Fatigue Crack Closure Model Research Articles

Equivalent thickness-based three dimensional stress fields and fatigue growth of part-through cracks emanating from a circular hole

Accurate characterization of stress states is essential to assess structural integrity and predict fatigue crack growth life. Strong three dimensional constraints always raise at cracks and holes, but have never been investigated in the frame of three dimensional fracture theory for part-through cracks emanating from a hole. Here the three dimensional constraint and its effect on crack tip fields of corner and surface cracks emanating from a circular hole in tensile plates are comprehensively analyzed using finite element method. Distributions of the out-of-plane constraint factor Tz are strongly dependent on relative circular hole size and relative thickness parameters, but the K-Tz description of the stress field remains efficient with the present of circular hole. The equivalent thickness conception based on Tz distributions is applied to crack tip stress field description. Based on the equivalent thickness conception and plasticity-induced fatigue crack closure model, evaluation of fatigue growth of corner crack emanating from a circular hole is demonstrated and validated against test data in the literature.

Prediction of fatigue crack growth rates using crack closure finite element analysis

A three-dimensional finite element fatigue crack closure model of a corner crack and of a through thickness crack has been developed to evaluate the range of effective stress intensity factor from the distribution of the range of stress ahead of the crack tip. The corresponding fatigue crack growth rate was evaluated from a Paris law fit to experimental data from high stress ratio tests. The point of origin for the range of stress distribution was adjusted in accordance with Irwin’s plastic zone correction. Encouraging comparisons of finite element predictions of fatigue crack growth rate incorporating closure effects with experimental measurements were obtained.

Fatigue crack propagation for a through thickness crack: a crack propagation law considering cyclic plasticity near the crack tip

A new parameter, which can quantitatively describe fatigue crack propagation, is proposed in this paper. This parameter reflects the cyclic plasticity behaviour near the crack tip, and the resulting built up of layers with the residual plastic deformations on the fatigue crack surfaces. A fatigue crack closure model suitable for an arbitrary applied stress distribution with an arbitrary residual stress distribution based on appropriately modified Dugdale’s concept of crack tip plasticity is developed. A re-tensile plastic zone generated (RPG) load, at which the tensile plastic zone starts to develop ahead of a crack tip, is defined. The effective stress intensity factor range is redefined by replacing the crack opening load with the RPG load. This redefined effective stress intensity factor is termed ΔKRPG. When ΔKRPG substitutes for ΔK or the crack opening load based on ΔKeff the “knee” in the threshold region of the crack growth data is not seen any longer. As a result, it is confirmed that a stopping phenomenon of a fatigue crack propagation can be quantitatively and appropriately described without the threshold value such as (ΔKeff)th. It is also confirmed that the proposed crack closure model can provide quantitative estimates of the fatigue life under various loading conditions and in pre-existing residual stress field.

A threshold fatigue crack closure model: Part I – model development

ABSTRACTA fatigue crack closure model is developed that includes the effects of, and interactions between, the three closure mechanisms most likely to occur at threshold; plasticity, roughness, and oxide. This model, herein referred to as the CROP model (for Closure, Roughness, Oxide, and Plasticity), also includes the effects of out‐of‐plane cracking and multi‐axial loading. These features make the CROP closure model uniquely suited for, but not limited to, threshold applications. Rough cracks are idealized here as two‐dimensional sawtooths, whose geometry induces mixed‐mode crack‐tip stresses. Continuum mechanics and crack‐tip dislocation concepts are combined to relate crack face displacements to crack‐tip loads. Geometric criteria are used to determine closure loads from crack‐face displacements. Finite element results, used to verify model predictions, provide critical information about the locations where crack closure occurs. The CROP model is verified with experimental data in part II of this paper.

A threshold fatigue crack closure model: Part II – experimental verification

ABSTRACTPredictions from an analytical model that considers contributions and interactions between plasticity, roughness, and oxide induced crack closure are presented and compared with experimental data. The analytical model is shown to correctly predict the combined influences of crack roughness, oxide debris, and plasticity in the near‐threshold regime. Furthermore, analytical results indicate closure mechanisms interact in a non‐linear manner such that the total amount of closure is not the sum of closure contributions for each mechanism.

Probabilistic Fatigue Crack Growth Analyses for Critical Structural Details

The damage tolerance method requires the assumption that cracks preexist at the critical structural details and that subsequent fatigue crack propagation could cover at least twice the design life before failure occurs. If fatigue crack propagation cannot meet these requirements, an inspection could be arranged to detect cracks at half of the fatigue life to prevent catastrophic failure. Fatigue tests using from coupons up to the whole structure should be performed to complement the damage tolerance analyses. Nevertheless, the damage tolerance method can still not guaranteean economical airframe dueto uncertaintiesin initial fatiguequality, material, usage, and maintenance. Probabilistic analyses are needed to cover major sources of these uncertainties. A procedure is presented based on several novel probabilistic fracture mechanics solutions for the analyses of fatigue crack propagation. A practical example is used in the discussion to illustrate the procedure and to address important issues when uncertainties are considered. It is shown that different consequences may appear if analyses of the fatigue life are based on the probabilistic consideration. O guarantee enough structural strength during the design life span, the damage tolerance is usually considered for critical structural details to achieve the maximum reliability with a mini- mum maintenance requirement. The damage tolerance method re- quiresspecifyingthatcracksshouldbeassumed inalloftheprimary structural details, and that these cracks should not grow to a size to cause loss of the structure within a specie ed service period. The damage tolerance method requires 1 ) a full-scale fatigue test to at least double the design life for an average usage load and 2 ) at least twice the design life for a crack started froma specie ed size to grow into the critical size. The damage tolerance method is often imple- mented by an inspection to detect fatigue cracks at half of the crack growth life. The fracture-mechanics-based damage tolerance method pro- vides information about the average crack growth behavior. It usu- ally does not account for uncertainties involved in the fatigue crack growth process for practical structural problems. Empirical safety factors are often adopted to cover uncertainties in crack propaga- tion.Whentherearenoadequatedatatosupportselectionofasafety factor, a large value is preferred, which may lead to uneconomical heavy structures and to rejection of reliable structures and com- ponents. The consequent maintenance programs are usually poorly dee ned,resultinginuneconomicalinspectionintervalsthatmaystill notguarantee a reliable structure in service. Aprobabilistic analysis ofthefatiguecrackgrowthisdesirableinthereliabilitymanagement of structural problems. The analysis can be used as a guideline for service conditions, where various uncertainties cannot be avoided. When accidental damages such as pilot error, maintenance dam- age, environmental attacks, production faults, etc., are excluded, probabilistic fatigue crack growth analyses should cover the effect ofpredictablevariablessuchasinitiale aws,stochasticcrackgrowth, crack growth threshold, production and loading, failure criteria, in- spection, e eet size, etc. In this paper, a crack growth analytical pro- cedure is developed based on Elber' s fatigue crack closure model 1 for nonstationary stochastic fatigue crack growth analyses under the general loading condition. The experimental data for the fa- tigue crack growth rate against the effective stress intensity factor for constant amplitude loading are used as intrinsic material data to represent the resistance of material to the fatigue crack growth. The

A probabilistic damage accumulation solution based on crack closure model

A total life probabilistic model has been developed based on both short and long crack growth data to analyse the fatigue crack growth under general loading conditions. The analysis is based on Elber's crack closure model. An effective stress intensity factor is used as the major crack growth driving force in the crack growth analyses. Statistical fatigue crack baseline data from the constant amplitude loading tests are used as a basic governing function in the probabilistic crack growth analyses. A strip yield fatigue crack closure model is used together with a modified Miner–Palmgren's damage accumulation model to account for uncertainties in the non stochastic crack growth process from the crack initiation to the final failure. In this model, effects of material inhomogeneity, initial flaws, and variations in geometry and applied load etc., have been considered for their individual effects. This model provides a probabilistic estimation of the fatigue crack growth for both small and large crack sizes. Several examples have been provided to illustrate a variety of problems that the model is capable of dealing with, and to clarify physical mechanisms behind some of the controversial experimental results.

Fatigue crack closure under triaxial stress constraint—II. Analytical model

An analytical model for fatigue crack closure under triaxial stress constraint is established based on a modified Dugdale model as well as the asymptotic solution of three dimensional cracks. The influence of mechanical parameters, geometries of specimens and properties of materials is critically analysed. Comparing with three dimensional finite element results shows that the error of the present model is less than 3.5% for a wide range of thickness (2–30 mm). An engineering conception for the sensitive zone of stress constraint for fatigue crack closure is proposed. By use of the model, fatigue crack propagation in materials where the striation mechanism is dominant can be explained very well.

A geometric model for fatigue crack closure induced by fracture surface roughness under mode I displacements: Li, S., Sun, L., Zang, Q. and Wang, Z. Mater. Sci. Eng. A 29 Feb. 1992 A150 (2) 209–212

In the past three decades ratcheting fatigue has attracted lots of research interest. Ratcheting can be defined as the directional progressive accumulation of plastic deformation of a material when it is subjected to a primary load along with a secondary cyclic load. The current article addresses the recent progresses made on the experimental front on the ratcheting behavior spanning from the specimen level to the component level and its correlation with microstructural evolution. The experimental aspects of ratcheting include the effect of stress levels, stress rate, temperature, planar anisotropy, previous loading history, and multiaxial loading paths. This work also discusses two test controlling modes engineering and true stress control ratcheting and their comparison, ratcheting-tensile, ratcheting-low cycle fatigue, ratcheting-ratcheting, ratcheting-creep interactions and ratcheting in component level. This summarized information clarifies why ratcheting is presently an important topic of engineering research.

A geometric model for fatigue crack closure induced by fracture surface roughness under mode I displacements

A geometric model dealing with the roughness-induced fatigue crack closure under mode I displacements is proposed. It is shown that roughness-induced crack closure can also be acquired without mode II and III displacements at the crack tip. In this mechanism, the severe contact region is near the crack tip. The average crack closure ratio is the result of discrete asperities which come into contact.

A fatigue crack closure model and measurement technique: Mirzaei, M. and Provan, J.W. Int. J. Fract. Jan. 1991 47, (1), R3–R10

A fatigue crack closure model and measurement technique: Mirzaei, M. and Provan, J.W. Int. J. Fract. Jan. 1991 47, (1), R3–R10

A fatigue crack closure model and measurement technique

A fatigue crack closure model and measurement technique

A mixed mode fatigue crack closure model

Fatigue crack closure conditions leading to mixed mode crack-tip stress states are discussed. A closure model based on contact between impinging fracture surface asperities is introduced. Asperity angle, magnitude of mode II interference, friction between contacting surfaces and distance of the contact surfaces from the crack-tip are features included in the model. The magnitudes of mode I and mode II stress intensity factors due to closure contact are found to vary substantially with asperity angle. Also, because of a reversal of friction force direction during cycle loading, the stress intensity factors exhibit a complex behavior. During the closure phase of the loading cycle, the mode II contribution is found to be quite significant. For loading through an entire cycle, which includes both the closure and crack open phases, nonproportional stress states are developed. Also, it is concluded that the mixed mode states developed could provide the conditions required for crack branching.

A model for fatigue crack closure

The phenomenon of fatigue crack closure has attracted continued interest over recent years. This paper concerns itself with one aspect of the phenomenon namely the effects of a single asperity on the crack face close to the crack tip and under dominantly plane strain Mode 1 loading conditions. The model as developed is two dimensional in character but the nature of the closure processes allows it to be applied to real materials. The model illustrates the influence of asperity height, the distance from the crack tip of the asperity and rigidty of the asperity on the crack closure stress intensity. Application of the model to the case of microstructural asperities in nickel alloys and to oxide asperities in steels has met with reasonable success.

A multiple asperity fatigue crack closure model

The plane strain, fatigue crack problem in which fracture surface asperities prevent closure is considered. A model in which closure contact can develop on a distribution of asperities is introduced. A comparison of closure behavior for one and for two asperities is made, and the effects of variations in the model parameters are examined. The relationships of these parameters to the value of the closure stress intensity factor and crack opening displacement are discussed. The possible use of the model in examining conditions in which asperity welding occur is considered. The resulting closure behavior is briefly described.

A geometric model for fatigue crack closure induced by fracture surface roughness

Mechanisms for fatigue crack closure under plane strain conditions have recently been identified at very low (near-threshold) stress intensities in terms of effects of excess corrosion deposits or fracture surface roughness in promoting premature closure of the crack. In the present paper, a geometric model is presented for crack closure induced by fracture surface roughness. This model specifically addresses the contribution from both Mode I and Mode II crack tip displacements in addition to considering the nature of the fracture surface morphology. The implications of this model are briefly discussed in light of the roles of grain size, yield strength, microstructure, and crack size in influencing near-threshold fatigue behavior in engineering alloys.

A model for fatigue crack closure based on surface roughness and residual strain

A model for fatigue crack closure based on surface roughness and residual strain