Simulate Fatigue Crack Research Articles

A cohesive model for fatigue failure of polymers

A cohesive failure model is proposed to simulate fatigue crack propagation in polymeric materials. The model relies on the combination of a bi-linear cohesive failure law used for fracture simulations under monotonic loading and an evolution law relating the cohesive stiffness, the rate of crack opening displacement and the number of cycles since the onset of failure. The fatigue component of the cohesive model involves two parameters that can be readily calibrated based on the classical log–log Paris failure curve between the crack advance per cycle and the range of applied stress intensity factor. The paper also summarizes a semi-implicit implementation of the cohesive model into a cohesive-volumetric finite element framework, allowing for the simulation of a wide range of fatigue fracture problems.

Fatigue threshold and crack growth in an electron beam weld made of steel and bronze

In this research topic some experimental tests with single-edge notched beams were performed to determine the threshold load value for fatigue crack growth and to characterize fatigue crack behaviour of an electron beam weld made of steel and bronze. Subsequently, numerical analyses were done to estimate the threshold value Δ K th and to simulate the fatigue crack growth. The calculated crack path was compared to those determined experimentally. The objective was to find out the necessary fracture properties for an analysis of an electron beam welded worm wheel and to asses the capability of usual fracture analysis software to simulate fatigue crack growth in welds.

A study of fatigue crack closure in polycarbonate CT specimens

Plane strain and plane stress finite element (FE) models were built to simulate fatigue crack closure behaviour in polycarbonate. Effective driving forces for crack growth were determined in terms of crack closure, where the opening load was taken either as corresponding to full opening of the two crack faces (Definition 1), or identified by the instant when the principal stress perpendicular to the crack-tip stress becomes tensile (Definition 2). Experimental work was conducted to determine crack growth rates and to characterise crack closure levels, using the compliance technique, in compact tension specimens either 2 mm (plane stress) or 10 mm (plane strain) thick. The FE predictions of crack closure using Definition 1 were found to agree reasonably with the experimental results. It was also found that higher crack closure levels were predicted from Definition 2. A two-parameter function of Δ K eff and K max was utilised to model the fatigue crack growth rate data. The equation derived from Definition 1 theoretical results described the growth rate data better than that obtained from Definition 2.

破壊力学 異種接合材中を伝ぱする疲労き裂の伝ぱ経路の等価試験片によるシミュレーション

A method of simulating the behavior of fatigue cracks propagating in bonded dissimilar materials by using equivalent specimens made of single constituent material was proposed. The equivalent specimens reproduced the same elastic characteristics with those of the bonded dissimilar materials by replacing the effect of elastic constant by that of the specimen thickness, and removed the effect of weakened strength of the bonded interface. Using the proposed equivalent specimens, experiments were conducted simulating fatigue crack paths propagating near or across the slant (15° and 45°) interface of bonded steel-copper specimens. When the cracks propagated from the thick (equivalent to steel) side to the thin (copper) side, they grew almost straight across the interface, while the initial cracks were in the thin (copper) side, they propagated along the interface without penetrating into the thick (steel) side. These behaviors were quite similar to the actual ones directly observed with the real bonded steel-copper specimens. The proposed concept of the equivalent specimen was confirmed to be useful in simulating the behavior of fatigue cracks in bonded dissimilar materials.

AMPLITUDE AND PHASE WAVELET MAPS FOR THE DETECTION OF CRACKS IN GEARED SYSTEMS

The newly developed wavelet transform enables one to look at the evolution in time of a signal's frequency content. This property makes it very suitable for the detection of vibration transients generated by developing localised faults in gear trains. Recent applications of the wavelet technique have focused on the use of the amplitude map only. In this study, both the amplitude and phase maps of the wavelet transform are used in conjunction to assess the condition of an instrumented gear test rig. The phase wavelet map is found to display distinctive features in the presence of a cracked tooth. Another key finding is that the amplitude wavelet map of the residual vibration signal offers a better indicator to the presence of faults than the map of the actual signal. A new polar representation is also introduced that makes pinpointing the precise location of a crack an easy task. The cases studied include a healthy gear, one with a simulated fatigue crack, and one with a simulated chipped tooth.

Effects of Flaw Sizing Errors on the Reliability of Vessels and Piping

This paper describes probabilistic fracture mechanics calculations that simulate fatigue crack growth, flaw detection, flaw sizing accuracy, and the impacts of flaw acceptance criteria. The numerical implementation of the model is based on a Latin hypercube approach. Calculations have been performed for a range of parameters. For representative values of flaw detection probability, flaw sizing errors, and flaw acceptance criteria, detection capability is the most limiting factor with regard to the ability of the inservice inspections to reduce leak probabilities. However, gross sizing errors or significant relaxations of current flaw acceptance standards could negate the benefits of outstanding probability of detection capabilities.

Visual simulation of fatigue crack growth

An attempt has been made to visually simulate fatigue crack propagation from a precrack. An integrated program was developed for this purpose. The crack-tip shape was determined at four load positions in the first load cycle. The final shape was a blunt front with an “ear” profile at the precrack tip. A more general model, schematically illustrating the mechanism of fatigue crack growth and striation formation in a ductile material, was proposed based on this simulation. According to the present model, fatigue crack growth is an intermittent process; cyclic plastic shear strain is the driving force applied to both state I and II crack growth. No fracture mode transition occurs between the two stages in the present study. The crack growth direction alternates, moving up and down successively, producing fatigue striations. A brief examination has been made of the crack growth path in a ductile two-phase material.

A study on the prediction of fatigue life in an axi-symmetric extrusion die

The present paper gives some results of the fatigue behavior of a typical axi-symmetric forward extrusion die. The extrusion process is analyzed by the rigid-plastic FEM and deformation analysis of the extrusion die is conducted by the elasto-plastic FEM. To approach the crack problem, LEFM (linear elastic fracture mechanics) is introduced. Using a special element in order to consider the singularity of stress-strain in the vicinity of the crack tip, the stress intensity factor and the effective stress intensity factor are calculated. Applying a proper fatigue crack propagation criterion such as the Paris-Erdogan fatigue law and maximum principal criterion to these data, the angle and the direction of fatigue crack propagation is then simulated. From the results, it is established that the simulated fatigue crack propagates in the zig-zag path along the radial direction and the fatigue life of the extrusion die is evaluated using the computed crack growth rate.

Shape growth simulation of surface cracks in tension fatigued round bars

The step-by-step three-dimensional finite element technique, developed recently by the present authors, was used to simulate fatigue crack shape developments, beginning from several elliptical-arc cracks with different aspect ratios and an irregular crack, in round bars under axial tension. A Paris type crack growth relation was employed as the basis of the simulating computations. The shape of growing cracks was quantitatively examined by two proposed measures: the relative residual and relative standard deviation, in order to reveal the shape difference between the numerically predicted crack profiles and the widely-assumed circular-arc shape. The aspect ratio changes for the initially part-elliptical cracks were predicted, and compared with some published experimental results. In addition, the effect of the exponent in the Paris law on the aspect ratio variation was investigated.

The influence of starter notches on flight simulation fatigue crack growth: Wanhill, R.J.H. and Schra, L. National Aerospace Laboratory Rep. NLR TP 95127 U (1995) 3–27

The influence of starter notches on flight simulation fatigue crack growth: Wanhill, R.J.H. and Schra, L. National Aerospace Laboratory Rep. NLR TP 95127 U (1995) 3–27

FATIGUE CRACK GROWTH SIMULATIONS BASED ON FREE FRONT SHAPE DEVELOPMENT

Abstract— A single‐crack evolution model with eight degrees of freedom and an isotropic Paris law constant was used to simulate fatigue crack growth at the surface of a plate, and from the toe of a transverse non‐load‐bearing fillet weld in a T‐joint. A planar crack was assumed. In the simulated cases fatigue cracks usually propagate through the plate thickness under the dominant effect of the mode I stress system. The crack front shape was modelled as a broken line. The straight sided crack tip elements were tangential to the direction of an initial elliptical crack front. It was found that the simple eight degrees of freedom model performed well and the predicted aspect ratio development was in good agreement with experimental data.

Flight simulation fatigue crack growth testing of aluminium alloys: Specific issues and guidelines

Flight simulation fatigue crack growth tests are necessary for verification of aircraft damage tolerance analyses and crack growth prediction methods, and also for comparing candidate materials for aircraft structural applications. However, such tests involve complicating issues that have emerged from many investigations on aluminium alloys since the late 1960s. These issues are reviewed to provide guidelines for further testing.

Retardation and arrest of fatigue crack growth in AISI 4340 steel by introducing rest periods and overloads: Kim, S.-H. and Tai, W.-P. Fatigue Fract. Eng. Mater. Struct. June 1993 15, (6), 519–530

The step-by-step three-dimensional finite element technique, developed recently by the present authors, was used to simulate fatigue crack shape developments, beginning from several elliptical-arc cracks with different aspect ratios and an irregular crack, in round bars under axial tension. A Paris type crack growth relation was employed as the basis of the simulating computations. The shape of growing cracks was quantitatively examined by two proposed measures: the relative residual and relative standard deviation, in order to reveal the shape difference between the numerically predicted crack profiles and the widely-assumed circular-arc shape. The aspect ratio changes for the initially part-elliptical cracks were predicted, and compared with some published experimental results. In addition, the effect of the exponent in the Paris law on the aspect ratio variation was investigated.

Evaluation of the Strength of Carburized Spur Gear Teeth Based on Fracture Mechanics

A method is developed to simulate fatigue crack growth in a carburized gear tooth based on two-dimensional linear fracture mechanics. In the simulation, the stress intensity factor is calculated by means of a finite-element method (FEM) which takes into account the effect of residual stress. The fatigue crack growth rates in the case layer are estimated experimentally, and they are expressed by an experimental formula. A strength evaluation procedure for carburized gears is then proposed on the basis of the developed method of simulation. In the procedure, the critical length of the initial crack which is obtained from the fatigue strength is assumed to be equal to the crack length evaluated from the threshold stress intensity factor, and the basic load capacity is estimated. The critical lengths are evaluated for variously treated gears and illustrated as a function of surface condition.

Reliability of detection of small defects in noisy weldments by advanced signal processing and pattern recognition techniques

Reliable detection of a defect (3 mm long × 1 mm deep) in the top mid-section of maraging steel weldment poses problems during conventional pulse-echo ultrasonic testing. Acoustic noise due to coarse and textured microstructure in the top mid-section adversely influences the signal-to-noise ratio and thus the detection. The reliable detection of a small defect in rocket motor components is essential to achieve the designed payload capacity of the space vehicle. Advanced signal analysis techniques such as autocorrelation, demodulation, etc., were applied to the detection of a simulated fatigue crack on the top mid-section of the weldment. Confidence levels of only 60 to 85% could be achieved. When a combination of cluster analysis of cross-power data and Gaussian distribution function were applied, a confidence level of 95% for defect detection could be achieved.

Reliability of Detection of Small Defects in Noisy Weldments by Advanced Signal Processing and Pattern Recognition Techniques

Load bearing capacity of any structure for a given dimension can be increased by improving the reliability of detection of smaller defects in weldments. This is highly desirable in aeronautical and space industries where the overall weight of the structure is a major constraint as it decides the pay load capacity. Maraging steels are widely used in space industries for fabrication of rocket motor casings. Conventional ultrasonic pulse echo technique is applied for defect detection in weldments. However, inspection by ultrasonic testing of top midsection of maraging steel weldments, which is acoustically noisy, poses problems for reliable detection of defects of size 3 mm long x 1 mm deep or less (a design requirement). This is because of small amplitude difference of echo signal (2dB) between the noise and defect signals. Reliability of detection of such defects is improved by adopting advanced signal processing and pattern recognition techniques, which in turn increases the load bearing capacity of the structures. A developmental work was undertaken for reliable detection of small defects in maraging steel weldments. For this purpose, a fatigue crack of 3 mm x 1 mm size was created in top midsection of the maraging steel weldments representing expected weld defects formed during fabrication. This paper discusses the application of advanced techniques like, autocorrelation, cross power spectral analysis, demodulation and cluster analysis for detection of the simulated fatigue crack. By adopting these techniques 95% reliability has been achieved for the detection of the fatigue crack. The approach has been assessed for shop floor adaptability. The approach would yield considerable enhancement in the pay lead of space vehicle thus resulting in enhanced capability and effective utilization.

Formation of Calcareous Deposits within Simulated Fatigue Cracks in Seawater

Abstract The potential profile and occurrence of calcareous deposits within simulated fatigue cracks of mild steel specimens has been investigated as a function of cathodic potential, cyclic frequency, and nominal electrolyte velocity. The experiments also included preliminary investigation of the chemistry and structure of the deposits. A model is presented to rationalize the observations, and it is deduced that dissolved oxygen concentration within the crack, as determined by mass transport associated with the crack electrolytic ejection-injection process and by the oxygen reduction reaction, is particularly important.

ENVIRONMENTAL FATIGUE CRACK PROPAGATION IN METAL/COMPOSITE LAMINATES

— Flight simulation fatigue crack propagation tests with gust spectrum loading were carried out on laminates of (i) aluminium alloy 2024-T3/carbon epoxy, (ii) aluminium alloy 7475-T761/carbon-epoxy and (iii) titanium alloy Ti–6Al–4V/carbon-epoxy, each with a nominal weight saving of 30% as compared to equivalent 2024-T3 panels. The performance of the 2024-T3/carbon-epoxy laminates was much superior to those of the other material combinations. Overall, there was a fairly strong effect of changing from an environment of normal air to an air plus water spray environment. Probable reasons for this strong effect are discussed.

Flight simulation fatigue crack propagation in 7010 and 7075 aluminium plate

The fatigue crack propagation resistances of 7010-T7651, 7010-T73651 and 7075-T7351 thick plate were compared for flight simulation (gust spectrum) loading conditions. The alloy 7075-T7351 was found to be slightly superior, and this superiority was not essentially due to its higher fracture toughness. The influence of specimen thickness on the crack propagation resistance was significant. Thinner specimens gave longer crack propagation lives and, generally, lower crack propagation rates and longer delays in crack growth following severe flights.

GUST SPECTRUM FATIGUE CRACK PROPAGATION IN CANDIDATE SKIN MATERIALS

Abstract— Flight simulation fatigue crack propagation tests were carried out on 2024‐T3, 7475‐T761 and mill annealed Ti‐6A1‐4V sheet in thicknesses up to 3 mm and representative for transport aircraft lower wing skin stiffened panels of end load capacities 1·5 and 3 MN/m. The performance of 2024‐T3 was much superior, owing mainly to greater retardation of crack growth after severe flights. The effect of load truncation was also greater for 2024‐T3. The significance of the results for the choice of advanced structural concepts and materials and the choice of truncation level is discussed. A recommendation for further investigation is given.