Crack Growth Rate Equation Research Articles

Constant-probability crack growth curves

This paper details a stochastic, time-inhomogeneous model that serves as a theoretical basis for the prediction of crack growth and its variability under constant-amplitude loading. Crack evolution is described as a set of constant probability curves, each of whose points possess equal probability of advancing from one position to another forward position. This probability is governed by a transition intensity parameter for which two mathematical interpretations are examined. A simplified crack growth rate equation, employing one of the definitions, is derived and applied to A17075-T6 material for different loading conditions. Results of this application are compared with those experimentally obtained.

Fatigue fracture toughness of maraging steel.

High-cycle fatigue tests, low-cycle fatigue tests, and static tensile tests on notched specimens of a maraging steel were conducted. not only is the fatigue fracture toughness Kfc approximately constant for high-cycle and low-cycle fatigue, regardless of applied stresses and strains, but also Kfc is approximately equal to the static fracture toughness KIC;Kfc<cong>KIC<cong>36 MPa·m1/2. Moreover, for its high tensile strength (yield stress σ0.2=2440 MPa, tensile stress σB=2490 MPa), the maraging steel has an extremely small value of KIC in comparison with other low-and medium-strength steels. Considering that the crack propagation period occupies only 20-30% of total life in high-cycle fatigue and also that the crack lengths at final fracture in low-cycle fatigue are very small in comparison with specimen size, the fatigue life prediction method on the basis of the integral of crack growth rate equation is inadequate and should not be applied to high-strength steels such as maraging steels. Instead, Kfc will be useful to predict the final fracture of maraging steels.

On the statistical characteristics of fatigue crack propagation

In order to investigate the governing factor which causes the statistical fluctuation in the fatigue crack growth process, various experimental and simulated results obtained based on the Paris-Erdogan equation of fatigue crack growth rate were surveyed. Then, the governing factors for the randomness in microscopic fatigue fracture process being reflected on the phenomenological crack growth characteristics were examined. As a result, the distribution of the resisting strength of material to crack propagation with a certain unit size US is considered to be important. Also, the significance of the restriction of crack plane, that it can not rotate remarkably around the crack growth direction axis, is also indicated.

疲労とクリープの重畳効果に関する研究 ＶＩＩ 高温クリープ疲労き裂進展のひずみ範囲分割法による取扱い

The strain range partitioning analysis of creep-fatigue cracks is conducted for the normalized and tempered 21/4 Cr-1 Mo steel at 550°C and for SUS 304 stainless steel at 700°C, assuming that creep-fatigue life relations can be simply obtained by integrating creep-fatigue growth rate equations. For Δeij straining, crack growth rate equations in air and vacuum are respectively given by (1/a) (da/dN)ij=ln(af/a0)ij(Δeij/Aij)1/mij and (1/a)(da/dN)ij=ln(af/a0)ij(Δeij/αijDi)2, where respective partitioned strain versus life relations are given by Δeij=AijNij-mij and Δeij=αijDiNij-0.5, and (af/a0)ij is the ratio of final half crack length to initial one. For (ΣΔeij) straining, it is assumed that the crack growth rate is given by Σ(da/dN)ij.It is shown based on air data that ln(af/a0)pp=8.3, ln(af/a0)pc=10.3, ln(af/a0)cp=2.6 and ln(af/a0)cc=4.0 for 21/4 Cr-1 Mo steel, and that ln(af/a0)pp=13.7, ln(af/a0)pc=5.5, ln(af/a0)cp=5.4 and ln(af/a0)cc=5.2 for SUS 304 steel.Furthermore, (a0)ij and (af)ij of very small size are evaluated on the basis of the obtained values of (af/a0)ij. It is suggested that four types of inelastic strain range, Δeij, are new and useful parameters that will help us to evaluate the crack initiation life, the remaining life and the material damage in future.

Crack growth rate under cyclic loading and effect of different singularity fields

The effect of two singularity fields: the HRR solution and a modified form of Rice's solution for the anti-plane shear, on the fatigue crack propagation are investigated. A unified crack growth rate equation is derived involving mechanical, cyclic, fatigue properties as well as a length parameter associated with the microstructure. The crack propagation model includes a function which demonstrates the effect of different types of singularity fields. The predictions of the rate of crack growth are compared with the experimental data of three different metals, and the agreement is found to be fairly good. It is shown that a broad class of the previously proposed crack growth relationships can be derived as a particular case of the present one.

Prediction of threshold and ultra-low fatigue crack growth rates

A model was derived to predict the true threshold value for fatigue crack growth in the absence of crack closure. The model, based only on the tensile and cyclic properties of the material, was successfully verified against a set of experimental data on medium and high strength steels and one aluminium alloy. Good agreement with experimental results was also obtained for Region I of the da/ dN vs ΔK curve using a fatigue crack growth rate equation based on the same model. Fatigue crack growth data obtained from the medium strength steel CK45 in the normalized state and two heat-treated conditions were analysed. Good data correlation was shown using a previously developed normalizing parameter, φ = (ΔK 2−ΔK 2 th )/(K 2 c −K 2 max ) , in the entire range of fatigue crack growth rates and for stress ratios ranging from 0.1 to 0.8.

EFFECT OF LASER BEAM RADIATION ON FATIGUE CRACK GROWTH BEHAVIOUR

AbstractThis paper studies the effect of laser beam radiation on the fatigue crack growth threshold and the crack growth rate in 25CrMnSi steel plate. A comparison of radiated and unradiated specimens permits the derivation of an equation for the fatigue crack growth rate. The results show that radiation can enhance the fatigue threshold and retard crack growth rate.

THE INFLUENCE OF AGE‐HARDENING ON FATIGUE CRACK PROPAGATION BEHAVIOUR IN 7075 ALUMINIUM ALLOY IN VACUUM

Abstract— The influence of age‐hardening on the middle and low crack growth rates of a 7075 Al alloy is studied in vacuum. A transition in fracture surfaces morphology and crack growth curves is observed with the T 651 and T 7351 treatments in the near‐threshold regime. Measurements of crack closure show its dependance on surfaces roughness and explain the lack of dependance of ΔKth with load ratio, except for the T 7351 alloy. An equation of crack growth rate to the fourth power of ΔKeff is in good agreement only with the crack propagation curves obtained for microstructure with an homogeneous deformation mode.

Change of fatigue parameters with temperature

AbstractA fatigue crack growth rate (FCGR) equation, had been proposed which predicts the observed R‐ratio effects correctly. Conceptually, this equation accounts for spectrum loading effects via the parameter “K”. The work presented deals with the temperature effect on the fatigue parameters entering the above FCGR‐equation. For materials which do not experience a microstructural or a fracture mode transition within the temperature range of interest, the effect of temperature on the fatigue parameters “C” and “ΔKT” can be interpolated or extrapolated from relatively few experimental data. Extrapolation of these fatigue parameters for Inconel X‐750 measured between 300° K and 900° K allowed a very accurate prediction of the FCGR at 4° K.At higher temperatures the end of fatigue controlled crack growth is clearly indicated by a rapid increase of the fatigue parameter “C”. There, the fatigue parameter “C” increases withing a temperature span of 100° K by a factor of 102. This kind of information is of utmost importance for materials application at elevated temperatures as in nuclear systems.

CRACK GROWTH AND PREDICTION OF ENDURANCE IN THERMAL‐MECHANICAL FATIGUE OF 12Cr—Mo—V—W STEEL

Abstract Fractography and fracture mechanics were used to study the behaviour of a crack that emanated from a starter notch on a specimen surface subjected to thermal cycles, and which grew in the direction perpendicular to the surface, under out‐of‐phase loading conditions. A 12Cr–Mo–V–W steel was used as representative of an elevated temperature material, and one that is frequently employed for vessels or heat‐exchanger tubes. A low power travelling microscope observed crack length changes on the specimen surface. It was shown that the growth rate of a part‐through crack could be expressed in terms of a strain intensity factor range and two constants, and that the striation spacings agreed with the microscopically observed crack growth rate. The integration of the crack growth rate equation gave an approximate evaluation of thermal fatigue life of smooth specimens.

Fatigue Crack Propagation in A533B Steels—Metallographic and Fractographic Analyses

Metallographic and fractographic analyses are performed on A533B low alloy plate steels made by three steelmaking practices. The fatigue crack growth rates of these steels had been previously established in all six possible testing orientations. By using quantitative image analysis to quantify the nonmetallic inclusion structures of these steels, graphical and statistical correlations were established between the two material constants of the fatigue crack growth rate equation and various inclusion parameters. The average area of an inclusion on the metallographic cross section corresponding to the plane of fracture was found to be the best single parameter for establishing a correlation applying to all testing orientations. Scanning electron microscopic investigations of the fracture surfaces of the fatigue crack propagation specimens indicated that the inclusions (Type II manganese sulfides and alumina galaxies) exerted a predominant effect on the fatigue crack propagation behavior. Both studies provide additional evidence that the differences in fatigue crack growth rates between and within the steels of this investigation can be a result of the nonmetallic inclusion structures of the materials.

Developing Normalized Crack Growth Curves for Tracking Damage in Aircraft

This paper directs attention to the interrelationship between crack growth rate equations and the Normalized Crack Growth (NCG) curve concept used in the F-4 fighter damage tracking program. Crack growth rate equations, based on linear elastic fracture mechanics assumptions, provide the capability for predicting the influences of geometrical changes or of stress scaling. For the crack growth rate equations that describe the flight-by-flight generated data presented herein, generalized integral (or inverted) formulas are suggested that provide the rationale for developing NCG curves. Subject to the limitations described within the body of the paper, the NCG curve invariance assumption for tracking damage at different locations in an aircraft appears reasonable.

Some viscoelastic crack growth relations for orthotropic and prestrained media

Equations are developed for predicting and sliding modes of crack growth along planes of geometric symmetry in viscoelastic orthotropic media with and without large prestrains. Except for the small failure zone at the crack-tip, the material is assumed to be linearly viscoelastic with respect to the changes in stress and strain which occur during crack propagation. For an orthotropic body in plane strain, an observation of Biot relating the Fourier transformed tractions and displacements on the surface of any homogeneous, elastic half-space is used in conjunction with Graham's extended correspondence principle to generate the viscoelastic crack face displacements. Application of a suitable energy criterion for failure leads to a nonlinear integro-differential equation for the crack tip speed in terms of material and loading parameters. The resulting equation is of the same generic form as in the previously published isotropic case except that the isotropic creep compliance is replaced by effective compliances formed from orthotropic moduli. Thus, just as in the isotropic case, a much simpler, approximate crack growth rate equation is deduced from the assumption that these effective compliances have small curvature when plotted logarithmically against logarithmic time. Included is a numerical example using constitutive properties of a fiber-reinforced plastic. Extension to fracture of prestrained media and crack growth between certain types of dissimilar media is then made. Again the growth equations have the same basic form, but for a prestrained medium the effective compliances involve the incremental moduli. The results indicate that crack growth is accelerated for initial stress states that create certain surface instabilities ahead of the crack tip. Finally, it is argued that these crack velocity relations can be employed in plane stress problems and in many three-dimensional cases, and, with a small change, can be used to predict the time of fracture initiation.

A theory for creep crack growth

The paper derives an analytical expression for creep crack growth rate based on a model in which the higher and concentrated stresses ahead of the crack tip enhance creep deformation, thus progressively causing stress rupture and continuous crack advance. The equation derived for creep crack growth rate is expressed in terms of a geometrical factor in the stress intensity expression and in terms of the crack tip radius whose lower limit estimate is the fracture mechanics crack-tip opening displacement. The functional features of the derived creep crack growth rate equation can be compared with those of a pertinent empirical equation. The analytical expression provides some guidelines for alloy and microstructure design.

The influence of stress intensity and microstructure on fatigue crack propagation in a 1% carbon steel

The influence of alternating and maximum stress intensity and microstructure on fatigue crack propagation in a 1% carbon steel has been investigated. Considerably higher growth rates were found for a pearlitic compared with a spheroidised microstructure on account of different fatigue crack growth mechanisms. A fatigue crack growth rate equation which is in good agreement with the experimental data is presented. The proposed equation is applicable even when the maximum value of the stress intensity approaches the critical stress intensity for failure under monotonic loading.