Fatigue propagation threshold of short cracks under constant amplitude loading

In this study a threshold for fatigue crack propagation as a function of crack length is defined from a depth given by the position d of the strongest microstructural barrier to crack propagation, which defines the plain fatigue limit. The material threshold is estimated from the plain fatigue limit Δσ_eR, the position d of the strongest microstructural barrier and the threshold for long cracks, ΔK_thR. The threshold for eight different materials for which experimental results can be obtained from the literature was estimated. Good agreement was observed in all cases. Some quantitative analyses of the fatigue propagation behavior of short cracks are carried out and discussed.     

LIMITATIONS ON THE USE OF THE STRESS INTENSITY FACTOR, K, AS A FRACTURE PARAMETER IN THE FATIGUE PROPAGATION OF SHORT CRACKS

Abstract— It is well known that for very short cracks the stress intensity factor K is not a suitable parameter to estimate the stress level over the small but finite Stage II process zone activation region of size r_s near the crack tip, within which crack growth events take place. A critical appreciation of the reasons for the limitations on the applicability of ΔK as a fatigue crack propagation (FCP) parameter, when the crack length a is of the same order of magnitude or smaller than the size of the ‘fatigue-fracture activation region’, r_s is presented. As an alternative to ΔK the range Δσ_s of the cyclic normal stress at a point situated at the fixed distance s=r_s/2, ahead of the crack tip, inside the fatigue-fracture activation region, is proposed. It is observed that the limitation on the use of ΔK when the crack is short, is mathematical (and not physical) but this inconvenience is easily circumvented if the stress Δσ_s at the prescribed distance is used instead of ΔK since nowadays Δσ_s can be obtained numerically by using finite element methods (FEM). It follows that the parameter Δσ_s is not restricted by the mathematical limitations on ΔK and so it would seem that there is, a priori, no reason why the validity of the parameter Δσ_s cannot be extended to short cracks. It is shown that if the Paris law is expressed in terms of Δσ_s (πrr_s)^½ instead of ΔK the validity of the modified Paris law can be extended to short cracks. A coherent estimate of the value of the fatigue-fracture activation region r_s is derived in terms of the fatigue limit Δσ_FL obtained from S-N tests and of the threshold value ΔK_th obtained from tests on long cracks where both relate to Stage II crack growth that ends in failure, namely, r_s= (ΔK_th/Δσ_FL)²/π. An overall, threshold diagram is presented based on the simple criterion that, for sustained Stage II FCP, Δσ_s must be greater than Δσ_FL. The study is based on a simple continuum mechanics approach and its purpose is the investigation of the suitability of both ΔK and Δσ_s to characterise the crack driving force that activates complex fracture processes at the microstructure's scale. The investigation pertains to conditions that lead to the ultimate failure of the component at values of Δσ_s > Δσ_FL.     

A NEW METHOD FOR PREDICTING FATIGUE LIFE IN NOTCHED GEOMETRIES

The objective of this paper is to develop a notch crack closure model, called NCCM, based on plasticity-induced effects and short fatigue crack growth in the vicinity of the notch, and to predict the fatigue failure life of notched geometries. By using this model the regime for non-propagating cracks (n.p.c.) and the relationship between the fatigue strength reduction factor, Kf , and the elastic stress concentration factor, Kt , under mean stress conditions, can be determined quantitatively. A crack closure model is assumed to apply in the notch regime based on an approach developed to explain the crack growth retardation behavior observed in smooth specimen geometries after an overload. Notch plasticity effects are also applied in the NCCM model. Fatigue failure life is calculated from both short fatigue crack growth in the notch region where elastic–plastic fracture mechanics (EPFM) is applied and from long fatigue crack growth remote from the notch where linear elastic fracture mechanics (LEFM) occurs. This prediction is obtained using a quantity called the effective plasticity-corrected pseudo-stress. The NCCM can be used to account quantitatively for various observed notch phenomena, including both the relationship between Kf and Kt and n.p.c. The effects of the tensile mean stress on the Kf versus Kt relationship is investigated and leads to the little recognized but technologically important observation that mean stress conditions exist where Kf can be greater than Kt . The role of notch radius and tensile mean stress on n.p.c. behavior is also explored. The model is verified using experimental data for notch geometries of aluminum alloy 2024-T3, alloy steel SAE 4130 and mild steel specimens tested at zero and tensile mean stress.     

Fatigue crack growth simulation in heterogeneous material using s-version FEM

A fully automatic fatigue crack growth simulation system is developed using the s-version Finite Element Method (s-FEM). This system is extended to fractures in heterogeneous materials. In a heterogeneous material, the crack tip stress field has a mixed-mode condition, and the crack growth path is affected by inhomogeneous materials and mixed-mode conditions. Stress intensity factors (SIFs) in the mixed-mode condition are evaluated using the virtual crack closure method (VCCM). The criteria for the crack growth amount and crack growth path are based on these SIFs, and the growing crack configurations are obtained. At first, the basic problem is solved, and the results are compared with some results available in the literature. It is shown that this system gives an adequate accurate estimation of the SIFs. Then, two-dimensional fatigue crack growth problems are simulated using this system. The first example is a plate with an interface between hard and soft materials. The cracks tend to grow in soft materials through the interface. A second example is a plate with distributed hard inclusions. The crack takes a zig-zag path by propagating around the hard inclusions. In each case, the crack growth path changes in a complicated manner. Changes of the SIFs values are also shown and discussed.     

Consideration of the mechanical behaviour of small fatigue cracks

The mechanical behaviour of small fatigue cracks is investigated for a low, medium and high strength material. At first an elastic consideration is performed which give a good impression how the stress fields change with crack size. In part 2 a full elastic-plastic analysis of short cracks is performed using a new numerical scheme to simulate the growth of shear bands emanating from the crack tip. The influence of material and loading paramters as well as of the crack size on the plastic crack tip opening displacement is discussed. It is also investigated how it is possible to get a conservative estimate of the crack tip deformation at small cracks.     

Multiaxial fatigue of a short glass fibre reinforced polyamide 6.6 – Fatigue and fracture behaviour

The multiaxial fatigue behaviour of a short glass fibre reinforced polyamide 6.6 (PA66-GF35) is investigated on hollow tubular specimens in the range of fatigue lives between 10² and 10⁷ cycles. Fatigue experiments included pure tension, pure torsion, combined tension–torsion at different biaxiality ratios and phase shifting angles between the stress components. Tests were carried out with load ratio R = 0 and R = −1 at room temperature as well as at 130 °C. The influence of biaxiality ratio, phase angle between load components and load ratio is discussed.An extensive analysis of the fracture behaviour is performed on the specimens to recognise the crack nucleation and propagation mechanisms; failure modes were evaluated via optical and scanning electron microscopy.     

Fatigue crack growth resistance of ECAPed ultrafine-grained copper

This work presents the experimental results of fatigue crack growth resistance of ultrafine-grained (UFG) copper. The UFG copper has a commercial purity level (99.90%) and an average grain size of 300 nm obtained by a 8-passes route Bc ECAP process. The fatigue propagation tests are conducted in air, at load ratios R = K_min/K_max varying from 0.1 to 0.7, on small Disk Shaped CT specimens. Both stage I and stage II regime of growth rate are explored. Results are partially in contrast with the few experimental data available in the technical literature, that are by the way about high purity UFG copper. In fact, the present material shows a relatively high fatigue crack resistance with respect to the unprocessed coarse-grained alloy, especially at high values of applied stress intensity factor ΔK. At higher R-ratio a smaller threshold intensity factor is found, together with a lower stage II fatigue crack growth rate. The explanation of such crack growth retardation is based on a diffuse branching mechanism observed especially at higher average ΔK.     

疲劳强度的发展及任务

疲劳破坏很早就被人们注意。经过二百多年的工作,已形成了由材料、力学和机械等组成的边缘学科——疲劳强度,疲劳一般指室温下的高周疲劳,考虑了温度、腐蚀介质和受载方式等的环境因素,有不同机理的疲劳。疲劳强度的研究应微观和宏观结合,从标准式样试验到整机试验,从常规疲劳设计到现代疲劳设计,并随科学技术的发展,不断深入。     

Fatigue Investigations on Steel Pipeline Containing 3D Coplanar and Non-Coplanar Cracks

Fluctuated loadings from currents, waves and sea ground motions are observed on offshore steel pipelines, and they will result in small cracks to propagate continuously and cause unexpected damage to offshore/geotechnical infrastructures. In spite of the availability of efficient techniques and high-power computers for solving crack problems, investigations on the fatigue life of offshore pipelines with 3D interacting cracks are still rarely found in open literature. In the current study, systematic numerical investigations are performed on fatigue crack growth behaviours of offshore pipelines containing coplanar and non-coplanar cracks. Extended finite element method (XFEM) is adopted to simulate the fatigue crack growth. The qualitative validations of numerical results are made for certain cases with available experimental results. Parametric studies are conducted to investigate the influences of various important parameters on fatigue crack growth. The results will be helpful to assess the fatigue behaviours of steel pipeline with 3D interacting cracks.     

Influence of interface on fatigue threshold values in elastic bimaterials

This paper describes a study of the behavior of a fatigue crack growing in one elastic material and penetrating through the interface into a second material. The study aims especially to quantify the influence of the elastic mismatch of both materials on the threshold value of a fatigue crack propagating perpendicularly to the interface. Special attention is devoted to the case of a crack touching the interface. It is shown that the corresponding threshold value is strongly influenced by the existence of an interface between the two materials. A tentative procedure suggested in the paper makes it possible to quantify the effect and determine the dependence of the threshold value of a fatigue crack growing through the interface on the Dundurs parameters and β.

The results are applied to a body with a protective layer, and the corresponding fatigue threshold value for a crack with its tip at the interface is estimated. This makes it possible to decide whether the crack will stop at the interface or continue growing into the second material.

The results generally contribute to a better understanding of the failure of bi-material bodies and of structures with protective layers.     

Fatigue crack propagation in cellular metals

Two types of cellular metals were investigated: a closed-cell aluminium foam with a cell size of about 3.5 mm and densities ranging from 0.25 to 0.40 g/cm³ and hollow sphere structures made of a stainless steel (316L) with sphere sizes of 2 and 4 mm and a density of about 0.3 g/cm³. Fatigue and fatigue crack propagation tests were performed on these materials using an electro-dynamic resonance fatigue testing machine. The crack extension was monitored by a potential drop technique. Additionally, investigations were carried out inside the scanning electron microscope (SEM) using an in situ loading device. All tests were accompanied by local deformation measurements and fracture surface analyses. From the fatigue crack propagation tests it is evident that these materials show a relatively high Paris-Exponent m in the range of 6 to 25 compared to common ductile solid metals. Additional tests were performed to estimate the influence of crack closure, crack bridging and micro cracking on the da/dN versus ΔK curve for these materials. The in situ fatigue tests and the fracture surface analyses revealed a difference in the fatigue crack propagation mechanisms between the closed-cell foam and the hollow sphere structure: in the closed-cell foam a contiguous fatigue crack can be found, where in the case of the hollow sphere structure the fatigue crack propagation is concentrated in the vicinities of the sintering necks.     

Fatigue growth of short cracks in Ti-17: Experiments and simulations

The fatigue behaviour of through thickness short cracks was investigated in Ti-17. Experiments were performed on a symmetric four-point bend set-up. An initial through thickness crack was produced by cyclic compressive load on a sharp notch. The notch and part of the crack were removed leaving an approximately 50 μm short crack. The short crack was subjected to fatigue loading in tension. The experiments were conducted in load control with constant force amplitude and mean values. Fatigue growth of the short cracks was monitored with direct current potential drop measurements. Fatigue growth continued at constant R-ratio into the long crack regime. It was found that linear elastic fracture mechanics (LEFM) was applicable if closure-free long crack growth data from constant K_Imax test were used. Then, the standard Paris’ relation provided an upper bound for the growth rates of both short and long crack.The short crack experiments were numerically reproduced in two ways by finite element computations. The first analysis type comprised all three phases of the experimental procedure: precracking, notch removal and fatigue growth. The second analysis type only reproduced the growth of short cracks during fatigue loading in tension. In both cases the material model was elastic-plastic with combined isotropic and kinematic hardening. The agreement between crack tip opening displacement range, cyclic J-integral and cyclic plastic zone at the crack tip with ΔK_I verified that LEFM could be extended to the present short cracks in Ti-17. Also, the crack size limits described in the literature for LEFM with regards to plastic zone size hold for the present short cracks and cyclic softening material.     

A model for short crack propagation in polycrystalline materials

A model for microstructurally short crack propagation in a grain structure of a polycrystalline material is developed. The crack propagation model is based on a crystal plasticity model and a microstructurally short crack propagation model in the spirit of the model by Navarro and de los Rios [A model for short fatigue crack propagation with an interpretation of the short-long crack transition. Fatigue Fract Eng Mater Struct 1987;10:169-86]. Numerical examples, where the combined crystal plasticity and crack propagation model is implemented in a model of a microstructure representing a duplex stainless steel, concludes the paper. Results showing how the misorientation of the crack- and slip-directions between two adjacent austenitic grains influences the crack propagation rate, as the crack propagates across their common grain boundary, are given.     

Fatigue crack growth behavior of X2095 Al–Li alloy

Microstructures and micro-textures of X2095 Al–Li alloy in as-received/superplastic state were characterized by means of SEM/BDS, X-ray diffraction and orientation imaging microscopy (OIM). It was observed that the microstructure of the alloy was typical of a particulate-reinforced composite material, consisting of aluminum matrix and homogeneously distributed T_B(Al₇Cu₄Li) particles with a volume fraction of about 10%. Brass-type texture was the dominant texture component. Both constant amplitude and near-threshold fatigue crack growth rates of the alloy in the L–T and T–L orientations were determined at different stress ratios. Particular attention was paid to the role of the T_B phase in the fatigue crack growth. When a fatigue crack approached a T_B particle, the crack basically meandered to avoid the particle. The T_B particles thus provided a strong resistance to the propagation of fatigue crack by promoting crack deflection and the related crack closure effects. The fatigue crack propagation behavior has been explained by the microstructural features, micro-textures, cracking characteristics and crack closure effects.     

Density Evolution of the Surface Short Fatigue Cracks of 1Cr18Ni9Ni Pipe—Weld Metal

The evolutionary density and the scatter of densities of the short fatigue cracks on the surface of 1 Cr18Ni9Ti pipe-weld metal were observed by local and overall viewpoints,respectively.The local viewpoint ,which is in accordance with a so-called “effectively short fatigue crack criterion“,paid attention to the dominant effective short fatigue crack (DESFC) initiation zone and the zones ahead of the DESFC tips.The overall viewpoint focused on the whole test piece of specimen.The results revealed that the density and scatter evolution exhibited a significant character of microstructural short crack and physical short crack stages.The evolutionary behavior by the local viewpoint was sensitive to the increase of DESFC size and tip location.The mechanism of the short crack growth associated with the general test observations that the DESFC acted gradually as a long crack and the scatter of DESFC growth rates tended gradually to that of a long crack was well revealed.Intrinsic causes of the random cyclic strain-life relations and stress-strain responses are appropriately given.In contrast ,the evolutionary behavior by the overall viewpoint was non-sensitive and violated the general test observations.Therefore,the intrinsic localization and randomization of material evolutionary fatigue damage should be more appropriately revealed from the observations by the local viewpoint.     

Density Evolution of the Surface Short Fatigue Cracks of 1Cr18Ni9Ti Pipe-Weld Metal

The evolutionary density and the scatter of densities of the short fatigue cracks on the surface of 1Cr18Ni9Ti pipe-weld metal were observed by local and overall viewpoints, respectively. The local viewpoint, which is in accordance with a so-called "effectively short fatigue crack criterion", paid attention to the dominant effective short fatigue crack (DESFC) initiation zone and the zones ahead of the DESFC tips. The overall viewpoint focused on the whole test piece of specimen. The results revealed that the density and scatter evolution exhibited a significant character of microstructural short crack and physical short crack stages. The evolutionary behavior by the local viewpoint was sensitive to the increase of DESFC size and tip location. The mechanism of the short crack growth associated with the general test observations that the DESFC acted gradually as a long crack and the scatter of DESFC growth rates tended gradually to that of a long crack was well revealed. Intrinsic causes of the random cyclic     

疲劳裂纹扩展预测模型及其应用

在分析了灰色预测方法和支持向量机各自的优缺点基础上,提出了将二者相结合的一种新的预测模型———灰色支持向量机裂纹扩展预测模型.新模型发挥了灰色预测方法中"累加生成"的优点,弱化了原始序列中随机扰动因素的影响,增强了数据的规律性,同时避免了灰色预测方法及模型存在的理论缺陷.工程实例表明,文章所提出的裂纹扩展预测模型较传统的GM(1,1)模型、等维GM(1,1)模型精度都有所提高,为预测疲劳裂纹扩展提供了一种新的方法.