X-ray tomography which are combined to study the fatigue mechanisms. The observations highlight the effect of defect distribution and temperature on the crack propagation path and in particular the change of the role of eutectic regions as the temperature increases. In addition, based on the defects population analyses by tomography, a fatigue crack initiation model is proposed to consider both temperature and defect effects on the total low-cycle fatigue life and fatigue crack growth rates.

Low cycle fatigue test and enhanced lifetime estimation of high-strength steel S550 under different strain ratios

This study investigates the low-cycle fatigue (LCF) behavior of the high-strength steel S550 (commonly used in ship and floating structures) under different strain amplitudes with different strain ratios at a room temperature. The test results characterize the cyclic stress-strain relationship, the mean stress relaxation behavior and the cyclic plasticity parameters of S550 steels. The scanning electron microscopy (SEM) examinations on the failure surface reveal the fatigue crack initiation and growth mechanism. Based on the experimental results, this study presents two enhanced approaches to estimate the low-cycle fatigue life of S550 steels. The energy-based approach modifies the original Smith-Watson-Topper model using the applied energy calculated in the first cycle to enhance the accuracy and facilitate engineering implementations. The damage mechanics-based approach calibrates the material parameters from the measured total fatigue life by combining the fatigue crack initiation model and the damage growth model. The computed fatigue life using the calibrated material parameters demonstrates a close agreement with the measured fatigue life in the experiment.

The energy‐based multistage fatigue crack growth life prediction model for DRMMCs

AbstractA complex closed form expression for the multistage fatigue crack growth life has been developed to predict the fatigue life of discontinuous reinforced metal matrix composites. The multistage fatigue crack growth model includes the microstructural features of composite such as aspect ratio, volume fraction of reinforcement, constraint of fibre in the matrix, and interfacial bonding strength. It characterizes the fatigue damage evolution in various stages of crack nucleation/initiation and the growth of crack culminating in failure. A fatigue crack initiation model is presented, using energy balance equation, considering the nucleation process of phase transformation. The short crack growth life is estimated using the dependency of cyclic crack‐tip opening displacement that is directly correlated with the fatigue crack growth rate whereas the long crack growth life is evaluated using Li and Ellyin model. The sensitivity analysis of crack initiation model is performed to provide in‐depth knowledge on the mechanistic aspect. The sensitivity analysis shows that the little variation in the parameters “cyclic strain hardening exponent” (n′), “cyclic strength coefficient” (K′), and short crack length (asc) significantly affects the total fatigue crack growth life. It is observed that reinforcement increases the cyclic plastic deformation level and cyclic plastic zone size near the crack tip, under the total strain‐controlled conditions. The effect of total fatigue crack growth life is found to be significant in low cycle fatigue applications.

Orientation Dependence of Low Cycle Fatigue Properties of a Ni-based Single Crystal Superalloy DD10

Low cycle fatigue (LCF) properties of a nickel-based single crystal (SX) superalloy DD10 with different orientation deviation angles from the [001] axis were investigated at 760 °C with an invariable total strain amplitude of 1.4%. Results reveal that the LCF behaviors of DD10 exhibit a strong orientation-dependence. The fatigue life decreases apparently with the increment of the orientation deviation angle. For specimens with the same orientation deviation angle from the [001] axis, those on the [001]-[011] boundary exhibit a longer fatigue life than ones on the [001]-[ 1 ¯ 11] boundary. It is found that the orientation-dependence of fatigue life stems from the difference of accumulated plastic deformation per cycle. On the other hand, both of total stress amplitude and plastic strain amplitude show a reverse orientation-dependence compared with the fatigue life. However, the orientation deviation shows no influence on the model of fatigue crack initiation and subsequent propagation.

A cyclic slip irreversibility based model for fatigue crack initiation of nickel base alloys

The opportunity to define a microscopic law of fatigue crack initiation using Manson-Coffin law formulated in terms of cyclic slip irreversibility deduced from AFM measurements is discussed for a polycrystalline superalloy with different grain sizes and precipitate sizes. The results show that the modified Manson-Coffin law, relating cyclic slip irreversibility parameter to fatigue crack initiation life, is sustained through a two-parameter power law: ε′f and c. The analysis suggests that the exponent c-value can be related to the degree of plastic strain incompatibility between grains, and the cumulative irreversible cyclic plastic strain to crack initiation is a relevant damage indicator for crack initiation. Consequently, our approach allows giving a physical base of engineering law.

Thermomechanical fatigue crack initiation in disc alloys using a damage approach

A fatigue crack initiation model based on damage accumulation via a fatigue memory surface in conjunction with a plastic strain energy parameter was evaluated for thermomechanical fatigue loading in a gas turbine disc alloy. The accumulated damage in each hysteresis loop was summed up, and it was assumed that the damage at the stable state is repeated until failure occurs. Crack initiation occurs when enough fatigue damage has been obtained, and the number of cycles can thus be directly determined. The fatigue damage is highly coupled to the constitutive behaviour of the material, where the constitutive behaviour was modelled using a non-linear hardening description. Based on this, a stable state was achieved and the obtained damage could be extracted. A user-defined material subroutine was implemented, incorporating both the constitutive description and the fatigue damage accumulation. The framework was adopted in a finite element context to evaluate the thermomechanical fatigue crack initiation life of the disc alloy RR1000. From the evaluation it could be seen that a good prediction of the thermomechanical fatigue life was achieved compared to performed experiments.

A cyclic slip irreversibility based model for fatigue crack initiation of nickel base alloys

The opportunity to define a microscopic law of fatigue crack initiation using Manson-Coffin law formulated in terms of cyclic slip irreversibility deduced from AFM measurements is discussed for a polycrystalline superalloy with different grain sizes and precipitate sizes. The results show that the modified Manson-Coffin law, relating cyclic slip irreversibility parameter to fatigue crack initiation life, is sustained through a two-parameter power law: εf′ and c. The analysis suggests that the exponent c-value can be related to the degree of plastic strain incompatibility between grains, and the cumulative irreversible cyclic plastic strain to crack initiation is a relevant damage indicator for crack initiation. Consequently, our approach allows giving a physical base of engineering law.