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.     

Mechanisms for corrosion fatigue crack propagation

ABSTRACT The corrosion fatigue crack growth (FCG) behaviour, the effect of applied potential on corrosion FCG rates, and the fracture surfaces were studied for high‐strength low‐alloy steels, titanium alloys, and magnesium alloys. During investigation of the effect of applied potential on corrosion FCG rates, polarization was switched on for a time period in which it was possible to register the change in the crack growth rate corresponding to the open‐circuit potential and to measure the crack growth rate under polarization. Due to the higher resolution of the crack extension measurement technique, the time rarely exceeded 300 s. This approach made possible the observation of a non‐single mode effect of cathodic polarization on corrosion FCG rates. Cathodic polarization accelerated crack growth when the maximum stress intensity (K_max) exceeded a certain well‐defined critical value characteristic for a given material‐solution combination. When K_max was lower than the critical value, the same cathodic polarization, with all other conditions (specimen, solution, pH, loading frequency, stress ratio, temperature, etc.) being equal, retarded or had no influence on crack growth. The results and fractographic observations suggested that the acceleration in crack growth under cathodic polarization was due to hydrogen‐induced cracking (HIC). Therefore, critical values of K_max, as well as the stress intensity range (ΔK) were regarded as corresponding to the onset of corrosion FCG according to the HIC mechanism and designated as K_HIC and ΔK_HIC. HIC was the main mechanism of corrosion FCG at K_max > K_HIC (ΔK > ΔK_HIC). For most of the material‐solution combinations investigated, stress‐assisted dissolution played a dominant role in the corrosion fatigue crack propagation at K_max < K_HIC (ΔK < ΔK_HIC).     

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.     

Fretting fatigue limit as a short crack problem at the edge of contact

This paper proposes a local stress concept to evaluate the fretting fatigue limit for contact edge cracks. A unique S–N curve based on the local stress could be obtained for a contact edge crack irrespective of mechanical factors such as contact pressure, relative slip, contact length, specimen size and loading type. The analytical background for the local stress concept was studied using FEM analysis. It was shown that the local stress uniquely determined the ΔK change due to crack growth as well as the stress distribution near the contact edge. The condition that determined the fretting fatigue limit was predicted by combining the ΔK change due to crack growth and the ΔK_th for a short crack. The formation of a non‐propagating crack at the fatigue limit was predicted by the model and it was experimentally confirmed by a long‐life fretting fatigue test.     

Parameters affecting the damage tolerance behaviour of railway axles

The paper provides a discussion on damage tolerance options applied to railway axles and factors influencing the residual lifetime as well as the required inspection interval. These comprise material properties such as the scatter of the da/dN–ΔK curve, the fatigue crack propagation threshold ΔK_th and the toughness of the material. Parameters affecting axle loading such as the press fit, rotating bending, load history and mixed crack opening modes are discussed. Finally the influence of the initial crack geometry on residual lifetime is simulated.     

Potential resistance to transgranular fatigue crack growth of Fe–C alloy with a supersaturated carbon clarified through FIB micro-notching technique

The threshold stress intensity factor range (ΔK_th) of water-quenched Fe–0.017C (wt.%) fully ferritic steel was determined using room-temperature fatigue tests on micro-notched specimens. The experimentally determined ΔK_th was approximately 40.5% higher than conventionally predicted results. This extraordinary resistance to transgranluar fatigue crack propagation likely results from the strain–age hardening.     

Elastic correction of fatigue crack growth laws

Fatigue crack growth (FCG) is usually studied assuming that ΔK is the driving parameter. An effective ΔK is considered in the presence of crack closure. However, after crack opening, there is an elastic regime that does not contribute to FCG. The objective here is to quantify this elastic range of ΔK, ΔK_el, for different loading conditions and material properties. The yield stress was found to be the most important material parameter, followed by the hardening exponent. A linear decrease of ΔK_el with ΔK was found for the 7050‐T6, 6082‐T6, and 6016‐T4 aluminium alloys, while the 304L stainless steel presented a slight increase. On the other hand, the increase of K_max was found to increase the elastic fatigue range. Relatively high values of elastic range were obtained for the plane strain state, compared with the plane stress state.     

Effect of sudden load decrease on the fatigue crack growth in cold drawn prestressing steel

This paper analyzes the overload retardation effect (ORE) on the fatigue crack growth (FCG) of cold drawn prestressing steel when different loading sequences are used. The ORE is more intense for elevated load decrease or for low initial stress intensity factor (SIF) range ΔK₀. A transient stage can be observed in the Paris curve (da/dN–ΔK) when the K_maxΔK value suddenly decreases, associated with the ORE and with the evolution of the plastic zone and compressive residual stresses near the crack tip. In tests with K_max decrease, a small zone appears related to FCG initiation, with a fatigue fractography resembling the tearing topography surface (TTS) mode, and associated with a decrease of crack tip opening displacement (CTOD).     

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.     

FATIGUE CRACK GROWTH UNDER MIXED MODES I AND II

Fatigue crack growth behaviour under mixed modes I and II was studied by applying in-phase alternating tensile and torsional loading to a thin-walled hollow cylindrical specimen with an initial crack. In the linear region of a log-log plot where da/dN=A(ΔK)^m, da/dN at first decreases with increasing ΔK₁₁₀ component and then approaches a minimum close to the value of ΔK₁₁₀/ΔK₁₀～ 0.58; here ΔK₁₁₀/ΔK₁₀ is the ratio of the initial ΔK_II to the initial ΔK₁., When ΔK₁₁₀/ΔK₁₀ increases further, da/dN increases. Under shear mode, da/dN becomes higher than that under mode I. The ΔK₁, and ΔK₁₁ components during fatigue crack growth under mixed mode loading increase and decrease, respectively, with an increase in da/dN In the low crack growth rate region the fatigue crack growth rates accelerate with an increase of the initial ΔK₁₁ component, ΔK₁₁₀. Fatigue life increases with increase of ΔK₁₁₀/ΔK₁₀ under the test condition of equivalent stress range being kept constant and the pre-crack length being the same.     

Short crack threshold estimates to predict notch sensitivity factors in fatigue

The notch sensitivity factor q can be associated with the presence of non-propagating fatigue cracks at the notch root. Such cracks are present when the nominal stress range Δσ_n is between Δσ₀/K_t and Δσ₀/K_f, where Δσ₀ is the fatigue limit, K_t is the geometric and K_f is the fatigue stress concentration factors of the notch. Therefore, in principle it is possible to obtain expressions for q if the propagation behavior of small cracks emanating from notches is known. Several expressions have been proposed to model the dependency between the threshold value ΔK_th of the stress intensity range and the crack size a for very small cracks. Most of these expressions are based on length parameters, estimated from ΔK_th and Δσ₀, resulting in a modified stress intensity range able to reproduce most of the behavior shown in the Kitagawa–Takahashi plot. Peterson or Topper-like expressions are then calibrated to q based on these crack propagation estimates. However, such q calibration is found to be extremely sensitive to the choice of ΔK_th(a) estimate. In this work, a generalization version of El Haddad–Topper–Smith’s equation is used to evaluate the behavior of cracks emanating from circular holes and semi-elliptical notches. For several combinations of notch dimensions, the smallest stress range necessary to both initiate and propagate a crack is calculated, resulting in expressions for K_f and therefore for q. It is found that the q estimates obtained from this generalization, besides providing a sound physical basis for the notch sensitivity concept, better correlate with experimental data from the literature.     

Fatigue behaviour of a box-welded joint under biaxial cyclic loads

Multiaxial fatigue behaviour of box-welded (wrap-around) joints in a JIS SM400B steel (12-mm-thick plate) was examined using a biaxial fatigue test facility. For the specimen, two stiffeners were attached to a main plate by a CO₂ semi-automatic welding procedure. Residual stress measurements and finite element (FE) analyses were also performed. Fatigue tests were performed under both uniaxial and biaxial (mainly out-of-phase) cyclic loads, and both results were compared and examined. It was found that fatigue cracks in the biaxial fatigue test specimens were initiated at the boxing-weld toes and propagated almost in the direction of the lateral loads. This is considered to be due to the dominant direction of tensile residual stresses from welding and the stress concentration in the vicinity of the boxing-weld toe. From the relation between the strain range near a weld toe, Δε₅ , and the fatigue lives, it was found that crack initiation life, N_c , was almost equivalent in the biaxial and uniaxial fatigue tests, while the failure life, N_f , was slightly longer in the biaxial tests. However, when the fatigue lives are put in order using the stress range near a weld toe, Δσ₅ , the crack initiation life, N_c , in the out-of-phase biaxial tests (phase difference of π) is ~30% lower than in the in-phase biaxial and uniaxial tests, while the failure life, N_f , was almost equivalent in the biaxial and uniaxial tests. From these results, it is concluded that an increase in Δσ₅ (lowering of the minimum value of σ₅ ), induced by the out-of-phase lateral loads, leads to an increase in fatigue damage where the high tensile welding residual stresses exist in the vicinity of the boxing-weld toe. Finally, a simple life estimation for the biaxial fatigue tests was made using FE analyses and the results of the uniaxial fatigue tests, proving that the effects of the lateral loads should be taken into consideration.     

Fatigue crack growth of AA2219 under different aging conditions

The fatigue crack growth of commercial AA2219 has been examined under different aging treatments, namely, naturally aged (NA), under aged (UA), peak aged (PA) and over aged (OA) conditions. From the near threshold stress intensity range (ΔK_NTH), the alloy in the NA condition is found to have the highest resistance to fatigue crack initiation. The crack growth rate increases and the near threshold stress intensity range decreases with advancing aging. This observation is found to be consistent with lower levels of crack closure and decreasing levels of tortuosity in crack path for PA and OA tempers. The inhomogeneous transcrystalline slip in the UA condition results in the slower crack growth at low stress intensity range (ΔK). The fracture morphology changes from crystallographic facets near the threshold region to clearly developed ductile striations in the Paris power-law regime to microvoid coalescence in the high ΔK regions.     

The effect of mean stress on delay in fatigue crack growth under load stepdown

The effect of mean stress together with decreasing stress range on fatigue crack propagation behaviour in mild steel is investigated. The delay period between crack arrest and reprogation is found to be a function of the maximum stress intensity factor stepdown ration, K_2max/K_1max. Delay only occurs when this ratio is less than unity. For specimen thicknesses of 1.6 to 6.4 mm, non-propagating cracks, where the affected delay cycles are 500 000 cycles or greater, appear to occur when K_2max/K_1max has a value of approximately 0.7 and the stepdown plastic zone size is about half the initial load plastic zone size, which is approximately equal to the affected crack length.     

Acceleration of FCP in toughened PMMA following a step increase in load amplitude

Fatigue crack growth measurements on rubber-toughened poly(methyl methacrylate) show that the relationship between crack growth rate da/dn and stress intensity range ΔK can be represented by two intersecting Paris curves of different slope. Sudden increases in load amplitude cause an acceleration in crack growth rate which is much greater than that predicted by the Paris law, but the rate falls sharply over the first 10 cycles at high stress amplitude, tending asymptotically to the ‘Paris values’ for mature crack growth. Results for crack extension during the first high load cycle indicate that accelerated growth occurs even when the increase in load amplitude is relatively small (there is no observable threshold) and that crack growth rates are dependent only on K_max for ΔK_high/ΔK_low above about 1.5.     

Small fatigue crack growth behavior of titanium alloy TC4 at different stress ratios

In this paper, the small fatigue crack behavior of titanium alloy TC4 at different stress ratios was investigated. Single‐edge‐notch tension specimens were fatigued axially under a nominal maximum stress of 370 MPa at room temperature. Results indicate that fatigue cracks in TC4 initiate from the interface between α and β phases or within α phase. More than 90% of the total fatigue life is consumed in the small crack initiation and growth stages. The crack growth process of TC4 can be divided into three typical stages, ie, microstructurally small crack stage, physically small crack stage, and long crack stage. Although the stress ratio has a significant effect on the total fatigue life and crack initiation life at constant σ_max, its effect on crack growth rate is indistinguishable at R = ?0.1, 0.1, and 0.3 when crack growth rate is plotted as a function of ?K.     

LIMITATIONS ON THE USE OF THE STRESS INTENSITY FACTOR, K, AS A FRACTURE PARAMETER IN THE FATIGUE PROPAGATION OF SHORT CRACKS

Abstract— It is well known that for very short cracks the stress intensity factor K is not a suitable parameter to estimate the stress level over the small but finite Stage II process zone activation region of size r_s near the crack tip, within which crack growth events take place. A critical appreciation of the reasons for the limitations on the applicability of ΔK as a fatigue crack propagation (FCP) parameter, when the crack length a is of the same order of magnitude or smaller than the size of the ‘fatigue-fracture activation region’, r_s is presented. As an alternative to ΔK the range Δσ_s of the cyclic normal stress at a point situated at the fixed distance s=r_s/2, ahead of the crack tip, inside the fatigue-fracture activation region, is proposed. It is observed that the limitation on the use of ΔK when the crack is short, is mathematical (and not physical) but this inconvenience is easily circumvented if the stress Δσ_s at the prescribed distance is used instead of ΔK since nowadays Δσ_s can be obtained numerically by using finite element methods (FEM). It follows that the parameter Δσ_s is not restricted by the mathematical limitations on ΔK and so it would seem that there is, a priori, no reason why the validity of the parameter Δσ_s cannot be extended to short cracks. It is shown that if the Paris law is expressed in terms of Δσ_s (πrr_s)^½ instead of ΔK the validity of the modified Paris law can be extended to short cracks. A coherent estimate of the value of the fatigue-fracture activation region r_s is derived in terms of the fatigue limit Δσ_FL obtained from S-N tests and of the threshold value ΔK_th obtained from tests on long cracks where both relate to Stage II crack growth that ends in failure, namely, r_s= (ΔK_th/Δσ_FL)²/π. An overall, threshold diagram is presented based on the simple criterion that, for sustained Stage II FCP, Δσ_s must be greater than Δσ_FL. The study is based on a simple continuum mechanics approach and its purpose is the investigation of the suitability of both ΔK and Δσ_s to characterise the crack driving force that activates complex fracture processes at the microstructure's scale. The investigation pertains to conditions that lead to the ultimate failure of the component at values of Δσ_s > Δσ_FL.     

Fatigue assessment using an integrated threshold curve method - applications

This paper deals with the analysis and prediction of a high-cycle fatigue behaviour in notched and damaged specimens, as well as butt-welded joints by using a threshold curve for fatigue crack propagation that includes the short crack regime (a function of crack length, a). The approach regards the effective driving force applied to the crack as the difference between the total applied driving force defined by the applied stress distribution corresponding to a given geometrical and loading configuration, ΔK(a), and the threshold for crack propagation, ΔK_th(a). Chapetti’s model is used to estimate the threshold for crack propagation by using the plain fatigue limit, Δσ_eR, the threshold for long cracks, ΔK_thR, and the microstructural characteristic dimension (e.g. grain size). Applications, predictions and results, in good agreement with experimental results from the literature, demonstrate the ability of the method to carry out quantitative analyses of the high cycle fatigue propagation behavior (near threshold) of short cracks in different geometrical, mechanical and microstructural configurations.     

Multiple mechanisms controlling fatigue crack growth

Recognizing that fatigue is a two‐parameter problem requiring two load parameters to define cyclic loads unambiguously, a unified approach has been developed to account for crack growth behaviour in terms of ΔK and K_max . Since both driving forces govern the crack growth rate, any analysis based on either ΔK or K_max will provide only partial information about the fatigue behavior of materials. It is shown that ΔK–K_max plots and the associated crack growth trajectory maps reflect the basic mechanisms that contribute to crack growth in a material. These plots also provide a convenient basis to recognize the changes in the micromechanisms that can occur as a function of load ratio or crack growth rate, or both. Taking examples from the literature, crack growth trajectory maps are provided showing such changes in the governing mechanisms of crack growth. It is shown that the ΔK–K_max approach is not an alternative to crack closure models, but it reflects the intrinsic material behaviour that must be understood before reliable crack prediction models can be developed.     

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.