Steady-state Fatigue Crack Growth Research Articles

An inverse method to reconstruct crack-tip cohesive zone laws for fatigue by numerical field projection

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loadings, but the functional form of such phenomenological models does not have a strong micromechanical basis. While numerical techniques have been developed to extract the crack-tip cohesive zone law for monotonic fracture from experimental strain information, elucidating the unloading-reloading hysteresis representing accumulated and irreversible damage under fatigue cycling is still challenging. Here, we introduce a novel field projection method (FPM) to reconstruct the cohesive zone laws for steady-state fatigue crack growth from elastic strain field information at various loading and unloading stages within a single steady-state fatigue cycle. The method is based on the Maxwell-Betti’s reciprocal theorem, which considers the material response to be linear elastic during loading and unloading, albeit with a reciprocity gap to account for the inhomogeneous residual elastic strain accumulated at the end of each fatigue cycle. Through numerical experiments, we demonstrate that this FPM is capable of accurately extracting the crack-tip cohesive tractions and separations, along with the elusive unloading-reloading hysteresis, which constitute the cohesive zone law for fatigue crack growth. We discuss the errors and uncertainties associated with this inverse approach.

Fatigue crack growth behavior of the quaternary 3d transition metal high entropy alloy CoCrFeNi

CoCrFeNi, a 3d transition metal high entropy alloy, has shown promising mechanical and corrosion resistance properties. CoCrFeNi was subjected to tension–tension fatigue at room temperature and the steady-state fatigue crack growth characteristics and underlying deformation mechanisms were investigated. CoCrFeNi exhibited good steady-state fatigue crack growth resistance with the Paris law exponent at the lower end of the ductile metals range, m ≈ 2.5, regardless of load ratio. TEM analysis performed at different locations revealed that the plastic deformation mechanism changed from dislocation slip to the addition of nano-twinning as ΔK increased over crack life.

Fatigue crack growth parameters of Laser Powder Bed Fusion produced Ti-6Al-4V

The value of fatigue predictive NASGRO models hinges on the quality of established parameters to describe the behaviour of the subject material. To establish these parameters for laser powder bed fusion (LPBF) produced Ti-6Al-4V the influence of process inherent microstructure, residual stress, and orientational dependant mesostructure needs to be considered. Examining near-threshold in combination with steady-state fatigue crack growth rates (FCGR's) offers insight into the impact of crack closure in the NASGRO formulation. This study investigates the influence of microstructure, residual stress and orientation of LPBF produced Ti-6Al-4V on establishing parameters for NASGRO models from a foundational perspective. Near-threshold crack growth rate data from Compact Tension (CT) coupons built in three orientations and as-fabricated (AF), stress-relieved (SR) and duplex annealed (DA) state are considered. Optical and scanning electron micrographs are used to consider morphological features. Results show anisotropy in material constraint, used in describing crack closure, between orientations in AF and SR state, lending to unique consideration for each orientation. DA is shown to relieve this effect. Overall, this study establishes and demonstrates the importance of uniquely considering NASGRO parameters for LPBF produced Ti-6Al-4V.

Environmentally Assisted Cracking of Subsea Pipelines in Oil & Gas Production Environments—Effect of Static Loading

Fatigue crack growth rate of line pipe steels in sour environments typically exhibits a steady-state value at low frequencies. However, in highly inhibited sour environments, there is no evidence of a steady-state fatigue crack growth at low frequencies. This is likely a result of static crack growth rate at Kmax. Stable static crack growth measured under constant stress intensity factor (K) conditions in inhibited sour environments was in the range of 10−7 mm/s to 10−8 mm/s. The crack growth rate in inhibited sour environments is likely associated with crack tip processes associated with metal dissolution/film formation and associated hydrogen evolution. The results obtained were modeled based on a crack tip strain rate based approach, where the rate limiting step was the metal dissolution/FeS formation and the corresponding hydrogen generation reaction.

Microstructural optimization through heat treatment for enhancing the fracture toughness and fatigue crack growth resistance of selective laser melted Ti[sbnd]6Al[sbnd]4V alloy

The yield strength (σy) of Ti6Al4V alloy, additively manufactured via selective laser melting (SLM) of powder beds, can exceed 1000 MPa while possessing a mode I fracture toughness (KIc) of ∼50 MPam. The possibility of enhancing KIc as well as fatigue crack growth resistance, without a significant penalty on σy, via a judicious heat treatment process that transforms martensitic α’, which is present in the as-SLM microstructure due to rapid cooling of the molten metal, into an α/β phase mixture is examined. It was demonstrated that duplex annealing at temperatures below the β transus temperature of the alloy would lead to such a microstructure while retaining the mesostructure, whose nature depends on the process parameter combinations utilized. Near-doubling of the fracture toughness with only a ∼20% reduction in σy was noted upon heat treatment. While the strength becomes isotropic after heat treatment, significant anisotropy in the fracture toughness of the heat-treated alloy with columnar prior β structure was noted. While the steady state fatigue crack growth (FCG) rates are comparable to corresponding values of the same alloy, but manufactured using conventional means, the threshold for fatigue crack initiation (ΔK0) increases by 34%–56%. The enhancement in ΔK0 was found to be a result of the transition in the near-threshold crack growth, from trans-to inter-granular and caused by the α/β basket weave microstructure, which imparts a high crack path tortuosity. Overall, this study demonstrates that post-processing heat-treatment can improve the damage tolerance of SLM Ti64 by increasing both KIc and ΔK0.

Plastic strain gradients and transient fatigue crack growth: A computational study

Fatigue crack growth is analyzed for steady state and overload conditions. The model combines an elastic-plastic strain gradient hardening material and an irreversible cohesive zone model. Plastic strain gradients are found not to affect steady-state fatigue crack growth but play a key role in the overload response. Plastic strain gradient hardening lowers plastic strain magnitudes and alters the spatial distribution of plastic strain. This leads to reduced crack closure and higher crack growth rates during and after the overload. Using classical plasticity alone to describe fatigue crack growth following an overload is thus nonconservative.

Micro-and meso-structures and their influence on mechanical properties of selectively laser melted Ti-6Al-4V

The tensile properties, mode I fracture toughness (KIc), fatigue crack growth behavior, and unnotched fatigue strength of additively manufactured Ti-6Al-4V (Ti64) alloy using selective laser melting (SLM) technique were investigated. Four different combinations of layer thickness (t) - scan rotation between successive layers (ϕ), which resulted in mesostructures that range from through-thickness columnar prior β grains with square cross-sections, whose side lengths equal to the scan spacing, to near-equiaxed mesostructures in both build and transverse directions, were explored. Possible anisotropy in mechanical properties was investigated by conducting tests on samples whose loading axis is either parallel or perpendicular to the build directions. In all cases, the microstructure consisted of fine α/α′ lath structure, where α′ is the metastable martensitic Ti phase that is acicular in shape, within the prior β grains. Experimental results show that the process parameter combinations of t = 60 μm and ϕ = 67° results in an alloy that exhibits high yield strength (>1100 MPa) and ductility (>12%) simultaneously, KIc of 58 MPa m , and unnotched fatigue strength, which is similar to that of the same alloy but manufactured using conventional techniques. The anisotropy in properties, overall, was found to be not substantial, even in the case where columnar growth of prior β grains occurs in the build direction. The values of the Paris exponents for steady state fatigue crack growth (FCG) are much lower than those reported for conventionally manufactured Ti64, suggesting higher FCG resistance in SLM Ti64. Analysis of the effective microstructural length scale that controls the near-threshold FCG rate suggests that it is the colony size that dominates this behavior. Overall, the results of this study indicate directions for process parameter optimization that would lead to SLM Ti64 that is not only has high strength, but also is damage tolerant.

Fatigue Crack Propagation and Fracture Toughness of Laser Rapid Manufactured Structures of AISI 316L Stainless Steel

Fatigue crack propagation, fracture toughness, and impact toughness of AISI 316L stainless steel fabricated by laser rapid manufacturing with a continuous wave CO2 laser have been systematically studied. Charpy impact toughness of laser rapid manufactured structures was found to be on par with its wrought counterpart. Steady state fatigue crack growth rate in laser rapid manufactured compact tension specimens of AISI 316L stainless steel, in the investigated stress intensity range (ΔK) of 11.4–24 MPa √m, was comparable to that of 20% cold worked wrought AISI 316 stainless steel. Fatigue crack propagation was found to be transgranular in nature. The initiation fracture toughness (J 0.2) was found to be in the range of 147–259 kJ/m2 while critical crack tip opening displacement (CTODc) fracture toughness values were found to be in the range of 0.5–0.64 mm. Fracture toughness values of laser rapid manufactured structures, although inferior to wrought 316 stainless steel, were comparable to that of its weld metal.

A numerical procedure for simulating delamination growth on interfaces of interconnect structures

A fracture mechanics based numerical approach is developed for modeling delamination growth on materials interfaces in integrated circuit (IC) interconnects. In this approach, the heterogeneous interconnect structures neighboring the cracked interface are approximated by homogenized layers with transversely isotropic elastic properties. Evolution of the interface crack under fatigue condition is modeled by using an incremental approach, in which the fracture mechanics parameters including the strain energy release rate, the normalized stress intensity factors and phase angles are first estimated by post-processing finite element solutions. The fracture mechanics parameters along the curvilinear front of the interface crack are then substituted into a steady-state fatigue crack growth model for obtaining the crack growth increments. The process is repeated to simulate subsequent crack growth for predicting interconnect structural reliability under fatigue condition. The evolution of an interface corner crack in a back-end-of-line (BEOL) Cu/low-k interconnect structure under temperature cycling condition is considered as an application example of the procedure.

Microstructural study of fatigue and dwell fatigue crack growth behaviour of ATI 718Plus alloy

A new superalloy, ATI 718Plus alloy (718Plus), has been developed to have a 55°C higher temperature capability over the traditionally used alloy 718, while maintaining favourable processing characteristics and intrinsic raw material costs. The fatigue and dwell fatigue behaviour of four microstructural variations of 718Plus are evaluated and compared with Waspaloy: standard heat treated condition (HT1), standard heat treated condition with thermal exposure at 732°C (1350°F) for 1000 h (HT2), fine grain condition with a modified δ phase (HT3) and fine grain overaged through modified heat treatment (HT4). Fatigue crack growth rate tests were performed at 649°C (1200°F) and 704°C (1300°F) under constant amplitude loading at 10 Hz or with a 100 s tension dwell. The results show that the steady state fatigue crack growth rates of each microstructural variation and both alloys are identical, with all of the 718Plus variations showing a clear advantage over Waspaloy in the fatigue crack threshold regime. The 718Plus variants HT1 and HT3 exhibited the highest fatigue crack growth threshold, followed closely by HT4 and finally HT2. At 649°C (1200°F), the 718Plus alloys had average threshold values ranging from 8·8 to 10·4 MPa m1/2 whereas the Waspaloy material was 6·1–7·5 MPa m1/2. At 704°C (1300°F), the advantage increased with the 718Plus alloys having average threshold values ranging from 10·1 to 11·6 MPa m1/2 compared with Waspaloy, which exhibited average threshold values of 6·6–7·7 MPa m1/2. Dwell fatigue results show that Waspaloy has better resistance to crack propagation under dwell conditions; however, optimisation of the precipitate phase (HT2) shows vast improvement in the dwell fatigue resistance of 718Plus.On a développé un nouveau superalliage, l’alliage ATI 718PlusÒ (718Plus), afin qu’il soit capable de supporter une température de 55°C plus élevée par rapport à l’alliage 718 utilisé traditionnellement, tout en maintenant des caractéristiques favorables de traitement et les coûts intrinsèques de métal brut. On évalue, et compare au Waspaloy, le comportement de fatigue et de pause-fatigue de quatre variations de microstructure du 718Plus. 1) Condition de traitement thermique standard (HT1); 2) condition de traitement thermique standard avec exposition thermique à 732°C (1350°F) de 1000 heures (HT2); 3) condition à grain fin avec une phase d modifiée (HT3); 4) grain fin avec vieillissement artificiel au moyen d’un traitement thermique modifié (HT4). On a effectué des essais de vitesse de croissance de fissure de fatigue à 649°C (1200°F) et à 704°C (1300°F) sous une charge à amplitude constante à 10 Hz ou avec une pause en traction de 100 secondes.Les résultats montrent que les vitesses de croissance de fissure de fatigue en régime permanent de chaque variation microstructurale et des deux alliages étaient identiques, alors que toutes les variations du 718Plus montraient un avantage clair sur le Waspaloy lors du régime seuil de fissure de fatigue. Les variantes HT1 et HT3 du 718Plus exhibaient le seuil de croissance de fissure de fatigue le plus élevé, suivies de près par HT4 et finalement par HT2. À 649°C (1200°F), les alliages 718Plus avaient des valeurs moyennes de seuil allant de 8·8 à 10·4 MPa-m1/2 alors que pour le matériau de Waspaloy, elles variaient de 6·1 à 7·5 MPa-m1/2. À 704°C (1300°F), l’avantage augmentait, les alliages 718Plus ayant des valeurs moyennes de seuil allant de 10·1 à 11·6 MPa-m1/2 comparés au Waspaloy, lequel exhibait des valeurs moyennes de seuil de 6·6 à 7·7 MPa-m1/2. Les résultats de pause-fatigue montrent que le Waspaloy a une meilleure résistance à la propagation de fissure sous des conditions de pause; cependant, l’optimisation de la phase de précipité (HT2) montre une vaste amélioration de la résistance à la pause-fatigue du 718Plus.

A comparison of fatigue crack growth in resin composite, dentin and the interface

Objectives The objective of this in vitro study was to evaluate the fatigue crack growth properties of the dentin/resin adhesive interface. Methods Compact tension (CT) specimens were prepared from coronal dentin, resin composite, and dentin bonded to resin composite using Optibond Solo Plus adhesive. All specimens were then subjected to cyclic Mode I loading while fully hydrated at a stress ratio of R = 0.1 and frequency of 5 Hz. Steady state fatigue crack growth was modeled using the Paris Law in terms of the exponent ( m) and coefficient ( C). Results The average fatigue crack growth rates in the resin composite ranged from 1.6E−06 to 3.8E–05 mm/cycle with growth occurring over a stress intensity range from 0.40 to 0.77 MPa m 1/2; the average growth exponent was 6.9 ± 3.1. Average fatigue crack growth rates for the dentin/resin interface specimens ranged from 5.5E−07 to 6.4E−03 mm/cycle with growth occurring over a stress intensity range from 0.37 to 0.64 MPa m 1/2. The Paris Law exponent for these specimens ranged from 16 ≤ m ≤ 25. Fatigue crack growth at the interface occurred primarily in the adhesive resin and at the adhesive–dentin interface. In addition, many of the dentin/resin specimens underwent unstable fracture at a comparatively low stress intensity range without undergoing cyclic crack growth. Significance The dentin/resin adhesive interface proved to be significantly more sensitive to fatigue crack growth than either dentin or resin composite. Variation in the cyclic crack growth responses of the dentin/resin interface specimens suggests that the interface, and particularly the adhesive resin, exhibits lower resistance to crack initiation and growth in comparison to dentin.

Modeling of facesheet crack growth in titanium–graphite hybrid laminates. Part II: Experimental results

Titanium–graphite hybrid composite laminates exhibit a coupled damage growth mode of facesheet cracking and delamination. Part I of this work modeled the growth of the coupled damage mode. Fatigue experiments were conducted on single edge notch tension specimens to measure the crack growth rate. This paper compares the model predictions with experimental data. The three-dimensional finite element model successfully captured the damage growth behavior for two of the lay-ups ([Ti/0/90/0 2] s and [Ti/90/0/90 2] s) in the experimental program. However, in a third lay-up, [Ti/0/90/±30] s, the underlying damage modes were found to be sufficiently different than the other two lay-ups and the model did not capture the steady-state growth behavior. The effects of temperature and specimen size were also investigated for TiGr laminates. Except for the effects of the load ratio, elevated temperatures did not affect the crack growth rate significantly. For wider specimens, the steady-state fatigue crack growth behavior was similar to the narrow specimens, indicating that the steady-state facesheet crack growth behavior is independent of specimen size.

The effect of hold-time on fatigue crack growth behaviors of WASPALOY alloy at elevated temperature

The effect of hold-time on fatigue crack growth behaviors of WASPALOY alloy was investigated. It was found that the role of hold-time depends on the competition between the harmful environmental effect and the beneficial effect of creep. If temperature is not higher than 705 °C, fatigue crack growth rate of WASPALOY alloy increases with hold-time. On the contrary, hold-time plays a beneficial role on steady state fatigue crack growth of WASPALOY alloy at 760 °C and lower stress intensity factor. The beneficial effect of hold-time was attributed to the creep caused stress relaxation during the hold-time. However, accumulated creep damages cause to cavity nucleation and growth at the grain boundaries, and then accelerate fatigue crack growth. Hold-time plays a harmful role during the final stage of fatigue crack growth.

Analysis of overload effects and related phenomena

Overloads and underloads perturb steady state fatigue crack growth conditions and affect the growth rates by retarding or accelerating the growth. Clear understanding of these transient effects is important for the reliable life prediction of a component subjected to random loads. The overload effects have predominately been attributed to either plasticity induced crack closure behind the crack tip, residual stresses ahead of the crack tip, or a combination of both. These effects are critically examined in the context of the Unified Approach proposed by the authors. Recent experimental and analytical evaluation of crack closure has confirmed its negligible contribution to crack growth and has demonstrated that changes in the stresses ahead of the crack tip are more important than closure behind the crack tip. It is shown that the overload effects and other transient effects arise due to perturbation of the stresses ahead of the crack tip, and these can be accounted for by the two parametric approach emphasized in the unified theory. It is shown that related phenomena including the role of K max, the existence of propagation threshold K pr, and effects of overloads on K pr and K max etc, are all accounted for by the Unified Approach.

Fatigue crack growth in ferroelectric ceramics below the coercive field

Perovskite-type ferroelectric ceramics have found many applications in actuators, sensors and memories. One critical limitation on their performance is due to electric fatigue, which refers to the deterioration of material properties associated with electric cycling. The degradation of electrical properties in ferroelectrics, which appears in the hysteresis loop in the form of a decrease of remanant polarization and an increase of the coercive field, is a serious concern in application [1]. Due to a strong electro-mechanical coupling effect, an electrical field may also degrade the mechanical properties of ferroelectrics. The performance of ferroelectric ceramics in smart structures is often hampered by the cracks propagating in the devices [2]. It is essential to characterize the failure behavior of ferroelectric ceramics when subjected to a cyclic electric field. Cao and Evans [3] first attacked the issue of electrical field– induced fatigue crack growth. They reported that the growth of indented cracks was governed by the magnitude of an applied electrical field Ea relative to the coercive field Ec: When Ea≤ 0.9Ec, there was only a minor amount of growth (about 50 μm), and then the crack arrested; when Ea≥ 1.1Ec, the crack continued to grow and settled into a steadily growing state. They concluded that the fatigue effect occurred only at fields above the coercive field. For Ea<Ec, however, the intensified electric field near the flaw may exceed the coercive field. The electrical field concentration may cause local degradation. The analysis by Zhu and Yang [4] indicated that, for Ea<Ec, steady-state fatigue crack growth could be induced due to the effect of electrical field–induced domain switching at the crack tip. We report here a detailed experimental study of electrical field–induced crack growth for ferroelectrics under an electrical field below the coercive field. In the experiment, a long-focal-length optical microscope was used to observe the crack propagation process. Optical micrographs were taken to show crack growth associated with each electrical field reversal. The reported experimental phenomenon was interpreted in terms of the domain switching model. The material used for the experiment was PZT-5 provided by the Institute of Acoustics, Chinese Academy of Science. The material has a tetragonal crystal structure at room temperature and an average 3 μm grain size. Specimens were cut to dimensions of 4× 2× 15 mm. Gold electrodes were sputtered onto the opposing 2× 15 mm faces. The side faces were polished with 7, 5, 3.5 and 1μm grain-sized diamond abrasive pastes. The specimens were poled at 130 ◦C with a poling direction along the 4 mm dimension. The specimens were poled for 0.5 h under an electrical field of 2 kV/mm. To get the coercive field, Ec, the polarization hysteresis loop was measured as a function of the electrical field. The electric displacement was monitored using the Sawyer–Tower circuit. The measured ferroelectric hysteresis loop is shown in Fig. 1. The coercive field Ec is 1100 V/mm. The Vickers indentation technique was used to introduce the initial cracks in the electrical fatigue test. A Vickers indenter was placed in the center of the polished 4× 15 mm surface with a load of 29.4N. This created a square pyramid-shaped indentation with cracks emanating from the corners. The poled ferroelectric ceramics exhibited fracture toughness anisotropy [5]. The crack perpendicular to the poling direction was much longer than the crack parallel to it. Denoting c as the measured crack length (from one corner of the indentation to the tip of the crack), the fracture toughness of the ferroelectric ceramics can be expressed as [6]

Corrosion fatigue of a 2024-T3 aluminum alloy in the short crack domain

It is well accepted that the steady-state fatigue crack growth rates of long cracks depend uniquely on AK for a fixed load ratio R and test environment. Anomalous growth behavior of short cracks in either inert or deleterious environments that has been reported [1-7], however, calls into question the validity of using only long-crack results in evaluating the service life of a structural component and argues for the need for considering the effects of crack size. Crack-size effects have been extensively studied from the perspectives of mechanical, metallurgical and chemical principles. Microstructurally and mechanically short cracks [1-3] are associated with the influences of fine-scale microstructure, the limitation of continuum mechanics (or LEFM-linear elastic fracture mechanics), or crack closure. Chemically short cracks [4-7], on the other hand, normally extend to longer lengths and are attributed to the differences in local crack-tip chemistry (e.g., pH, [Oz], potential) between the long and short cracks and also, perhaps, from the bulk solution. The objective of this study is to explore the effect of crack size in various environments and to identify the key variables that affect crack growth behavior. The crack size investigated herein was chemically short but microstructurally and mechanically long. A 1.6 mm thick 2024-T3 (bare) aluminum alloy was used and its chemical composition (in wt%) is as follows: 4.24 Cu, 1.26 Mg, 0.65 Mn, 0.15 Fe, 0.08 Zn, 0.06 Si, 0.031 Ti, <0.01 Cr and balance A1. The elongation, 0.2% offset yield strength and tensile strength are 17.0%, 355 MPa (51 ksi) and 480 MPa (70 ksi), respectively. The specimens were cut in the L-T orientation as dog-bone shaped, center-pin-loaded, single-edge-cracked specimens with a 31.75 mm wide and 76.2 mm long (final dimension) mid-section. A 1.6 mm long electro-discharge machined (EDM) starter notch was introduced at the center of one edge of each specimen. The specimens were precracked by fatigue in air to a crack length of 3.42 mm (including the notch). Extra material (2.92 mm wide) was included on the notched side, and was removed by EDM to produce the final specimen, with a symmetrical test section and an approximaely 0.5 mm long edge crack. The following K calibration equation was used:

Empirical Formulations for the Analysis and Prediction of Trends for Steady-State Fatigue Crack Growth Rates

AbstractThe general characteristics of steady-state fatigue crack growth rates are discussed. An empirical formulation is described where two constants form a basic crack growth rate versus maximum stress intensity Kmax curve, which is a straight line on a log-log graph. The constants that form the base curves for various materials are correlated to Young's modulus. A third parameter that is sensitive to material alloy and environment is described and methods for obtaining this value are presented. Crack growth rate data for several stress ratios can then be projected to the basic modulus-dependent curve, where straight line scatter bands and statistical information pertaining to the overall accuracy of the formulations can be determined.