Showing papers on "Paris' law published in 1998"
TL;DR: In this article, a summary of reported trends in fatigue crack growth observed in variable amplitude fatigue tests on metallic materials, specifically on steels, under both simple and complex load histories are considered.
Abstract: A summary is given of reported trends in fatigue crack growth observed in variable amplitude fatigue tests on metallic materials, specifically on steels, under both simple and complex load histories. The effects of load variables, specimen geometry, material properties, microstructure and environment are considered. Attention is given to the threshold behaviour and small crack effects. The reviewed data suggest that, depending on a particular combination of load parameters, material, geometry and environment, variable amplitude load sequences of the same type can produce either retardation or acceleration in fatigue crack growth.
215 citations
Book•
31 Mar 1998
TL;DR: Rice et al. as mentioned in this paper proposed a method for growing cracks under elastic-plastic conditions and found that the size of the cracks in a crack is correlated with the severity of the crack growth.
Abstract: Overview Introduction Classification of Fracture Mechanics Regimes History of Developments in Fracture Mechanics Review of Solid Mechanics Stress Strain Elasticity Plasticity Consideration of Creep Component Analysis in the Plastic Regime Fully Plastic/Limit Loads Review of Linear Elastic Fracture Mechanics Basic Concepts Crack Tip Plasticity Compliance Relationships Fracture Toughness and Predictive Fracture in Components Subcritical Crack Growth Limitations of LEFM Analysis of Cracks under Elastic-Plastic Conditions Introduction Rice's J-Integral J-Integral, Crack Tip Stress Fields, and Crack Tip Opening Displacement J-Integral as a Fracture Parameter and Its Limitations Methods of Estimating J-Integral Analytical Solutions J-Integral for Test Specimens J for Growing Cracks Numerically Obtained Solutions Tables of J-Solutions Crack Growth Resistance Curves Fracture Parameters under Elastic-Plastic Loading Experimental Methods for Determining Stable Crack Growth and Fracture Special Considerations for Weldments Instability, Dynamic Fracture, and Crack Arrest Fracture Instability Fracture under Dynamic Conditions Crack Arrest Test Methods for Dynamic Fracture and Crack Arrest Constraint Effects and Microscopic Aspects of Fracture Higher Order Terms of Asymptotic Series Cleavage Fracture Ductile Fracture Ductile-Brittle Transition Fatigue Crack Growth under Large-Scale Plasticity Crack Tip Cyclic Plasticity, Damage, and Crack Closure ?J-Integral Test Methods for Characterizing FCGR under Large Plasticity Conditions Behavior of Small Cracks Analysis of Cracks in Creeping Materials Stress Analysis of Cracks Under Steady-State Creep Analysis of Cracks under Small-Scale and Transition Creep Consideration of Primary Creep Effects of Crack Growth on the Crack Tip Stress Fields Crack Growth in Creep-Brittle Materials Creep Crack Growth Test Methods for Characterizing Creep Crack Growth Microscopic Aspects of Creep Crack Growth Creep Crack Growth in Weldments Creep-Fatigue Crack Growth Early Approaches for Characterizing Creep-Fatigue Crack Growth Behavior Time-Dependent Fracture Mechanics Parameters for Creep-Fatigue Crack Growth Methods of Determining (Ct)avg Experimental Methods for Characterizing Creep Crack Growth Creep-Fatigue Crack Growth Correlations Case Studies Applications of Fracture Mechanics Fracture Mechanics Analysis Methodology Case Studies Appendices Index
203 citations
TL;DR: Small-crack theory has unified “fatigue” and “fracture mechanics” concepts; and has bridged the gap between safe-life and durability/damage-tolerance design concepts, so that fatigue damage can now be characterized by “crack size”.
171 citations
TL;DR: In this paper, the fatigue growth of an edge flaw in a round bar under cyclic tension or bending loading is examined, using a two-parameter numerical model, and it is shown that the crack front evolution is defined by a very small number of parameters, which varies during crack growth.
107 citations
TL;DR: In this paper, a series of experimental investigations concerning the residual stress fields at coldexpanded fastener holes and the behavior of fatigue cracks at such holes has been conducted, including measurement of the initial, cold-work-induced residual stress field at both uncracked and cracked holes and performance of both constant amplitude and spectrum fatigue crack growth tests.
Abstract: A series of experimental investigations concerning the residual stress fields at cold-expanded fastener holes and of the behavior of fatigue cracks at such holes has been conducted. These studies have included measurement of the initial, cold-work-induced residual stress fields at both uncracked and cracked holes and the performance of both constant amplitude and spectrum fatigue crack growth tests.
105 citations
TL;DR: In this article, the authors considered the strain energy density generated ahead of a fatigue crack as predicted by elastic and non-linear plastic theory and derived a simple expression for LEFM/EPFM crack growth, demonstrating how appropriate energy values may be obtained from low cycle fatigue (LCF) tests.
105 citations
TL;DR: In this paper, the impact of NDE on condition assessment and reliability of structures, in which fatigue crack growth is occurring as a result of cyclic random service loads, is examined.
98 citations
TL;DR: In this paper, the authors provided a mechanistic explanation for the electric-field-induced fatigue crack growth in ferroelectrics under cyclic electric loading, showing that the crack starts to grow if the stress intensity factor is higher than the fracture toughness of the material, but decreases as the crack extends and eventually results in crack arrest.
Abstract: Fatigue crack growth has been observed recently in ferroelectrics under cyclic electric loading. Does the crack grow by electric breakdown, or by the stress field near the crack tip? The present paper provides a mechanistic explanation for the electric-field-induced fatigue crack growth. The non-uniform electric field near an insulated crack tip might cause domain switching which in turn produces a concentrated stress field characterized by a stress intensity factor. For ferroelectrics poled along a direction perpendicular to the crack, we are able to show quantitatively that: (1) the stress intensity factor under a negative electric field is nine times as large as the stress intensity factor under a positive electric field; (2) the crack starts to grow if the stress intensity factor is higher than the fracture toughness of the material, but the stress intensity factor decreases as the crack extends and eventually results in crack arrest; (3) by reversing the electric field, the stress intensity factor is increased and crack growth resumes; and (4) this model can predict the extent of fatigue crack growth. In contrast to the conventional perception of (mechanical) fatigue, the fatigue crack growth in ferroelectrics under cyclic electric loading is a step by step cleavage process caused by a domain switching sequence that generates a cyclic driving stress field near the crack tip.
97 citations
15 Dec 1998-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this paper, the effects of LSP on the microstructure, hardness, surface roughness, residual stress, fatigue life, fatigue crack growth (FCG) of 2024-T62 aluminum alloy were investigated.
Abstract: Laser shock processing (LSP) is a relatively new technique for strengthening metals. A method developed for optimizing the LSP parameters is reported in this paper. The effects of LSP on the microstructure, hardness, surface roughness, residual stress, fatigue life, fatigue crack growth (FCG) of 2024-T62 aluminum alloy were investigated. The fatigue life of the laser-shocked specimens was two times greater than that of the unshocked specimens. The fatigue crack growth rates (FCGRs) at a given stress intensity were reduced by over one order of magnitude. The fatigue behavior improvements were attributed to a combination of increased dislocation density, decreased surface roughness and compressive residual stress induced by the laser shock waves.
89 citations
TL;DR: In this article, the authors modeled the fatigue crack growth for various cracks in both unnotched and notched round bars by using an automated numerical technique, which calculates the stress intensity factors at a set of points on the crack front through the three-dimensional finite element method and then applies an appropriate fatigue crack growing law to this set of pointed points to obtain a new crack front.
79 citations
TL;DR: In this paper, an analytic model for fatigue crack life prediction in fiber reinforced concrete (FRC) is presented, which elucidates fatigue crack growth in cementitious matrix material under the influence of external cyclic load and fiber and aggregate bridging.
Abstract: This paper presents an analytic model for fatigue crack life prediction in fiber reinforced concrete (FRC). The model elucidates fatigue crack growth in cementitious matrix material under the influence of external cyclic load and fiber and aggregate bridging. It is shown that fiber-matrix interface damage must be accounted for in order to properly simulate the three experimentally observed stages of matrix crack growth, involving a decelerated stage, a steady state stage, and an accelerated stage towards final fracture failure. This model, which explicitly accounts for the positive role of fibers on fatigue life, predicts the existence of the well-known fatigue limit load in standard S-N curve tests of FRCs. The basic framework of this analysis can be used to address fatigue life of FRC structures subjected to high cycle fatigue loading, as well as providing a basis for material design of fatigue resistant FRC at the microstructure level.
TL;DR: In this article, the effect of stress ratio and thickness on the fatigue crack growth rate of CK45 steel according to DIN 17200 was investigated and the results were obtained for constant amplitude load in tension with three stress ratios of R=0, 0.2 and 0.4.
TL;DR: In this article, the opening and closure behavior of a semi-circular moving crack has been studied using an elastic-plastic finite element model and the effects of different node release schemes, the refinement of the finite element mesh and the initial crack length have been studied.
TL;DR: In this paper, an analytical model for the distribution of bridging traction in fiber-reinforced metal laminates (FRMLs) is proposed to predict fatigue crack growth in CCT specimens of FRMLs.
Abstract: This paper is concerned with the development and application of an analytical model for predicting fatigue crack growth in fibre-reinforced metal laminates (FRMLs). An analytical model for the distribution of bridging traction is first introduced. Based upon observations of the delamination shapes in FRMLs under fatigue loading and a model for characterizing delamination growth in FRMLs, a model for predicting crack growth rates in CCT specimens of FRMLs is developed. The model is applied to two GLARE laminates (2/1, 3/2 lay-ups) under various cyclic stress levels and stress ratios. The predicted crack growth rates are compared with experimental data. The predicted crack growth rates agree well with the experimental results.
TL;DR: In this paper, it was shown that the effective fatigue threshold is uniquely correlated to the Young's modulus for a wide range of metallic and composite materials (ΔKth,eff=164·10−2·E) and that the crack closure level Kcl increases with increased roughness of the fracture surface H Kcl and H are quantitatively related via the equation K cl =12· H 1/3 for steels with widely different mechanical properties and grain sizes.
01 Jan 1998
TL;DR: In this article, the authors used fractographic evidence to analyze prediction problems offatigue crack growth under variable-amplitude (VA) loading and found that the predicted growth rate per spectrum block can still agree with the experimental value.
Abstract: Fatigue crack growth tests were carried out on 2024-T3 and 7075-T6 central cracked specimens. Variable-amplitude (VA) load spectra were used with periodic overload (OL) cycles added to constant-amplitude (CA) cycIes. The fatigue fracture surfaces were examined in the SEM to obtain more detailed information on crack growth contributions of different load cycles. The striation pattems could be related to the load histories. SEM observations were associated with delayed retardation, the effect of 10 or a single OL on retardation, crack growth during the OL cycIes, and crack growth arrest after a high peak load. Fractographs exhibited local scatter of crack growth rates and sometimes a rather tortuous 3d geometry of the crack front. Indications of structural sensitive crack grwoth under VA loading were obtained. Fractography appears to be inadmissable for the evaluation of fatigue crack growth prediction models in view of similarities and dissimilarities between crack growth and V A and CA loading. Nomenclature a BL cycles CA-loading daidN OL cyc1es VA loading A~ff ASeff Introduction crack length base line cyc1es constant-amplitude loading crack growth rate overload cycle variable"amplitude cycles effective stress intensity factor effective stress range The problem addressed in this paper is the potential usefulness of fractographic evidence to analyze prediction problems offatigue crack growth under variable-amplitude (VA) loading. Verifications of prediction models can be made on different levels. The most global one is a comparison of predicted and experimental crack growth lives. If they do agree, it is possible that an underprediction in the fust part of the crack growth life is compensated by an overestimation in the second part. In other words, in the first part the crack growth rate daidN is overestimated, whereas daidN is underestimated in the second part. The prediction model is apparently not accurate. A more precise verification of a prediction model requires that the crack growth rate is correctly predicted for the entire crack growth life. Such verifications are made by comparing predicted and experimental da/dNvalues as a function ofthe crack length a. Ifthe predicted relation and the experimental one are similar, the prediction model could be supposed to be accurate. However, da/dN values as obtained from crack growth records are calculated slopes. Such da/dN values still have a kind of a global nature. Fig.l shows the load spectra applied in the present test series. The spectra contain small base line (BL) cycles and intermittent larger overload (OL) cycles. Ifthe crack rate during the large cycles is higher than predicted by a cycleby-cycle prediction model, and the crack rate during the small cycles is lower than predicted, then the predicted growth rate per spectrum block can still agree with the experimental value. Local under-predictions can he canceled by local over-predictions. The prediction model might appear to he acceptabie, but it is physically still not correct. Prediction models should he verified by still more detailed crack growth measurements. Ultimately, the crack rate should he measured in each individual cycle. Experimentally it implies that striation spacings have to be measured. Fractographic observations in the electron microscope are essential for that purpose. Experiments were carried out on 2024-T3 (bare) and 7075-T6 (clad) specimens with simple VA load histories (Fig.l). Simple load spectra were chosen to be sure about striation pattems which might be vi si bie in the scanning electron microscope (SEM). The experimental conditions and load histories are described first, followed by results, a discussion and some conclusions. It is not the the aim as yet to compare the observations with results of aprediction model. Experimental conditions Crack growth fatigue tests were carried out in an electro-hydraulic fatigue machine equipped with MTS TestStar computer controlled load monitoring. The tests occurred in normal lab air. Central cracked tension specimens were used, see Fig.2. The specimens were produced from 4 mm thick plates. A lower thickness might have given shear lips in a too early stage ofthe crack growth. Plates of2024-T3 bare and 7075-T6 Clad material were used as they were available
TL;DR: In this paper, the results of these environmental tests were compared with those obtained in laboratory air to characterize the effect of aging treatment on corrosion fatigue susceptibility and showed that overaging treatments used to improve grain boundary characteristics and increase the intergranular SCC resistance might not guarantee an equivalent improvement in the resistance to transgranular CF cracking.
TL;DR: In this paper, a fracture mechanics test method based on fracture mechanics concepts is applied to measure fatigue crack growth rates for an adhesive material in a bondline double cantilever beam specimen containing a cohesive crack.
TL;DR: In this article, a neural network approach is developed to determine the crack opening load from differential displacement signal curves, which is applied in practical to constant amplitude loading tests and is found to provide good results.
TL;DR: In this article, a spur gear pair from the first stage of an industrial vehicle gear box has been subjected to experimental testing and the effects of different load distributions along the gear tooth width on the fatigue crack growth in gear tooth root were measured on an appropriate testing device.
15 Mar 1998-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this article, in-situ observation on fatigue cracking processes was made on a fatigue testing machine mounted in a scanning electron microscope, and the observed fatigue behavior in both the long and short life regimes was discussed in terms of metallurgical factors responsible for the fatigue behavior of the present materials.
Abstract: Fatigue crack initiation and early stage of crack growth for Ti–6Al–4V and Ti–4.5Al–3V–2Fe–2Mo were investigated on notched specimens. In-situ observation on fatigue cracking processes was made on a fatigue testing machine mounted in a scanning electron microscope. It was found that Ti–4.5Al–3V–2Fe–2Mo alloy with very fine α grains of ≈2 μm exhibited a much higher fatigue strength at 107 cycles than that of Ti–6Al–4V alloy. However, an opposite trend in fatigue life was obtained in the short life regime for the materials tested in the present study. The observed fatigue behavior in both the long and short life regimes is discussed in terms of metallurgical factors responsible for the fatigue behavior of the present materials.
TL;DR: In this paper, the behavior of a circumferential external surface defect in a metallic round pipe under cyclic axial loading is examined, where the defect is assumed to present an elliptical-arc shape with aspect ratio α=a/b (a, b are the ellipse semi-axes), whereas the relative depth ξ of the deepest point on the front is equal to the ratio between the maximum crack depth, a, and the pipe wall thickness, t.
TL;DR: In this article, a 3D FE model of the rail Rolling-Contact-Fatigue (RCF)'squat'-type crack, which tends to be common in tracks with high-speed passengers and mixed traffic, is presented.
Abstract: The analysis is based on the 3D FE model of the rail Rolling-Contact-Fatigue (RCF) 'squat'-type crack, which tends to be common in tracks with high-speed passengers and mixed traffic. The model incorporates the section of rail and a wheel of real geometry, in which the wheel is rolling over the running band of rail containing the 'squat'-type crack. The state of stress in the vicinity of the crack front is determined, and consequently the values and ranges of the stress intensity factors (SIFs) K 1 , K II and K III at the crack front are calculated for the cycle of rolling. To simulate loading conditions occurring in practice, residual, bending and thermal stresses acting in the presence of the tractive force were taken into account. The results indicate a significant role of face friction and tractive force in the loading mechanism at the'squat'. The longitudinal and lateral residual stresses may also influence the loading cycles, especially for the cases with reduced friction between the crack faces. Reduction of the face friction coefficient to values close to zero creates conditions for crack propagation driven by the shear mode mechanism. These results were obtained under a project sponsored by the ERRI D173 Committee, Utrecht, The Netherlands.
TL;DR: In this article, a nonlinear dynamic model of fatigue crack growth in the state-space setting based on the crack closure concept under cyclic stress excitation of variable amplitude and random loading is proposed.
Abstract: This paper proposes a nonlinear dynamic model of fatigue crack growth in the state-space setting based on the crack closure concept under cyclic stress excitation of variable amplitude and random loading. The model state variables are the crack length and the crack opening stress. The state-space model is capable of capturing the effects of stress overload and underload on crack retardation and acceleration, and the model predictions are in fair agreement with experimental data on the 7075-T6 aluminum alloy. Furthermore, the state-space model recursively computes the crack opening stress via a simple functional relationship and does not require a stacked array of peaks and valleys of stress history for its execution; therefore, savings in both computation time and memory requirement are significant. As such, the state space model is suitable for real-time damage monitoring and control in operating machinery.
TL;DR: In this article, a series of three-dimensional finite element analyses from which the stress intensity factors along the front of growing cracks were estimated was used to predict the crack shape without making the usual assumption of semi-elliptical shape.
Abstract: Fatigue crack growth was numerically simulated for various internal surface cracks with initially either semi-elliptical or irregular crack fronts. The simulation was directly based on a series of three-dimensional finite element analyses from which the stress intensity factors along the front of growing cracks were estimated. The fatigue crack growth law obtained from small laboratory specimens was incrementally integrated at a set of points along the crack front, and a new crack front was then re-established according to the local advances at this set of points by using a cubic spline curve. This method enabled the crack shape to be predicted without having to make the usual assumption of semi-elliptical shape. Fatigue analysis results are presented and discussed for fatigue shape developments and deviations from the semi-elliptical shape, aspect ratio changes, stress intensity factor variations during crack growth, and fatigue life predictions. Some of the results were also compared with those obtained by two simplified methods based on one and two degree-of-freedom models, respectively.
TL;DR: In this paper, the effects of residual microstresses and tensile residual macrostresses on fatigue crack propagation were examined in a high-carbon steel and phase-specific diffraction measurements showed that uniaxial deformation and radial cold expansion produce predominantly microstress and macrostress fields, respectively.
Abstract: The effects of residual microstresses and tensile residual macrostresses on fatigue crack propagation (FCP) are examined in a high-carbon steel. Phase-specific diffraction measurements show that uniaxial deformation and radial cold expansion produce predominantly microstress and tensile macrostress fields, respectively. Microstresses are found to have little effect on FCP rates, while tensile macrostresses increase crack growth rates in a manner that depends systematically on ΔK. The increases are partly attributed to crack closure, which was found to be appreciable near the surface of control samples but absent in the presence of tensile residual stresses. Both the ΔK dependence and absence of microstress effects were explored by X-ray microbeam measurements around propagating fatigue cracks and found to stem from fading and/or redistribution of residual macrostresses and microstresses during fatigue crack growth.
TL;DR: In this article, the authors generalize previous stochastic fatigue crack growth models by incorporating a time-dependent noise term described by arbitrary marginal distributions and autocorrelations to model the uncertainty in the crack growth under constant amplitude loading.
TL;DR: In this paper, a general computational model for modeling subsurface fatigue crack growth under cyclic contact loading of mechanical elements is described, where the model assumes that the initial fatigue crack develops along the slip line in a single crystal grain at the point of the maximum equivalent stress.
TL;DR: In this article, the effects of microstructure on the initiation of micro-cracks and their subsequent growth into large cracks were studied in a TiAl sheet alloy, heat treated to the lamellar and equiaxed microstructures.
Abstract: The fatigue mechanisms in a TiAl sheet alloy, heat treated to the lamellar and equiaxed microstructures, were studied to determine the effects of microstructure on the initiation of microcracks and their subsequent growth into large cracks. The nucleation and growth history of individual microcracks were followed. For comparison, fatigue crack growth and fracture toughness were also characterized using specimens containing a machined notch with a fatigue precrack. The results indicated that microcracks initiated at grain/colony boundaries and at slip bands. Most microcracks were arrested after nucleation, but a few grew at stress intensity ranges below the large crack threshold. The populations of nonpropagating and propagating cracks varied with life fractions. Ligaments in the wake of a fatigue crack were more severely strained than the crack-tip region of the main crack, and, as a result, they were more prone to fatigue failure. The destruction of the crack-wake ligaments is expected to result in lower fracture resistance in materials under cyclic loading than those under monotonic loading.
TL;DR: In this paper, a mechanical explanation of plasticity-induced crack closure under plain strain conditions is given first by means of dislocation mechanics and then by the methods of continuum mechanics.
Abstract: A mechanical explanation of plasticity-induced crack closure under plain strain conditions is given first by means of dislocation mechanics and then by the methods of continuum mechanics. In plane strain, the event of crack closure is due to transport of material from the wake to the crack tip. It is an elastic effect caused by the response of the matrix surrounding the plastic wake. The transported material produces a wedge which follows the crack tip, and unlike the plane stress condition it does not leave a remaining layer on the crack flanks. The length of the produced wedge at the crack tip is of the same scale as the plastic zone. It is then shown that in spite of its smallness this wedge is able to cause the experimentally observed shielding effect. The results also suggest that the discrepancies concerning the interpretation of fatigue crack growth and closure experiments are likely to be due to differences in accuracy in the detection of such small but nevertheless effective wedges.