Showing papers on "Paris' law published in 1989"
TL;DR: In this article, a model for the elastic-plastic finite element simulation of fatigue crack growth and crack closure is presented and evaluated, showing that careful attention must be given to a series of critical decisions about mesh and model design if the analysis is to be reliable.
301 citations
TL;DR: In this paper, the role of crack bridging by uncracked ligaments is examined with specific emphasis on the role in the growth of fatigue cracks in metal-matrix composites, and simple analytical models are developed for such bridging induced by both overlapping cracks and by coplanar ligaments in the wake of the crack tip.
Abstract: Micro-mechanisms of crack-tip shielding associated with the growth of fatigue cracks in metalmatrix composites are examined with specific emphasis on the role of crack bridging by uncracked ligaments. Simple analytical models are developed for such bridging induced by both overlapping cracks and by coplanar ligaments in the wake of the crack tip; the models are based on respective notions of a critical tensile strain or critical crack-opening displacement in the ligament. The predicted degree of shielding derived from these mechanisms is not large, but is found to be consistent with experimental observations in high-strength P/M aluminum alloys reinforced with 15 to 20 vol pct of SiC particulate.
156 citations
TL;DR: In this paper, an experimental and numerical study has been made of the mechanisms of fatigue crack growth and crack-closure behavior in an αβ titanium alloy Ti-4A1-4Mo-2Sn-0.5Si (IMI 550), following both single and block tensile overloads.
149 citations
TL;DR: In this article, a power-law dependence on the peak stress intensity factor (Kmax) was found for cyclically induced crack propagation in alumina subjected to direct tension, and it was suggested that direct compressive loads and crack length are both factors that affect cyclic fatigue behavior.
Abstract: Cyclically induced crack propagation occurs in alumina subjected to direct tension—compression loading. The crack increment per cycle (da/dN) has a power-law dependence on the peak stress intensity factor (Kmax). Cyclic crack growth can occur at lower values of Kmax than are required to produce static fatigue effects. Subcritical crack-growth behavior was found to be dependent on specimen geometry: it is suggested that direct compressive loads and crack length are both factors that affect cyclic fatigue behavior, and that the use of K alone to characterize fatigue crack growth in ceramics may be questionable.
130 citations
TL;DR: In this article, the authors examined the crack propagation behavior in a 2024-T3 aluminum alloy/aramid-fiber epoxy 3 2 laminated composite, ARALL®-2 LAMINATE, with the objective of quantitatively evaluating the primary mechanisms of crack-tip shielding.
119 citations
TL;DR: In this article, the authors measured the growth rate of fatigue cracks in 12 variations of particulate silicon carbide reinforced aluminum alloy composites and found that they exhibited an approximately linear, or Paris law, region, fitting the function da/dN = BΔK s, and a threshold stress intensity factor, ΔK th.
88 citations
TL;DR: In this article, the relationship between frictional stress of filament/matrix interface and fracture toughness of SiC monofilament/Si3N4 matrix composites was investigated.
Abstract: SiC-monofilament-reinforced SiC or Si3N4 matrix composites were fabricated by hot-pressing, and their mechanical properties and effects of filaments and filament coating layers were studied. Relationships between frictional stress of filament/matrix interface and fracture toughness of SiC monofilament/Si3N4 matrix composites were also investigated. As a result, it was confirmed experimentally that in the case of composites fractured with filament pullout, the fracture toughness increased as the frictional stress increased. On the other hand, when frictional stress was too large (>about 80 MPa) for the filament to be pulled out, fracture toughnesses of the composites were almost the same and not so much improved over that of Si3N4 monolithic ceramics. The filament coating layers were found to have a significant effect on the frictional stress of the SiC monofilament/Si3N4 matrix interface and consequently the fracture toughness of the composites. Also the crack propagation behavior in the SiC monofilament/Si3N4 matrix composites was observed during flexural loading and cyclic loading tests by an in situ observation apparatus consisting of an SEM and a bending machine. The filament effect which obstructed crack propagation was clearly observed. Fatigue crack growth was not detected after 300 cyclic load applications.
81 citations
TL;DR: In this paper, the effect of residual stresses on fatigue crack growth is investigated by paying attention to a fatigue crack that initiates at the weld metal and propagates perpendicular to the weld line, and the experimental results indicate that the crack growth rates are equivalent by use of the effective stress intensity range, based on the measurements of crack opening ratio.
74 citations
TL;DR: In this article, the authors developed a general parameter based on the deformation intensity at a mixed mode crack tip to predict crack growth behavior, especially in the near threshold region, which is defined as a vector summation of CTOD and CTSDc which act, respectively in the directions of mode I and mode II fatigue crack growth.
Abstract: — This work is aimed at developing a general parameter based on the deformation intensity at a mixed mode crack tip to predict crack growth behaviour, especially in the near threshold region. Being a mechanisms-related parameter, the vector crack tip displacement (CTD) is defined as a vector summation of CTOD and CTSDc which act, respectively in the directions of mode I and mode II fatigue crack growth. The basic assumption is that both direction and rate of mixed mode fatigue crack growth are governed by the vector ΔCTD, which represents the resultant of the “driving force”at the crack tip. The analytical predictions obtained by using the vector ΔCTD are in good agreement with the reported experimental results of mixed mode I and II fatigue cracks.
67 citations
TL;DR: In this paper, the interlaminar fracture behavior of composite materials under static and cyclic loadings has been studied using a width tapered double cantilever beam specimen and the fracture energy is evaluated by compliance, beam and area methods.
Abstract: Interlaminar fracture behavior of composite materials under static and cyclic loadings has been studied using a width tapered double cantilever beam specimen. The fracture energy is evaluated by compliance, beam and area methods. The comparison results show that the initial fracture energy could be evaluated either by beam or area method while the crack growth resistance could be calculated by compliance method. Increases in the criti cal load and fracture energy due to fiber bridging are predicted by a power function of fracture area. The interlaminar fatigue crack growth behavior is studied through the con stant cyclic strain energy release rate range test. A modification of Paris' power law is made to interpret fatigue crack growth under the influence of fiber bridging. The predicted fatigue life by the modified power law is reasonably close to the experimental data. Frac tography study shows that the interlaminar failure mechanism of a composite beam in volves fiber breakage, matrix tearing and transv...
65 citations
TL;DR: In this paper, the authors reported the results of an experimental and numerical investigation of the interaction and coalescence of two coplanar semi-elliptical cracks and showed good agreement between experimental fatigue crack growth data and the finite element predictions.
Abstract: — This paper reports the results of an experimental and numerical investigation of the interaction and coalescence of two coplanar semi-elliptical cracks. Fatigue crack growth data were obtained from a four-point bend specimen using the direct current potential difference method and a beachmarking technique. A finite element simulation of the experimental conditions was also performed. Crack advance was computed from the Paris equation on a step by step basis. Good agreement between experimental fatigue crack growth data and the finite element predictions is demonstrated.
TL;DR: In this article, the interaction and coalescence of twin coplanar semi-elliptical cracks under both tension and bending loadings are investigated by numerical methods, where crack advance is computed on a step-by-step basis from the Paris equation using stress intensity factors calculated by the finite element method.
TL;DR: In this article, a three-dimensional elastoplastic finite element analysis of fatigue crack growth and closure in a center-crack tension specimen was performed in order to investigate the crack opening stress as a function of specimen thickness under constant amplitude loading conditions.
TL;DR: In this paper, an experimental method for introducing residual stress in a specimen by local plastic deformation and a technique to measure and delineate the residual stress field is discussed, and the role of residual stress redistribution as the crack grows is also discussed.
TL;DR: In this article, stitching yarns were used to improve delamination resistance in composite laminates by using thermoplastic matrix resins and stitching yarn yarns, which showed a 20 to 30% increase in critical crack-opening load, a 20 times higher fatigue threshold, and a two-orders-of-magnitude increase in fatigue life.
Abstract: This paper shows how to improve delamination resistance in composite laminates by the use of thermoplastic matrix resins and by stitching Discussed are fatigue crack growth characteristics in thermoplastic matrix composites as well as the differences between the crack growth processes in thermoplastic and thermosetting matrix composites under cyclic fatigue and monotonically increasing loads Further improvement of delamination resistance achieved by stitching shows a 20 to 30% increase in the critical crack-opening load, a 20 times higher fatigue threshold, and a two-orders-of-magnitude increase in fatigue life Fractography evidence is presented to illustrate the role of the stitching yarns in resisting delamination A fracture model was constructed to simulate delamination crack propagation in the presence of stitching yarns The effects of geometric stitching parameters, as well as intrinsic and extrinsic yarn properties, were simulated with this fracture model Finally, practical issues on the effective and economical application of stitching to composite structures are discussed
TL;DR: This paper reviewed the probabilistic modeling of fatigue crack growth from 1980 to the present, focusing on evolutionary models that start with the randomization of a deterministic differential equation by the introduction of random variables or random functions, and directly generate the evolution of distributions.
TL;DR: In this article, fracture and fatigue crack propagation behavior of Ni78Si10B12 was investigated in thin ribbons of a nickel-base metallic glass: Ni78si10b12.
Abstract: This work is an investigation of fracture and fatigue in thin ribbons of a nickel-base metallic glass: Ni78Si10B12. The fracture and fatigue crack propagation behavior of this high tensile strength and high toughness amorphous alloy is of interest for two reasons: (1) the alloy, has no normal microstructure, and (2) the alloy shows an unusual form of plastic deformation which proceeds by nucleation and propagation of localized shear bands. On uniaxial tensile loading, failure of uniform ribbons occurs instantaneously at the yield stress by shear rupture through an intense shear band inclined at 55 deg to the loading axis. The development of a local plastic zone at the crack tip in single edge-notched specimens under monotonic tensile loading has been studied by a replication technique. Under plane stress conditions, these plastic zones are dominated by shear bands elongated in the direction of crack extension. Dugdale's “strip yield” model offers a reasonable description of the plastic zone sizes and displacements at the crack tip. The relationship between fatigue crack growth per, cycle,da/dN, and the alternating stress intensity factor, ΔK, has been determined atR=0.1. For growth rates in the range 10−6 through 5×10−4 mm/cycle, the Paris law (with an exponentm∼-2) is obeyed. The mechanism of fatigue crack extension is shown to depend on the deformation microstructure of the alloy. At intermediate growth rates, the plastic zone consists of a number of shear bands similar in shape to the Prandtl slip line field for nonhardening materials. Decohesion along these bands produces undulating fracture morphologies. At near threshold values of ΔK, growth rates deviate from the Paris law producing an extremely low ΔK
TH (=0.5 MPa {
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$$\sqrt m $$
}). This is attributed to the ease of shear band nucleation, and a simple geometrical model of crack growth at low ΔK levels is proposed.
01 Jan 1989
TL;DR: In this article, the micromechanisms responsible for the transition in the fracture mode from transgranular to intergranular are reviewed and two interrelated mechanisms are discussed.
Abstract: This paper is concerned with the micromechanisms and the metallurgical factors controlling the high temperature behavior of Alloy 718. The presentation is divided into two parts. In the first one the micromechanisms responsible for the transition in the fracture mode from transgranular to intergranular are reviewed. Two interrelated mechanisms are discussed : (i) slip-induced intergranular cracking and (ii) oxidation-assisted crack growth. A strong emphasis is laid upon the later one. Results of Auger spectrometry showing the formation of two types of oxides : a spine1 type (Ni, Fe, 0) and Cr,03 oxide, are given. These results are used to discuss transient effects in crack growth behavior reported in the literature and the effect of hold time at minimun load observed during fatigue crack growth measurements. The second part of the paper deals with the study of metallurgical factors which control the elevated temperature resistance of Alloy 718. The effects of both heat treatment and compositional modifications on the strength and thermal stability are discussed. The requirements (composition, heat-treatment) to achieve a compact morphology consisting of cube shaped Y' precipitates covered on there six faces by 7" precipitates are given. A number of factors controlling more specifically the grain boundary strength (grain size, grain boundary morphology and chemistry) are also reviewed and discussed. Superalloy 718-Metallurgy and Applications Edited by E.A. Loria The Minerals, Metals & Materials Society, 1989
TL;DR: In this paper, the authors examined the constant amplitude fatigue crack growth behavior of a conventionally (α + β ) solution treated and aged Ti-6Al-4V fan disc forging by fractographic and microstructural analysis.
TL;DR: In this article, a new model based on cumulative random jump processes is proposed, where the fatigue crack length (at arbitrary time t ) is represented as a random sum of random (non-negative) increments.
TL;DR: In this paper, a theoretical analysis of the thermal fatigue of MAR-M509, a typical cast superalloy for vanes in jet engines, was carried out using a finite element analysis of plane strain small scale yielding.
TL;DR: In this paper, a tensile residual stress field was used to predict fatigue crack growth and closure under an applied compressive loading by carrying out various applied stress ratio tests ranging from R= 0 to R= R=
Abstract: — —Fatigue crack growth and closure through a tensile residual stress field under an applied compressive loading is investigated by carrying out various applied stress ratio tests ranging from R= 0 to R= It is found that even under applied compressive loading, fatigue crack growth rates are well correlated with the effective stress intensity factor range and the behaviour of crack closure through a tensile residual stress field is uniquely controlled by an effective stress ratio which takes account of residual stresses. Consequently, the method of predicting fatigue growth rates, using da/dN vs ΔK data from residual stress-free specimens, can be successfully applied to crack growth through a tensile residual stress field. However, previously used simple assumptions may lead to non-conservative estimates of crack growth rates.
TL;DR: In this paper, a two-state stochastic model for fatigue crack growth problems is presented and solutions are given which will, for the first time, provide the distribution of the random time to reach a critical crack size directly.
01 Jan 1989
TL;DR: In this paper, the authors present a review of Fatigue prediction methods in the Regime where Inelastic Strains Dominate- Fatigue Crack Initiation at Notches: Techniques, Experiments and Interpretations.
Abstract: I - Fundamentals of Fatigue- Short Fatigue Cracks- The Influence of The Microstructure on Fatigue- Modelling of Fatigue Crack Growth- Statistical Analysis of Fatigue Crack Growth- Fatigue Threshold Behaviour Part I: Modelling of FCG Near Threshold- II: Theoretical Aspects and Open Questions- Fatigue at Notches- A Review of Fatigue Life Prediction Models for the Crack Initiation and Propagation Phases- Environmentally Assisted Fatigue Crack Growth- Non-Propagating Fatigue Cracks: The True Fatigue Limit- Experimental Techniques to Observe and Monitor Short Fatigue Cracks- Mechanisms of Creep-Fatigue Interactions- Elevated Temperature Life Prediction Methode- Multiaxial Fatigue Failure- Multiaxial Fatigue Crack Propagation Behaviour- Analysis and Design Methods in Multiaxial Fatigue- A Review of Fatigue Predictive Methods in the Regime where Inelastic Strains Dominate- Fatigue Crack Initiation at Notches: Techniques, Experiments and Interpretations- Creep and Low Cycle Fatigue Analysis of Engineering Alloys - A Review- The J Integral Approach in Elastic-Plastic Fatigue Crack Propagation- II - Engineering Applications- The SAE Round-Robin Fatigue Program with A356-T6 (A17 SiMg) Cast Aluminum Alloy- Methodology of Variable Amplitude Fatigue Tests- How to Improve Fatigue Strength of Vehicle Components Employing Different Test Methods- Fatigue Behaviour of Welded Joints- Fatigue Design Optimisation in Welded Joints- Fatigue Life Prediction Methods in Welded Joints: Case Studies- Fatigue Analysis in Offshore Structures- The Damaging of Composite Materials: Mechanisms and Detection- The Fatigue of High Performance Composite Materials- Damage Assessment in Fatigue of Reinforced Structural Composites- Mechanical Aspects Related to Fibre Fracture in ARALL 2 Laminates- Development in Fatigue Design in Automotive Industry Using New Materials- Damage Evaluation and Life Extension of Structural Components- Optimisation of Component Design by Fatigue Analysis and Testing- III - Research Contributions- Cyclic Hardening and Softening of [001] Al Single Crystals- Fatigue Crack Growth of Short Cracks in an A1MGSI Alloy- Generalization of the Kitagawa Diagram to V-Notched Members- Separate Contributions of Corrosion-Froduct Induced and Roughness-Induced Crack Closure to the Fatigue Threshold of Al Alloys- Dynamic Analysis of Plasticity - Induced Fatigue Crack Closure- Fatigue Crack Growth in Textured Metals- Inelastic Modelling for Engineering Design for High Temperature Conditions- Total Strain Energy Density as a Fatigue Damage Parameter- Fatigue Crack Extension, A General Mechanism- Interaction Between Fatigue Crack Growth, Yielding and Nonlinearly Viscous Material Response- Multiaxial Fatigue: Damage Mechanisms and Life Predictions- Cyclic Deformation Behaviour of a Fe-28Cr-4Mo-2Ni-o43Nb Superferritic Stainless Steel- Fatigue and Brittle Fracture in Tubular Joints - A Probabilistic Fracture Mechanics Analysis- Fatigue Investigation on Preloaded Welded Connections- Influence of Surface Treatment on Fatigue Resistance of Aircraft Alloys- The In Service Multi-Axial-Stress Situation in an Uncooled Gas Turbine Blade- Time Dependent Effects on High Temperature bow Cycle Fatigue and Fatigue Crack Propagation of Nickel Base Superalloys
TL;DR: In this paper, a finite element model has been developed that simulates crack growth under time dependent loading conditions and accounts for the hold time and frequency effect under high temperature fatigue crack growth.
01 Jan 1989
TL;DR: In this paper, the effect of the stress ratio on the threshold value for fatigue crack growth was investigated over a wide range of mean stresses ( − 10 ) for pure Cu, the age-hardened alloy Al-2024 and the mechanically alloyed pm Al-alloy IN-905XL.
01 Feb 1989-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this paper, the authors have shown that morphologies of martensite have a strong effect on threshold values and FCP rates in both near-threshold and higher regions of stress intensity range ΔK in as-rolled and heat-treated dual-phase steels with different morphologies.
Abstract: Fatigue crack propagation (FCP) behaviour in both near-threshold and higher regions of stress intensity range ΔK in as-rolled and heat-treated dual-phase steels with different morphologies of martensite has been studied in the laboratory air and in a 3.5% NaCl solution at a stress ratio of R = 0. It is shown that morphologies of martensite have a strong effect on threshold values (ΔKth) and FCP rates. Microstructures with acicular and netted martensite posess higher threshold values and lower FCP rates than do those with granular martensite. In specimens in the 3.5% NaCl solution, ΔKth is much larger than it is in specimens in the laboratory air for both as-rolled and heat-treated dual-phase steels. Observation by scanning electron microscopy shows that in the near-threshold region, fracture surfaces are mainly characterized by cyclic cleavage in specimens in the laboratory air and by integranular cracking in specimens in the 3.5% NaCl solution. However, in the higher ΔK region, fracture surfaces are composed of mixed cracking modes. It is suggested that the enhancement of the threshold values in specimens in the 3.5% NaCl solution arises from the higher crack closure induced by the rough fracture surface and by the strong wedge effect of corrosion products.
TL;DR: In this paper, the effect of biaxial loading on the fatigue crack growth properties for a stainless steel has been examined, and significant acceleration of crack growth was observed just after the uniexial or equibiaxial stress condition was changed to the shear stress condition.
Abstract: — The effect of biaxial loading on the fatigue crack growth properties for a stainless steel has been examined. From comprehensive experiments, a significant biaxial stress effect on crack growth was found when the stress level was high and the crack was short. In this paper, the critical region where the effect of biaxial stress appears was clarified quantitatively. Moreover, the effect of changing the biaxial stress condition on fatigue crack growth behaviour was investigated. Significant acceleration of crack growth was observed just after the uniaxial or equibiaxial stress condition was changed to the shear stress condition. This acceleration seems to be due to the change of plastic zone shape at the crack tip.