Small Crack Sizes Research Articles

A study of life prediction differences for a nickel-base Alloy 690 using a threshold and a non-threshold model

In this paper we compare and contrast the crack growth rate of a nickel-base superalloy (Alloy 690) in the Pressurized Water Reactor (PWR) environment. Over the last few years, a preponderance of test data has been gathered on both Alloy 690 thick plate and Alloy 690 tubing. The original model, essentially based on a small data set for thick plate, compensated for temperature, load ratio and stress-intensity range but did not compensate for the fatigue threshold of the material. As additional test data on both plate and tube product became available the model was gradually revised to account for threshold properties. Both the original and revised models generated acceptable results for data that were above 1 × 10 −11 m/s. However, the test data at the lower growth rates were over-predicted by the non-threshold model. Since the original model did not take the fatigue threshold into account, this model predicted no operating stress below which the material would effectively undergo fatigue crack growth. Because of an over-prediction of the growth rate below 1 × 10 −11 m/s, due to a combination of low stress, small crack size and long rise-time, the model in general leads to an under-prediction of the total available life of the components.

The true toughness of human cortical bone measured with realistically short cracks

Bone is more difficult to break than to split. Although this is well known, and many studies exist on the behaviour of long cracks in bone, there is a need for data on the orientation-dependent crack-growth resistance behaviour of human cortical bone that accurately assesses its toughness at appropriate size scales. Here, we use in situ mechanical testing to examine how physiologically pertinent short (<600 microm) cracks propagate in both the transverse and longitudinal orientations in cortical bone, using both crack-deflection/twist mechanics and nonlinear-elastic fracture mechanics to determine crack-resistance curves. We find that after only 500 microm of cracking, the driving force for crack propagation was more than five times higher in the transverse (breaking) direction than in the longitudinal (splitting) direction owing to major crack deflections/twists, principally at cement sheaths. Indeed, our results show that the true transverse toughness of cortical bone is far higher than previously reported. However, the toughness in the longitudinal orientation, where cracks tend to follow the cement lines, is quite low at these small crack sizes; it is only when cracks become several millimetres in length that bridging mechanisms can fully develop leading to the (larger-crack) toughnesses generally quoted for bone.

Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue

The enhanced ability to detect and measure very short cracks, along with a great interest in applying fracture mechanics formulae to smaller and smaller crack sizes, has pointed out the so-called anomalous behavior of short cracks with respect to their longer counterparts. The crack-size dependencies of both the fatigue threshold and the Paris’ constant C are only two notable examples of these anomalous scaling laws. In this framework, a unified theoretical model seems to be missing and the behavior of short cracks can still be considered as an open problem. In this paper, we propose a critical reexamination of the fractal models for the analysis of crack-size effects in fatigue. The limitations of each model are put into evidence and removed. At the end, a new generalized theory based on fractal geometry is proposed, which permits to consistently interpret the short crack-related anomalous scaling laws within a unified theoretical formulation. Finally, this approach is herein used to interpret relevant experimental data related to the crack-size dependence of the fatigue threshold in metals.

The Crack Growth Life Predictions for High Cycle Dynamic Components

Using of a safe life approach is necessitated by the small critical crack sizes and rapid crack growth rates resulting from the severe vibratory environment of rotorcraft. However Based on the success of damage tolerance initiative for airframe structure, a crack growth based on damage tolerance approach is being examined for implementation into the design and management of dynamic components. In this paper the crack growth behavior in low cycle fatigue (LCF) and high cycle fatigue (HCF) are compared and the accuracy of several damage tolerance analysis methods in determining the crack growth life from an initial detectable crack size 1.25 mm to 12 mm for a rotorcraft main rotor yoke are investigated. The real rotorcraft materials measured by experiment and the fatigue load mean frequency spectrum based on statistical usage spectrum are adopted. The crack growth equations used in the programs are discussed to provide a basis for understanding the results. The results show that the load less than the safe fatigue limit has an important effect on crack growth life and it is reasonable for the material that the cut-off stress ratio for the threshold stress intensity factor range is set 0.7.

Kitagawa‐Takahashi diagrams define the limiting conditions for cyclic fatigue failure in human dentin

As cyclic fatigue is considered to be a major cause of clinical tooth fractures, achieving a comprehensive understanding of the fatigue behavior of dentin is of importance. In this note, the fatigue behavior of human dentin is examined in the context of the Kitagawa-Takahashi diagram to define the limiting conditions for fatigue failure. Specifically, this approach incorporates two limiting threshold criteria for fatigue: (i) a threshold stress for fatigue failure, specifically the smooth-bar (unnotched) fatigue endurance strength, at small crack sizes and (ii) a threshold stress-intensity range for fatigue-crack growth at larger crack sizes. The approach provides a "bridge" between the traditional fatigue life and fracture mechanics based damage-tolerant approaches to fatigue-life estimation, and as such defines a "failure envelope" of applied stresses and flaw sizes where fatigue failure is likely in dentin This approach may also be applied to fatigue failure in human cortical bone (i.e. clinical "stress fractures"), which exhibits similar fatigue behavior characteristics, and in principle may aid clinicians in making quantitative evaluations of the risk of fractures in mineralized tissues.

Scaling relationship of initiations for moderate to large earthquakes

We investigate the initiation sizes of earthquakes over a wide range of moderate to large events. Using the model of Sato and Kanamori, which is based on Griffith crack theory for a circular fault, we estimate the initial crack sizes of earthquakes, using high‐quality data recorded at close hypocentral distances. Taking into account the local attenuation and the dynamic stress drop of the earthquakes, we estimate trigger factors and initial crack radii for 35 events in Japan and Taiwan with magnitudes of 3.5 to 7.9. Our results show that all of the earthquakes can be explained with a small trigger factor and initial crack sizes of 12–96 m. For the large range of earthquake sizes, this is a small range of initial crack sizes. There does not appear to be a clear scaling relationship between initial crack size and final earthquake size. Instead, our results show that all the moderate to large earthquakes initiate with initial crack radii on the order of tens of meters.

Fretting fatigue analysis using a fracture mechanics based small crack growth prediction method

A complete life model for the nucleation and growth of a fretting fatigue crack has been developed. The nucleation of a fretting crack is predicted by superimposing the crack growth rate experienced under fretting conditions onto S–N fatigue data for the alloy. The growth model utilizes small crack growth rate data and a fretting fatigue stress intensity factor to account for the small crack sizes and higher stresses experienced under fretting fatigue conditions. The development of the propagation model within the established fatigue crack growth code AFGROW allows this approach to be readily used by members of the aerospace industry.

Fatigue Behavior and Life Prediction for Argon-Arc Weld Joints Based on Small Crack Methodology

Experimental and analytical studies were made on the fatigue behavior and life prediction for argon-arc welded titanium alloy joints, TA15. High cycle fatigue tests at two stress ratios, R=0.5 and 0.06, were carried out on smooth specimens with the argon-arc weld joint located at the specimen center section. Through macroscopic observation and SEM fractographic analysis, it was found that most of the cracks were initiated at weld defects such as voids and inclusions at the edge of weld and in the heat affected zone (HAZ). A small crack methodology based on the plasticity-induced crack-closure concept and the effective stress intensity factor range, ΔKeff , was used to predict the total fatigue life of the weld joints. Large crack growth curve for cracks in the HAZ area was employed as the da/dN-ΔKeff base-line of the TA15 alloy. From fractographic measurements, an average defect size of 100 microns was assumed as the initial small crack size in the life predictions. Predicted total fatigue life by solely considering small crack growth stage agreed well with the experimental data.

Fretting Fatigue Strength under High Local Contact Pressure and Its Fracture Mechanics Analysis

Fretting fatigue fractures of industrial machines often occur at the point where high contact pressure occurs due to an uneven contact. In this study, fretting fatigue tests were performed under high contact pressure applied by line-contact conditions using 12-Cr steel with parameters of the mean stress and the material strength. It was shown that the fretting fatigue strength decreased slightly with increasing the contact pressure and became minimum when Hertz's average contact pressure is about 1.5 times of 0.2% proof stress, σ0.2. I also showed that test results concerning the fretting fatigue strength and the non-propagating crack length can be successfully explained by the micro-crack propagation model in which a micro-crack can propagate when its stress intensity factor range, ΔK is greater than the threshold value, ΔKth considering small crack size effects and mean stress effects.

Fatigue damage calculated by ratio-method to metallic materials with small crack under unsymmetric cyclic loading

Based on the standpoint to take for the crack size also to be a damage variable like the damage variable, by means of the two-directions coordinate system, several new calculation equations on the small crack growth rate are suggested for describing the elastic-plastic behavior of some metallic materials. And the estimation formulas of life are also suggested relative to varied small crack size at each loading history, which is unsymmetric cyclic loading. In the calculation method, as a loaded stress-strain parameter to adopt the ratio with plastic strain range to elastic strain range, and as the material constants using the typical material parameters in damage calculation expression, a new concept of the compositive material constant, which has functional relation with the typical material constants, average stress, average strain, critical loading time is given out. In addition, the fatigue damage of a part of car is put up to calculate as an example, its calculation results are accordant with the Landgraf's equation, and calculation precision is more rigorous, so could avoid unnecessary fatigue tests and will be of practical significance on saving times, manpower and capitals, as well as the convenience for engineering applications.

A practical investigation to solving the inverse problem of crack identification through vibration measurements

PurposeTo investigate the feasibility of using single/multi variable optimisation techniques with vibration measurements in solving the inverse crack identification problem.Design/methodology/approachThe finite element method is used to solve the forward crack problem with a special nodal crack force approach. The multi‐variable optimisation approach is reduced to a much more efficient single‐variable one by decoupling the physical variables in the problem.FindingsIt is shown that, for the crack identification problem, global optimisation algorithms perform much better than other algorithms relying heavily on objective function gradients. Simultaneous identification of crack size and location proved to be difficult. Decoupling of the physical variable is introduced and proved to provide efficient results with single‐variable optimisation algorithms.Research limitations/implicationsNeed for improving the reliability and accuracy of the procedure for smaller crack sizes. Need for developing and investigation more rigorous and robust multi‐variable optimisation algorithm.Practical implicationsAny information about approximate crack size and location provides significant aid in the maintenance and online monitoring of rotating equipment.Originality/valueThe paper offers practical approach and procedure for online monitoring and crack identification of slow rotating equipment.

Fatigue Damage of Materials with Small Crack Calculated by the Ratio-Method under Cyclic Loading

This paper offers some new calculating equations on the small crack growth rate for describing the elastic-plastic behavior of materials under symmetric or un-symmetric cyclic loading. And it yet suggests the estimating formulas of the life relative to varied small crack size aoi at each loading history. The method is to adopt the ratio e p e e D D / by plastic strain range to elastic strain range as a stress-strain parameter, using some staple material parameters as the material constants in damage calculating expression. And it gives out a new concept of the composite material constant, that it is functional relation with each staple material constants, average stress，average strain and critical loading time. The calculated results are accordant with the Landgraf’s equation, so could avoid unnecessary fatigue tests and will be of practical significance to stint times, manpower and capitals, the convenience for engineering applications.

Indentation fracture mechanics toughness dependence on grain size and crack size: Application to alumina and WC–Co

Measurements, for alumina, of the indentation fracture mechanics stress intensity, K, at different grain sizes show a reversed trend in the material toughness property: at small crack sizes, although larger than the material grain size, K increases with decrease in grain size in accordance with a Hall–Petch (H–P) type dependence of being linearly dependent on the inverse square root of the grain diameter; whereas, at larger crack sizes, K reverses itself and increases with increase in grain size. The experimental results are interpreted here in terms of approximate equations obtained from the Bilby/Cottrell/Swinden (BCS) model for critical crack growth with an associated plastic zone size, s, at the crack tip. The particular variations in s associated with the two types of K dependencies, nevertheless, give a positive H–P grain size dependence, at sensibly constant crack size, for computed pre-crack fracture stresses, though of lesser H–P slope than the reference crack-free fracture stress. By comparison, K measurements for WC–Co cemented carbide systems show lower values both at smaller WC particle sizes and, especially, at smaller mean free path, λ, of the fracture-prone Co binder phase. Such result is predicted to occur if s is proportional to λ. The WC–Co system is of special interest, also, because H–P dependencies for the WC and Co constituent components in different alloy compositions make an important contribution, along with the contiguity of the WC particles, to determining the corresponding material hardness properties.

Crack Initiation at a Notch under Constant and Selected Variable Amplitude Loading Conditions

Abstract In a previous study, we showed that crack initiation life at a notch tip can be modeled as the micro crack propagation life from an initial microstructural defect up to a crack size of about 500 µm. This model is based upon the assumption that short cracks at a notch propagate without any significant closure effects. In our present experimental study, the results of fatigue tests to verify this hypothesis are presented and discussed. The fatigue tests were conducted in ambient air on single edge notched specimens with a theoretical stress concentration factor of 3.14 on thin sheets of 1.2 mm thick Aluminum alloy 2024 T351. The test conditions studied are: constant amplitude tests at stress ratios of 0.1, 0.3, and 0.5 and variable amplitude tests using an extract from the TWIST spectrum. The tests were carried out at a nominal frequency of 10 Hz. At selected intervals, micro crack advance (if any) was determined using replicas. The measurements were made at the maximum stress for constant amplitude tests and at a chosen positive stress for variable amplitude tests (avoiding any overload). The smallest crack size detected is about 10 µm.

Effects of particle size on fatigue crack initiation and small crack growth in SiC particulate-reinforced aluminium alloy composites

Fatigue crack initiation and small crack growth were studied under axial loading using powder metallurgy 2024 aluminum-matrix composites reinforced with SiC particles of three different sizes of 5, 20 and 60 μm. The 5 and 20 μm SiC p/Al composites exhibited nearly the same fatigue strength as the unreinforced alloy, while the 60 μm SiC p/Al composite showed a significantly lower fatigue strength due to its inferior crack initiation resistance that could be attributed to interface debonding between particles and the matrix. Small crack growth behaviour was different depending on stress level. At a low applied stress, the addition of SiC particles enhanced the growth resistance, particularly in the composites reinforced with coarser particles, while at a high applied stress, the 60 μm SiC p/Al composite showed a considerably low growth resistance, which could be attributed to interaction and coalescence of multiple cracks. In the 5 μm SiC p/Al composite, small cracks grew avoiding particles and thus few particles appearing on the fracture surfaces were seen, particularly in small crack size region. In the 20 and 60 μm SiC p/Al composites, they grew along interfaces between particles and the matrix and the number of particles appearing on the fracture surfaces increased with increasing crack size or maximum stress intensity factor.

Some Peculiarities of Fatigue Crack Growth at Various Stages of Its Development

The author considers some peculiarities of fatigue crack growth in metals at the stages of its initiation and initial development, and stable and unstable growth that precedes final fracture. It is shown that at the stage of initial growth of fatigue cracks, the stress state, nonlocalized fatigue damage that precedes initiation of the main fatigue crack, residual surface stresses, surface manufacturing and in-service defects, and contact interactions are the factors that determine the crack paths. Stable growth of a fatigue crack is primarily determined by the stress-strain state of a structure as a whole and by the stress-strain state at the crack tip with allowance for its variation due to crack propagation, which is evaluated by the criteria of fracture mechanics. The author also studied peculiarities of fatigue crack development in compressor blades of marine gas turbines. It is shown that for embrittled steels, when fatigue cracks develop under plane strain conditions, final fracture occurs at very small crack sizes. In this case, the characteristics of fatigue fracture toughness are appreciably lower than the static values. The paper also considers peculiarities of unstable fatigue crack propagation.

On the application of the Kitagawa–Takahashi diagram to foreign-object damage and high-cycle fatigue

The role of foreign-object damage (FOD) and its effect on high-cycle fatigue (HGF) failures in a turbine engine Ti–6Al–4V alloy is examined in the context of the use of the Kitagawa–Takahashi diagram to describe the limiting conditions for such failures. Experimentally, FOD is simulated by firing 1 and 3.2 mm diameter steel spheres onto the flat specimen surface of tensile fatigue specimens at velocities of 200 and 300 m/s. Such damage was found to markedly reduce the fatigue strength of the alloy, primarily due to four factors: stress concentration, microcrack formation, impact-induced plasticity and tensile residual stresses associated with the impact damage. Two groups of fatigue failures could be identified. The first group initiated directly at the impact site, and can be readily described through the use of a fatigue-crack growth threshold concept. Specifically, a Kitagawa–Takahashi approach is presented where the limiting threshold conditions are defined by the stress-concentration corrected smooth-bar fatigue limit (at microstructurally small crack sizes) and a “worst-case” fatigue-crack growth threshold (at larger crack sizes). The second group of failures was caused by fatigue cracks that initiated at locations far from the impact site in regions of high tensile residual stresses, the magnitude of which was computed numerically and measured experimentally using synchrotron X-ray diffraction. Specifically, these failures could be rationalized due to the superposition of the residual stresses on the far-field applied mean stress, leading to a locally elevated load ratio (ratio of minimum to maximum loads). The effects of residual stress, stress concentration, and microstructurally small cracks are combined in a modified Kitagawa–Takahashi approach to provide a mechanistic basis for evaluating the detrimental effect of FOD on HCF failures in Ti–6Al–4V blade alloys.

Foreign-object damage and high-cycle fatigue of Ti–6Al–4V

Recent high-cycle fatigue (HCF) related failures of gas-turbine jet engines have prompted a re-examination of the design methodologies for HCF-critical components, such as titanium alloy turbine blades. As foreign-object damage (FOD) from ingested debris is a key concern for HCF-related failures of such blades, the current study is focused on the role of simulated high velocity FOD in affecting the initiation and early growth of small surface fatigue cracks in a Ti–6Al–4V alloy, processed for typical blade applications. It is found that resistance to HCF is markedly reduced, primarily due to earlier fatigue crack initiation. The mechanistic effect of FOD on such premature fatigue crack initiation and the subsequent crack growth is discussed in terms of four prominent factors: (i) the presence of small microcracks in the damaged zone; (ii) the stress concentration associated with the FOD indentation; (iii) the localized presence of tensile residual hoop stresses at the base and rim of the indent sites; and (iv) microstructural damage from FOD-induced plastic deformation. In view of the in-service conditions, i.e., small crack sizes, high frequency (>1 kHz) vibratory loading and (depending on the blade span location) high mean stress levels, a damage-tolerant design approach, based on the concept of a threshold for no fatigue-crack growth, appears to offer a preferred solution. It is shown that FOD-initiated cracks that are of a size comparable with microstructural dimensions can propagate at applied stress-intensity ranges on the order of Δ K∼1 MPa√m.

Comparison of the fatigue and fracture of α+β and β titanium alloys

The present study compares the fatigue and fracture properties of the high-strength β titanium alloy β-Cez with the conventional α+β titanium alloy Ti-6Al-4V, because of increasing interest in replacing α+β titanium alloys with β titanium alloys for highly stressed airframe and jet engine components. This comparison study includes the Ti-6Al-4V alloy in an α+ β-processed condition (for a typical turbine blade application) and the β-Cez alloy in two distinctly different α+β-processed and β-processed conditions (optimized for a combination of superior strength, ductility, and fracture toughness). The comparison principally showed a much lower yield stress for Ti-6Al-4V (915 MPa) than for both β-Cez conditions (1200 MPa). The Ti-6Al-4V material also showed the significantly lower high-cycle fatigue strength (resistance against crack initiation) of 375 MPa (R=−1) as compared to the β-Cez alloy (∼600 MPa, R=−1). Particularly in the presence of large cracks (>5 mm), the fatigue crack growth resistance and fracture toughness of the Ti-6Al-4V material is superior when compared to both β-Cez conditions. However, for small crack sizes, the conditions of both the alloys under study show equivalent resistance against fatigue crack growth. For the β-Cez material, where microstructures were optimized for high fracture toughness (conventional large crack sizes) by thermomechanical processing, maximum K Ic-values of 68 MPa√m of the β-processed β-Cez condition (tested in the longitudinal direction) decreased by ∼50 pct in the presence of small cracks (1 mm). A similar decrease in fracture toughness was obtained by loading the β-processed β-Cez condition perpendicular to the flat surfaces of the pancake-shaped β grain structure (tested in the short transverse direction). These results were discussed in terms of the effectiveness of the crack front geometry in hindering crack propagation. Further, the results of this study were considered for alloy selection and optimized microstructures for fatigue and fracture critical applications. Finally, the advantage of the α+β-processed β-Cez condition in highly stressed engineering components is pointed out because of its overall superior combination of fatigue crack initiation and propagation resistance (especially against small fatigue cracks).

Fatigue Behavior of Alumina with Surface Crack. Effects of Initial Surface Crack Size and Multiple Surface Cracks.

In this paper, the effect of crack size, number and distance between the centers of surface cracks on the fatigue behavior of alumina has been investigated. A single crack and two or three collinear surface cracks were introduced by Vickers indenter. The crack size was changed by several indentation load. The fatigue tests were carried out under static tensile loading (stress ratio R=1) and cyclic loading (R=0 and -1). The main results were as follows. ( 1 ) For any surface crack size, appreciable decrease in fatigue lifetime due to cyclic load was observed, and the degree of the decrease was almost the same for each crack size. ( 2 ) No appreciable effect of stress ratio was observed in the decrease in fatigue lifetime due to cyclic loading. ( 3 ) An interaction of multiple surface cracks, that is to say, the decreasing fatigue lifetime by the interaction with the increase in the nurnber of crack or the decrease of the distance between those cracks was more clearly observed in the case of small crack size, while no interaction was observed In the case of large crack. Such a result seems to be caused by the reason that the interaction of multiple surface cracks may be cancelled by the higher crack propagation resistance owing to bridging effect in crack tip.