A crack propagation criterion based on ΔCTOD measured with 2D‐digital image correlation technique

The fatigue cracks growth rate of a forged HSLA steel (AISI 4130) was investigated using thin single edge notch tensile specimen to simulate the crack development on a diesel train crankshafts. The effect of load ratio, R, was investigated at room temperature. Fatigue fracture surfaces were examined by scanning electron microscopy. An approach based on the crack tip opening displacement range (ΔCTOD) was proposed as fatigue crack propagation criterion. ΔCTOD measurements were carried out using 2D‐digital image correlation techniques. J‐integral values were estimated using ΔCTOD. Under test conditions investigated, it was found that the use of ΔCTOD as a fatigue crack growth driving force parameter is relevant and could describe the crack propagation behaviour, under different load ratio R.     

Crack growth behavior and fatigue-life prediction based on worst-case near-threshold data of a large crack for 9310 steel

ABSTRACT Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks, near‐threshold growth behavior of large cracks at constant R‐ratio/decreasing ΔK and constant K_max/decreasing ΔK, respectively, for 9310 steel. The results showed that a pronounced small‐crack effect was not observed even at R = ?1, small cracks initiated by a slip mechanism at strong slip sites. Worst‐case near‐threshold testing results for large cracks under several K_max values showed that an effect of K_max on the near‐threshold behavior does not exist in the present investigation. A worst‐case near‐threshold test for a large crack, i.e. constant K_max/decreasing ΔK test, can give a conservative prediction of growth behavior of naturally initiated small cracks. Using the worst‐case near‐threshold data for a large crack and crack‐tip constraint factor equations defined in the paper, Newman's total fatigue‐life prediction method was improved. The fatigue lives predicted by the improved method were in reasonable agreement with the experiments. A three‐dimensional (3D) weight function method was used to calculate stress‐intensity factors for a surface crack at a notch of the present SENT specimen (with r/w = 1/8) by using a finite‐element reference solution. The results were verified by limited finite‐element solutions, and agreed well with those calculated by Newman's stress‐intensity factor equations when the stress concentration factor of the present specimen was used in the equations.     

Comparison of retardation behaviour of 2024-T3 and 7075-T6 Al alloys

Retardation in fatigue crack growth rate following the application of single and periodic tensile overloads was studied for 2024‐T3 and 7075‐T6 aluminium alloys. Tests were performed at constant stress and at constant stress intensity factor ranges, at a load ratio of R= 0.1, at a baseline ΔK in the 10–20 MPa√m range which corresponds to the Paris regime. Overload ratios of 1.3–1.65 were studied with overload spacing, n, varying from 20 to 10 000 cycles. 2024‐T3 displayed an order of magnitude higher retardation, N_d, due to single tensile overloads compared to 7075‐T6. Periodic overloads induced maximum retardation when n/N_d≈ 0.5 for both alloys, the magnitude being only 15% higher for 2024‐T3.     

SMALL FATIGUE CRACK GROWTH IN A LOW CARBON STEEL UNDER TENSION–COMPRESSION AND PULSATING-TENSION LOADING

The growth behaviour of small fatigue cracks has been investigated in a low carbon steel under axial loading at the stress ratios R of –1 (tension-compression) and 0 (pulsating-tension). Crack closure was measured to evaluate the effects of stress ratio and stress level on small crack growth. Except for the accelerated growth at stress levels close to the yield stress of the material, at R=–1 small cracks grow faster than large cracks below a certain crack length, but at R= 0 the crack growth rates for small cracks are coincident with those for large cracks in the whole region of crack length investigated. The critical crack length, 2c_c, above which the growth behaviour of small cracks is similar to that of large cracks depends on stress ratio, being 1–2 mm at R=–1 and smaller than 0.7 mm at R=0. The 2c_c value at R=–1 agrees with that obtained under rotating bending (R=–1). The small crack data are closely correlated with large crack growth rates in terms of the effective stress intensity range, ΔK_eff; thus ΔK_eff is found to be a characterizing parameter for small crack growth including the growth at the higher stress levels.     

Elastic–plastic fatigue crack growth in 18G2A steel under proportional bending with torsion loading

The paper presents the results of fatigue crack growth on low‐alloy 18G2A steel under proportional bending with torsion loading. Specimens with square sections and a stress concentration in the form of external one‐sided sharp notch were used. The tests were performed under the stress ratios R=?1, ?0.5 and 0. The test results were described by the ΔJ‐integral range and compared with the ΔK stress intensity factor range. It has been found that there is a good agreement between the test results and the model of crack growth rate, which includes the ΔJ‐integral range.     

Fatigue crack growth law of API X80 pipeline steel under various stress ratios based on J‐integral

Load‐controlled three‐point bending fatigue tests were conducted on API X80 pipeline steel to investigate the effects of stress ratio and specimen orientation on the fatigue crack growth behaviour. Because of the high strength and toughness of X80 steel, crack growth rate was measured and plotted versus ΔJ with stress ratio. The fatigue crack length is longer in the transverse direction, whereas the fatigue crack growth rates are nearly the same in different orientations. Finally, a new fatigue crack growth model was proposed. The effective J‐integral range was modified by ΔJ_p in order to correlate crack closure effect due to large‐scale yield of crack tip. The model was proved to fit well for fatigue crack growth rate of API X80 at various stress ratios of R > 0.     

TRANSIENT RETARDATIONS IN FATIGUE CRACK GROWTH FOLLOWING A SINGLE PEAK OVERLOAD

Retardation in the fatigue crack growth rate following the application of a single peak overload in a fatigue loading sequence has been studied for a low carbon structural steel. Tests have been performed at load ratios of R= 0.2 and R= 0.6 at a baseline stress intensity range, ΔK_b, corresponding to fatigue crack growth rates in the Paris regime. Single peak overloads were applied at a crack-length to specimen-width ratio of a/W= 0.5. At the load ratio of R= 0.6 monotonic or “static” fracture modes were observed upon application of the overload, and these produced an immediate increase in growth rate. A subsequent retardation is attributed to the presence of a residual compressive stress field ahead of the crack tip. A similar retardation was observed at a load ratio of 0.2. The importance of residual stress was established by performing stress relieving experiments. In addition, removal of the surface deformation after an overload by machining “T” sidegrooves resulted in an extended transient, which could not be explained by residual machining stresses.     

Analysis of fatigue crack growth behavior of SS 316(N) welds using the unified approach

Fatigue crack growth (FCG) behavior of SS 316(N) weld has been evaluated at different R‐ratios at room temperature and compared with that of the base metal. The FCG resistance of weld is better than that of the base material and is due to the residual stresses developed during the welding. The data were analyzed using the unified approach that considers the two‐parametric (ΔK and K_max) nature of fatigue. The R‐ratio effects in both the base and weld metals are accounted for without invoking the extrinsic parameters, such as plasticity‐induced crack closure. Since the residual stresses are of the monotonic type, they affect the crack growth via the K_max‐parameter. The crack growth trajectory plots were developed, and they show how the two crack tip driving forces, ΔK and K_max, change to overcome the FCG resistance of the weld in relation to that of the base metal. The results also show that the effects from the compressive residual stresses are more dominant at low R‐values and occur via the K_max parameter.     

Fatigue crack propagation in API 5L X‐70 pipeline steel longitudinal welded joints under constant and variable amplitudes

Fatigue crack propagation (FCP) under constant and variable amplitude loading in base metal (BM), weld metal (WM) and heat affected zone (HAZ) of longitudinal welded joints of an API X‐70 pipeline steel was investigated. Constant amplitude loading tests were performed at R = 0.1 and 0.5, whereas for variable amplitude testing single peak tensile overloads (OLs) alternating between 75 and 100% of maximum load were applied at 2.5 mm intervals in crack growth. Results of SE(B) specimens tested under constant and variable amplitude loading revealed that BM, WM and HAZ regions subjected to R = 0.5 and low ΔK‐values presented the highest crack growth rates. At higher ΔK values FCP rates in all the studied regions were similar and the R effect on FCP rate was no more observed. Crack growth retardation due to OLs was observed at the three studied regions, showing a decrease on the FCP delay with a decreasing on ΔK.     

Examination of fatigue crack driving force parameter

Most of the previous parameters that utilized as a crack driving force were established in modifying the parameter K_op in Elber's effective SIF range ΔK_eff(=K_max?K_op). However, the parameters that replaced the traditional parameter K_op were based on different measurements or theoretical calculations, so it is difficult to distinguish their differences. This paper focuses on the physical meaning of compliance changes caused by plastic deformation at the crack tip; the tests were carried out under different amplitude loading for structural steel. Based on these test results, differences of several parameter ΔK_eff in literature are analysed and an improved two‐parameter driving force ΔK_drive(=(K_max)ⁿ(ΔK^∧)^1‐n) has been proposed. Experimental data for several different types of materials taken from literature were used in the analyses. Presented results indicate that the ΔK_drive parameter was equally effective or better than ΔK(=K_max?K_min), ΔK_eff(=K_max?K_op) and ΔK*(= (K_max)^α(ΔK⁺)^1?α) in correlating and predicting the R‐ratio effects on fatigue crack growth rate.     

Further developments in <Emphasis Type="Italic">J</Emphasis> evaluation procedure for growing cracks based on LLD and CMOD data

Laboratory testing of fracture specimens to measure resistance curves (J − Δa) have focused primarily on the unloading compliance method using a single specimen. Current estimation procedures (which form the basis of ASTM E1820 standard) employ load line displacement (LLD) records to measure fracture toughness resistance data incorporating a crack growth correction for J. An alternative method which potentially simplifies the test procedure involves the use of crack mouth opening displacement (CMOD) to determine both crack growth and J. However, while the J-correction for crack growth effects adopted by ASTM standard holds true for resistance curves measured using load line displacement (LLD) data, it becomes unsuitable for J-resistance measurements based upon the specimen response defined in terms of load-crack mouth opening displacement (CMOD). Consequently, direct application of the evaluation procedure for J derived from LLD records in laboratory measurements of resistance curves using CMOD data becomes questionable. This study provides further developments of the evaluation procedure for J in cracked bodies that experience ductile crack growth based upon the eta-method and CMOD data. The introduction of a constant relationship between the plastic components of LLD (Δ _p ) and CMOD (V _p ) drives the development of a convenient crack growth correction for J with increased loading when using laboratory measurements of P-CMOD data. The methodology broadens the applicability of current standards adopting the unloading compliance technique in laboratory measurements of fracture toughness resistance data (J resistance curves). The developed J evaluation formulation for growing cracks based on CMOD data provides a viable and simpler test technique to measure crack growth resistance data for ductile materials.     

Empirical model for plasticity‐induced crack closure based on Kmax and ΔK

The mean stress has a significant effect on crack propagation life and must be included in prediction models. However, there is no consensus in the fatigue community regarding the dominant mechanism explaining the mean stress effect. The concept of crack closure has been widely used and several empirical models can be found in literature. The stress ratio, R, is usually the main parameter of these models, but present numerical results showed a significant influence of K_max. A new empirical model is therefore proposed here, dependent on K_max and ΔK, with four empirical constants. The model also includes the effect of material's yield stress, and two additional parameters were defined to account for stress state and crack closure parameter. A comparison was made with Kujawski's and Glinka's parameters, for a wide range of loading conditions. ΔK_eff lies between Kujawski's and Glinka's parameters, and some agreement is evident, although the concepts are quite different. The crack opening model was applied to literature results and was able to collapse da/dN–ΔK curves for different stress ratios to a single master curve.     

J integral and COD fracture criteria in 40CrNiMo steel under mixed mode I+II loading

Abstract

By defining the J integral and crack opening displacement (COD) under mixed mode I + II loading, a mixed J integral fracture criterion is proposed and the relationship between the J integral and COD in 40CrNiMo steel is discussed. The mixed J integral J _M and its mode I and II components J _I and J _II were calculated by the finite element method, while the mixed COD and its mode I and II components CTOD and CTSD were measured using a duplicated grid. The critical values J _Mc and COD_c for mixed crack initiation were determined by a resistance curve. The results show that mode II loading lowers both J _Mc and COD_c for 40CrNiMo steel. The variation of J _Mcfrommode I tomode II loading is found to be in accordance with the linked equations J _Mc=J _Ii+J _IIi;(J _Ii/J _Ic)+(J _IIi/J _IIc)=1, where J _Icand J _IIcare the critical J integrals of pure mode I and II cracks,and J _Iiand J _IIiare the mode I and II components of J _Mc at arbitrary mixed K_I/K_II ratio respectively; the J _Mc value for a given K_I/K_II ratio can be obtained if J _Ic and J _IIc are known. Finally, under valid loads, J_M and the mixed COD satisfy the relation J _M=J _I+J _II=dσ₀CTOD+d _sτ₀CTSD. When unified by yield stress σ_y the relation becomes J _M=dσ_yCOD, where d _n, d _s and d are coefficients, and σ₀ and τ₀ are the tensile and shear stress at the crack tip strip respectively. While d _n and d _s vary with K_I/K_II ratio and materials, d was found to have a constant value of about 0.98.     

The non-constant CTOD/CTOA in stable crack extension under plane-strain conditions

Contrary to the previous work that successfully applied the constant CTOD/CTOA fracture criteria to relatively thin structures, this paper demonstrates that the initial non-constant portion of the CTOD/CTOA plays an essential role in predicting fracture behavior under plane-strain conditions. Three- and two-dimensional finite element analyses indicate that a severe underestimation of the load would occur as the crack extends if a constant CTOD/CTOA criterion were used. However, the use of a simplified, bilinear CTOD/CTOA criterion to approximate its non-constant portion will closely duplicate the test data. Furthermore, using the experimental data from J-integral tests with various crack length to specimen width ratios (a/W), it is demonstrated that the critical CTOD/CTOA is crack tip constraint dependent. The initial high values of the CTOD/CTOA are in fact a natural consequence of crack growth process that is reflected by, and consistent with, the J-resistance (J-R) curve and its slope (tearing modulus).     

The prediction of crack growth rates from total endurances in high strain fatigue—thirty years on

McClintock 1 , 2 was one of the first to model continuous‐cycling fatigue crack growth by assuming a succession of miniature low‐cycle‐fatigue (LCF) specimens at the crack tip. Elements ahead of the crack amass damage until the arrival of the tip itself. Such models had been summarized by Majumdar and Morrow, 3 but the author was unaware of these papers at the time. The ideas were pursued further by Chakrabortty 4 whose paper, again unknown to the author, was published in the same issue (1979, Vol. 2) of FEMS. In the original paper 5 crack propagation is represented by successive regeneration at the crack tip, the process becoming progressively easier as the crack grows owing to an increase in strain concentration. These ‘initiation’ cycles were related to the ‘Coffin’ expression for crack initiation, thereby introducing two empirical constants k and α. The paper is of the class ‘ρ/N’ where ρ is the assumed size of a crack‐tip process zone and N is the cycles required to traverse that zone. Expressions had been previously derived linking LCF with linear‐elastic fracture‐mechanics (LEFM) crack growth, using the parameter ΔJ. 6 (It was later shown that this was identical to using an equivalent stress intensity parameter. 7 ) It has been shown that the approach does not apply for crack depths < 180 μm. 6 At elevated temperature the ΔJ approach was successful for describing crack growth in the range 0.2–1.2 mm for the cobalt‐based alloy MAR‐M509 at 600 °C. 8 Other studies have in fact shown 9 that crack growth rates are approximately constant below a depth of 200 μm. Even to this day short crack growth relations in LCF and their practical use are not as familiar as those in LEFM. It may justifiably be argued that for every paper published on LCF short crack growth, several hundred have appeared dealing with LEFM crack growth in terms of the ‘Paris’ law. One of the original referees' comments was that the paper 5 should have been presented in terms of LEFM. The author nevertheless defended his approach because for small cracks it was thought useful to retain the crack depth explicitly. It will be shown that LCF crack growth data have a definite part to play in the assessment of components and structures.     

NON-PROPAGATION CONDITIONS (ΔKth) AND FATIGUE CRACK PROPAGATION THRESHOLD (δKT)

Abstract— Fatigue crack propagation threshold values have been determined with two experimental methods, it., the constant R method and the constant K_max method. Three materials, namely A17075-T7351 and Ti6A14V STA in the LT- and TL-orientations, and a Ti-turbine disk material (IMI 685) in the CR-orientation, were investigated. The paper is divided into 3 parts. In the first part the test conditions, the experimental results and the conclusions drawn from the experimental results are presented, namely that the three different functional dependencies of ΔK_th on R cannot be reconciled with present continuum mechanics concepts. In the second part, some facts used in conjunction with the da/dN–ΔK_eff methodology are applied to the non-propagation condition ΔK_th. Parameters such as K_Op, the threshold ΔK_T, and a parameter “K_LL” are investigated by numerical modelling of their individual influence on the ΔK_th versus R curves. This modelling work shows that the individual ΔK_th versus R curves are primarily dependent on the K_op behavior of the respective material. Further, it is shown that the threshold ΔK_T is a constant value, independent of any particular cyclic loading condition. In the third part of the paper, the ΔK_eff concept is applied to the experimental results obtained in the first part. Using either experimentally or semi-empirically determined K_op functions and the measured ΔK_T values, the ΔK_th versus R curves of the three materials investigated were accurately reconstructed. It follows that the ΔK_th versus R curves of the individual materials are the natural consequence of the driving force for fatigue crack propagation, namely ΔK_eff     

Fracture toughness and growth of short and long fatigue cracks in ductile cast iron EN‐GJS‐400‐18‐LT

Heavy components of ductile cast iron frequently exhibit metallurgical defects that behave like cracks under cyclic loading. Thus, in order to decide whether a given defect is permissible, it is important to establish the fatigue crack growth properties of the material. In this paper, results from a comprehensive study of ductile cast iron EN‐GJS‐400‐18‐LT have been reported. Growth rates of fatigue cracks ranging from a few tenths of a millimetre (‘short’ cracks) to several millimetres (‘long’ cracks) have been measured for load ratios R=?1, R= 0 and R= 0.5 using a highly sensitive potential‐drop technique. Short cracks were observed to grow faster than long cracks. The threshold stress intensity range, ΔK_th, as a function of the load ratio was fitted to a simple crack closure model. Fatigue crack growth data were compared with data from other laboratories. Single plain fatigue tests at R=?1 and R= 0 were also carried out. Fracture toughness was measured at temperatures ranging from ?40 °C to room temperature.     

Crack closure under high load-ratio conditions for Inconel-718 near threshold behavior

Fatigue-crack-growth (FCG) rate tests were conducted on compact specimens made of an Inconel-718 alloy to study the behavior over a wide range in load ratios (0.1 ? R ? 0.95) and a constant K_max test condition. Previous research had indicated that high R (>0.7) and constant K_max test conditions near threshold conditions were suspected to be crack-closure-free and that any differences were attributed to K_max effects. During a test at a load ratio of 0.7, strain gages were placed near and ahead of the crack tip to measure crack-opening loads from local load-strain records during crack growth. In addition, a back-face strain (BFS) gage was also used to monitor crack lengths and to measure crack-opening loads from remote load-strain records during the same test. The BFS gage indicated that the crack was fully open (no crack closure), but the local load-strain records indicated significant amounts of crack closure. The crack-opening loads were increasing as the crack approached threshold conditions at R = 0.7. Based on these measurements, crack-closure-free FCG data (ΔK_eff against rate) were calculated. The ΔK_eff-rate data fell at lower ΔK values and higher rates than the constant K_max test results. In addition, constant R tests at extremely high R (0.9 and 0.95) were also performed and compared with the constant K_max test results. The constant R test results at 0.95 agreed well with the ΔK_eff-rate data, while the R = 0.9 data agreed well with constant K_max test data in the low-rate regime. These results imply that the R = 0.7 test had a significant amount of crack closure as the threshold was approached, while the R = 0.9 and K_max test results may have had a small amount of crack closure, and may not be closure free, as originally suspected. Under the high load-ratio conditions (R ? 0.7), it is suspected that the crack surfaces are developing debris-induced crack closure from contacting surfaces, which corresponded to darkening of the fatigue surfaces in the near-threshold regime. Tests at low R also showed darkening of the fatigue surfaces only in the near-threshold regime. These results suggest that the ΔK_eff against rate relation may be nearly a unique function over a wide range of R in the threshold regime.     

Fatigue crack growth resistance of 7075 Al alloy after equal channel angular pressing

This work presents experimental results on effects of severe plastic deformation (SPD) and subsequent natural ageing on tensile mechanical properties and fatigue crack growth resistance of fine‐grained 7075 Al alloy. The alloy was subjected to equal channel angular pressing (ECAP) after solution treatment. Fatigue crack propagation tests were conducted in room condition, at load ratio R = 0.1 and different load ranges on small disk shaped compact tension specimens. Fatigue fracture surface is also investigated using scanning electron microscopy observations and showed more ductile fatigue crack growth in the unECAPed specimen. Despite the increased tensile strength after ECAP, the ductility that controls low‐cycle fatigue behaviour has decreased. It is found that ECAP has resulted in a remarkable change in Paris regime parameters and a significant increase in fatigue crack growth rate. The decrease in fatigue crack growth resistance and ΔK_c after ECAP can be attributed to the decrease in alloy's ductility.     

Effect of residual stresses on crack behaviour in single edge bending specimens

Residual stresses due to manufacturing processes, such as welding, change the load bearing capacity of cracked components. The effects of residual stresses on crack behaviour in single edge bending specimens were investigated using Finite element analyses. Three parameters (J, Q and R) were used to study the crack behaviour. The J‐integral predicts the size scale over which large stresses and strains exist, the constraint parameter Q describes the crack‐tip constraint as a result of geometry, loading mode and crack depth and the constraint parameter R is used to describe the constraint resulting from residual stresses. To carry out a systematic investigation on the effect of residual stresses on the J‐integral and crack‐tip constraints, models under different combinations of residual stresses and external loads with different crack depths were analysed. It has been shown that the crack‐tip constraint R increased by tensile residual stresses around the crack‐tip. On the other hand, the constraint parameter R decreased and tended to zero at high external load levels.