Showing papers on "Paris' law published in 1981"

A crack-closure model for predicting fatigue crack growth under aircraft spectrum loading

Abstract: The development and application of an analytical model of cycle crack growth is presented that includes the effects of crack closure. The model was used to correlate crack growth rates under constant amplitude loading and to predict crack growth under aircraft spectrum loading on 2219-T851 aluminum alloy sheet material. The predicted crack growth lives agreed well with experimental data. The ratio of predicted to experimental lives ranged from 0.66 to 1.48. These predictions were made using data from an ASTM E24.06.01 Round Robin.

Oxide-Induced Crack Closure: An Explanation for Near-Threshold Corrosion Fatigue Crack Growth Behavior

Abstract: The concept of oxide-induced crack closure is utilized to explain the role of gaseous and aqueous environments on corrosion fatigue crack propagationat ultralow, near-threshold growth rates in bainitic and martensitic 2 1/4 Cr-1 Mo pressure vessel steels. It is shown that at low load ratios, near-threshold growth rates are significantly reduced in moist environments (such as air or water), compared to dry environments (such as hydrogen or helium gas), due to the formation of excess corrosion deposits on crack faces which enhances crack closure. Using Auger spectroscopy, it is found that at the threshold stress intensity, ΔKo, below which cracks appear dormant, the maximum thickness of excess oxide debris within the crack is comparable with the pulsating crack tip opening displacement. The implications of this model to near-threshold fatigue crack growth behavior, in terms of the role of load ratio, environment, and microstructure are discussed.

Methods and models for predicting fatigue crack growth under random loading

Abstract: Papers are presented in the volume summarizing the baseline data, methodology, procedures, and results of a round-robin analysis which was conducted to predict the fatigue crack growth in 2219-T851 aluminum center-cracked specimens subjected to flight loading in random cycle-by-cycle format. The objective of the analysis was to assess whether data from constant-amplitude fatigue crack growth tests on center-cracked specimens can be used to predict fatigue crack growth lives under random loading. The following approaches are discussed in detail: a root-mean-square approach, a crack-closure model, a multi-parameter yield zone model, and a load-interaction model.

A Simple Crack Closure Model for Prediction of Fatigue Crack Growth Rates Under Variable-Amplitude Loading

Abstract: A model for the prediction of growth rates of fatigue cracks in aluminium alloys is presented. The model is based on an approximate description of the crack closure behavior and can be used to predict effects of crack growth acceleration and retardation observed experimentally under variable-amplitude loading. A computer program was developed for analysis of fatigue crack growth. It was used to analyze the effect of certain parameter variations in a flight simulation load spectrum on the crack growth rate. For 7075-T6 thin sheet material the results are compared with experimental data.

Recent progress in understanding environment assisted fatigue crack growth

Abstract: Metal fatigue has been well recognized as an important cause for failure of engineering structures. In most applications, fatigue damage results from the conjoint actions of the cyclically applied stress and the external (chemical) environment, and is therefore time dependent. Understanding of this load-environment interaction is essential to the formulation of rational life prediction procedures and to the development of realistic materials evaluation and qualification tests. Research over the past 15 years has led to the suggestion that the rate of fatigue crack growth in an aggressive environment, (da/dN)e, is the sum of three components—the rate of fatigue crack growth in an inert environment, (da/dN)r, which represents the contribution of “pure” fatigue, a cycle-dependent component, (da/dN)cf, that requires the synergistic interaction of fatigue and environmental attack, and the contribution by sustained-load crack growth (i.e., stress corrosion cracking) at K levels above K Iscc, (da/dN)scc. Recent fracture mechanics and surface chemistry studies have provided a clearer understanding of the cycle-dependent term, and, hence, a more complete understanding of environment assisted fatigue crack growth. (da/dN)cf results from the reaction of the environment with fresh crack surfaces produced by fatigue, and is a function of the extent of reaction during one loading cycle. For highly reactive alloy-environment systems, this contribution depends also on the rate of transport of the aggressive environment to the crack tip. The experimental basis and the development of models for transport and surface reaction controlled fatigue crack growth are reviewed. Interpretation of the effects of partial pressure of the aggressive environment and cyclic load frequency in terms of surface reaction and transport processes is discussed. Implications in terms of service performance and life prediction procedures are considered.

A critical review of crack tip stress intensity factors for semi-elliptic cracks*

Abstract: Several crack tip stress intensity factor solutions have been published for semi-elliptic, surface breaking cracks in plates subjected to tension or bending forces. These solutions do not agree with each other particularly well and the basis for choosing which one is the best has not been established. In this paper, the development of fatigue crack shape is used as a diagnostic tool to test the accuracy of these theoretical stress intensity solutions in predictive fatigue crack growth calculations. Those solutions giving the best engineering estimate of crack tip stress intensity factors are identified. Single equations are also given for each loading case at the deepest point or surface intersection point of semi-elliptic cracks in order to facilitate calculations on programmable calculators. A rational basis for calculating the progress of a crack which snaps through the thickness and continues to propagate in a stable way by fatigue is suggested.

Effect of Density on Tensile Strength, Fracture Toughness, and Fatigue Crack Propagation Behaviour of Sintered Steel

Abstract: The tensile strength, fatigue crack propagation behaviour, and fracture toughness of a low-alloy sin tered steel were determined for the porosity range 11–17%. Static and cyclic strength were found to increase with density in a non-linear fashion. The pores both exerted a stress-concentrating influence and reduced the load-bearing section. The micromechanism of failure was always ductile fracture in the necks between sintered steel particles. It was concluded that the stress state at the tips of cracks subjected to static or cyclic loading was closer to plane stress than to plane strain. Retardation of fatigue crack propagation appeared to occur due to the blunting action of the pores. The presence of a wear mechanism had little influence upon fatigue crack growth rates. A companion paper (following) attempts to model the static and cyclic behaviour of the steel, based on the known micromechanisms of failure. PM/0172

An analysis of several fatigue crack growth rate (FCGR) descriptions

Abstract: This report presents the results of a round-robin life-prediction effort conducted by ASTM Task Group E24.04.04 on FCGR Descriptions. The fatigue crack growth rate (FCGR) data supplied to the task group participants for description purposes are provided along with the definition of the life-prediction effort and results. It is shown that the majority of the participants could describe the FCGR data well enough that the resulting constant amplitude life predictions were within ′20 percent of the test lives for more than 80 percent of the tests.

Multi-Parameter Yield Zone Model for Predicting Spectrum Crack Growth

Abstract: A systematic technique is presented for modeling crack growth load interaction effects due to spectrum loading. The Multi-Parameter Yield Zone (MPYZ) model accounts for crack growth retardation, acceleration, and underload effects. The load interactions are attributed to the residual stress intensity due to the plastic deformation at the crack tip. Fatigue crack growth was predicted and compared with test data for a variety of spectrum loadings.

A Root-Mean-Square Approach for Predicting Fatigue Crack Growth under Random Loading

Abstract: A method for predicting fatigue crack growth under random loading which employs the concept of Barsom (1976) is presented. In accordance with this method, the loading history for each specimen is analyzed to determine the root-mean-square maximum and minimum stresses, and the predictions are made by assuming the tests have been conducted under constant-amplitude loading at the root-mean-square maximum and minimum levels. The procedure requires a simple computer program and a desk-top computer. For the eleven predictions made, the ratios of the predicted lives to the test lives ranged from 2.13 to 0.82, which is a good result, considering that the normal scatter in the fatigue-crack-growth rates may range from a factor of two to four under identical loading conditions.

A New Parameter for Characterizing Corrosion Fatigue Crack Growth

Abstract: The role of mechanical factors, such as ΔK, R, and K (loading rate), and its significance on corrosion fatigue crack growth acceleration were discussed in terms of crack tip strain rate and/or nucleation rate of fresh metal surface. A new parameter for characterizing corrosion fatigue crack growth was proposed, paying attention to rates of crack tip mechanochemical reactions, i.e., oxide film rupture rate, passivation rate, and solution renewal rate, which are influenced by the crack tip mechanical condition, microstructure of material, and environment. Hence a new parameter da/dt] air , the time base pure fatigue crack growth rate which was related closely to crack tip deformation rate, was introduced as a measure of actual crack tip strain rate. In various combinations of materials and environments, it was shown that the value of da/dt] air determines a crack growth rate in the environment, irrespective of mechanical factors such as ΔK, Kmax , R, and K, or frequency.

Fatigue crack growth in polyurethane foam

Abstract: The growth of fatigue cracks in compact tension specimens of rigid polyurethane foam has been studied at room temperature under conditions of constant load-amplitude cycling. The growth of the cracks at the frequencies employed (∼0.2 Hz) is found to be reasonably reproducible and the growth rate can be related to the cyclic stress intensity range in the conventional way. The rate of growth of the cracks is also found to depend on the mean stress level and an attempt has been made to separate out the effects of stress-intensity range, ΔK, and the maximum stress intensity in each cycle, K max, by combining the data obtained under a variety of loading conditions.

Random Spectrum Fatigue Crack Life Predictions With or Without Considering Load Interactions

Abstract: The validity of using constant amplitude crack growth rate data for the prediction of fatigue crack growth behavior and lives of center-cracked tension (CCT) specimens under random spectrum loadings was assessed. Analytical predictions obtained from the EFFGRO computer program were the results from two different approaches. One approach did not account for the load interaction effects to the fatigue crack growth, while the other approach considered both the tensile overload retardation and the compressive load acceleration effects as well as the reduction of overload retardation effect caused by the compressive load immediately following the tensile overload. This paper describes the fatigue crack growth rate equation, the load interaction model, the numerical procedure, and the cycle counting technique used in the EFFGRO program. Results from other studies, including the sensitivity of the overload shut-off ratio, the crack growth rate constants determination procedure, and the range-pair counting effects to the prediction accuracies, are also presented.

Effect of residual stress on fatigue crack growth rate measurement

Abstract: Examples are given where influence of residual stress leads to erroneous interpretation of fatigue crack growth rate measurements made in accordance with ASTM Method E 647-78T. The experimental data presented form a basisfor modification of applicable ASTM documents to give recognition to problems caused by residual stress, and to suggest guidelines for minimization of their effect on fracture property measurement.

Development of a Proposed ASTM Standard Test Method for Near-Threshold Fatigue Crack Growth Rate Measurement

Abstract: Results are summarized which provide the basis for development of the proposed ASTM standard test method for measuring and presenting very slow cyclic rates of fatigue crack propagation. The technique for obtaining very slow rate data as K decreases with crack extension is described. Data are reviewed that show the individual and combined effects of various precracking and testing procedures, loading rates, and other testing parameters. The data are used to demonstrate the utility of the method and its limitations. Guidelines are given for the minimization of transient growth rate processes which can confound interpretation of the data. Analytical procedures for fitting near-threshold data are also discussed.

A Critical Analysis of Grain-Size and Yield-Strength Dependence of Near-Threshold Fatigue-Crack Growth in Steels.

Abstract: : Though a number of investigators have examined the influence of microstructural variables on near-threshold fatigue-crack growth rates in steels, a comprehensive understanding of the dependence of near-threshold growth rates on grain size, yield strength and microstructural morphology in steels has yet to emerge -- as noted in an excellent review by Ritchie. Recently, however, from our own extensive studies with alpha/beta titanium alloys, the basis for microstructural dependence of widely different fatigue crack growth rates was established for titanium alloys. Inasmuch as the micromechanistic model from that work does not depend uniquely on alloy family, it is of great interest to explore its applicability to steels -- especially since it predicts quantitatively the influence of yield strength and grain size in the near-threshold region for steels. Thus, the purpose of this paper is to critically analyze the near-threshold fatigue crack growth behavior, as reported in the literature, for steels of widely different strength level, grain size and microstructural morphology -- in the search for a systematic ordering of near-threshold fatigue crack growth rates that pertains to the whole gamut of steels. (Author)

The engineering fatigue properties of wrought copper

Abstract: — The paper presents a comprehensive review, supplemented by original data, of the engineering fatigue behaviour of copper. Variations in manufacturing route and softening treatments are shown to have little effect on the fatigue of annealed copper but the high cycle fatigue strength is increased by cold work. The high strain fatigue behaviour is defined in terms of the plastic strain range and the cyclic stress-strain characteristics are documented. Fatigue behaviour in bending and torsion is defined by data and related to that in tension by simple design rules. Notches are found to reduce the laboratory measured fatigue strength of copper by ∼ 30% and the effect of surface finish, surface distortion and surface residual stress is defined in the literature. Fatigue crack growth is defined in terms of stress intensity factor range ΔK by an upperbound law and, together with the conditions for non-growth (ΔK0), shown to relate to the equivalent conditions for steels via the ratio of the respective elastic moduli. The effect of environment on the fatigue of copper has received scant attention in the literature, such results as exist suggesting little if any reduction in strength to be brought about by gaseous or aqueous environments. The most dramatic change is the improvement of about an order of magnitude which results when tests in vacuum are compared with equivalent tests in air. Results of fatigue tests on copper in ammoniacal environments are conspicuously absent from the literature. As the test temperature is reduced below room temperature there is a predictable increase in high cycle fatigue strength, a reduction in fatigue strength occurring above room temperature. High strain fatigue test results presented in terms of plastic strain range appear insensitive to temperature although at very low strain rates and high temperatures a reduction in fatigue strength occurs. A linear life fraction cumulative damage creep-fatigue law appears sometimes to be non-conservative but much more testing is needed to evaluate fatigue damage summation laws generally for copper. Numerical data are given in support of all the aspects of the engineering fatigue behaviour reviewed in the paper.

Fatigue crack growth under mixed mode loading

Abstract: —Mixed mode fatigue crack growth is analysed using Sih's strain energy density approach. A centre crack panel geometry loaded under uniaxial cyclic tension is considered. The crack angle is varied from 30° to 90°. A procedure for the determination of crack propagation life is outlined. The crack trajectory due to cyclic loading is predicted. The crack growth rate, the cyclic life and the cyclic life ratio are discussed, for an aluminium alloy and a steel, as a function of initial crack angle, crack length, stress amplitude, and the strain energy density factor.

Theoretical model for FCGR near the threshold

Abstract: A theoretical model for fatigue crack growth rate at low and near threshold stress intensity factor is developed. The crack tip is assumed to be a semicircular notch of radius ρ and incremental crack growth occurs along a distance 4ρ ahead of the crack tip. After analysis of the stress and strain distribution ahead of the crack tip, a relationship between the strain range and the stress intensity range is proposed. It is then assumed that Manson-Coffin cumulative rule can be applied to a region of length 4ρ from the crack tip, where strain reversal occurs. Finally, a theoretical equation giving the fatigue crack growth rate is obtained and applied to several materials (316L stainless steel, 300M alloy steel, 70-30 α brass, 2618A and 7025 aluminum alloys). It is found that the model can be used to correlate fatigue crack growth rates with the mechanical properties of the materials, and to determine the threshold stress intensity factor, once the crack tip radius α is obtained from the previous data.

Analysis of Crystallographic High Temperature Fatigue Crack Growth in a Nickel Base Alloy

Abstract: Crack growth behavior of a nickel-base alloy, Udimet 700, was studied at room temperature and 850 °C in air and vacuum. Crack growth rates were higher in air than in vacuum but this increase in growth rates was nearly the same at both temperatures. In contrast to the effect of environment, an increase of temperature from 25 to 850 °C has a much larger effect on growth rates although the mode of crack growth did not change with temperature or with environment. A detailed analysis of the fracture surfaces indicated that the growth rates under all of the above experimental conditions occurs by a crystallographic faceted mode with the plane of the facet identified to be the {100} cleavage plane rather than a slip plane. Also the increase in growth rates with temperature appears not to be directly related to an environmental effect, creep effect or variation of elastic modulus with temperature.

The early stage of fatigue crack growth in martensitic steel

Abstract: In low ductility and high strength steels, the early stage fatigue behavior associated with non-metallic inclusions is a highly localized phenomenon near the inclusions. However, the nature of the fatigue crack initiation process is not clear. In this paper, a special emphasis is placed on the possible differences in the mechanism of initiation and the early growth of fatigue cracks between a martensitic steel and ordinary ductile materials. The poor adhesion between matrix and aluminum oxide inclusion leads to the formation of an inclusion pit which serves as a simple stress raiser. The fatigue crack originates at the periphery of this inclusion pit at an angle of 45 degrees to the principal stress direction. Metallurgical and micro-fractographical observations revealed that the initiation and early growth of fatigue cracks from non-metallic inclusion are of the shear rather than the tensile mode. Thus, it is concluded that, though the fatigue process is quite localized in the vicinity of inclusion, the mechanism for an initiation and early growth of fatigue cracks is essentially the same as that for ductile materials. The effects of metallurgical heterogeneities in the martensite, such as the prior austenite grain boundaries, packets, and plates on the initiation and early growth of the cracks, are also discussed from the mechanical-metallurgical viewpoint.

Some Aspects of Fatigue Crack Closure in Two Contrasting Titanium Alloys

Abstract: Fatigue crack growth at intermediate rates was measured in compact tension specimens of the microstructurally contrasting alloys Ti-6Al-4V (Imperial Metal Industries, Ltd. [IMI] titanium 318) and Ti-6Al-5Zr-0.5Mo-0.25Si (IMI titanium 685). Sinusoidal loading was used with a ratio of minimum load to maximum load R of 0.1. The incidence of crack closure was examined during fatigue with both direct current potential drop and crack-opening-displacement (COD) methods; COD was found to be more reliable for closure measurement than potential drop. In contract to the fine-grained IMI 318, the coarse-structured IMI 685 showed substantial load transfer across the crack faces during fatigue and this was attributed to mismatch of the fracture faces. It was shown that the large differences in crack growth rate between the two alloys could be substantially accounted for by an effective stress intensity factor range concept. Marked reductions in growth rate produced by variable amplitude loading of the IMI 318 could not be explained in terms of crack closure.