Time-dependent Crack Growth Research Articles

Contributions of Time Dependent and Cyclic Crack Growth to the Crack Growth Behavior of Non Strain-Crystallizing Elastomers

Abstract Engineering components are observed to fail more rapidly under cyclic loading than under static loading. This reflects features of the underlying crack growth behavior. This behavior is characterized by the relation between the tearing energy, T, and the crack growth per cycle, dc/dn. The increment of crack growth during each cycle is shown here to result from the sum of time dependent and cyclic crack growth components. The time dependent component represents the crack growth behavior that would be present in a conventional constant T crack growth test. Under repeated stressing additional crack growth, termed the cyclic crack growth component, occurs. For a non-crystallizing elastomer, significant effects of frequency have been found on the cyclic crack growth behavior, reflecting the presence of this cyclic element of crack growth. The cyclic crack growth behavior over a wide range of frequencies was investigated for unfilled and swollen SBR materials. The time dependent crack growth component was calculated from constant T crack growth tests and the cyclic contribution derived from comparison with the observed cyclic growth. It is shown that decreasing the frequency or increasing the maximum tearing energy during a cycle results in the cyclic crack growth behavior being dominated by time dependent crack growth. Conversely at high frequency and at low tearing energy, cyclic crack growth is dominated by the cyclic crack growth component. A large effect of frequency on cyclic crack growth behavior was observed for highly swollen SBR. The cyclic crack growth behavior was dominated by the time dependent crack growth component over the entire range of tearing energy and/or crack growth rate. The origin of the cyclic component may be the formation/melting of quasi crystals at the crack tip, which is absent at fast crack growth rates in the unswollen SBR and is absent at all rates in the swollen SBR.

Fatigue crack-growth behavior of Sn-Ag-Cu and Sn-Ag-Cu-Bi lead-free solders

Fatigue crack-growth behavior and mechanical properties of Sn-3Ag-0.5Cu, Sn-3Ag-0.5Cu-1Bi, and Sn-3Ag-0.5Cu-3Bi solders have been investigated at room temperature (20 °C). The tensile strength and hardness of the solders increased with increasing Bi content. However, the yield strengths of Sn-3Ag-0.5Cu-1Bi and Sn-3Ag-0.5Cu-3Bi solders were nearly similar, but the 3Bi solder exhibited the lowest ductility. Fatigue crack-growth behavior of the solders was dominantly cycle dependent in the range of stress ratios from 0.1-0.7 at a frequency of 10 Hz, except for the Sn-3Ag-0.5Cu solder tested at a stress ratio of 0.7. Mixed intergranular/transgranular crack propagation was observed for the Sn-3Ag-0.5Cu solder tested at the stress ratio of 0.7, indicating the importance of creep in crack growth. The Sn-3Ag-0.5Cu-1Bi and Sn-3Ag-0.5Cu-3Bi solders had higher resistance to time-dependent crack growth, resulting from the strengthening effect of the Bi constituent. It appears that the addition of Bi above a certain concentration is harmful to the mechanical properties of Sn-3Ag-0.5Cu.

크리프 역전 변수 도입에 의한 9Cr강의 크리프 피로 균열성장 거동의 평가

Creep-fatigue crack growth models have been proposed employing (C_1)_avg as a crack tip parameter characterizing the time-dependent crack growth. The basic assumptions made in these previous models were ideal creep reversal conditions such as no creep reversal and complete creep reversal condition. Due to this assumption, the applicability of the models was limited since they did not consider partial creep reversal condition which is usually observed in many engineering metals at high temperature. In this paper the creep reversal parameter, C_R, which was defined by Grover, is critically evaluated to quantity the extent of partial creep reversal at the crack tip. This approach does not rely on any simplifying assumptions regarding the extent of the amount of creep reversal during the unloading part of a trapezoidal fatigue cycles. It is shown that the (C_1)_avg value calculated for 9Cr steel agrees well with the experimentally measured one. It is argued that the extent of improvement is not significant when the result is compared with that of the conventional model which has an assumption of full creep reversal behavior.

Creep and Fatigue at Elevated Temperatures. On Time-dependent Crack Growth Parameters in Plasticity and Creep Fields.

Rate and non-rate parameters are examined for correlation of time-dependent crack growth rates under static control conditions. Experimental data on single edge notch specimens of IN718 at 593°C, compact tension specimens of stainless steel 304 at 538°C and X20CrMoV 12 1 steel at 545°C are used to examine the performance of rate parameters Cpc, J^·, J·* and non-rate versions of these parameters which are computed either from approximate equations or finite element analyses. It is found that rate parameters can correlate time-dependent crack growth rates whether the crack tip field is dominated by plasticity or by creep. Non-rate parameters are found inadequate in either circumstance.

Fatigue and R-curve behavior of an Al2O3-10vol%Cr3C2 composite

The static and dynamic fatigue properties of an Al2O3-10 composite were studied. The R-Curve behavior was determined using the indentation strength in bending (ISB) technique. Results indicated that both alumina and the Al2O3-Cr3C2 composite exhibit time-dependent slow crack growth under static fatigue test conditions. In addition, the resistance for slow crack growth in the Al2O3-Cr3C2 composite is higher than that in monolithic alumina. The toughness of alumina was substantially increased and R-curve behavior became evident after the incorporation of Cr3C2 particles.

High temperature fatigue of a polycrystalline nickel base superalloy

A high temperature fatigue crack growth study on an experimental disc alloy of approximate composition Ni-14.75Cr-14-19Co-4.75Mo-3Al-3.75Ti-1.75Ta-0.7Hf-0.06Zr-0.02C-0.0175B wt- has been undertaken. Comparison of constant load fatigue crack growth tests conducted in air and a vacuum at 725C and in air at room temperature indicate that an oxidising environment has a major influence on crack growth rates over a wide range of applied stress intensity range. In particular it contributes to enhanced embrittlement of grain boundary regions, promoting an early transition to intergranular failure along with a concomitant increase in growth rate. Constant stress intensity factor range tests at high R ratio showed that a decrease in frequency at 725C in both air and a vacuum caused an increase in the crack growth rate per cycle due to time dependent crack growth. This was most significant in air at 725C rather than in vacuo, although in both instances low frequency tests were accompanied by wholly intergranular crack growth. At lower R ratios the influence of time dependent processes is less pronounced, especially in a vacuum. For the purposes of prediction a straightforward linear summation model using sustained load crack growth results combined with high frequency growth rates was found to model reasonably the influence of frequency on crack growth rates for the air tests at 725C. This can be rationalised by the observation that in air intergranular failure proceeds by linking of prior cracked or embrittled grains some distance ahead of the crack tip. At lower values of stress intensity range a slight under prediction of growth rates was evident, but improvements could be made through the use of triangular waveform data. For the vacuum tests, the linear summation model was consistently found to over predict growth rates due to the transitory nature of the sustained load crack growth rates under repeated loading and was not generally deemed suitable. Under these conditions damage occurs close to the crack tip and direct interaction between time dependent and time independent mechanisms will occur. This is not taken into account by a summation approach and more accurate modelling of damage formation in the varying strain fields ahead of the crack tip is required to predict this.

Creep, fatigue and oxidation in crack growth in advanced nickel base superalloys

This paper presents some of our recent results from an ongoing collaborative research programme on creep-fatigue behaviour of two advanced nickel base superalloys for turbine disc applications. The role of creep, fatigue and oxidation in crack growth has been investigated at 650°C under typical loading waveforms at selected loading frequencies. Load-line deflections were monitored in selected tests under static and long dwell loading conditions. Scanning electron microscopy was adopted to identify the fracture mode and to facilitate the evaluation of oxidation. The results show that mixed time and cycle dependent crack growth seems to be the predominant crack growth mode in the two PM nickel alloys studied. Whilst limited creep may be present at the crack tip, particularly under static and long dwell loading conditions, oxidation appears to be the predominant mechanism for crack growth under the test conditions examined.

New evaluation method of crack growth in SiC/SiC composites using interface elements

Crack propagation behavior in SiC/SiC composites was analyzed using a new computer simulation method that included time-dependent interface elements. The simulation method was used to describe the time-dependent crack growth in SiC/SiC composites under four-point bending of single-edge-notched beam bend-bars. Two methods were used to simulate time-dependent crack growth in SiC/SiC composites due to fiber creep. In one method, the creep property was introduced into the interface elements by the general method of finite element method (FEM) analysis. In the second method, a new technique making the best use of the potential function was used to represent crack closure tractions due to creeping fibers. The stage-II slow crack growth of a general creep deformation was simulated by both methods. Additionally, stage-III crack growth and the transition from stage-II to stage-III could be simulated by the new method. The new method has the potential to completely simulate time-dependent crack growth behavior in SiC/SiC composites due to fiber creep.

Time-dependent crack growth in stainless steel 304 in the plasticity-dominant field

Time-dependent crack growth is investigated at 538°C on compact tension specimens of stainless steel 304 under constant loads and alternating tensile loads with identical hold times. Finite element analyses of crack growth are performed following the experimental crack growth history. It is found, for the load levels employed, that plastic deformation is dominant around the crack tip throughout the test duration. Test results indicate that, for alternating load tests, most of crack growth occurs at the upper load and that crack growth is retarded by periodic load changes. It is shown that crack growth rates are not correlated with J, but with rate parameters J ̇ and C pc proposed in this study. The minimum crack extension for validity of the correlation varied from test to test but was always less than 0.35 mm.

High temperature fatigue crack growth in Inconel 718

The nickel base superalloys are extensively used in high temperature applications, so it is important to know their behaviour under conditions of high-temperature fatigue. This paper studies the influence of ΔK, loading frequency, stress ratio and temperature on the high temperature fatigue crack growth rate of nickel base superalloys. This study is based on fatigue tests carried out in corner crack specimens of Inconel 718 at 600°C and at room temperature. Three stress ratios (R = 0.05, 0.5 and 0.8) and loading frequencies ranging from 0.0017 to 15 Hz were considered in the tests. For frequencies below 0.25 Hz, the load wave shape was trapezoidal with different dwell times at maximum load. At relatively high frequencies the propagation is cycle dependent, while for lower frequencies it is time dependent. At intermediate frequencies a mixed crack growth occurs. The transition frequencies from cycle dependent to mixed regime and from mixed to time dependent regime were obtained for each R. The increase of R increases the transition frequencies, i.e., extends the time dependent crack growth to higher frequencies. The increase of R also produces an increase of cyclic crack growth rate for all regimes of crack growth. In the time dependent regime, a higher variation is observed, that can be explained by an acceleration of oxidation damage promoted by the increase of maximum stress. An approach for modelling the high-temperature fatigue crack growth in nickel base superalloys is presented. A good agreement was observed between time dependent fatigue results and mathematical models based on static load results.

Creep-Fatigue Crack Growth at CrMo Steel Weld Interface

Creep-fatigue crack growth behavior was experimentally measured particularly when a crack was located in the heat affected region of lCr-5Mo steel. Load hold times of the tests for trapezoidal fatigue waveshapes were varied among 0, 30, 300 and 3,600 seconds. Time-dependent crack growth rates were characterized by the parameter. It was found that the crack growth rates were the highest when the crack path was located along the fine-grained heat affected zone(FGHAZ). Cracks located in other heat affected regions had a tendency to change the crack path eventually to FGHAZ. Creep-fatigue crack growth law of the studied case is suggested in terms of (da/dt) vs. () for residual life assessment.

Explanation of an apparent abnormality in fatigue crack growth rate curves in titanium alloys

A surprising phenomenon is investigated where titanium alloys exhibit no threshold fatigue crack growth value if K max in the K max-constant testing procedure exceeds a certain value. The crack growth rate increases with decreasing Δ K up to final fracture. The phenomenon was found repeatedly for Ti–6Al–2Sn–4Zr–6Mo above K max=21 MPa√m (equal to 72% of K IC), and its causes were investigated. The same crack growth rates as in the K max-constant test were reproduced by two independent experimental procedures, the so-called “jump” test and sustained K cracking experiments along with a calculation. It is demonstrated that the observed phenomenon is not a special crack growth feature or a new phenomenon, but simply caused by time-dependent crack growth, which is known to exist in titanium alloys or steels. Fractographic work revealed that intergranular crack growth along α and transformed β grain boundaries increases with decreasing Δ K and increasing K max value, accompanied by creep deformation in the transformed β grains. The conditions for time-dependent cracking are believed to be a sufficiently high stress and strain field in the crack tip region, along with hydrogen-assisted cracking.

Environmentally assisted crack growth in a Ni–18Cr–18Fe ternary alloy at elevated temperatures

Fatigue crack growth experiments were conducted on a Ni–18Cr–18Fe ternary alloy under trapezoidal loading, in high-purity argon and oxygen at 873, 923 and 973 K, as a part of a broader study to elucidate the mechanism and rate controlling process for crack growth in nickel-base superalloys. The data were analyzed in terms of a new superposition model which facilitates the decomposition of data into the time-dependent and cycle-dependent contributions, as well as the respective mechanical and environmental components. The results demonstrated the effectiveness of the model, and showed that oxygen only affected cycle-dependent (or fatigue) crack growth, increasing the growth rates by about 2X. The time-dependent (or sustained-load) crack growth was principally associated with grain boundary cavitation and controlled by creep at these temperatures, with an apparent activation energy of 210±10 kJ mol−1. These results suggest that the pressure mechanism proposed by Bricknell and Woodford for oxygen enhanced crack growth in nickel-base superalloys did not operate at these temperatures. The near absence of environmental sensitivity in this Nb-free, Ni–Cr–Fe ternary alloy suggested the internal oxidation of Ni, Cr and Fe was not a significant contributor to the enhancement of crack growth. The results, instead, provided complementary support for the embrittling role of Nb that had been proposed by Gao et al.

Time-Dependent Crack Initiation and Growth in Ceramic Matrix Composites

Matrix cracking in ceramic matrix composites with fine grained fibers at high temperatures will be governed by fiber creep, as relaxation of the fibers eliminates crack tip shielding. Using a time dependent bridging law that describes the effect of creeping fibers bridging a crack in an elastic matrix, crack growth initiation and history have been modeled. For a stationary crack, crack tip stress intensity factors as a function of time are presented to predict incubation times before subcritical crack growth. Two crack growth studies are reviewed: a constant velocity approximation for small-scale bridging, and a complete velocity history analysis which can be used to predict crack length as a function of time. The predictions are summarized and discussed in terms of identifying various regimes of crack growth initiation, subcritical growth, and catastrophic matrix cracking.

Growth of pores during the creep of a single crystal nickel-base superalloy

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.

CREEP CRACK GROWTH WITH SMALL SCALE BRIDGING IN CERAMIC MATRIX COMPOSITES

Time-dependent crack growth in ceramic matrix composites with linearly creeping fibers in an elastic matrix is predicted for bridged regions that are much smaller than the crack length. The relationship between crack openings and bridging tractions was modeled previously and accounts for the mechanics of fiber pull-out while fibers are creeping. The length of the bridged zone is determined by a fiber failure criterion and the condition that the stress intensity factor at the crack tip equals the matrix toughness. Solutions that relate constant crack velocities to applied stress intensity factors are presented. Two fiber failure criteria are considered: a critical crack opening and a critical total strain in the fiber at the crack plane. When fiber failure is governed by a critical crack opening, bridging lengths will decrease with increasing velocity. For the case of a critical strain, the steady-state bridge length will increase with increasing velocity. Asymptotic analytical solutions are presented for cases where the crack velocity is small. © 1997 Acta Metallurgica Inc.

Crack Growth and Lifetime of Concrete under Long Time Loading

Edge-notched eccentrically compressed fracture specimens made of aggregate of reduced size are loaded in standard creep test frames. Measurements of the time rate of crack mouth opening in notched concrete specimens subjected to constant load of almost one month duration are reported and analyzed. To reveal the size effect, geometrically similar specimens of four sizes in the ratio I :2:4:8 are tested. The results are success­ fully described by a previously proposed time-dependent generalization of the R-curve model, in which the rate of crack growth is a function of the ratio of the stress intensity factor to the R-curve, and linear aging viscoelastic creep in the bulk of the specimen is treated according to the operator method. Good predictions are also obtained with a simplified method in which the R-curve is replaced by a constant asymptotic value of the critical stress intensity factor and creep is handled in similarity to the effective modulus method, neglecting the history effect. The time curves of crack opening terminate with an infinite slope, indicating the lifetime. The finiteness of the lifetime is not caused by creep, but by time-dependent crack growth, which dominates the final stage of crack opening. The initial stage of crack opening, on the other hand, is dominated by creep. Tests are conducted both for concretes of normal strength of 33.4 MPa (4,847 psi) in compression and relatively high strength of 46.4 MPa (6,442 psi). For the stronger concrete, the lifetimes are found to be longer. An increase of specimen size is found to decrease the lifetime. Since the same type of model was previously shown capable of describing all other known time-dependent fracture phenomena in concrete, a rather general applicability may be expected.

Time dependent cracks in ceramic matrix composites: Crack growth initiation

Ceramic matrix composites at high temperatures exhibit time-dependent behavior due to fiber creep, even though the matrix remains elastic. The time-dependent behavior of bridged cracks for such materials is modeled using a bridging law developed previously which describes the effects of fibers bridging a matrix crack and accounts for frictional sliding between the fibers and the matrix. Approximations which simplify the bridging law are presented for short cracks or high loads. In particular, regimes are identified where the history-dependence of the crack opening rate can be neglected. Using a simplified form of the bridging law, results are presented for the general evolution of bridged stationary cracks. Determination of the bridging stress profile at a given instant in time allows calculation of the crack tip stress intensity factor as a function of time, leading to estimates for the time to initiate time-dependent crack growth. The results indicate that for very high loads and very short cracks, a simple form of bridging law can be used to produce accurate estimates for the initiation time to begin growing matrix cracks.

Viscoelastic creep crack growth: A review of fracture mechanical analyses

The study of time dependent crack growth in polymers using a fracture mechanics approach has been reviewed. The time dependence of crack growth in polymers is seen to be the result of the viscoelastic deformation in the process zone, which causes the supply of energy to drive the crack to occur over time rather than instantaneously, as it does in metals. Additional time dependence in the crack growth process can be due to process zone behavior, where both the flow stress and the critical crack tip opening displacement may be dependent on the crack growth rate. Instability leading to slip-stick crack growth has been seen to be the consequence of a decrease in the critical energy release rate with increasing crack growth rate due to adiabatic heating causing are duction in the process zone flow stress, a decrease in the crack tip opening displacement due to a ductile to brittle transition at higher crack growth rates, or an increase in the rate of fracture work due to more rapid viscoelastic deformation. Finally, various techniques to experimentally characterize the crack growth rate as a function of stress intensity have been critiqued.

Effect of temperature on small fatigue crack growth in nickel-base superalloys : Okazaki, M., Nohmi, S. and Yamada, H. J. Soc. Mater. Sci., Jpn. (1995) 44 (498), 348–354

This paper presents some of our recent results from an ongoing collaborative research programme on creep-fatigue behaviour of two advanced nickel base superalloys for turbine disc applications. The role of creep, fatigue and oxidation in crack growth has been investigated at 650°C under typical loading waveforms at selected loading frequencies. Load-line deflections were monitored in selected tests under static and long dwell loading conditions. Scanning electron microscopy was adopted to identify the fracture mode and to facilitate the evaluation of oxidation.The results show that mixed time and cycle dependent crack growth seems to be the predominant crack growth mode in the two PM nickel alloys studied. Whilst limited creep may be present at the crack tip, particularly under static and long dwell loading conditions, oxidation appears to be the predominant mechanism for crack growth under the test conditions examined.