Propagation Curve Research Articles

Analysis Approach to Durability Based on Material Initial Fatigue Quality and S-N Curve

Based on probabilistic fracture mechanics approach, a new concept of material initial fatigue quality (MIFQ) is developed. Then, the relation between S-N curve and crack propagation curve is studied. From the study, a new durability analysis method is presented. In this method, S-N curve is used to determine crack growth rate under constant amplitude loading and evaluate the effects of different factors on durability and then the structural durability is analyzed. The tests and analyses indicate that this method has lower dependence on testing, and higher accuracy, reliability and generality and is convenient for application.

Effect of Microstructure on Small Fatigue Crack Initiation and Propagation Behavior of Ti-6Al-4V Alloy

Fatigue tests were performed in laboratory air using extruded Ti-6Al-4V to determine the effect of microstructure on S-N curve, and the crack initiation and crack propagation behavior of the alloy. A modified linear elastic fracture mechanics approach was used in the analysis of the short crack propagation behavior to predict the S-N curve and the crack propagation curve. The predictions agreed well with the experimental results.

Application of Lambda Distributions and Bootstrap analysis to the prediction of fatigue lifetime and confidence intervals

Dealing with fatigue lifetime prediction, this paper aims to report on a new statistical method combining the Lambda Distributions and the Bootstrap technique. This method is first applied for determining the Probability Density Function (PDF) of the C and n coefficients in the Paris relationship of a fatigue crack propagation curve. Then, introducing the initial crack's length distribution, the fatigue lifetime prediction is obtained and discussed considering various standard deviations of the initial crack's length. It is shown that the scattering of the initial crack's length needs to be taken into account in predicting lifetime, and that the stochastic nature of the crack's propagation is not self-sufficient to explain completely the experimental asymmetry of the PDF lifetime. This paper shows that the Lambda Distributions are a powerful tool for modelling the PDF lifetime, compared with traditional Gaussian or lognormal PDF.

Notch Effect on Fatigue Strength of Porous Ceramics

Smooth specimens, semi-circular notched and V-notched specimens of porous silicon carbide with porosity of 35% were fatigued under cyclic four-point bending at a stress ratio of 0.1. The reduction of the fatigue strength due to notches can be estimated from the reduction of the crack initiation stress in static bending fracture tests. The crack propagation curve in V-notched specimens was divided into stages I, II and III. In stage I, the crack propagation rate decreased even though the applied stress intensity factor got larger with crack extension. The crack propagation rate was nearly constant in stage II, and then increased in stage III. The anomalous behavior in stages I and II was caused by crack-tip shielding due to microcracking and asperity contact, while the crack tip shielding was minimal in stage III. For the case of semi-circular notched specimens, stage I was followed by stage III without stage II. The crack length at the end of stage I took a constant value of about 0.068 mm for semi-circular notched specimens and 0.12 mm for V-notched specimens. The stress intensity factor at the onset of unstable fracture was about 1 MPa·m 1/2 for both types of notched specimens.

Method for measuring velocity of shallow water flow for soil erosion with an electrolyte tracer

Measurement of the velocity of shallow water flow on a hill slope is of great importance in soil erosion studies. Electrolyte tracers have been tried to estimate mean velocity of water flow with the velocity of the leading edge of the solute propagation multiplied with a somewhat arbitrary correction factor. In this study, an analytical solution of solute (tracer) transport was formulated to serve as the mathematical foundation for measuring shallow water flow velocity. To estimate the flow velocity, a procedure was advanced. In the procedures, the analytical solution is fitted with the measured propagation curve and given the ‘the least square’ estimation of velocity. A detailed mathematical description is outlined for this purpose. Experimental results are given to show the feasibility of the method, including the analytical solution and the estimation procedures. This study provides the theoretical foundation for measuring the velocity of shallow water flow and for studies of overland solute transport.

Experimental study on the influence of overload induced residual stress field on fatigue crack growth in aluminium alloy

The aim of this study is to investigate current methods in linear elastic fracture mechanics (LEFM) and determine a new experimental procedure for their suitability to predict crack growth in aluminium alloy, i.e. Al 7050–T7451, when a compressive residual stress field is introduced by an overload. A basic study has been made on the effect of varying levels of tensile overloads on the crack growth rate in aluminium alloy that are being used extensively in fighter jet aircraft. To the knowledge of the researchers no such results available on Al 7050–T7451 materials. Experiments are performed on the centre-cracked tension specimens at various levels of range of stress intensity factors (ΔK). Typical overload ratios of 1.4, 1.6 and 1.8 that are generally used in service conditions, are investigated for each ΔK level using load shedding to maintain the ΔK value required. Crack growth measurements are performed using both special crack propagation gauges and a newly designed, purpose-built travelling microscope. The average crack growth rate is used to determine an effective ΔK value for each interval using the fatigue crack propagation curve. After the application of overloads, experimental measurements revealed a period of significant retardation before the crack growth rates returned to their original baseline levels. The results from the numerical predictions are compared with the experimental results. The prediction model produces conservative results for both constant amplitude crack-growth and overload induced retarded growth. Wheeler retardation model produces larger improvements and the over predicts the fatigue life in comparison to experimental values.

The Friction and Wear of Rubber Part 2: Micro-Mechanical Description of Intrinsic Wear

Abstract The concept of a Damage Orientation Distribution Function was introduced in Part 1 of this series to describe the transient affect on wear generated by a dynamically changing slip orientation. In this Part an analytical model of the micro-mechanical processes that occur in a slipping rubber/abrasive interface is offered and serves as the basis for a new relation for the prediction of rubber wear. The description considers the fatigue fracture processes that occur at the intrinsic nodule level. The assumption is made that each intrinsic nodule undergoes intermittent fractures which are driven by Strain Energy Release Rate levels that range from a minimum at or below the linear region of the material's Fatigue Crack Propagation curve, through the Power Law Region and finally to the catastrophic tear value. The proposed description is tested against the early data of Schallamach. It is shown that the simple relationships offered in the analytical study can be used to predict rubber wear performance over a wide range of pressures and abrasive asperity sizes. In light of this analysis, the Damage Orientation Distribution Function of Part 1 is revisited and found to be a useful tool when considering the fundamental processes that occur during unidirectional wear. Changes in slip direction are found to affect the instantaneous wear rate by affecting the Distribution Function in a different manner than changes in pressure or abrasive size. Changes in slip direction are shown to affect the population of intrinsic nodules immediately available for rupture while changes in pressure or abrasive size are shown to influence wear by changing the rate at which nodules move through the Distribution.

Toughness Optimization of SBR Elastomers – Use of Fracture Mechanics Methods for Characterization

AbstractElastomer materials are used in a wide application range and subjected to different loading from which failure of the material results. Because this failure is caused by initiation and propagation of cracks, the application of fracture mechanics methods for the assessment of the material is obvious. A short summary of the methods of technical fracture mechanics including possibilities of determination of crack resistance curves is given. Vulcanizates on the basis of SBR 1500 with various sulfur and carbon black contents were investigated. For describing the crack initiation and crack propagation behavior, several fracture mechanics examination methods were applied. Tear‐analyzer results were used to assess the crack propagation behavior under fatigue‐like loading conditions. Furthermore, for the characterization of the crack resistance of the materials under impact‐like loading conditions, instrumented tensile‐impact tests were performed. To obtain information about the initiation and propagation of a stable crack, quasi‐static fracture mechanics tests were applied. The results of the several tests are discussed in dependence on sulfur and carbon black contents. We found a non‐monotonous behavior of the toughness as a function of carbon black loading. An explanation is given in connection with a percolation‐like transition in filler morphology on larger length scales. Schematic crack propagation curve for characterizing the fatigue behavior of the vulcanizates recorded in a TFA test.magnified imageSchematic crack propagation curve for characterizing the fatigue behavior of the vulcanizates recorded in a TFA test.

Common-Pb corrected in situ U–Pb accessory mineral geochronology by LA-MC-ICP-MS

LA-MC-ICP-MS is shown to be a rapid, precise and accurate method for determination of U–Pb ages of accessory minerals. For the protocol described, total analysis time is <3 min with a main acquisition sequence of only 30 s. Using a raster ablation protocol, within-run inter-element fractionation can be effectively eliminated and an external ablation standard used to quantify an overall error for the analysis. Reproducibilities of 206Pb/238U = ca. 3% and 207Pb/206Pb = <1% (2 σ) are achieved, with the resulting age accurate to within 1% as determined using in-house samples previously characterised by TIMS. A key control on the Pb/Pb reproducibility is shown to be the size of the 207Pb peak and an error propagation curve is determined for the accurate representation of this data. Propagation of these errors allows each individual sample analysis to be considered a stand-alone result, removing the need for statistical averaging of multiple data points. Simultaneous collection of flat-topped peaks enables precise measurement and correction of isobaric interference from 204Hg and a procedure for the consistent correction of common-Pb using 204Pb is described. Determination and correction of the common-Pb component is shown to be critical to the reliable interpretation of the data for certain minerals including those phases where a correction is often deemed unnecessary. Combined with time-resolved analysis of the data, this allows the Pb-loss history and nature of discordance within individual crystal domains to be ascertained. Successful analyses of zircons using a non-matrix matched (monazite) standard are also demonstrated suggesting that particle size distribution, ionisation efficiency and plasma loading, are more important issues in controlling inter-element fractionation in the plasma than absolute matrix matching.

Acoustics of industrial buildings

Industrial halls have significantly different shapes as rooms for other purposes. Typically these enclosures are very large and/or flat, which means that the room height is usually very much smaller than width and length. Sound fields in these types of enclosures cannot be expected to have an approximate diffuse sound field. Instead, the decay curves are bent, while sound level versus distance (sound propagation curve) is declining. This contribution summarizes physical properties of sound fields in flat and long rooms, gives some examples of predictions based on image sources, on Kuttruffs integral equation, results of scale model experiments and ray-tracing algorithms with two different levels of complexity. It can be shown that in many cases predictions can yield sufficiently accurate results. However, problems will occur in cases where rooms are heavily filled with scattering objects (fittings). On the other hand, the exact spatial distribution of sound in these nondiffuse cases has shown to have less influence on the perceived annoyance than expected. Accordingly, predictions of sound levels with reasonable accuracy should be sufficient to describe the subjective effect of listening, unpleasantness and annoyance in industrial halls.

Fatigue Mechanisms of Porous Silicon Carbide under Cyclic Loading(Ceramics &amp; Rocks 1)

Notched specimens of porous silicon carbide with porosity 37% were fatigued under four-point bending at frequencies of 30 and 0.3 Hz. The fatigue life expressed in terms of time was rather insensitive to the test frequency, while that expressed in terms of cycles was much shorter for the case of 0.3Hz than for 30 Hz. A time-dependent stress corrosion mechanism was mainly responsible for crack propagation, and stress cycling enhanced the crack propagation mechanism. The crack length was estimated from the change of the compliance of the specimen. The crack propagation curve was divided into Stages I and II. In Stage I, the crack propagation rate decreased even though the applied stress intensity factor got larger with crack extension, and turned to increase in Stage II. The transition from Stage I to II took place at the crack extension of around 0.8 mm. This anomalous behavior is caused by crack-tip shielding due to microcracking and asperity contact. Fractographic observations showed that the fracture path was along the binder phase between SiC particles, more precisely along the interface between particles and binders.

Elastic and fracture parameters of Etna, Stromboli, and Vulcano lava rocks

The results of a series of experiments aimed at characterizing the elastic and failure parameters of lava specimens from Mount Etna, Vulcano and Stromboli volcanos is presented. The double torsion—constant configuration—load relaxation method has been employed to obtain the behavior of the stress intensity factor versus mode I subcritical crack velocity. The experimental technique has been optimized in several respects. First, a very stiff machine, expressly designed and built, has been used. Second, all samples have been carefully machined to low tolerance. Third, the experimental conditions have been carefully controlled, with temperature variations within 1°C and humidity within 10%. Fourth, high resolution electronic measuring systems have been used together with a pulse stacking procedure. Fifth, the length of the prefracture has been optically checked. This optimization allowed us to measure the slope of the subcritical fracture propagation curve in the III region, which extends from velocities of 10−7m/s to catastrophic, with a standard deviation around 20%, suggesting that the results can be effectively used for modeling purposes. As a by-product, we could measure the elastic parameters with an accuracy of a few percent.

Spannungsrißkorrosion des Chromstahles X 210 Cr 12 in chloridund sulfathaltigen Lösungen Teil 1: SpRK-Belastungsverhalten

Es wird das SpRK-Verhalten des Kaltarbeitsstahles X 210 Cr 12 mit martensitischem und perlitischem Gefüge in reinem Wasser sowie in wäßrigen Chlorid- und Sulfatlösungen bruchmechanisch bei Raumtemperatur untersucht. Der Stahl ist in beiden Gefügevarianten in den untersuchten Medien SpRK-anfällig und weist in seinem SpRK-Belastungsverhalten dehnungsinduzierte SpRK (ε-iK) auf. Der Korrosionsprozeß im Riß führt im Zusammenwirken mit der Dehnung zur Wasserstoffversprödung an der Rißspitze. Bei zu geringer Dehnrate kann es zu anormalen Verläufen der Rißausbreitungskurven kommen. Die stark ausgeprägte Gefügeinhomogenität des Werkstoffs begünstigt ebenfalls dieses Verhalten. Um die erforderliche Dehnrate bei der ε-iK zu erreichen, sind bei der Erfassung der 3 Bereiche der Rißausbreitungskurve unterschiedliche Belastungsregimes anzuwenden: Zur Bestimmung des Schwellwertes KISCC und des Bereiches I der Rißausbreitungskurve ist die Belastung im CR-Modus (Constant Displacement Rate) mit hinreichend großer Dehnrate erforderlich. Dagegen kann es bei CL-Modus (Constant Load) im Bereich I wegen zu geringer Dehnrate zu anormaler Rißausbreitung mit temporärem Rißstillstand („Einschlafeffekt”︁) kommen. Zur Bestimmung des Plateaubereiches (Bereich II) sowie des Überganges zum Bereich III des instabilen Bruchs ist der CL-Modus bei zunehmendem K-Wert erforderlich. Der CR-Modus im Plateau führt infolge zu geringer Dehnrate zur Erniedrigung der Plateaurißgeschwindigkeit mit diskontinuierlichem Rißwachstums. Der CD-Modus (Constant Displacement) ist wegen Dehnrate nahezu Null weder zur Bestimmung des Plateaus noch für den Schwellwert KISCC geeignet. Stress corrosion cracking of the chromium steel X 210 Cr 12 in chloride and sulphate containing solutions Part 1: Influence of loading conditions on SCC – behaviour The stress corrosion cracking behaviour of the cold work steel X 210 Cr 12 with both martensitic and pearlitic structure has been investigated in distilled water as well as in aqueous chloride and sulphate solutions at room temperature by means of a fracture mechanics method. This steel is found to be sensitive to stress corrosion cracking and this behaviour points to strain induced SCC. The crack propagation is caused by hydrogen embrittlement by interaction of the corrosive produced hydrogen at the crack tip with material straining. Abnormal crack propagation can be caused by both large inhomogeneities of the structure and strain rates below threshold values. For realisation of a demanded strain rate it is necessary to use different loading conditions as follows: The CR-mode (Constant Displacement Rate) with a sufficiently high strain rate is necessary for the determination of KISCC-value as well as the region I of the crack propagation curve. On the other hand, the CL-mode (Constant Load) can lead in the region I to abnormal crack propagation with temporary crack stop (“resting effect”) because of too low strain rate. However, the CL-mode with increasing K-value is required to determine the plateau of crack propagation rate in region II as well as to the transition into the region III of instable cracking. The use of the CR-mode in region II would lead to a lower plateau of crack rate combined with discontinuous crack growth. The CD-mode (Constant Displacement) with strain rate of about zero is not applicable to determine the plateau value as well as the threshold value KISCC.

Lower Limit of Cumulative Fatigue Damage of 0.25%C Annealed Steel under Two-Step Loading.

Rotating bending fatigue tests were performed using smooth and precracked 0.25%C annealed steel specimens. The initiation and propagation of fatigue cracks were successively observed by the replication method, and the cumulative fatigue damage under two-step loading was investigated. Precracked specimens with four different precrack lengths, 150, 300, 450 and 700μm, were examined and the S-N curves for the precracked specimens with arbitrary crack lengths were estimated. The fatigue damage defined by Miner's rule under two-step loading was estimated from the crack propagation curve, the S-N curve of the smooth specimen and the estimated S-N curve for the precracked specimen. The estimated average value of the lower limit was 0.97, but it was 0.60 when the scatter of the experimental data in each specimen was considered.

Numerical prediction of fracture for TPB specimen of No. 45 steel

In the present paper, the fracture initiation, crack propagation and resistance curve J R- Δα for a three point bending (TPB) specimen made of no. 45 steel have been predicted by applying the combinatorial work density model [K. S. Zhang, C. Q. Zheng and N. S. Yang, Proc. ICM 6] associated with the finite element analysis. The model's parameters were obtained from the axial simple tension experiment [K. S. Zhang and Z. H. Li, Engng Fracture Mech. 49, 235–241 (1994)]. The reasonable results by simulation show that the prediction method, in which the damage criterion can be determined only using the simple tension experiment data, seems to be applicable for a ductile material which has a large constrictive ratio (necking deeply) at fracture when this material is tensioned axially.

Fatigue Crack Propagation in a Specimen with a Complicated Cross-Section; Characterization of the Stress Intensity Factor

Abstract In order to predict the fatigue life of machine equipment, the fatigue crack propagation law has up to now been investigated using specimens with a simple cross-section shape. In this study, a specimen with three grooves cut in the loading direction was used to clarify crack propagation and crack closure behavior at points of discontinuous change in thickness. It was found that the crack propagation curve showed a complicated variation in the vicinity of the grooves and that the variation of crack closure behavior correlated well with it. The stress intensity factor was evaluated using the calibration curve between the crack propagation rate and the effective stress intensity factor range obtained from a similar smooth specimen. Results showed that the stress intensity factor of the grooved specimen was higher in front of the first groove and lower behind it, compared to the smooth specimen. As the crack crossed the first groove, the crack propagation rate exhibited a local maximum as a function of the maximum value of stress intensity factor.

Ｔｉ‐６Ａｌ‐４Ｖ合金における単一過大荷重下の低サイクル疲労き裂進展特性

In this study, the low cycle fatigue deformation properties and the surface crack propagation behaviour of α/β-rolled plates of Ti-6Al-4V alloy with conventionally annealed equiaxial microstructure were investigated under the constant strain amplitude and the single over-straining conditions. Two types of the single over-straining were performed; that is, tension only (T waveform) and tension-compression (T-C waveform) over-straining, and the effects of the overstraining ratio λ on the cyclic deformation and the crack acceleration or the crack retardation behavior were also studied from the stand-point of the changes in crack opening displacement Φ and tensile peak stress σpt. As the results, in the T waveform test in the range of λ≥1.62, the crack ratardation occurred when compared with the crack propagation of the constant amplitude test, and the retardation effect increased with the ratio λ. On the other hand, in the T-C waveform test, the crack propagation curve after over-straining was almost coincident with the curve of the constant amplitude test. It became clear that the retardation behaviour of surface crack propagation after the over-straing of the T waveform resulted from both of the changes in Φ and σpt after the over-straining. The relation between the crack propagation rate da/dN and the J integral range ΔJ under the over-straining conditions was in good agreement with the da/dN and ΔJ relation of the constant strain amplitude test.

The influence of coating thickness on lubricated rolling contact fatigue life

The effect of coating thickness on the fatigue life of TiN-coated rollers under lubricated contact was investigated with a twin-disk machine. TiN films of various thicknesses (0.25–5 μm) were deposited on AISI 4118 steel rollers by high rate reactive sputtering. The ratio of the spalled area ( A sp) to the observed area ( A ob was used as the fatugue damage index for different coating thicknesses at selected cycles. The experimental results revealed that coating thicknesses of 0.25 μm give the best fatigue resistance. On the basis of the test data, fatigue life charts of coated contact are established. The behavior of spalling initiation is described according to the stress state and the coating thickness. The relatively thick coatings have larger initial spalls. The process of spalling propagation can be illustrated by the progressive measurement of spalling areas as related to length of rolling contact cycles. The spalling propagation curve shows a slow propagation mode followed by a fast growth to contact failure.

引張残留応力場にある溶接継手の設計疲労き裂伝ぱ曲線

Fatigue crack propagation properties of welded joints were investigated for five types of steels, SB42, SM50B, SPV50, HT80 and SUS304. Propagation data for all materials were found to be coinciding with each other. This was due to the presence of tensile residual stress around the crack tip which made the crack surfaces to open. A total of 3, 335 data plots were used to fit a regression curve. For design purpose, it is advisable to adopt the fatigue crack propagation curve at 99.5% confidence limit. It is also shown that the proposed curve is applicable to random loadings.

繰返し衝撃曲げを受けるモルタル試験体の疲労挙動について

The purpose of this investigation is to examine the S-N diagram and the fatigue process, and the fracture toughness of cement mortar specimens under repeated impact bending load. Here, S is impact load level and N is numbers of repeated stroke. This investigation is divided into three tests. The S-N diagram of cement mortar specimens was clarified by the first test which we struke the falling ball with stell on the center of simple beams (shape of beam = 4×4×16cm, span = 15cm) to obtain impact fatigue life data. The second test is the fatigue process test which was performed by the same method as the first test to obtain the relation between numbers of repeated stroke and impact flexural strain, and residual strain as well. The third test is the fracture mechanics test which was performed on two simple beams with notch and without notch to clarify the crack propagation process under repeated impact bending load and to expect impact fatigue life of cement mortar specimens. The main results obtained by this investigation are summarized as follows. (1) From the first test, relations between S and N can be showen by two straight lines on the S-N diagram. When S is larger than an intersecting point which is named the specific impact load level S_0, the impact breakage is the predominant behavior on the S-N diaram. When S is smallar than S_0, impact damage is very little, then the fatigue process ia observed. Here, S_0 is about 55 % of impact bending strength. (2) In the case of S>S_0, the crack propagation under repeated impact bending load is in proportion to S and the propagation process of impact flexural strain and residual strain change remarkably. Therefore, the fatigue process under repeated impact bending load can be estimated by the crack propagation and impact flexural strain and residual strain. (3) When the linier fracture mechnics applies to cement mortar specimens under repeated impact bending load, the fatigue life of specimens, that is, the crack propagation curve and numbers of repeated stroke into fracture, is estimated by statical stress intensity factor K and physical constant c and m. Here, the values of c and m can be obtained by the experimental results.