Time-dependent Crack Growth Research Articles

Time-dependent subcritical crack growth and its mechanism in Ni-based single crystal superalloys at 500 °C

The subcritical crack growth behavior under sustained loading and its microscopic mechanism in <100> oriented single crystal (SC) Ni-based superalloys subjected to a relatively low temperature condition (500 °C) are critically investigated. An evident time-dependent crack growth (TDCG) phenomenon is observed even at such a temperature condition, but its rate (da/dt) is significantly small and weakly dependent on the crack length, i.e. the stress intensity (K) value. The cross-sectional observation of a crack tip region by electron microscopy (SEM/TEM), together with the conventional fractography, reveals the following points: the macroscopic crack path shows pronounced branching influenced by the {100} planes; most dislocations in the γ’ phase near the crack tip are rectilinearly aligned and locked on the {100} planes; the crack tip dislocations provide the microscopically preferable oxidation paths. These points strongly suggest that the dislocation-mediated micro-oxidation process plays a major role in the observed anisotropic TDCG mechanism that eventually leads to the anomalous da/dt - K property.

Sensitivity of crack-growth lives to sustained thermal gradients

This paper investigates the effect of path-dependent material properties on predicted crack-growth lives with material properties set at the instantaneous crack-tip location. Specifically, we focus on cracks advancing through thermal gradients with temperature-dependent crack-growth properties. Here, material properties that describe fatigue crack growth under cyclic load and time-dependent crack growth under sustained load have been set to capture the response of the high-temperature alloy ME3. This study investigates the effect of peak temperature, peak stress, temperature gradient, hold time, and time to reach full loading. To perform this investigation, we design a simple example problem that captures key features of fatigue crack growth without introducing unnecessary complexity. Results indicate that increasing lives are associated with lower crack-tip temperatures due to cooling thermal gradients that reduce crack growth per cycle. Furthermore, these results reveal minimal impacts on lives for temperatures with negligible time-dependent crack growth, and larger increases in lives are expected for cracks with more appreciable time-dependent crack growth. Designers may employ these ideas to extend useful lives of applications with strong spatial gradients in the material response, e.g., recent efforts to design internal cooling passages into gas-turbine engines using additive manufacturing.

Numerical 3D‐bifurcation analysis of star‐shaped crack patterns using the energy method

AbstractThe present research deals with a three‐dimensional (3D) Finite Element Method (FEM) bifurcation analysis based on the global mechanical potential that can be used to find the parameters at which a crack pattern changes. In our case we want to analyze at which point the star‐shaped shrinkage cracks in an aqueous colloidal suspension filled in a glass cylinder change from four to three or two cracks growing. The driving force for the crack growth is shrinkage caused by diffusion controlled drying. The 3D crack front geometry is described efficiently by using a Fourier series approach. Based on steady‐state crack growth, the Fourier coefficients are determined in a first step using an optimization algorithm. As a result, the time dependent crack growth can be determined. In a second step, the bifurcation point is determined by an eigenvalue analysis of the second order derivatives of the potential energy of the system. If the lowest eigenvalue reaches zero the fundamental solution becomes unstable and a transition will occur. Our analysis shows that the transition from four to two cracks is preferred over the transition from four to three cracks.

Time-dependent crack growth mechanism in Ni-based single crystal superalloys at high-temperature

The microscopic mechanism of time-dependent crack growth (TDCG) in single crystal (SC) Ni-based superalloys under a relatively high-temperature condition (900 °C) is critically investigated. Two alloy types are compared: alloy A containing 3% rhenium (Re) and alloy B containing no Re. With an initial stress intensity (K) value of 40 MPam1/2, both alloys show similar two step TDCG, i.e. a steady stage followed by an acceleration stage. The total life to failure (tf) of alloy B is, however, an order of magnitude shorter than alloy A. In addition to the conventional fractography, cross-sectional analyses (EBSD and EDS) are also conducted for an interrupted crack tip. Two distinct fracture modes are then identified in both alloys: {111}<112> twin-induced shear fracture and non-crystallographic fracture along dendrite boundaries. The twin systems observed are the secondary ones having a relatively smaller Schmid factor compared to the primary ones that remain inactive under the <100> tension. In the case of alloy A, the twin induces local phase transformation involving TCP precipitation, decomposition of γ (Ni)/γ’ (Ni3Al) structure and recrystallization, which eventually enhances local ductility and dominates the crack growth rate. In the case of alloy B, the macroscopic appearances of these fracture modes are much the same, but they are significantly facilitated by micro-voids formed exclusively in γ channel whose stability is much lower than that in alloy A. The apparently brittle TDCG nature of alloy B compared to alloy A can be interpreted as an enhanced localization of plasticity at the crack tip.

The Effect of Unloading Path on the Time-Dependent Behavior of Beishan Granite

Abstract Understanding the time-dependent characteristics of Beishan granite after excavation is critically important for the long-term stability and disaster control of the high-level radioactive waste repository. In this context, a series of creep tests under different unloading paths are designed to simulate the time-dependent behavior of rock mass after excavation. Results show that the instantaneous volume deformation under each loading step is greatly influenced by the unloading path. Moreover, the unloading path has minor effects on the creep strain. The axial and lateral creep strain is dominated by creep fracture potential, which can be characterized by a unified time-dependent fracture potential index (ξTFPI) for different stress states. It is observed that the creep strain generally increases with increasing ξTFPI. In order to describe the fracture mechanism during the creep process, a damage mechanical model based on time-dependent subcritical crack growth theory is adopted. It reveals that the strain hardening behavior dominates the granite creep process, and the strain softening effect is gradually strengthened with increasing ξTFPI.

Micromechanics of Void Nucleation and Early Growth at Incoherent Precipitates: Lattice-Trapped and Dislocation-Mediated Delamination Modes

The initial stages of debonding at hard-particle interfaces during rupture is relevant to the fracture of most structural alloys, yet details of the mechanistic process for rupture at the atomic scale are poorly understood. In this study, we employ molecular dynamics simulation of a spherical Al2Cu θ precipitate in an aluminum matrix to examine the earliest stages of void formation and nanocrack growth at the particle-matrix interface, at temperatures ranging from 200–400 K and stresses ranging from 5.7–7.2 GPa. The simulations revealed a three-stage process involving (1) stochastic instantaneous or delayed nucleation of excess free volume at the particle-matrix interface involving only tens of atoms, followed by (2) steady time-dependent crack growth in the absence of dislocation activity, followed by (3) dramatically accelerated crack growth facilitated by crack-tip dislocation emission. While not all three stages were present for all stresses and temperatures, the second stage, termed lattice-trapped delamination, was consistently the rate-limiting process. This lattice-trapped delamination process was determined to be a thermally activated brittle fracture mode with an unambiguous Arrhenius activation energy of 1.37 eV and an activation area of 1.17 Å2. The role of lattice-trapped delamination in the early stages of particle delamination is not only relevant at the high strain-rates and stresses associated with shock spallation, but Arrhenius extrapolation suggests that the mechanism also operates during quasi-static rupture at micrometer-scale particles.

Modeling and effect analysis on crack growth behavior of Hastelloy X under high temperature creep-fatigue interaction

The crack growth behavior of Hastelloy X under creep-fatigue interaction at high temperature is investigated by a nonlinear creep-fatigue interaction damage model. Multiaxial stress is considered both in the fatigue and creep damage models. The effect of the variance of fatigue damage parameters is analyzed in a quantitative method and some linear effects were observed. The influence of hold time, crack depth ratio and load level on the crack growth behavior are studied and results under different hold time indicate that the increase of hold time, crack depth ratio and load level enhances the creep damage and accelerates the time-dependent crack growth rate. When the hold time varies from 1 to 60 min, the creep damage always dominates the damage accumulation, which can explain the overlap of the curves between da/dt and (Ct)avg observed in the experiment very well. The damage contributions of creep, fatigue, and their interaction are quantized thanks to the independent damage model for each part: (1) when the hold time increases from 1 min to 60 min, the creep damage ratio rises from 70% to 99% and the interaction damage ratio decreases from 25% to 1%. (2) when the crack depth ratio increases from 0.35 to 0.5, the creep damage ratio rises from 80% to 90% and the interaction damage ratio decreases from 15% to 10%; (3) when the load level increases from 4200 N to 5000 N, the creep damage ratio rises from 75% to 90% and the interaction damage ratio decreases from 25% to 10%. It is also shown the increase of load level and crack depth ratio lead to the increase of equivalent stress and therefore enhances the creep damage and accelerates the crack growth rate.

Solving Recent Challenges for Wrought Ni-Base Superalloys

This paper reviews the status of technology in design and manufacture of new wrought polycrystalline Ni-base superalloys for critical engineering applications. There is a strong motivation to develop new alloys that are capable of operating at higher temperatures to realize improvements in thermal efficiency, which are necessary to achieve environmental targets for reduced emissions of harmful green-house gases. From the aerospace sector, the development of new powder metallurgy and ingot metallurgy alloys is discussed for disk rotor and static applications. New compositions for powder metallurgy contain about 50 to 55 pct of gamma prime (γ′) strengthening precipitates to ensure components operate successfully at temperatures up to 788 °C (1450 °F). In contrast, new compositions for ingot metallurgy aim to occupy a design space in temperature capability between Alloy 718 and current powder alloys that are in-service, and show levels of γ′ of about 30 to 44 pct. The focus in developing these alloys was design for manufacturability. To complement the aerospace developments, a review of work to understand the suitability of candidate alloys for multiple applications in Advanced-Ultra Supercritical (AUSC) power plants has been undertaken by Detrois, Jablonski, and Hawk from the National Energy Technology Laboratory. In these power plants, steam temperatures are required to reach 700 °C to 760 °C. The common thread is to develop alloys that demonstrate a combination of high-temperature properties, which are reliant on both the alloy composition and microstructure and can be produced readily at the right price. For the AUSC applications, the emphasis is on high-temperature strength, long-term creep life, phase stability, oxidation resistance, and robust welding for fabrications. Whereas for powder disk rotors in aircraft engines, the priority is enhanced resistance to time-dependent crack growth, phase stability, and resistance to environmental damage, while extending the current strength levels, which are shown by existing alloys, to higher temperatures.

Demonstrating Structural Integrity under Challenging Load and Material Conditions

Since the industrial revolution when a German mining engineer August Wohler first studied the frequent breaking of chains causing several casualties and developed the concept of what we now know as the S-N curve, many experimental, theoretical and software-aided simulation techniques have been developed to study ageing material behaviour and to design new materials. Over time the demands placed on new materials have required operation under more severe temperatures and loads in order to conserve natural resources and minimise emissions. Fracture mechanics based finite element algorithms to simulate 3D cracks in components / structures have proved very useful in assessing the residual life and developing repair and maintenance strategies as mandatorily required by various licensing authorities for the continuous operation of infrastructure projects in Aerospace, Power, Transportation, Oil and Chemical industries under the ever more demanding operating conditions. Here one such software tool for crack simulation of industrial applications is presented with examples including combined fatigue and time dependent crack growth under thermo-mechanical loading including hold-time and weld defect assessment with inclusion of dis-similar materials.

Cyclic and time-dependent crack growth mechanisms in Alloy 617 at 800 °C

Crack growth mechanisms for Alloy 617 at 800 °C were investigated in air with specific emphasis on the transition from cycle-dependent to time-dependent crack growth mechanisms in the creep-fatigue regime. Crack growth studies were conducted using compact tension samples, a load ratio of 0.5, and triangular 5 Hz, 0.33 Hz, and 0.05 Hz waveforms, a trapezoidal 0.05 Hz waveform with 17 s hold time, and sustained loading. Fatigue crack growth rates were relatively insensitive to changes in frequency and hold times in air up to ∆K ≈ 11.5 MPa√m for R = 0.5, i.e, Kmax = 23 MPa√m. Above this threshold, the onset of time dependent crack growth was observed via a creep void nucleation and coalescence mechanism for triangular and trapezoidal waveforms with a loading frequency of 0.05 Hz, and during sustained loading. An estimate of the threshold for stress assisted grain boundary oxidation (SAGBO) crack growth was calculated to be 23 MPa√m, and oxidized grain boundaries observed near the crack tip were mostly uncracked, suggesting the SAGBO threshold was not reached before the onset of the void nucleation mechanism. A comparison of results across all available studies suggests that a threshold-based transition from cycle- to time-dependent crack growth at 800 °C likely exists. However, the stress intensity factor does not maintain similitude to accurately define a threshold across studies. Thus, gaining an understanding of the crack tip stress states that define the various time dependent mechanisms should be considered in future work.

A frequency dependent embrittling effect of high pressure hydrogen in a 17-4 PH martensitic stainless steel

The effects of hydrogen on tensile and fatigue-life properties of 17-4PH H1150 steel have been investigated by using a smooth, round-bar specimen for tensile tests and circumferentially-notched specimen for fatigue-life tests. The specimens were precharged by an exposure to 35-100 MPa hydrogen gas at 270°C for 200 h. For the 100 MPa hydrogen exposure, the steel showed a significant degradation in ductility loss, translated by a relative reduction in area, RRA, of 0.31. The fatigue-life test of the present notch specimen (stress concentration factor of 6.6) reflects the fatigue crack growth (FCG) for long cracks. The fatigue limit of the non-charged and H-charged notched specimens, defined by the threshold of non-propagation for long cracks, was not affected by hydrogen. At a higher stress amplitude, the H-charged specimen showed a significant FCG acceleration ratio compared to the non-charged specimen. Although, an upper bound of the FCG acceleration seemed to exist, this ratio was approximately 100. The fracture surface of the H-charged specimen was covered with quasi-cleavage (QC) at a lower stress amplitude and with a mixture of QC and intergranular (IG) facets at higher stress amplitudes. It has been suggested that a cycle-dependent crack growth accompanied by QC occurs at a lower stress amplitude, whereas a mixture of cycle-dependent crack growth (accompanied by QC) and time-dependent crack growth (accompanied by IG) occurs otherwise. This mixture justifies the 100 times FCG acceleration ratio in spite of the existence of the upper bound.

Characterizing crack growth behavior and damage evolution in P92 steel under creep-fatigue conditions

The present paper characterized crack growth behavior and damage evolution in P92 steel under creep-fatigue interaction conditions. Creep-fatigue crack growth tests were conducted at a constant load amplitude with various hold times. To reveal the role of constraint in creep-fatigue regime, specimens with different crack depths and thicknesses were used. Combination with a non-linear creep-fatigue interaction damage constitutive model, the crack growth and damage evolution behaviors were simulated using finite element method. Under creep-fatigue condition, time dependent crack growth rate increased as the duration period was reduced. This was attributed to the role of enhanced fatigue damage with the decreasing of the dwell time. Moreover, the deviation of crack growth rate with different dwell times became small as crack grew. With the crack length increasing, the creep damage level was improved regardless the dwell time, which may be due to the fact that the creep damage dominated crack growth in this stage. Furthermore, the crack growth rate increased as the crack depth became deep and the specimen thickness became large, as a result of the increased constraint level. A load-independent constraint parameter Q* was introduced to correlate the crack growth rate, which provided a good prediction for specimens under different constraint conditions.

Molecular design of confined organic network hybrids with controlled deformation rate sensitivity and moisture resistance

We demonstrate molecular design strategies for engineering the deformation rate sensitivity and fracture resistance of organic-inorganic hybrid films in moist environment. Hybrids with intimate mixing of inorganic and organic molecular networks were synthesized with an epoxy-functionalized silane, (3-glycidoxypropyl) trimethoxysilane and an acetate-stabilized zirconium alkoxide, tetra-n-propoxyzirconium. The highly confined non-hydrolysable organic molecular network connectivity was systematically manipulated by tuning the epoxy ring opening polymerization reaction and the incorporation of carbon bridges of selected lengths. By investigating the corresponding time-dependent crack growth in moist environments, new insights into the fundamental molecular-scale relaxation and cracking mechanisms of the hybrids are provided. These processes were found to be impacted by the confined organic network connectivity which results in significant changes in the deformation rate sensitivity and fracture resistance. With increasing non-hydrolysable organic network connectivity, mechanical behavior that varied from almost perfectly elastic to increasingly viscoelastic could be obtained in a controlled fashion. The related resistance to cracking in moist environments was found to be significantly improved. These findings provide a basis for the rational design of functional hybrids with precisely defined mechanical properties.

Thermo-Mechanical Fatigue Crack Growth of RR1000

Non-isothermal conditions during flight cycles have long led to the requirement for thermo-mechanical fatigue (TMF) evaluation of aerospace materials. However, the increased temperatures within the gas turbine engine have meant that the requirements for TMF testing now extend to disc alloys along with blade materials. As such, fatigue crack growth rates are required to be evaluated under non-isothermal conditions along with the development of a detailed understanding of related failure mechanisms. In the current work, a TMF crack growth testing method has been developed utilising induction heating and direct current potential drop techniques for polycrystalline nickel-based superalloys, such as RR1000. Results have shown that in-phase (IP) testing produces accelerated crack growth rates compared with out-of-phase (OOP) due to increased temperature at peak stress and therefore increased time dependent crack growth. The ordering of the crack growth rates is supported by detailed fractographic analysis which shows intergranular crack growth in IP test specimens, and transgranular crack growth in 90° OOP and 180° OOP tests. Isothermal tests have also been carried out for comparison of crack growth rates at the point of peak stress in the TMF cycles.

Environmentally Assisted Cracking in Silicon Nitride Barrier Films on Poly(ethylene terephthalate) Substrates.

A singular critical onset strain value has been used to characterize the strain limits of barrier films used in flexible electronics. However, such metrics do not account for time-dependent or environmentally assisted cracking, which can be critical in determining the overall reliability of these thin-film coatings. In this work, the time-dependent channel crack growth behavior of silicon nitride barrier films on poly(ethylene terephthalate) (PET) substrates is investigated in dry and humid environments by tensile tests with in situ optical microscopy and numerical models. The results reveal the occurrence of environmentally assisted crack growth at strains well below the critical onset crack strain and in the absence of polymer-relaxation-assisted, time-dependent crack growth. The crack growth rates in laboratory air are about 1 order of magnitude larger than those tested in dry environments (dry air or dry nitrogen). In laboratory air, crack growth rates increase from ∼200 nm/s to 60 μm/s for applied stress intensity factors, K, ranging from 1.0 to 1.4 MPa·m1/2, below the measured fracture toughness Kc of 1.8 MPa·m1/2. The crack growth rates in dry environments were also strongly dependent on the prior storage of the specimens, with larger rates for specimens exposed to laboratory air (and therefore moisture) prior to testing compared to specimens stored in a dry environment. This behavior is attributed to moisture-assisted cracking, with a measured power law exponent of ∼22 in laboratory air. This study also reveals that much larger densities of channel cracks develop in the humid environment, suggesting an easier initiation of channel cracks in the presence of water vapor. The results obtained in this work are critical to address the time-dependent and environmental reliability issues of thin brittle barriers on PET substrates for flexible electronics applications.

Mechanistic modelling of time-dependent fatigue crack growth in Ni-based superalloys

Advanced Ni-based superalloys for aero-engine disk applications can experience multiple damage mechanisms that include oxidation, creep and stress corrosion in additional to cycle-dependent fatigue crack initiation and growth. Interactions of these various damage mechanisms can lead to the occurrence of frequency, temperature, heat dwell and environmental effects on the fatigue crack growth response and service life of Ni-based superalloys. In this overview paper, the development of a set of generic microstructure-based fatigue crack growth models for treating concurrent time-dependent and cycle-dependent damage mechanisms at the microstructural levels is summarised. Key features of the mechanistic models are highlighted and utilised to assess the variability of time-dependent fatigue crack growth response in the threshold and power-law regimes due to variations in microstructure such as grain size, and γ′ size. This methodology provides a pathway for evaluating microstructural effects on multiple damage modes and extending the service lives of hot-section components.

Micro–macro modeling of brittle creep and progressive failure subjected to compressive loading in rock

A major challenge of rock mechanics is to link the time-dependent crack growth with macroscopic mechanical behavior. A new micro–macro method is presented to model the brittle creep and progressive failure of rock in compression. The Ashby’s microcrack model, Charles’ crack growth law and a new theoretical relation are incorporated into this method. This new relation is suggested to establish the linkage between microcrack growth and macroscopic strain based on the macroscopic and micromechanical definition of rock damage in this paper. The long-term strength of rock could also be calculated using this suggested micro–macro method. Rationality of the suggested method is verified through the theoretical and experimental results. Furthermore, effects of confining pressure on brittle creep and progressive failure of Sanxia granite is investigated. Theoretical corresponding relation between crack growth, damage and strain is investigated. And theoretical foundation of deep-buried construction design is also discussed in this paper.

A Hydrogen-Induced Decohesion Model for Treating Cold Dwell Fatigue in Titanium-Based Alloys

Cold dwell fatigue in near-alpha Ti alloys is a time-dependent fracture process at ambient temperature that involves fatigue in the presence of creep to produce cracking on low-energy fracture (e.g., cleavage) facets in hard alpha grains. In this article, cold dwell fatigue is treated as a hydrogen-induced decohesion process by using a nonlinear cohesive stress-strain relation to describe the decrease in the cohesive strength with increasing local hydrogen contents. It is postulated that during cold dwell fatigue, time-dependent deformation occurs by 〈a〉 slip that results in dislocation pileups in soft alpha grains. The stress and dilatational fields of the dislocation pileups assist the transport of internal hydrogen atoms from soft grains to neighboring hard grains. The accumulation of internal hydrogen atoms at the trap sites leads to decohesion along crystallographic planes, which can be slip or hydride habit planes. The decohesion model is applied to treat cold dwell fatigue in Ti-6Al-4V with a basal-transverse texture by modeling the effects of hydrogen-induced decohesion on the stress-fatigue life (S-N f) response, the time-dependent crack growth response (da/dt), and the fracture toughness (K c) as functions of grain orientation. A probabilistic time-dependent fatigue crack growth analysis is then performed to assess the influence of microtexture on the dwell fatigue life of a Ti-6Al-4V ring disk subjected to a long-duration hold at the peak stress of the loading cycle. The results of the probabilistic life computations indicate that dwell fatigue resistance in Ti-6Al-4V may be improved and the risk of disk fracture may be reduced significantly by controlling the microtexture or reducing the size and volume fraction of hard alpha grains in the microstructure.

Numerical simulation of time-independent and -dependent fracturing in sandstone

A grain-based model has been developed to simulate both the time-independent and -dependent damage evolution leading to ultimate failure. The mechanical behaviors of the Coconino sandstone during uniaxial compression, Brazilian splitting and fracture toughness tests were simulated. Simulation results are in satisfying agreement with the lab results. Mode-I, Mode-II and mixed mode subcritical crack growth mechanisms considering randomly distributed initial microcracks have been used in the calibrated time-independent model. One-edged time-dependent crack growth in the sandstone specimen due to stress corrosion has been analyzed both theoretically and numerically. It reveals that the lifetime of the specimen decreases nonlinearly with increasing length of the initial microcracks and the applied tensile load. In order to validate the developed numerical simulation scheme, a series of simulations only considering the influence of stress were conducted for a landscape arch which was assumed to be composed by the intact sandstone. The safety factor and the final failure pattern of the arch (time-independent) were determined using the strength reduction method. In parallel, the failure process of the arch due to stress corrosion (time-dependent) was studied in detail. Both approaches revealed similar final failure patterns. The proposed modeling scheme not only exhibits macroscopic mechanical response of the sandstone, but also provides deeper insight into the microscopic damage process, and allows time-related prediction of damage evolution.

Mitigating time-dependent crack growth in Ni-base superalloy components

Advanced Ni-based gas turbine disks are expected to operate at higher service temperatures in aggressive environments for longer time durations. Exposures of Ni-base alloys to these aggressive environments can lead to cycle-dependent and time-dependent crack growth in superalloy components for advanced turbopropulsion systems. In this article, the effects of tertiary γ′ on the crack-tip stress relaxation process, oxide fracture and time-dependent crack growth kinetics are treated in a micromechanical model which is then incorporated into the DARWIN® probabilistic life-prediction code. Using the enhanced risk analysis tool and material constants calibrated to powder-metallurgy (PM) disk alloy ME3, the effects of grain size and tertiary γ′ size on combined time-dependent and cycle-dependent crack growth in a PM Ni-alloy disk is demonstrated for a generic rotor design and a realistic mission profile using DARWIN. The results of this investigation are utilized to assess the effects of controlling grain size and γ′ size on the risk of disk fracture and to identify possible means for mitigating time-dependent crack growth (TDCG) in hot-section components.