Fatigue Crack Propagation Model Research Articles

Model of fatigue crack propagation by damage accumulation at the crack tip

Modelling fatigue crack propagation by damage accumulation at the crack tip originally proposed by McClintock is reworked out using metallurgical considerations. On a physical basis it is shown that the validity of such models is actually confined to the low crack growth rate range corresponding to stage I growth such as along crystallographic planes. At higher crack growth rates there is a transition to plastic stretching mechanisms which could be described by crack opening displacement models. An evaluation of two models has been carried out on a 33Co Ni alloy where extensive information was available: both are based on the strain singularity as computed by Tracey from a finite element analysis of plane strain small scale yielding and as adapted to cyclic loading under Rice's hypothesis and taking the grain as the critical element below which size continuum mechanics do no longer apply. It is pointed out that the use of this strain singularity which is not able to account for crack closure, renders models unable to predict experimental crack growth rates curves but only intrinsic curves relating the growth rate to the effective stress intensity amplitude as defined by Elber. The first model which assumes fatal cracking of a grain with an average uniform cyclic equivalent strain, underestimates the crack growth rates and in addition it yields results very sensitive to the shape and size of the grain. The second model which assumes progressive cracking in a grain with a cyclic equivalent strain gradient is able to predict the intrinsic crack growth rate curve in the 33Co Ni alloy and to yield predictions consistent with other experimental data.

疲労き裂過程に現れる統計的変動の支配因子について

Since fatigue is essentially the manifestation of continuous local fracture caused by cyclic stressing, it has been pointed out that fatigue shows the statistical characteristics reflecting the stochastic feature of each fatigue process. Thus, the factors governing this fluctuation can be studied on the basis of both extreme theory and the stochastic process theory. The similar fluctuation also appears in the fatigue crack propagation process, and consequently a number of crack growth curves may be obtained.In this paper, the Monte-Carlo simulation was conducted by assuming the microstructural heterogeneity model as well as the stochastic process model of fatigue crack propagation, and the factors governing the statistical fluctuation in the fatigue crack propagation process were investigated.The results show clearly that such a factor as the difference in resisting power of structure caused by the change in size distribution of structural units like crystal grains, influences considerably the stochastic feature of the fatigue crack propagation process.

Fatigue Crack Propagation Model with consideration for Crack Opening/Closing Phenomena

It is well known that fatigue cracks remain closed during part of the load cycle under constant- and variable-amplitude loading. It seems that Elber's effective stress intensity factor range produced by a crack opening stress is in successfully good agreement with experimental fatigue crack propagation behaviour under various loading including constant-, block-, and spike-loading from a huge amount of tests. Recently, J. C. Newman introduced the interesting calculation model of the crack opening stress which was based on the Dugdale model, but was modified to leave plastically-deformed material along the crack surfaces as the crack advances.However in his model, he neglected the stress re-distribution in the region of crack ahead in the calculation of crack opening load which leads to the occurrence of the re-distribution. Moreover, he also neglected the elastic deformation for the materials along the crack surfaces.In this paper, Newman's calculation model is modified to solve the above problems. By the way, from the physical point of view, the idea that crack-opening stress is a limit stress for a fatigue crack propagation proposed by Elber comes to question. We considered that a fatigue crack does not propagate if a local part in the vicinity of a crack tip remains elastic, i. e., a plastic strain does not accumulate at a crack tip. This limit loading stress is named “consuming stress Scs” which was confirmed to have nearly the same value as the crack opening stress by our calculation results. Various kind of case studies including constant-amplitude, spike and step down (for the threshold phenomenon) loading were carried out by using the model. These calculation results suggest the following phenomena.(1) Scs value increases rapidly just after fatigue crack initiates from a natural sharp defect. This result supports the phenomenon that fatigue crack can easily initiate from a sharp crack even if the length is small because of a large effective stress range.(2) Scs value reaches constant value approximately as a crack advances under constant-amplitude loading.(3) Scs value changes in accordance with the behaviour of acceleration and delayed retardation of a crack propagation after a spike over-loading.Scs(4) Phenomenon of threshold crack propagation seems to be able to be explained by the Scs value under step down loading.

Mean stress effect in fatigue crack propagation

Crack propagation rates in three different grades of mild steel and two types of age hardening aluminium alloys have been measured for different stress ratios. The results show a pronounced stress ratio effect for all these materials. A model of fatigue crack propagation is formulated in terms of the size of the cyclic plastic instability zone at the crack tip rather than the zone of plastic yielding. The micro-plastic instability zone is measured by a parameter involving the ratio of the maximum stress intensity and the stress level at which macro-plastic instability occurs in the S N curve of plain fatigue test pieces. Such a parameter provides a means of normalizing crack propagation results obtained for various stress ratios.

The effect of hold time on the fatigue properties of a β-processed titanium alloy

Several recent papers have demonstrated that dwell periods at peak stress can significantly reduce the number of cycles to failure in LCF tests on titanium alloys and can cause enhanced growth rates in fatigue crack propagation tests. In all cases cleavage or quasi-cleavage facet formation has been intimately linked with the dwell sensitive fatigue response. The present paper demonstrates that facets can also form during creep deformation at ambient temperatures and it proposes that the LCF dwell effect and facet formation under cyclic conditions is dependent on time dependent plastic strain accumulation. If hydrogen contributes to the failure process it is suggested this must be through an interaction with dislocations. The significance of the model for dwell sensitive fatigue crack propagation is discussed.

A regression model of fatigue crack propagation under flight simulation loading

A multi-variable regression analysis is made of crack propagation data under flight simulation loading for the 2024-T3 and 7075-T6 alloys. The study is made using an effective stress range concept based on cracl closure considerations. A two-variable regression model of the equivalent stress range is suggested. The model is used to calculate fatigue crack propagation lives. Predictions using the proposed model are compared with empirical results. It is shown that the model accounts for the influence of maximum, minimum and mean stress levels of the load spectrum.

A mathematical model of fatigue crack propagation under variable amplitude loading

A mathematical model of fatigue crack propagation based on the crack closure concept is proposed. It allows prediction of fatigue crack growth under complex loading sequences on the basis of data obtained under constant amplitude and simple Low-High, High-Low loading sequences. The model explains the influence of single and multiple positive overloads and the interaction of positive and negative overloads. An algorithm for cycle-by-cycle calculation of crack growth is proposed.

<I>bcc</I>金属における疲れき裂伝播の結晶方位依存性

A study has been made of the crystallographic dependence of fatigue crack propagation in bcc metals using Fe-3%Si alloy coarse grain specimens. A significant crystallographic dependence in fatigue crack propagation is observed. Fatigue cracks do not propagate stably along an unspecific plane normal to the loading axis but incline to change the propagation plane gradually to propagate along a specific plane ({110} or {100}). In this grain, the fatigue striation arrangement direction is changed according to the change of the fatigue crack plane. Analyzing this result, it is revealed that the striations are arranged parallel to the cross-line between a macroscopic crack plane and the {110} or {100} plane.Various fatigue crack propagation models are discussed in the light of this study, and it is shown that no fatigue crack propagation model can explain adequately this crystallographic dependence. This may be explained by modifying the so-called slip-off process.

ＢＣＳモデルに基づく疲労き裂伝ぱのシミュレーション

A model of fatigue crack propagation has been proposed. The model is essentially based on the following four assumptions:(1) The displacement along the crack line follows the BCS-model solution.(2) Every point along the crack line has a maximum amount of residual plastic deformation that it received in its history.(3) The rate of the fatigue crack propagation is given by the equation da/dN=C(ΔKeff)m, where ΔKeff is the effective range of the stress intensity factor and C and m are the material constants.(4) The effective stress range is evaluated by the stress at which the point rp* behind the crack tip opens or closes. The parameter rp* denotes the size of the cyclic plastic zone.Based on this model, a computer simulation of fatigue crack propagation has been carried out. The summary of the results is as follows:(1) When the applied stress range and the stress ratio R are held constant, the effective stress range ratio U has a constant value and it is independent of the crack length. The relation between U and R is in good agreement with Elber's equation, i. e., U=0.5+0.4R.(2) In the case of the decreasing ΔK test, the model can describe well the effect of R. The threshold stress intensity factor is given by the assumption that the crack will stop propagating when the COD at the crack tip is less than a certain characteristic value.(3) When there is a sudden change in the applied stress range, an accelerating or retarding effect occurs for a certain period.In these three cases, the model can express the essential features observed in the experiments. Then the simulation technique is considered to be useful for the estimation of fatigue lives.

A fatigue crack propagation model for strain hardening materials

In this paper a crack propagation model based on Tomkins concept ( dl dN ∝ Δϵ p · ω ) has been developed using the theoretically developed cyclic plastic zone sizes. The crack propagation rates are found to be functions of stress intensity factor, Elber's effective stress range ratio, cyclic yield strength of material, crack length, specimen width and cyclic strain hardening exponent. Suitably grouped to give the crack growth rate in terms of five constants termed as Loading Constant, Material constant, Crack size constant, specimen Width Constant and Stress Intensity Exponent. The crack growth rates found by theory are compared with the experimental results available in literature and a good agreement is found.

The Development of Fatigue Crack Propagation Models for Engineering Applications at Elevated Temperatures

The value of modelling the fatigue crack propagation process is discussed and current models are examined in the light of increasing knowledge of crack tip deformation. Elevated temperature fatigue is examined in detail as an area in which models could contribute significantly to engineering design. A model is developed which examines the role of time-dependent creep cavitation on the failure process in an interactive creep-fatigue situation.

On the effect of cyclic stress ratio on the fatigue crack propagation

A new model of fatigue crack propagation is proposed which takes the effect of cyclic stress ratio into account. In the model it is assumed that the fatigue crack propagation rate is proportional to the absorbed hysterisis energy per stress cycle at the tip of a crack. The energy is calculated from stress field resulting from the Dugdak-Barenblatt Model and strain field from an experimental result. The model was applied to analyse the experiments on several materials.

Low cycle fatigue, fatigue crack propagation and substructures in a series of polycrystalline Cu-Al alloys

Low Cycle Fatigue (LCF) on smooth hour glass specimens and Fatigue Crack Propagation (FCP) studies on Single Edge Notch (SEN) specimens were carried out at room temperature on four Cu-Al polycrystalline alloys to investigate the effects of Stacking Fault Energy (SFE) and mechanical property variations on fatigue characteristics. Significant improvements in fatigue properties were observed for alloys of low SFE. A microhardness technique was used to delineate the fatigue plastic zone ahead of stopped cracks at several stress intensity ranges for all the alloys. Planar slip was associated with a less than a second power dependence of plastic zone size on the stress intensity range. Transmission Electron Microscopy (TEM) was used to observe the substructures that developed both in LCF at different strain ranges and also ahead of fatigue cracks at different stress intensity ranges. Fractography was carried out to study the micromechanisms of crack propagation using a two stage replication technique. The experimental results were in good agreement with a theoretical model for FCP developed previously by the authors which incorporates mechanical and microstructural variables.

A model for fatigue crack propagation

A model for fatigue crack propagation is presented which incorporates low cycle fatigue, mechanical properties and a microstructurally-associated process zone. Comparison of the model to published date for 4340 (hard and soft), a series of TRIP steels, Ti-6A1-4V, 2024-T6 and 300 grade maraging steel shows good agreement.

Fatigue crack propagation from a crack inclined to the cyclic tensile axis

Cyclic stresses with stress ratio R = 0.65 were applied to sheet specimens of aluminium which have an initial crack inclined to the tensile axis at angles of 30°, 45°, 72° or 90°. The threshold condition for the non-propagation of the initial crack was found to be given by a quadratic form of the ranges of the stress intensity factors of modes I and II. The direction of fatigue crack extension from the inclined crack was roughly perpendicular to the tensile axis at stress ranges just above the threshold value for non-propagation. On the other hand, at stress ranges 1.6 times higher than the threshold values the crack grew in the direction of the initial crack. The rate of crack growth in the initial crack direction was found to be expressed by the following function of stress intensity factor ranges of mode I, K 1, and mode II, K 2: dc dN = C(K eff)sum , where K eff = [K 1 4 + 8K 2 4] 1 4 . This law was derived on the basis of the fatigue crack propagation model proposed by Weertman.

The geometry of slip processes at a propagating fatigue crack—II

A previously published model of fatigue crack propagation is refined and the resulting slip geometry at the crack tip is calculated. The essential features of this refined model are: The slip on both sides of the crack is assumed to occur on slip bands instead of the discrete slip planes used in the old model. Slip is represented by finite matrices, shape changes of the crack tip as well as the anisotropy of slip are fully taken into account. It is shown, that the geometric mean of the average strains on both sides of the crack cannot be chosen independently but is a unique function of material parameters c 1, c 2 (characterizing the inhomogeneity of slip on both slip systems involved) and the angle α between the two slip planes. Whenever such strains—which must typically be of the order of one—can be produced by the applied stress, ductile crack propagation is possible (ductile fracture criterion). The crack tip angle and the ratio of crack advance per cycle and crack opening displacement are also given in terms of c 1, c 2 and α. Finally it is demonstrated that only the surface production by slip on intersecting slip planes cannot be reversed by slip reversal in the compression phase.

A Consideration on the Fatigue Crack Propagation

A simple model of fatigue crack propagation is offered which takes the effeet of stress ratio into account. In the model it is assumed that fatigue crack propagation rate is proportional to the absorbed hystereisis energy per a stress cycle at the tip of a crack. The energy is calculated from stress and strain field around a crack. Stress distribution is determined by Dugdale model and strain field is done from the experimental results shown by some researchers. It is affirmed that the model can be applied to the experiments on several materials.

Two theoretical models of fatigue crack propagation

A generalized theory of fatigue crack propagation recently published is applied to a dislocation model of fatigue for the anti-plane mode of deformation. By using the results of this model as a guide, reasonable approximations can be made which allow the generalized growth law to be written in a simple form similar to growth laws currently used in the literature.

Shear crack propagation in the residual stress field

The problem of propagation of a longitudinal shear crack in a medium with a random field of internal stresses is considered and solved with the use of the theory of quasi-brittle failure. Local criterion of crack propagation under cyclic loading is derived, and its application as a model of fatigue crack propagation is investigated.

Fatigue crack propagation in trip steels

The fatigue crack propagation behavior of a class of metastable austenitic steels called TRIP steels has been investigated. The alloy composition was chosen to have theMs well below room temperature and theMD above room temperature after thermomechanical processing. A simple theoretical model of fatigue crack propagation (FCP) based on fracture mechanics was developed. Fatigue crack propagation tests on SEN specimens at various stress intensity ranges (ΔK) were carried out, and two stage plastic-carbon replica were used to observe the fracture surface of the FCP specimens. To a first approximation, both the experimental and theoretical results followed the usual relationship between ΔK and FCP rates;i.e. da/dn ∝ (ΔK).4 The fatigue fracture surface contained fatigue striations, quasicleavage and elongated dimples; a reflection of the complex structure of TRIP steels. A beneficial effect of strain induced martensite transformation with regards to fatigue crack propagation was found. TRIP steels showed better FCP properties than a number of alloy steels of similar strength levels and compared favorably with mar aging steels in the low ΔK range.