Initial Flaw Size Research Articles

Availability of gamma distribution as initial distribution of flaw size

To demonstrate availability of gamma distribution as the initial distribution of flaw size, three kinds of initial flaw size data of alumina ceramics were employed. Compared with a power function, gamma distribution was better fit to the data in every case. For practical use, an approximate expression of the initial distribution of flaw size was proposed by taking out a major part of the gamma distribution relating to the shape parameter. Finally, a positive correlation between the average fracture strength of the alumina ceramics and the shape parameter of the gamma distribution was discussed.

Fatigue crack formation and growth from localized corrosion in Al–Zn–Mg–Cu

The effect of precorrosion on the fatigue life of aluminum alloy 7075-T6511 was measured, physical characteristics of corrosion topography plus fatigue damage were established by microscopy, and a corrosion modified equivalent initial flaw size (CM-EIFS) was established using fracture mechanics modeling. Fatigue life is reduced by clustered corrosion pits on the L–S surface from laboratory-EXCO exposure. Cracks initiate from pits clustered as a semi-elliptical surface micronotch rather than the deepest pits, consistent with shape-dependent stress intensity. Marker band analysis establishes that the number of cycles to form a crack about a pit cluster can be a significant fraction of total fatigue life. The CM-EIFS, back-calculated from fracture mechanics analysis of measured fatigue life, equals measured initiating-pit cluster size provided that important inputs are provided; such favorable comparison validates this approach to corrosion-fatigue interaction. Calculated CM-EIFS provides a metric to characterize alloy corrosion damage, and can be used to forward-model the effects of stress and loading environment on fatigue life distribution, critical for efficient alloy development. Use in prognosis of the fatigue performance of a service-corroded surface is hindered by uncertain non-destructive characterization of corrosion topography.

Long-Term Outcome of Acellular Dermal Matrix When Used for Large Traumatic Open Abdomen

The purpose of this study is to prospectively examine the use of Human Acellular Dermal Matrix (HADM) in trauma patients with large open abdominal wounds and assess the long-term outcome. Previous studies have not examined the long-term outcomes in trauma patients with abdominal wall reconstructions. An institutional review board approved prospective case series of consecutive patients admitted to a level I university trauma center, who were unable to have their abdomen closed primarily after trauma laparotomy. These patients had HADM placed to attain closure of the abdomen with skin advancement flaps to cover the HADM when possible. Our primary outcome measure was hernia formation and our secondary outcomes were laxity, fistulae, and infections associated with HADM. Ten patients were enrolled during a 1-year period. Mean time to HADM placement was 17.2 days +/- 3.6 days. Mean initial defect size was 425.1 cm2 +/- 75.9 cm2 with the largest 770 cm2. Thirty day follow-up showed no recurrence in 100% patients. Six patients remained for long-term follow-up. Follow-up at 60 days demonstrated significant laxity or recurrent hernia or both in 67% of patients, and this increased to 100% by the end of 1 year follow-up. There were no bowel fistulae in these patients closed with HADM but 20% with infection. HADM is an alternative available to reconstruct the unclosable open abdomen with no fistulae formation, however, it is associated with a high rate of laxity in large abdominal wounds.

Probabilistic fatigue life prediction using an equivalent initial flaw size distribution

A new methodology is proposed in this paper to calculate the equivalent initial flaw size (EIFS) distribution. The proposed methodology is based on the Kitagawa–Takahashi diagram. Unlike the commonly used back-extrapolation method for EIFS calculation, the proposed methodology is independent of applied load level and only uses fatigue limit and fatigue crack threshold stress intensity factor. The advantage of the proposed EIFS concept is that it is very efficient in calculating the statistics of EIFS. The developed EIFS methodology is combined with probabilistic crack growth analysis to predict the fatigue life of smooth specimens. Model predictions are compared with experimental observations for various metallic materials.

Micro/macro-crack growth due to creep–fatigue dependency on time–temperature material behavior

The implicit character of micro-structural degradation is determined by specifying the time history of crack growth caused by creep–fatigue interaction at high temperature. A dual scale micro/macro-equivalent crack growth model is used to illustrate the underlying principle of multiscaling which can be applied equally well to nano/micro. A series of dual scale models can be connected to formulate triple or quadruple scale models. Temperature and time-dependent thermo-mechanical material properties are developed to dictate the design time history of creep–fatigue cracking that can serve as the master curve for health monitoring. In contrast to the conventional procedure of problem/solution approach by specifying the time- and temperature-dependent material properties as a priori, the desired solution is then defined for a class of anticipated loadings. A scheme for matching the loading history with the damage evolution is then obtained. The results depend on the initial crack size and the extent of creep in proportion to fatigue damage. The path dependent nature of damage is demonstrated by showing the range of the pertinent parameters that control the final destruction of the material. A possible scenario of 20 yr of life span for the 38Cr2Mo2VA ultra-high strength steel is used to develop the evolution of the micro-structural degradation. Three micro/macro-parameters μ ∗, d ∗ and σ ∗ are used to exhibit the time-dependent variation of the material, geometry and load effects. They are necessary to reflect the scale transitory behavior of creep–fatigue damage. Once the algorithm is developed, the material can be tailor made to match the behavior. That is a different life span of the same material would alter the time behavior of μ ∗, d ∗ and σ ∗ and hence the micro-structural degradation history. The one-to-one correspondence of the material micro-structure degradation history with that of damage by cracking is the essence of path dependency. Numerical results and graphs are obtained to demonstrate how the inherently implicit material micro-structure parameters can be evaluated from the uniaxial bulk material properties at the macroscopic scale. The combined behavior of creep and fatigue can be exhibited by specifying the parameter ξ with reference to the initial defect size a 0. Large ξ (0.90 and 0.85) gives critical crack size a cr = 11–14 mm (at t < 20 yr) for a 0 about 1.3 mm. For small ξ (0.05 and 0.15), there results critical a cr = 6–7 mm (at t < 20 yr) for a 0 about 0.7–0.8 mm. The initial crack is estimated to increase its length by an order of magnitude before triggering global to the instability. This also applies ξ ≈ 0.5 where creep interacts severely with fatigue. Fine tuning of a cr and a 0 can be made to meet the condition of t = 20 yr. Trade off among load, material and geometric parameters are quantified such that the optimum conditions can be determined for the desired life qualified by the initial–final defect sizes. The scenario assumed in this work is indicative of the capability of the methodology. The initial–final defect sizes can be varied by re-designing the time–temperature material specifications. To reiterate, the uniqueness of solution requires the end result to match with the initial conditions for a given problem. This basic requirement has been accomplished by the dual scale micro/macro-crack growth model for creep and fatigue.

A Semi-empirical Mathematical Model to Estimate the Duration of the Atmosphere within a Double Oxide Film Defect in Pure Aluminum Alloy

It has been shown that the oxygen and nitrogen within the atmosphere of a double oxide film defect can be consumed by the surrounding Al melt. Experimentally determined reaction rates were used to construct a semi-empirical model to predict the change in volume with time of a bubble of air trapped in an Al melt, with the model including the diffusion of H from the metal into the bubble. Comparison with experimental results showed that the model predicted the change in volume well. The model was then used to estimate the duration of the internal atmosphere within double oxide film defects, which suggested that these would be consumed in a time of up to 3 minutes, depending upon assumptions made about the initial defect size.

Fretting behaviour of AISI 301 stainless steel sheet in full hard condition in contact with AISI 52100 steel

The fretting behaviour of thin sheets of AISI 301 stainless steel in the full hard condition in contact with an AISI 52100 cylindrical body was evaluated. The relationship between fretting conditions and residual fatigue life was used to characterise fretting damage. The influence of normal force and displacement amplitude on fretting damage was considered with emphasis on the latter. An equivalent initial flaw size calculated using the NASGRO crack growth rate equation was used to quantify the fretting damage.

高炭素クロム軸受鋼の転がり疲れにおける内部欠陥からのき裂発生挙動

It is important to clarify the effects of nonmetallic inclusions on rolling contact fatigue life to extend or to predict the life of the rolling bearings. The observation of initial cracks from internal defects is desirable from this point of view. In this study, high carbon-chromium bearing steel, SUJ2, with a number of artificial pores as internal defects was prepared. Initial cracks around pores under rolling contact were observed and the stress was CAE analyzed with the following results:- The exposure of the initial crack surface by forced breaking and the subsequent fracture observation in this study were effective to identify the mode of the initial crack generation.- The tensile stress around the pores initiated mode-I crack, and the pore with cracks is subjected to crack propagation process by internal stress under rolling contact fatigue.- Rolling contact fatigue life is not simply dominated by the size of initial defects in steels. As observed in this study, the sum of initial defect size and rim crack size may control the fatigue life. This suggests that the inclusion types and the interfacial adhesiveness between inclusions and matrix may influence rolling contact fatigue.

Hygrothermal Failures From Small Defects in Lead-Free Solder Reflowed Electronic Packages

Steam-driven delamination failure is a main failure mode in electronics packages during solder reflow. Steam pressures built up within interfaces in packages are sensitive functions of the reflow temperature. The switch to lead-free soldering will raise re-flow temperature by more than 20degC and double the equilibrium saturated steam pressure within defects in the package. The effects of saturated steam driven interfacial failure was analyzed using finite element in this study. Analyses revealed that packages which are thin and made using high thermal conductivity materials are at higher risk of failure than conventional packages made using standard materials. This suggests that electronics made with thick and inexpensive encapsulants are less prone to failure when switched to lead-free solder. Portable and mobile electronics which have low profiles and are made of high thermal conductive encapsulants are at higher risk when switched to lead-free solder reflow. Moreover, the study found that the critical temperature for failure is dependent on the defect size in the package. Reduction of initial defect size can reduce failures in high risk packages in lead-free solder reflow.

An improved model for predicting fatigue S–N (stress–number of cycles to fail) behavior of glass fiber reinforced plastics

In a previous study a model to predict the fatigue S–N behavior of glass fiber reinforced thermoplastics by using a fracture mechanics approach was presented. Using a single flaw size model, some degree of success was observed, particularly for a reinforced polyamide. The model was not successful in predicting the S–N behavior of a reinforced polyester. The earlier study also employed flexural fatigue rather than tensile fatigue data in the calculations because the calculated flaw sizes were more nearly constant as a function of stress level. Subsequently it was shown that the flexural fatigue stress calculations were in error for these types of short glass fiber reinforced plastics owing to the nonlinearity of their stress–strain behavior. In this report we reexamine the utility of the fracture mechanics approach to predict fatigue S–N behavior for both materials using an improved model. Whereas previously a single initial surface flaw was assumed, here we assume multiple flaws growing simultaneously across the sample thickness. The new model is applied to both flexural and tensile fatigue loading. Results demonstrate that this new approach provides accurate predictions of the S–N behavior for both materials under both loading conditions. This reflects the fact that the calculated initial flaw sizes are relatively independent of stress level. No additional adjustable parameters are required if one uses the initial breaking strength of the material as part of the model calculations.

Efficient damage sensitivity analysis of advanced Cu/low- k bond pad structures by means of the area release energy criterion

For integrated circuit (IC) wafer back-end development, state-of-the-art CMOS-technologies have to be developed and robust bond pad structures have to be designed in order to guarantee both functionality and reliability during waferfab processes, packaging, qualification tests, and, of course, usage. It is now well established that for future CMOS-technologies (CMOS065 and beyond), low- k dielectric materials will be integrated in the back-end structures. However, bad thermal and mechanical integrity as well as weak interfacial adhesion result in major thermo-mechanical reliability issues. Especially the forces resulting from packaging related processes such as dicing, wire bonding, bumping and molding are critical and can easily induce cracking, delamination and chipping of the IC back-end structure when no appropriate precautions are taken. This paper presents an efficient method to describe the damage sensitivity of three-dimensional multi-layered structures. The index that characterizes this failure sensitivity is an energy measure called the Area Release Energy, which predicts the amount of energy that is released upon crack initiation at an arbitrary position along an interface. The benefits of the method are: (1) the criterion can be used as damage sensitivity indicator for complex three-dimensional structures; (2) the criterion is energy-based, thus more accurate than stress-based criteria; (3) unlike recent fracture mechanics approaches, no initial defect size and location has to be assumed a priori. A mesh objectivity condition is formulated resulting from numerical experiments. The method is applied to advanced IC back-end structures, revealing not only the most critical back-end design but also the critical interfaces in the bond pad structures at which delamination might occur. In order to bridge the length scale difference between the wafer level and the back-end structures, a multi-scale method has been implemented in the finite element code MSC.Marc. In this way, effects of e.g., packaging and wire bond loading at the global level can be studied while taking into account the possibility of occurring failure phenomena at the local, back-end level. The validity and applicability of the method will be demonstrated by considering several Cu/low- k back-end structures. The obtained results are in good agreement with experimental observations.

Three-dimensional shape of the early stages of fatigue cracks nucleated in nodular cast iron

High resolution synchrotron X-ray tomography has been used to obtain three-dimensional (3D) images of the early stages of fatigue crack nucleation in a nodular cast iron. Microcracks were observed to initiate at casting defects (microshrinkage) and graphite nodules. The 3D observations have shown that the microcracks form in the material ligament comprised between the specimen surface and the defect. The probability of a defect to initiate a crack was correlated with the size of the defect and its position with respect to the surface. This correlation has been explained on the basis of local stress concentrations in the vicinity of the defect. The 3D observations of samples submitted to different fatigue cycles revealed that a large part of the fatigue life consisted in the progressive fracture of the ligament. The majority of the observed cracks stopped after this fracture process and, therefore, their size did not exceed the initiating defect size even if the crack seemed larger than the defect on the optical surface observations. Only few microcracks, nucleated on the largest defects, continued to grow with short-crack behaviour.

Effect of increased interfacial strength on the fatigue crack growth resistance and crack opening displacement of β Ti21S/SCS 6 composites

Fatigue crack growth resistance of metastable β titanium composite was investigated in different heat treatment conditions. The effects of increased interfacial strength due to peak ageing on the fatigue crack growth, crack opening displacement and fibre bridging were examined and results of fibre fractures monitored by acoustic emission and fibre push back tests were correlated with fatigue crack growth and crack opening behaviour of the composites. It is shown that at maximum applied intensity factor values higher than crack arrest/catastrophic failure transition, peak ageing reduces the fatigue crack growth resistance of composite due to higher number of fibre fractures which occurs as fibre stress is increased due to increased interfacial shear stress. However, below transition heat treated composite shows better crack growth resistance compared to as-received condition under fixed K max,ini values. This favourable effect of increased interfacial strength on the crack growth behaviour is prominent in the composites with smaller initial unbridged defect size.

Aircraft life management using crack initiation and crack growth models – P-3C Aircraft experience

In this paper, we present our experience in applying crack initiation and crack growth models to aircraft life predictions and fleet management. The first section of the paper discusses general fleet life assessment methods followed by a description of traditional US Navy method of fleet fatigue life assessment and individual aircraft fatigue tracking. The next section focuses on the history of life estimation methods of P-3C aircraft, with brief descriptions of recently conducted full-scale fatigue test. We then discuss limitations of safe-life methods for aging aircraft such as P-3C and then describe a deterministic total life approach for continued operations beyond crack initiation up to a safe limit using full-scale test as a basis. In the context of crack growth sensitivity to various factors, the need to conduct risk assessment supported by service examples is then presented. Details of risk assessment effort using service data as a basis are briefly described next. Equivalent mathematical formulations for probability of failure analysis are presented with lessons learnt in applying this to field problems. The paper discusses lessons learnt mainly from the standpoints of equivalent initial flaw size distributions, final crack length distributions, and probability of failure calculation methods. The last section of the paper focuses on current crack initiation and crack growth models and their use in aircraft life assessment. Recent coupon test results are used to make general observations about the use of crack initiation and crack growth models. The limitations of applying crack initiation models for different classes of spectrum such as tension dominated and tension–compression type spectrum are then discussed. Similarly, limitations of current crack growth models for application to wide classes of spectra and stress severities are presented. We show the need for calibration of crack growth models when applying to long spectrum histories, using results from recent crack growth coupon tests. The paper concludes with a discussion on the need of better predictive models for both crack initiation and growth for application to a wide variety of aircraft problems.

Tensile strength degradation of ceramic fibres due to cyclic loading

Interfacial strength of Ti β 21S/SCS 6 composite was increased via ageing. Composite specimens with ao/W ratios of 0.24 and 0.07 were prefatigued in three point bending at ambient and at 500 °C both in the air and vacuum. Bridging fibres were extracted from the pre-fatigued specimens and tested in tensile loading to monitor the strength degradation due repeated opening and closing of the fatigue crack. A tri-modal Weibull distribution was employed to express strength distribution of the SCS 6 fibres. Results have shown that cyclic loading of the composites lower the mean tensile strength of the fibres by 20%, compared to the unfatigued composite. A marked effect of initial unbridged defect size was observed, when the tensile strength data were divided into two sub-population using the fatigue crack length values. Compared to unfatigued composite, tensile strength reductions of 41 and 22% were measured from the prefatigued composites with ao/W of 0.24 and 0.07, respectively.

界面初期欠陥を有するＩＴＥＲ用第一壁の亀裂進展の評価

The first wall of the International Thermonuclear Experimental Reactor (ITER) will be fabricated by means of the Hot Isostatic Pressing (HIP) method for the bonding of cooling tubes and a copper alloy heat sink. A ultrasonic testing (UT) is adopted as a non-destructive inspection method for the bonding interface as one of the acceptance tests of the first wall components. Therefore, clarification of a defect size criteria is one of the critical issues for the soundness of the first wall. In this paper, a thermo-mechanical behavior of an initial defect at the bonded interface of the ITER first wall was numerically analyzed. An elastoplastic fracture mechanical parameter, J-integral, was calculated to evaluate the propagation behavior of the interfacial defects under thermal loading. As a result, it was found that the initial defect size of 10 mm×20 mm in semi-elliptic shape was unlikely to propagate under the thermal loading of ITER. This defect size is more than ten times larger than a detection limit of present UT techniques, and it can be resulted that the UT method presently available is sufficient to detect such harmful initial defects of the ITER first wall.

Simultaneous uncertainty quantification of fracture mechanics based life prediction model parameters

A Bayesian technique is developed for simultaneous estimation of the equivalent initial flaw size (EIFS) and crack growth rate distributions in fracture mechanics based life prediction models from inspection data. The inference method separately quantifies the different sources of variability to obtain a data set independent EIFS distribution without the requirement for prior knowledge of the uncertainties in other parameters. The ability to simultaneously and accurately predict the EIFS distribution and crack growth rate noise from a small, highly-scattered data set is demonstrated in a numerical example.

Application of a total life prediction model for fretting fatigue in Ti–6Al–4V

A method for predicting the total fretting fatigue life is applied for Ti–6Al–4V dog-bone fretting fatigue specimens. The total life model incorporates a dual mechanism approach of including the crack initiation life and propagation life while simultaneously determining an associated initial flaw size. This technique adds autonomy to existing fretting fatigue models by releasing the dependence on estimating an initiation flaw size. The model is exercised on two sets of Ti–6Al–4V fretting fatigue experiments and compared to existing results and life prediction methods. The variable initiation crack length model predicts the experimental data and proves to be a new advancement in total fretting fatigue life prediction.

A fracture mechanics approach to estimate the fatigue endurance of welded t‐joints including residual stress effects

ABSTRACTResidual stresses and weld defects play a major role in the fatigue behaviour of welded structures, so these effects need to be accounted for in a theoretical analysis. A simplified engineering procedure based on linear‐elastic fracture mechanics is applied to estimate the fatigue behaviour, particularly the limit of endurance. Local geometrical irregularities and pre‐existing flaws, which are typical for this kind of weld, are covered by an overall notch intensity factor instead of a specific stress intensity factor, so the initial flaw size is not needed explicitly in the analysis. The effect of residual stresses can be easily included. The cut‐compliance method was applied to measure the residual stress distribution on the cross‐section of the weld. A welded T‐joint was used as a benchmark. Unexpectedly, compressive residual stresses were found to prevail in the root region. According to the analysis, they contribute to the endurance limit of the considered joint by about 50%. This result was confirmed by fatigue tests where a significant decrease in the fatigue strength after a post‐weld stress relieving heat treatment was observed.

Characterisation of equivalent initial flaw sizes in 7050 aluminium alloy

ABSTRACTThis paper summarises a collation of crack growth related data from a significant number of fatigue tests on commercial quality 7050‐series aluminium alloy tested under various F/A‐18 aircraft spectra. The data presented consist of quantitative fractography measurements of the fracture surfaces including effective initiating defect size and type (mechanical, environmental or chemical). Three different surface conditions were considered: chemically etched, glass bead peened and machined. The purpose of providing these data was to facilitate analyses on the parameters governing the propagation of fatigue cracks in the 7050‐series aluminium alloy. Here an investigation to determine whether surface finish or applied stress and spectra have any bearing on the initial defect size or the damage type is summarised. Based on this investigation, it appears that the applied stress and spectra have no correlation to the size of the equivalent initiating flaw; however, the surface finish appears to influence the various crack‐initiating mechanisms and to govern the formation of the damage type.