Crack-closure behavior of 2324-T39 aluminum alloy near-threshold conditions for high load ratio and constant Kmax tests

Fatigue-crack-growth rate tests were conducted on compact specimens made of 2324-T39 aluminum 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 were suspected to be crack-closure free and that any differences were attributed to K_max effects. During the tests, strain gages were placed near and ahead of the crack tip to measure crack-opening loads from local strain records on all tests, except R = 0.95. In addition, a back-face strain gage was used to monitor crack lengths and also to measure crack-opening loads from remote strain records. From local gages, significant amounts of crack closure were measured at the high-R conditions and crack-opening loads were increasing as the threshold condition was approached. Crack-closure-free data, ΔK_eff (= U ΔK) against rate, were calculated. These results suggest that the ΔK_eff against rate relation may be nearly a unique function over a wide range of R even in the threshold regime, if crack-opening loads were measured from local strain gages and not from remote gages. At low R, all three major shielding mechanisms (plasticity, roughness, and fretting debris) are suspected to cause crack closure. But at high R and K_max tests, roughness and fretting debris are suspected to cause crack closure above the minimum load.     

Fatigue crack growth behavior of silica particulate reinforced epoxy resin composite

In the present work, fatigue crack growth tests of epoxy resin composite reinforced with silica particle under various R-ratios were carried out to investigate the effect of R-ratio on crack growth behavior and to discuss fatigue crack growth mechanism. Crack growth curves arranged by ΔK showed clear R-ratio dependence even under no crack closure, where the values of ΔK_th were 0.82 and 0.33 MPa √m for R = 0.1 and 0.7 respectively. However, crack growth curves arranged by K_max merged into almost one curve regardless of R-ratio, which indicated that crack growth behavior of the present composite was time-dependent. The value of K_max,th were in the range from 0.78 to 1.12 MPa √m. In situ crack growth observation revealed the crack growth mechanism: micro-cracking near the interface between silica particle and resin matrix occurs ahead of a main crack and then micro-cracks coalesce with a main crack to grow. The crack path was in the epoxy matrix, which was consistent with the time-dependent crack growth.     

Analysis of vacuum fatigue crack growth results and its implications

Conventionally, the reduction of ΔK_th with load ratio R has been interpreted in terms of crack closure arising from plasticity, oxide or crack surface roughness. Since, plane-strain conditions exist near-threshold, plasticity-induced closure is absent. Therefore, to account for R-ratio effects near-threshold, the oxide and roughness closure mechanisms have been proposed. Further analysis has shown that these other two closure effects also are small, when the results taken in vacuum were included. The present analysis shows that there is a unique relation of the oxide thickness with a threshold K_max, rather than with a threshold ΔK. This threshold K_max (K*_max,th) depends on environment. When the applied K_max<K*_max,th, the crack is stationary in the presence of the oxide formation and grows only when the applied K_max>K*_max,th. Thus, the oxide thickness—K_max relation seems to have a bearing on the criterion for crack growth in the presence of the environment. Oxide formation passivates the crack surfaces and retards the environmental damage ahead of the crack-tip. Examples from CrMo and NiCrMo steels support this viewpoint and suggest that there is a pressing need for quantifying the crack-tip environmental effects and fatigue thresholds.     

Fatigue crack growth resistance of ECAPed ultrafine-grained copper

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

Crack closure and fatigue crack growth near threshold of a metastable austenitic stainless steel

In this paper R-ratio effects on fatigue crack growth near threshold region of a metastable austenitic stainless steel (MASS) in two different conditions, i.e. annealed and cold rolled, is investigated. The authors present two approaches to correlate FCGR data for R = 0.1, 0.3, 0.5, 0.7 and K_max = 23 MPa√m using a two-parameters approach (ΔK, K_max and α in Kujawski’s model) and crack closure model (using Elber’s K_op and in Donald’s ACRn2 approaches). The K_op and ACRn2 were experimentally measured on a single edge tension specimens. The K_op measurements were performed using a modified method and based on ASTM standards. While the two driving force approaches correlate data well in the Paris region, they fail to correlate them in the threshold region. However, this correlation can be improved in the threshold region when a different α value from the Paris region is used. The authors indicated that two different mechanisms operate; one in the Paris region and another in the near threshold. Hence, they proposed to combine the two-parameter and crack closure approaches where ΔK is replaced by ΔK_eff (estimated by a new method proposed in this paper), which is shown to correlate the FCGR data for different stress ratios for annealed steel. The correlation for cold rolled condition shows improvement with the new approach but is not as good as for the annealed one. The author further suggests to modify K_max in the two-parameter approach.     

Mode I fatigue crack-propagation mechanism based on the renewal stochastic damage-accumulation model

A mechanism of mode I fatigue-crack propagation, which involves the initiation and opening of the cleavage-mode crack, is proposed. This approach uses a renewal stochastic damage-accumulation model for crack propagation, in which the parameters are defined based on the dislocation density and the elastic energy of dislocation. The calculated results of ΔK_eff for da/dn agree with the experimental data. ΔK_eff th is calculated under the condition that the energy of cleavage-crack initiation is equal to that given from the outside of material. The plastic-zone size is calculated based on the number of dislocations on each slip line contained within it.     

Three-dimensional stress state around quarter-elliptical corner cracks in elastic plates subjected to uniform tension loading

Detailed full-field three-dimensional (3D) finite element analyses have been conducted to study the out-of-plane stress constraint factor T_z around a quarter-elliptical corner crack embedded in an isotropic elastic plate subjected to uniform tension loading. The distributions of T_z are studied in the forward section (0° ? θ ? 90°) of the corner cracks with aspect ratios a/c of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. In the normal plane of the crack front line, T_z drops radially from Poisson’s ratio at the crack tip to zero beyond certain radial distances. Strong 3D zones (T_z > 0) exist within a radial distance r/a of about 4.6-0.7 for a/c = 0.2-1.0 along the crack front, despite the stress-free boundary conditions far away. At the same radial distance along the crack front in the 3D zones, T_z increases from zero on one free surface to a peak value in the interior, and then decreases to zero on another free surface. The distributions of T_z near the corner points are also discussed. Empirical formulae describing the 3D distributions of T_z are obtained by fitting the numerical results, which prevail with a sufficient accuracy in the valid range of 0.2 ? a/c ? 1.0 and 0° ? θ ? 90° except very near the free surfaces where T_z is extremely low. Combined with the K-T solution, the transition of approximate plane-stress state near the surfaces to plane-strain state in the interior can be characterized more accurately.     

Analysis of high temperature fatigue crack growth behavior

High temperature fatigue crack growth has been examined in the light of the new concepts developed by the authors. We observe that the high temperature crack growth behavior can be explained using the two intrinsic parameters ΔK and K_max, without invoking crack closure concepts. The two-parameter requirement implies that two driving forces are required simultaneously to cause fatigue cracks to grow. This results in two thresholds that must be exceeded to initiate the growth. Of the two, the cyclic threshold part is related to the cyclic plasticity, while the static threshold is related to the breaking of the crack tip bonds. It is experimentally observed that the latter is relatively more sensitive to temperature, crack tip environment and slip mode. With increasing test temperature, the cycle-dependent damage process becomes more time-dependent, with the effect that crack growth is dominated by K_max. Thus, in all such fracture processes, whether it is an overload fracture or subcritical crack growth involving stress corrosion, sustained load, creep, fatigue or combinations thereof, K_max (or an equivalent non-linear parameter such as J_max) remains as one essential driving force contributing to the final material separation. Under fatigue conditions, cyclic amplitude ΔK (or an equivalent non-linear parameter like ΔJ) becomes the second necessary driving force needed to induce the characteristic cyclic damage for crack growth. Cyclic damage then reduces the role of K_max required for crack growth at the expense of ΔK.     

IN SITU SEM MEASUREMENTS OF CRACK CLOSURE FOR SMALL FATIGUE CRACKS IN ALUMINIUM 2024-T351

Abstract Crack closure has been measured for a range of small, self-initiated fatigue cracks using in situ SEM loading. Cracks were grown at positive R ratios in the aluminium alloy 2024-T351 and at nominal ΔK levels that extend substantially below the corresponding long crack threshold. The crack closure stress of the small cracks decreased and the K_cl level increased with increasing crack size until the long crack value near threshold was reached. For cracks of depth larger than about one grain size, a good correlation was obtained between small and long crack growth rate data in terms of ΔK_eff     

Acoustic emission study of fatigue crack closure of physical short and long cracks for aluminum alloy LY12CZ

Crack closure of physical short and long cracks of LY12CZ aluminum alloy during fatigue process was investigated using acoustic emission (AE) technique. Results showed that the effective fatigue crack growth curve (da/dN vs. ΔK_eff) of physical short and long cracks obtained by the AE technique was consistent with the effective fatigue crack growth curve at high stress ratio (R = 0.8), which implied that the AE technique could measure the crack closure level, especially for physical short crack. The growth rate of physical short crack was much higher than that of long crack at the same ΔK, and the lower crack closure level of short crack was the main reason.     

On the dominant role of crack closure on fatigue crack growth modeling

Crack closure is the most used mechanism to model thickness and load interaction effects on fatigue crack propagation. But assuming it is the only mechanism is equivalent to suppose that the rate of fatigue crack growth da/dN is primarily dependent on ΔK_eff=K_max−K_op, not on ΔK. But this assumption would imply that the normal practice of using da/dN×ΔK curves measured under plane-stress conditions (without considering crack closure) to predict the fatigue life of components working under plane-strain could lead to highly non-conservative errors, because the expected fatigue life of “thin” (plane-stress dominated) structures could be much higher than the life of “thick” (plane-strain dominated) ones, when both work under the same stress intensity range and load ratio. However, crack closure cannot be used to explain the overload-induced retardation effects found in this work under plane-strain, where both crack arrest and delays were associated to an increase in ΔK_eff. These results indicate that the dominant role of crack closure in the modeling of fatigue crack growth should be reviewed.     

THE INFLUENCE OF AGE-HARDENING ON FATIGUE CRACK PROPAGATION BEHAVIOUR IN 7075 ALUMINIUM ALLOY IN VACUUM

Abstract— The influence of age-hardening on the middle and low crack growth rates of a 7075 Al alloy is studied in vacuum. A transition in fracture surfaces morphology and crack growth curves is observed with the T 651 and T 7351 treatments in the near-threshold regime. Measurements of crack closure show its dependance on surfaces roughness and explain the lack of dependance of ΔK_th with load ratio, except for the T 7351 alloy. An equation of crack growth rate to the fourth power of ΔK_eff is in good agreement only with the crack propagation curves obtained for microstructure with an homogeneous deformation mode.     

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.     

A TECHNICAL NOTE. INFLUENCE OF MEAN STRESS ON FATIGUE IN SEVERAL ALUMINIUM ALLOYS UTILIZING Kcmax THRESHOLD PROCEDURES

Recent interest in the constant K_max (K^c_max) threshold testing procedure has resulted in a more in-depth study of the influence of K_max level on fatigue response and ΔK_th in aluminium alloys. Under R^c= 0.1 conditions, which cause large amounts of closure, ΔK^th levels were typically 2 to 4 Mpam. However, under K^c_max test procedures, associated with no measurable closure at threshold, ΔK_th was typically 1 Mpam. A slight K^c_max level effect on ΔK_th was observed at high K_max values for some of the alloys, and was deemed to be a pure mean stress effect, separate from closure arguments.     

Correlation and prediction of fatigue crack growth for different R-ratios using Kmax and ΔK parameters

This paper summarizes a study which has been conducted to examine the recently proposed fatigue crack driving force parameter, , and its ability to predict the crack growth rate for different R-ratios. A validation of the effectiveness of the proposed K∗ parameter relative to the existing crack closure approach, ΔK_eff, is analyzed and discussed. Experimental data for ten different types of materials taken from literature were used in the analyses. Presented results indicate that the K∗ parameter is equally effective or better than ΔK_eff in correlating and predicting the R-ratio effects on crack growth rate.     

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.     

Crack closure and influence of cycle ratio R on fatigue crack growth in type 304 stainless steel at room temperature

Crack growth rate and crack closure during fatigue of type 304 stainless steel are measured with an optical microscope and television camera. Based on the crack closure data an effective stress intensity range ΔK_eff is calculated. The da/dn vs ΔK_eff-curves indicate that crack closure could account for the R-influence as normally derived from da/dn vs ΔK-curves. Measurements of striation spacing lead to the conclusion that at higher da/dn values crack growth mechanisms dependent on K_max play an important role; these mechanisms are probably responsible for the R-influence in the range of the higher da/dn-values.     

Effect of welding residual stresses on fatigue crack growth thresholds

Fatigue crack growth thresholds ΔK_th were determined for friction stir welded butt joints made from aluminium alloys AA2024 and AA6013. Plotting the thresholds as a function of load ratio R showed distinctly higher amounts for welded joints as compared to those for parent material at small load ratios, but differences became smaller with increasing load ratio, until thresholds became finally identical for the highest R values. Applying Döker’s concept of two controlling parameters, namely ΔK and K_max [1], and plotting ΔK_th versus K_max, however, revealed that the effective threshold ΔK_th,eff determined at very high R ratios was nearly independent on the alloy and, simultaneously, was identical for parent material and respective welded joints. Thus, differences in threshold behaviour were only caused by the second threshold K_max,th, which was significantly higher for welded joints as compared to parent material. Differences in K_max,th coincided with compressive residual stresses determined by cut-compliance measurements in terms of stress intensity factors K_rs acting at the crack tip. Based on the analytical approach described by Döker [1], only one characteristic K_rs value was needed to calculate all thresholds of welded joints for 0 ⩽ R ⩽ 1 provided a base material master curve is available.     

On the development of crack closure at high R levels after an overload

ABSTRACT In a 1999 paper it was asserted that crack closure cannot be of major importance in the mechanism of crack retardation following an overload, particularly since the authors found no evidence for crack closure at high R‐values, although crack retardation was observed. In the present work, overload experiments were carried out at R = 0.5 and crack closure was observed. In addition, the rate of fatigue crack growth in both constant amplitude and overload tests was found to be a function of ΔK_eff. It is concluded that crack closure is an important part of the retardation mechanism.     

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