Prediction of Fatigue Lives of MAR‐M247 LC Based on the Crack Closure Concept

Low cycle fatigue (LCF), high cycle fatigue (HCF), and combined LCF and HCF tests are carried out on MAR‐M247 LC at 650 °C in air environment. Under combined LCF and HCF loading, block striations form on the fracture surface which are used to complete an effective crack growth curve by using the linear summation model. Crack growth lives starting from equivalent initial flaw sizes are calculated by the crack closure code FASTRAN and compared with experimental fatigue lives. Under HCF loading, predicted and experimental fatigue lives agree well for lifetimes above 10⁵ cycles. Lower lifetimes are overestimated indicating that the linear summation model is not valid for MAR‐M247 LC in this loading range. Interactions between the non‐crystallographic HCF crack growth and striated crack growth that is caused by the LCF loading are probably responsible for this behavior.     

Probabilistic high cycle fatigue behaviour of nodular cast iron containing casting defects

Theoretical and experimental investigations were combined to characterize the influence of surface casting defects (shrinkages) on the high cycle fatigue (HCF) reliability. On fracture surfaces of fatigue samples, the defect is located at the surface. The shape used for the calculation is a spherical void with variable radius. Finite-element simulations were then performed to determine stress distribution around defects for different sizes and different loadings. Correlated expressions of the maximum hydrostatic stress and the amplitude of the shear stress were obtained by using the response surface technique. The loading representative point in the HCF criterion was then transformed into a scattering surface, which has been obtained by a random sampling of the defect sizes. The HCF reliability has been computed by using the Monte Carlo simulation method. Tension and torsion fatigue tests were conducted on nodular cast iron with quantification of defect size on the fracture surface. The S – N curves show a large fatigue life scattering; shrinkages are at the origin of the fatal crack leading to the final failure. The comparison of the computed HCF reliability to the experimental results shows a good agreement. The capability of the proposed model to take into account the influence of the range of the defect sizes and the type of its statistical distribution has been demonstrated. It is shown that the stress distribution at the fatigue limit is log-normal, which can be explained by the log-normal defect distribution in the nodular cast iron tested.     

Multiaxial small fatigue crack growth in metals

Observations related to the formation and growth of small cracks ranging from subgrain dimension up to the order of 1 mm are summarized for amplitudes ranging from low cycle fatigue (LCF) to high cycle fatigue (HCF) conditions for polycrystalline metals. Further efforts to improve the accuracy of life estimation which address LCF, HCF and LCF–HCF interactions must consider various factors that are not presently addressed by conventional elastic–plastic fracture mechanics (EPFM) or linear elastic fracture mechanics (LEFM) approaches based on long, self-similar cracks in homogeneous, isotropic materials, nor by conventional HCF design tools such as the ε–N curve, the S–N curve, modified Goodman diagram and fatigue limit.Development of microstructure-sensitive fatigue crack propagation relations relies on deeper understanding of small crack behavior, including (a) interactions with microstructure and lack of constraint for microstructurally small cracks, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) local mode mixity effects on small crack growth. The basic technology is not yet sufficiently advanced in these areas to implement robust damage tolerant design for HCF. This paper introduces an engineering model which approximates the results of slip transfer calculations related to crack blockage by microstructure barriers; the model is consistent with critical plane concepts for Stage I growth of small cracks, standard cyclic stress–strain and strain–life equations above threshold, and the Kitagawa diagram for HCF threshold behaviors. It is able to correlate the most relevant trends of small crack growth behavior, including crack arrest at the fatigue limit, load sequence effects, and stress state effects.     

Failure probability of borosilicate glass under Hertz indentation load

The objective of this work is to test the hypothesis that the failure probability prediction model by Fischer-Cripps and Collins can be used without introducing an empirically derived parameter and therefore can serve as a predictive tool. We examined this hypothesis by Hertz cone crack initiation tests of flat borosilicate glass statically loaded through a spherical indenter. The Weibull parameters characterizing the surface flaw distribution were determined from biaxial flexure experiments using specimens with the same surface condition as in the indentation tests. Elastic moduli of the specimens were determined by using ultrasonic methods. In addition, the crack initiation was determined using stereo microscopy at 20× magnification.The results demonstrated that the model can predict the minimum critical load and cumulative failure probability for small indenters within the 90% confidence level. Therefore, the current work demonstrates that the model can be used as a predictive tool provided the parameters necessary for the model accurately reflect those of the actual sample populations that are used for the experimental setup.     

Simulation of plasticity-induced fatigue crack closure in part-through cracked geometries using finite element analysis

The part-through semi-elliptical surface flaw is commonly encountered in engineering practice. Proper characterization of plasticity-induced crack closure is necessary to predict both flaw growth and flaw shape evolution under cyclic loading. Three-dimensional elastic-plastic finite element analyses are used to model the plasticity-induced closure developed along the surface flaw crack front, and the subsequent crack opening behavior under constant amplitude loading. Resulting crack opening stresses are compared with results from a strip-yield model and with experimentally measured values reported in the literature. It was found that the computed values were larger than those measured.     

Micro-mechanical theory of macroscopic stress-corrosion cracking in unidirectional GFRP

A micro-mechanical theory of macroscopic stress-corrosion cracking in a unidirectional glass fibre-reinforced polymer composite is proposed. It is based on the premise that under tensile loading, the time-dependent failure of the composite is controlled by the initiation and growth of a crack from a pre-existing inherent surface flaw in a glass fibre. A physical model is constructed and an equation is derived for the macroscopic crack growth rate as a function of the apparent crack tip stress intensity factor for mode I. Emphasis is placed on the significance of the size of inherent surface flaw and the existence of matrix crack bridging in the crack wake. There exists a threshold value of the stress intensity factor below which matrix cracking does not occur. For the limiting case, where the glass fibre is free of inherent surface flaws and matrix crack bridging is negligible, the relationship between the macroscopic crack growth rate and the apparent crack tip stress intensity factor is given by a simple power law to the power of two.     

A fracture mechanics approach to high cycle fretting fatigue based on the worst case fret concept – I. Model development

An integrated analytical and experimental approach was taken to develop a fracture mechanics-based methodology for predicting the limiting threshold stress of high-cycle fretting fatigue in structural alloys. The contact stress field for two flat surfaces under fretting was analyzed via an integral equation technique. The local fretting stress field of the uncracked body was then utilized to obtain the stress intensity factor of an arbitrarily oriented fatigue crack using a continuum dislocation formulation. The limiting threshold stress ranges for the nonpropagation of fretting fatigue cracks were predicted on the basis that the fretting fatigue cracks are small cracks that exhibit a size-dependent growth threshold and propagate at stress intensity ranges below the large-crack threshold. In part I, the development of the worst-case fret (WCF) model is described. The influence of the limiting high-cycle fatigue (HCF) threshold stress on a variety of fretting fatigue parameters such as bearing pressure, pad geometry, shear stress, mode mixity, and coefficient of friction are elucidated by parametric calculations. In part II, the WCF model is applied to treating HCF of Ti-6Al-4V where model predictions are compared against critical experiments performed on a kilohertz fretting-fatigue rig.     

Effect of LCF on HCF crack growth of Ti-17

An improved understanding of fatigue crack growth phenomena applicable to titanium engine disks was developed through complimentary experimental and analytical investigations of Ti-17. The effect of low cycle fatigue (LCF) on the high cycle fatigue (HCF) threshold and rate of crack propagation was studied. A simplified variable-amplitude spectrum, consisting of high-R cycles, corresponding to HCF loading, and periodic R=0.1 cycles, corresponding to LCF loading, was used to demonstrate a load-interaction effect. When the ratio of HCF to LCF cycles was 100 or more the fatigue crack growth lifetimes were significantly lower than predicted using linear damage summation methods assuming no load-interaction effect. Thus, it was concluded that the LCF cycle accelerated the fatigue crack growth rate of subsequent HCF cycles, even when closure was concluded to be negligible. A phenomenological model was formulated based on hypothesized changes in the propagation resistance, K_PR, and fit to the test data. The model confirmed that the periodic LCF cycles increased fatigue crack growth rates of subsequent HCF cycles.     

Microstructure-based fatigue modeling of cast A356-T6 alloy

High cycle fatigue (HCF) life in cast Al-Mg-Si alloys is particularly sensitive to the combination of microstructural inclusions and stress concentrations. Inclusions can range from large-scale shrinkage porosity with a tortuous surface profile to entrapped oxides introduced during the pour. When shrinkage porosity is controlled, the relevant microstructural initiation sites are often the larger Si particles within eutectic regions. In this paper, a HCF model is introduced which recognizes multiple inclusion severity scales for crack formation. The model addresses the role of constrained microplasticity around debonded particles or shrinkage pores in forming and growing microstructurally small fatigue cracks and is based on the cyclic crack tip displacement rather than linear elastic fracture mechanics stress intensity factor. Conditions for transitioning to long crack fatigue crack growth behavior are introduced. The model is applied to a cast A356-T6 Al alloy over a range of inclusion severities.     

Microstructure-sensitive HCF and VHCF simulations

This paper provides some background and historical review of how microstructure-sensitive finite element simulations can play a role in understanding the effects of stress amplitude, R-ratio, and microstructure on fatigue crack formation and early growth at notches, including pores and non-metallic inclusions for Ti alloys and Ni-base superalloys. The simulations employ fatigue indicator parameters (FIPs) computed over finite volumes that relate to processes of fatigue crack formation and early growth at the scale of individual grains. It is argued that both coarse scale (uncracked, mesoscale) and fine scale FIPs (computed in the vicinity of cracks in single grains or crystals) serve as a driving force for crystallographic fatigue crack growth, and correlate directly with the cyclic crack tip displacement (CTD). Furthermore, variability in high cycle fatigue (HCF) and very high cycle fatigue (VHCF) responses is computationally assessed using multiple statistical volume elements and the distribution of FIPs of extreme value character. The concepts of marked correlation functions and weighted probability density functions are reviewed as a means to quantify the role of multiple microstructure attributes that couple to enhance the extreme value FIPs in the HCF regime. An algorithm for estimation of the cumulative probability distribution of cycles for crack formation and growth from notches in HCF and VHCF is also described.     

Analysis of stress intensity factors for three-dimensional finite cracked bodies by a variational alternating method

A variational alternating method which is suitable for analyzing finite three dimensional cracked solid is presented. The stress analysis of the unracked solid is performed by the functional variable displacement solution and the variational method. The stress intensity factor solution for an embedded elliptical crack and a surface flaw in a finite plate for the case of mode-I loading are obtained by the variational alternating method. The results are compared with that of reference.     

Fatigue crack propagation for defects near a free surface

The fatigue crack growth associated with an internal flaw as it approaches a free surface was studied. Previous researchers recommended when the plastic zone at the crack tip nearest the free surface reaches one-tenth of the ligament size which exists between the free surface and the crack tip that the flaw be treated as an edge crack. The results of this study show that the assumption of an edge crack can prove to be exceptionally conservative when employed for design purposes. Underestimates of fatigue life of as much as 1000% were observed. Improved methods for predicting the fatigue growth of near surface defects are offered in the paper.     

On the life-controlling microstructural fatigue mechanisms in ductile metals and alloys in the gigacycle regime

The high-cycle fatigue (HCF) behaviour of ductile metals and alloys, and the life-controlling microstructural fatigue mechanisms known from HCF are reviewed critically with respect to their possible role in the gigacycle or ultra-high-cycle fatigue (UHCF) regime. Arguments are presented to support the hypothesis that, at the very low amplitudes of the UHCF regime, fatigue crack initiation, resulting from cyclic strain localization, and slow early Stage I fatigue crack propagation are the life-controlling mechanisms and that these processes can essentially be described in terms of the microstructurally irreversible portion of the cumulative cyclic plastic strain. Emphasis is placed on the important role of the so-called slip irreversibility which decreases as the amplitude becomes lower and lower. Finally, the Manson–Coffin law is reformulated for very low amplitudes in terms of microstructurally relevant parameters, and a fatigue life diagram is developed, based on these preceding microstructural considerations. Important features of this diagram are: (i) the plastic strain fatigue limit in the HCF regime which is related to the threshold for cyclic strain localization in persistent slip bands; and (ii) the transition from this plastic strain fatigue limit to a threshold of negligible slip irreversibility at still lower amplitudes in the UHCF regime.     

Modified Kitagawa–Takahashi diagram accounting for finite notch depths

The Kitagawa–Takahashi diagram in its commonly used form allows to predict, for cracks of given length and stress range, the allowable stress range for infinite life. However, caution is advised if a crack emanates not directly from the plane surface but from a sharp, crack-like notch instead. In this contribution, it is shown that taking the crack length equal to the total flaw depth (sum of notch depth and crack length) gives non-conservative results. Based on a simple mechanical model, a 3-dimensional Kitagawa–Takahashi diagram considering the build-up of crack growth resistance as well as the influence of the notch depth is developed. Comparison of model predictions and experimental results shows good agreement.     

Weight function calculation for surface cracks using the line-spring model

A numerical method for calculating weight functions for surface cracks in plates and shells is proposed. Thick-shell finite elements are used to create the discrete model of a body with a through-wall flaw. Line-spring elements transform the through-wall flaw into a surface crack. A quadratic line-spring element is presented. Weight functions for some semielliptical surface cracks in a plate have been calculated. The weight functions obtained may be used for computing stress intensity factors related to two-dimensional stress fields at the crack surface.     

Probabilistic prediction of high cycle fatigue reliability of high strength steel butt‐welded joints

The aim of this paper is to develop a probabilistic approach of high cycle fatigue (HCF) behaviour prediction of welded joints taking into account the surface modifications induced by welding and the post‐welding shot peening treatment. In this work, the HCF Crossland criterion has been used and adopted to the case of welded and shot peened welded parts, by taking into account the surface modifications which are classified as follows: (i) the compressive residual stresses, (ii) the surface work‐hardening, (iii) the geometrical irregularities and (iv) the superficial defects. The random effects due to the dispersions of: (i) the HCF Crossland criterion material characteristics (ii) the applied loading and (iii) the surface modifications parameters are introduced in the proposed model. The HCF reliability has been computed by using the ‘strength load’ method with Monte Carlo simulation. The reliability computation results lead to obtain interesting and useful iso‐probabilistic Crossland diagrams (PCD) for different welding and shot peening surface conditions. To validate the proposed method, the approach has been applied to a butt‐welded joint made of S550MC high strength steel (HSS). Four types of specimens are investigated: (i) base metal (BM), (ii) machined and grooved (MG) condition, (iii) As welded (AW) condition and (iv) as welded and shot peened (AWSP) condition. The comparison between the computed reliabilities and the experimental investigations reveals good agreement leading to validate the proposed approach. The effects of the different welded and post‐weld shot peened specimen's surface properties are analysed and discussed using the design of experiments (DoE) techniques.     

Cohesive zone modelling of interface fracture near flaws in adhesive joints

A cohesive zone model is suggested for modelling of interface fracture near flaws in adhesive joints. A shear-loaded adhesive joint bonded with a planar circular bond region is modelled using both the cohesive zone model and a fracture mechanical model. Results from the models show good agreement of crack propagation on the location and shape of the crack front and on the initial joint strength. Subsequently, the cohesive zone model is used to model interface fracture through a planar adhesive layer containing a periodic array of elliptical flaws. The effects of flaw shape are investigated, as well as the significance of fracture process parameters. The results from simulations of fracture in a bond containing circular flaws show that localization of crack propagation in the vicinity of a flaw has significant effect on the joint strength and crack front shape. The localization effects are highly dependent on the fracture process zone width relative to the flaw dimensions. It is also seen that with increasing fracture process zone width, the strength variation with the flaw shape decreases, however, the strength is effected over a wider range of propagation.     

Probabilistic modeling of threshold stress intensity factor for fatigue endurance reliability prediction

This study develops a probabilistic model for the threshold stress intensity factor range, which is a critical parameter in infinite fatigue life design under material flaws. The model is based on the proposed concept of probability of propagation in the probabilistic framework, allowing for deriving the probability density function of the threshold intensity factor range. The uncertainty in fatigue crack growth can naturally be incorporated into the resulting distribution. By further introducing the derived distribution into the Kitagawa–Takahashi diagram, the fatigue endurance reliability model can be established in a rational manner. With the first-order asymptotic approximation, the analytical form of fatigue endurance reliability index is obtained. The usefulness of the overall method is demonstrated using realistic engineering application examples.     

SURFACE FLAWS IN CYLINDRICAL SHAFTS UNDER ROTARY BENDING

The propagation of a surface flaw in a cylindrical shaft subjected to rotary bending is analysed using a two-parameter theoretical model. The stress-intensity factor distribution along the crack front is numerically determined for any position of the flaw with respect to the bending moment axis. The crack front is assumed to present an elliptical-arc shape with aspect ratio α = a / b ( a ,   b = ellipse semi-axes), whereas the relative depth ξ of the deepest point on the front is equal to the ratio between the maximum crack depth, a , and the bar diameter, D . The results for rotary bending are compared to those for reversed cyclic bending.     

Predicting fatigue S-N (stress-number of cycles to fail) behavior of reinforced plastics using fracture mechanics theory

The present study describes a model to predict fatigue S-N behavior, and thus fatigue life, of glass fiber reinforced thermoplastics by using a fracture mechanics approach. The model assumes the presence of an inherent initial flaw in the molded plastic parts and thus ignores crack initiation contributions. In this paper we describe how fatigue crack propagation rate data were obtained for the same three glass fiber reinforced plastics whose S-N behavior was previously described in detail. Using the measured constants from the crack growth data, and corresponding S-N data for uncracked specimens, the validity of the single initial flaw hypothesis was evaluated. From the analyzed results it is concluded that accurate S-N predictions are possible using this simple fracture mechanics model for some materials. The best results are obtained for glass filled polyamide, PA (nylon 66) and polycarbonate, PC; however, with polybutylene terephthalate, PBT, predictions were poor. It is also shown that S-N data for different glass fiber orientations can be predicted by combining the single flaw model with predicted fatigue crack propagation rate measurements. The latter are calculated from a generalized crack growth rate expression utilizing the strain energy release rate fracture mechanics parameter, which was previously described.