Initial Flaw Size Research Articles

Fatigue limit evaluation considering crack initiation for lamellar pearlitic steel

In order to evaluate the fatigue limit of lamellar pearlitic steel used for railroad rails, tensile tests and fatigue tests are performed. Although the fatigue ratio of the lamellar pearlitic steel is lower than that of general steels, the reason for this has not been clarified. The fatigue cracks of the pearlitic steel initiate at a very early stage during the fatigue test. It is speculated that the steel should be treated as a steel with initial defects. In order to determine the initial defect size of the ultra-low cycle fatigue test, tensile tests are performed. Based on the test results, it was clarified that the crack initiation size depends on the crystal structure. In order to predict the fatigue limit of the pearlitic steel, Murakami's prediction method is applied to the steel. The measured defect sizes are applied to the method, and the fatigue tests are performed. The predicted fatigue limits and the test results have good agreement. In addition, from the SEM observations, the initial crack causing the fatigue failure was found to be a pearlite block. We then concluded that the fatigue limit of the pearlitic steel can be predicted by Murakami's method and the defect size is the pearlite block size. If the pearlite block sizes then become small, the fatigue limit of the pearlitic steel will increase.

System reliability of corroding pipelines

A methodology is presented in this paper to evaluate the time-dependent system reliability of a pipeline segment that contains multiple active corrosion defects and is subjected to stochastic internal pressure loading. The pipeline segment is modeled as a series system with three distinctive failure modes due to corrosion, namely small leak, large leak and rupture. The internal pressure is characterized as a simple discrete stochastic process that consists of a sequence of independent and identically distributed random variables each acting over a period of one year. The magnitude of a given sequence follows the annual maximum pressure distribution. The methodology is illustrated through a hypothetical example. Furthermore, the impact of the spatial variability of the pressure loading and pipe resistances associated with different defects on the system reliability is investigated. The analysis results suggest that the spatial variability of pipe properties has a negligible impact on the system reliability. On the other hand, the spatial variability of the internal pressure, initial defect sizes and defect growth rates can have a significant impact on the system reliability.

Delamination of moisture saturated graphite/polyimide composites due to rapid heating

In this study, experimental methods and a theoretical model are developed with aim of understanding and predicting the onset of steam pressure-induced delamination. Experiments are performed by rapid heat-up of moisture saturated T650-35/HFPE-II-52 graphite/polyimide laminates, pre-implanted in the midplane with circular starter cracks. The deformation of these flaws and subsequent delamination growth is measured using custom designed, transverse extensometers. A theoretical model for calculation of internal steam pressure within a deforming circular cavity is derived and combined with a linear elastic fracture mechanics approach to predict the onset of delamination growth. The experimental results and theoretical calculations are used to highlight the effect of heating rate, initial flaw size, initial moisture content, and material toughness on steam-induced delamination. A parametric study is conducted and used to identify conditions required for transition between steam-induced delamination and steam-induced blistering damage.

Inference of equivalent initial flaw size under multiple sources of uncertainty

A probabilistic methodology is proposed in this paper to estimate the equivalent initial flaw size (EIFS) distribution accounting for various sources of variability, uncertainty and error, for mechanical components with complicated geometry and multi-axial variable amplitude loading conditions. A Bayesian approach is used to calibrate the distribution of EIFS, where the likelihood function is constructed from model-based fatigue crack growth analysis and inspection results. The variability, uncertainties and errors in the above procedures are quantified, and the distribution of EIFS is calibrated by explicitly accounting for the various sources of uncertainty. Three types of uncertainty are considered: (1) natural variability in loading and material properties; (2) data uncertainty, due to crack detection uncertainty, measurement errors, and sparse data; (3) modeling uncertainty and errors during crack growth analysis, numerical approximations, and finite element discretization. A Monte Carlo simulation-based approach is developed for uncertainty quantification in the crack growth analysis and for constructing the likelihood function of EIFS. The proposed methodology is illustrated by a numerical example.

The Economical Life of Titanium Alloy Fasten Holes Structure

This paper outlined the experimental and theoretical study on the TC4 alloy fasten holes structure to assess the first inspection and maintenance period for structures. The initial fatigue quality of the fastener holes was represented by an equivalent initial flaw size distribution. Based on the experimental results of crack size, the life of fasten structure detail in which 5% crack happened was provided and the resulted life was suggested as the structure economical life. The predicated economical life of titanium alloy fasten hole structure are helpful to the economical repair of the airframe structure.

Statistical inference of equivalent initial flaw size with complicated structural geometry and multi-axial variable amplitude loading

This paper presents several efficient statistical inference techniques to calibrate the equivalent initial flaw size (EIFS) of fatigue cracks for mechanical components with complicated geometry and multi-axial, variable amplitude loading. Finite element analysis is used to address the complicated geometry and calculate the stress intensity factors. Multi-modal stress intensity factors due to multi-axial loading are combined to calculate an equivalent stress intensity factor using a characteristic plane approach. During cycle-by-cycle integration of the crack growth law, a Gaussian process surrogate model is used to replace the expensive finite element analysis, resulting in rapid computation. Experimental data (crack size after a particular number of loading cycles) and statistical methods are used to calibrate the EIFS. The methods of least squares and maximum likelihood method are extended to evaluate the entire probability distribution of EIFS. Bayesian techniques are also implemented for this purpose. A fast numerical integration technique is developed as an efficient alternative to the expensive Markov Chain Monte Carlo sampling approach in the Bayesian analysis. An application problem of cracking in a cylindrical structure is used to illustrate the proposed methods.

The history, logic and uses of the Equivalent Initial Flaw Size approach to total fatigue life prediction

Total fatigue life is traditionally composed of the time to crack initiation plus the time for the initiated crack to grow to a critical crack size. Fracture mechanics does reasonably well in predicting the growth portion but there is still a lot of uncertainty about the definition of an initiated crack and scatter associated with the number of cycles to “initiation”. This paper will review some of the history, logic and uses of the Equivalent Initial Flaw Size (EIFS) approach to total life prediction. In short, this is a method where found cracks are analytically grown backwards to time equal zero (time or cycles) to determine an initial flaw, referred to as an EIFS. By growing a number of found cracks back to time equal zero a distribution of EIFS can be established. Example of establishing this distribution are given for the C-130 aircraft with a 7075 aluminum structure and for gas powered turbine blades made of directional solidified super-alloys.

Fatigue crack growth of cable steel wires in a suspension bridge: Multiscaling and mesoscopic fracture mechanics

Intrinsically, fatigue failure problem is a typical multiscale problem because a fatigue failure process deals with the fatigue crack growth from microscale to macroscale that passes two different scales. Both the microscopic and macroscopic effects in geometry and material property would affect the fatigue behaviors of structural components. Classical continuum mechanics has inability to treat such a multiscale problem since it excludes the scale effect from the beginning by introducing the continuity and homogeneity assumptions which blot out the discontinuity and inhomogeneity of materials at the microscopic scale. The main obstacle here is the link between the microscopic and macroscopic scale. It has to divide a continuous fatigue process into two parts which are analyzed respectively by different approaches. The first is so called as the fatigue crack initiation period and the second as the fatigue crack propagation period. Now the problem can be solved by application of the mesoscopic fracture mechanics theories developed in the recent years which focus on the link between different scales such as nano-, micro- and macro-scale. On the physical background of the problem, a restraining stress zone that can describe the material damaging process from micro to macro is then introduced and a macro/micro dual scale edge crack model is thus established. The expression of the macro/micro dual scale strain energy density factor is obtained which serves as a governing quantity for the fatigue crack growth. A multiscaling formulation for the fatigue crack growth is systematically developed. This is a main contribution to the fundamental theories for fatigue problem in this work. There prevail three basic parameters μ ∗, σ ∗ and d ∗ in the proposed approach. They can take both the microscopic and macroscopic factors in geometry and material property into account. Note that μ ∗, σ ∗ and d ∗ stand respectively for the ratio of microscopic to macroscopic shear modulus, the ratio of restraining stress to applied stress and the ratio of microvoid size ahead of crack tip to the characteristic length of material microstructure. To illustrate the proposed multiscale approach, Hangzhou Jiangdong Bridge is selected to perform the numerical computations. The bridge locates at Hangzhou, the capital of Zhejiang Province of China. It is a self-anchored suspension bridge on the Qiantang River. The cables are made of 109 parallel steel wires in the diameter of 7 mm. Cable forces are calculated by finite element method in the service period with and without traffic load. Two parameters α and β are introduced to account for the additional tightening and loosening effects of cables in two different ways. The fatigue crack growth rate coefficient C 0 is determined from the fatigue experimental result. It can be concluded from numerical results that the size of initial microscopic defects is a dominant factor for the fatigue life of steel wires. In general, the tightening effect of cables would decrease the fatigue life while the loosening effect would impede the fatigue crack growth. However, the result can be reversed in some particular conditions. Moreover, the different evolution modes of three basic parameters μ ∗, σ ∗ and d ∗ actually have the different influences on the fatigue crack growth behavior of steel wires. Finally the methodology developed in this work can apply to all cracking-induced failure problems of polycrystal materials, not only fatigue, but also creep rupture and cracking under both static and dynamic load and so on.

Effect of Drilling Process on Fatigue Life of Open Holes

In this paper, a series of fatigue tests were performed to study the effect of drilling process on fatigue behavior of open holes in dog-bone specimens drilled by the traditional drilling process and advanced Winslow drilling process. The evaluations of initial fatigue qualities of the two types of holes were carried out based on the equivalent initial flaw size method and coincidence criterion. Fatigue fracture surfaces were observed by stereomicroscope. The results show that the location where the fatigue crack initiates is unchanged when these two different drilling processes are used. A longer fatigue life shows a more severe dispersibility. When the Winslow drilling process is adopted, the equivalent initial flaw size is smaller than 0.125 mm. The Winslow drilling process meets the requirement of coincidence criterion.

Effect of corrosion severity on fatigue evolution in Al–Zn–Mg–Cu

The effect of existing-localized corrosion on fatigue cracking of 7075-T6511 was established using crack surface marker-band analysis and a fracture mechanics model. The substantial reduction of fatigue life due to EXCO solution L–S surface pre-corrosion is nearly independent of exposure time after initial-sharp degradation, scaling with the evolution of pit-cluster size and initial stress intensity range with exposure time. Independent of exposure time, formation of a resolvable fatigue crack (∼10 μm) accounts for a similar-low (∼5%) fraction of total fatigue life at low stress range ( σ max = 150 MPa, R = 0.1). Crack formation occurs at microscopic protrusions into the corroded volume. A corrosion-modified-equivalent initial flaw size (CM-EIFS); predicted with the AFGROW tool using measured initial aspect ratio, initiation cycles, and total fatigue life inputs; accurately represents the corrosion damage effect on fatigue for a range of exposures. The similar deleterious effect of several corroding environments for various-exposed surfaces is described by a lower-bound CM-EIFS with a 300 μm depth and 1200 μm surface length suggesting fatigue is governed by a microscopic pit-based topography. Either an approximate lower-bound, or specific CM-EIFS calibrated by limited measurements of fatigue life for service-environment exposed specimens, can be used to assess the impact of corrosion in a damage tolerant framework. Complexities (e.g., local H embrittlement, 3D pit geometry, topography dependent initiation, and microstructure sensitive small-crack growth) do not compromise the CM-EIFS estimation, but must be better understood for refined modeling.

Calibration, validation, and verification including uncertainty of a physically motivated internal state variable plasticity and damage model

In this paper, we illustrate a formal calibration, validation, and verification process that includes uncertainty in an internal state variable plasticity-damage model that is implemented in a finite element code. The physically motivated continuum model characterizes damage evolution by incorporating material uncertainty due to microstructural spatial clustering. The uncertainty analysis is performed by introducing material variation through model validation and verification. The effect of variability in microstructural clustering and boundary conditions on the sensitivities and uncertainty of the plasticity-damage evolution for the 7075 aluminum alloy is characterized. The results show the potential of this methodology in the evaluation of material response uncertainty due to microstructure spatial clustering and its effect on damage evolution. For damage evolution, we have shown that the initial isotropic damage evolved into an anisotropic form as the deformation increased which is consistent with experimentally observed behavior for 7075 aluminum alloy in literature. Also, the sensitivities were found to be consistent with the physics of damage progression for this particular type of material. Through the sensitivity analysis, the initial defect size and number density of cracked particles are important at the beginning of deformation. As damage evolves, more voids are nucleated and grow and the sensitivity analysis illustrates this as well. Then, voids combine with each other and coalescence becomes the main driver, which is also confirmed by the sensitivity analysis. This work also shows that the microstructurally based damage evolution equations provide an accurate representation of the damage progression due to large intermetallic particles. Finally, we illustrate that the initial variation in the microstructure clustering can lead to about ±7.0%, ±8.1%, and ±9.75% variation in the elongation to failure strain for torsion, tensile, and compressive loading, respectively.

Osteochondral Lesion of the Talus

Background Identifying factors associated with favorable or unfavorable outcomes would provide patients with accurate expectations of the arthroscopic marrow stimulation techniques. Purpose To investigate the prognostic significance and optimal measures of defect size in osteochondral lesion of the talus as treated with arthroscopy. Hypothesis A critical, or threshold, defect size may exist at which clinical outcomes become poor in the treatment of osteochondral lesion of the talus. Study Design Cohort study; Level of evidence, 3. Methods In sum, 120 ankles underwent arthroscopic marrow stimulation treatment for osteochondral lesion of the talus and were evaluated for prognostic factors. Clinical failure was defined as patients’ having osteochondral transplantation or an American Orthopaedic Foot and Ankle Society (AOFAS) Ankle-Hindfoot Scale score less than 80. Linear regression analysis and the Kaplan-Meier method were used to identify optimal cutoff values of defect size. Results Eight ankles (6.7%) required osteochondral transplantation, and 22 ankles (18.4%) were considered failures because of AOFAS scores less than 80, which indicated fair or poor results. Linear regression analysis showed a high prognostic significance of defect area and suggested a cutoff defect size of 150 mm 2 for the optimum identification of poor clinical outcomes (P < .001). Only 10 of 95 ankles (10.5%) with a defect area <150 mm 2 showed clinical failure, whereas in patients with an area ≥150 mm 2 , the clinical failure rate was significantly higher (80%, 20/25). There was no association between outcome and the patient’s age, duration of symptoms, trauma, associated lesions, and location of lesions (P > .05). Conclusion Initial defect size is an important and easily obtainable prognostic factor in osteochondral lesions of the talus and so may serve as a basis for preoperative surgical decisions. A cutoff point exists regarding the risk of clinical failure at a defect area of approximately 150 mm 2 as calculated from magnetic resonance imaging.

Crack growth-based fatigue-life prediction using an equivalent initial flaw model. Part II: Multiaxial loading

A general methodology is proposed in this paper for fatigue-life prediction using crack growth analysis. This is the part II of the paper and focuses on the fatigue-life prediction under proportional and nonproportional multiaxial loading. The proposed multiaxial fatigue-life prediction is based on a critical plane-based multiaxial fatigue damage model and the Equivalent Initial Flaw Size (EIFS) concept. An equivalent stress intensity factor under general multiaxial proportional and nonproportional loading is defined. The fatigue life is predicted by integration of the crack growth rate curve from the EIFS to the critical crack length. The proposed model can automatically adapt for different materials experiencing different local failure modes. The numerical fatigue-life prediction results calculated by the proposed approach are validated with experimental data for a wide range of metallic materials available in the literature. Reasonable agreements are observed between the model predictions and the experimental observations under proportional and nonproportional loading.

Predicting corner crack fatigue propagation from cold worked holes

We predict the fatigue propagation of corner cracks from cold worked holes using three dimensional finite element models. The models account for the through thickness variation in residual stress left after cold working. The predictions are compared to experimental results in aluminum 2024-T351 and 7075-T651. The models show the evolution of P-shaped crack fronts similar to those observed in experiments. Predictions based on the initial residual stress field left after cold working were nonconservative, predicting either slower than experimental crack growth or crack growth that arrests. Predictions based on an estimate of the stable relaxed residual stress field near the hole were conservative, and predicted 5–10 times greater life than the current Department of Defense reduced initial flaw size approach.

The Behavior of Shallow Cracks in a Pipeline Steel Operating in a Sour Environment

Setting conditions for the avoidance of in-service crack growth in aggressive corroding environments has long been a major challenge due to the number of variables that have a significant effect on material behavior. One area where both experimental data and a validated assessment methodology are lacking is the behavior of shallow cracks. This paper describes the early results of an ongoing research program aimed at addressing the shortfall in experimental data to characterize material behavior in the shallow-crack regime, with the long-term aim of improving the understanding and assessment of the early stages of environment assisted cracking. There is an industry need for a better understanding of material behavior under these conditions and for the development of a more robust assessment methodology. API 5L X65 pipeline steel parent material was tested in a sour environment with initial flaw sizes in the range 1–2 mm. Fatigue crack growth rate tests have been performed to investigate the influence of crack depth on crack growth rate (da/dN). Initial results suggest that crack growth rates for deep flaws can increase by a factor of 5–100 compared with air depending on the applied stress intensity factor range (ΔK). Shallow cracks have been shown to grow up to 130 times faster in a sour environment than in air and up to an order of magnitude faster than deep cracks in a sour environment at the same value of ΔK. Constant load tests have also been performed to investigate the influence of crack depth on the threshold stress intensity factor for stress corrosion cracking (KISCC). Preliminary results suggest that in this case there is no crack depth dependence in the range of flaw sizes tested. While further experimental work is required, the results obtained to date highlight the potential nonconservatism associated with extrapolating deep-crack data. Guidance is therefore provided on how to generate appropriate experimental data to ensure that subsequent fitness for service assessments are conservative.

Reflections on ‘The effect of elevated temperature and environment on the fatigue crack growth characteristics of Ti‐6Al‐2Sn‐4Zr‐2Mo‐0.1Si’ by J. A. Ruppen and A. J. McEvily, FFEMS, Vol 2, Issue 1, 1979, pp. 63–72

A principal finding of the study was that at 538 °C fatigue crack growth tests in air and in vacuum showed that oxidation rather than creep was more important in affecting the fatigue crack growth rate in the range of test frequencies from 1 to 30 Hz. Similar results have also been found for steel, as shown in Fig. 1. Effect of testing conditions on the fatigue crack growth behaviour of a 9Cr-2Mo steel.1 Figure 2 shows long crack growth behaviour as a function of Eq. (2) and R value. The transition in growth behaviour occurs where the plastic zone size is about equal to the grain size of the α-phase, 10 μm. The rate of fatigue crack growth in Ti-6Al-4V as a function of (ΔKeff−ΔKeffth)2, modified for static modes of separation which occur at the highest value of the parameter. A comparison of experimental and predicted values of the fatigue strength, σw, as a function of the initial flaw size, a0.4 Note that the smallest flaw is but 15 μm in length. After some 60 year of intense research by many investigators, it is beginning to look as though we can deal with fatigue crack propagation on a quantitative basis, based upon the understanding of the basic mechanisms involved.

DDSim: A hierarchical, probabilistic, multiscale damage and durability simulation system – Part I: Methodology and Level I

Current tools for fatigue life prediction of metallic structural components are limited in some or all of the following capabilities: geometry of, and boundary conditions on, the affected structural component, automation of the simulation process, randomness of the primary variables, and physics of the damage evolution processes. DDSim, a next-generation damage and durability simulator, addresses each of these limitations with a hierarchical, multiscale, “search and simulate” strategy. This hierarchical strategy consists of three levels. Level I, described in this paper, performs an initial, reduced order, conservative screening, based on a linear finite element analysis of the uncracked component, to determine the most life-limiting locations for intrinsic material flaws. Initial flaw size can be specified deterministically, or generated randomly from statistical descriptions of the microstructure and used in Monte Carlo simulation. The result is a scalar field of predicted life over the entire domain of the structure. The benefits of the Level I analysis include a high degree of automation, solution speed, and easy implementation of high performance parallel computing resources. A validation case study of Level I is described. Levels II and III are outlined herein, but will be described in further detail in subsequent papers. The Level II analysis uses FRANC3D to accurately predict the number of cycles consumed by microstructurally large crack growth processes. Level III performs multiscale analyses to accurately predict the cycles consumed in microstructurally small crack growth processes.

Fatigue Life Prediction for Porosity-Containing Cast 319-T7 Aluminum Alloy

In this study, the linear elastic fracture mechanics (LEFM) approach, including use of the equivalent initial flaw size (EIFS) concept and fatigue crack propagation (FCP) rates, da/dN, as a function of either ΔK or ΔK eff, was used to predict the fatigue life of a porosity-containing 319-T7 specimen. The uniaxial fatigue tests were conducted on a 319-T7 specimen at a stress ratio (R) of −1. For the LEFM-based fatigue life prediction, da/dN-ΔK data were obtained for the 319-T7 specimen at R = 0.1. The shape and the size of the porosity were analyzed based on the fractographic and the micrographic analyses for each fatigued specimen. The LEFM concept, including the use of the EIFS value, back-calculated by using da/dN-ΔK eff data, successfully predicts the porosity-affected stress vs the number of cycles to failure (S-N) fatigue behavior of cast 319-T7 specimens. The LEFM models presently available for predicting the fatigue life of porosity-containing alloys were evaluated and a simple modification was proposed based on extensive fractographic analysis results.

結合力要素を用いた分散形複合材料の損傷進展解析

In this paper, a simple numerical analytical method is proposed for simulating crack extension in a particulate-reinforced composite material. The numerical method is based on finite element analysis with the homogenization method, where crack extension is expressed using embedded cohesive elements. We first present the formulation of the numerical model and verify the model's validity by comparing the simulated crack extension with the linear fracture mechanics. Next we simulate damage extension for a composite reinforced with spherical particles. We consider the cracks in the particles and on particle–matrix interfaces. The analytical results reveal the effect of crack extension on the macroscopic material properties of the composite. The particle crack extends unstably and sharply decreases the tangent modulus of the material, irrespective of the initial flaw size. In contrast, the interfacial crack invariably grows stably and decreases the tangent modulus gradually.

Asymptotic Characteristic of Exact Distribution of Fracture Strength Based on Gamma Distribution as Initial Flaw Size Distribution

In this paper, an exact distribution of fracture strength was derived from extreme value statistics for an initial distribution of flaw size, via conversion to an exact distribution of largest flaw size. Gamma distribution was shown as a better function to approximate the initial distribution data measured by immersion liquid technique. The exact distribution of fracture strength was obtained as a function of the number of links in the weakest link theory. With increasing the number of links, the exact distribution gradually became linear on Weibull plot, and almost coincided to Weibull distribution at the number of links larger than 1000. Compared to actual distributions of fracture strength, the number of links in the specimens was estimated to be in the range from 104 to 105. The above discussion showed a verification of this theory.