Fatigue crack propagation and cyclic deformation at a crack tip

The fatigue crack propagation relation da/dN = f(R)ΔK² can be derived with three assumptions: small scale yielding, material homogeneity and that crack tip stresses and strains are not strongly affected by plate thickness. f(R) is a constant at a given stress ratio, R. The effects of plate thickness and stress ratio on crack tip deformation and fatigue crack growth in 2024-T351 aluminum alloy were studied. High ΔK level in a thin specimen causes crack tip necking. Necking is more pronounced at high stress ratio. Necking causes high maximum strain near a crack tip, ε_max, and fast crack growth rate. In order to avoid the effects of crack tip necking, plates thicker than 2.5 (ΔK/σ_Y(c))² should be used.     

FRACTOGRAPHIC ANALYSES OF FATIGUE CRACK GROWTH IN D16T ALLOY SUBJECTED TO BIAXIAL CYCLIC LOADS AT VARIOUS R-RATIOS

Abstract Fractographic peculiarities of fatigue crack development are studied in cruciform specimens of D16T aluminium alloy under biaxial tension and tension-compression. In the range of the biaxial load ratios λ from - 1 to +1.5, and in the range of R-ratios 0.05 to 0.8, fatigue striation formation took place over a crack growth rate near to 4×10^?8 m/cycle. The striation spacing and the crack growth rate decrease as the ratios λ and R increase. The ratio between the increment of crack growth, da/dN, and the striation spacing, δ, is approximately 1:1 when da/dN is greater than 4×10-^?8 m/cycle. The relationship between the number of cycles from the beginning of a test up to the growth rate of 2.14×10^?7 m/cycle (N_d), and the crack growth period, _Np, from when the crack initiates up to the instant when that growth rate is reached, was determined for different λ and R-ratios. The value of N_d increases as the stress ratio, λ, is increased. Cycle loading parameters must be taken into account in order to describe the crack growth period when using a unified method involving an equivalent stress intensity factor K_e, =K₁,F(λ, R_s). The values of F(λ, R) for the growth rate (F(λ, R)_s) and for the striation spacing (F(λ, R_s) were determined and compared. The fatigue crack growth period, N^t_p, applicable to the stage of fatigue striation formation, (predicted by using both of the F(λ, R) values) is correlated with the experimental data and the error is of the order of 15%.     

Relationship between fatigue crack growth behaviour and local hydrogen concentration near crack tip in pipeline steel

The work is dedicated to evaluation of fatigue crack growth rate in pipeline steel under hydrogenating conditions with taking into account of local hydrogen concentration near the crack tip. The measurement of local hydrogen concentration C_H in metal was made by special technique of mass-spectroscopy with laser microprobe. It has been found that fatigue crack growth rate da/dN is the function of some critical combination of following parameters: local hydrogen concentration at the crack tip C_H(t), hydrogen concentration in bulk of metal C_H(v) and range of stress intensity factor ΔK. The application of derived formula for fracture risk assessment of defected pipeline is shown.     

An investigation of the edge-sliding mode in fracture mechanics

A boundary collocation procedure has been applied to the Williams stress function to determine the elastic stress distribution for the crack tip region of a finite, edge-cracked plate subjected to mode II loading at the crack tips. The asymmetric specimen selected was particularly suitable for the determination of plane strain fracture toughness for mode II loading. Numerical solutions for stress intensity factors for the edge-sliding mode obtained by the boundary collocation method were in close agreement with values obtained from photoelastic experiments.Fracture tests of several compact shear specimens of 2024-T4 aluminum were conducted in order to experimentally investigate the behavior of the edge-sliding mode. In each case a brittle shear failure was observed and mode II fracture toughness values were obtained. The average value for K_IIc obtained from two tests was 39.5 ksi(in)^{$\text{1}\text{2}$}. No K_Ic. data for 2024-T4 were available for comparison purposes; however, K_Ic values for a similar alloy, 2024-T351, have been reported as 34ksi(in)^{$\text{1}\text{2}$} which is only about 15 per cent below the corresponding K_IIc value.     

Experimental estimation of the probability distribution of fatigue crack growth lives

This paper deals with a method to estimate numerically the reliability of fatigue sensitive structures with respect to fatigue crack growth. A method is proposed to experimentally determine the probability distribution functions of material parameters of the Paris law, da/dN = C(ΔK/K₀)^m, using stress intensity factor controlled tests. The auto-correlation function of the resistance to fatigue crack growth, 1/C, is also estimated from the experimental data. The results of a high tensile strength steel show that the distribution of the parameter, m, is approximately normal and that of 1/C is a 3-parameter Weibull. The merit of the proposed method is that only a small number of tests are required to determine these functions. The probability distribution of the fatigue crack length after a given number of load cycles or the number of load cycles for a crack to reach a given length can be estimated by simulations of non-Gaussian random processes having these functions.     

Temperature effects on the fatigue of highly filled PMMA

The modulus and fracture toughness of an ATH-filled PMMA composite are determined as a function of temperature. The modulus can be modelled as a series addition of the two phases, giving a decreasing modulus with temperature tending to zero at 110°C. The K_1C value remains constant. Fatigue crack growth data in the form of da/dN versus K were obtained as a function of temperature and modelled using the Paris Law. The power index remained constant at 7.5, but the coefficient had a maximum at 50°C. It is suggested that this arises from microcracks generated by interparticle thermal stresses which are shown to have a maximum at the same temperature (50°C). A two-stage zone fatigue crack growth model was also applied to the data and gave a damage stress which correlated with the thermal stress and suggested a criterion based on achieving a constant energy per unit area.     

Cyclic fatigue crack growth of SiCw/Y-TZP composites: long- and short-crack behaviour

Cyclic fatigue crack growth behaviour has been investigated for 10 vol % SiC_w/Y-TZP composites with grain sizes varying from 1.50–2.00 m in a residual stress field. To investigate the effect of precracking procedure, cyclic fatigue tests were performed on unannealed specimens using the four-point bending method under two conditions: (a) with a sharp crack and precracking procedure, and (b) with a natural sharp flaw. For all specimens in both conditions, an overall V-shaped da/dN versus K _app relation was obtained. However, for the specimens without precracking, the da/dN had an unusual dependence on the applied stress intensity, giving a zigzag V-shaped curve. Explanations for these different results for the two conditions are discussed in terms of crack-tip shielding effects and residual stress field.     

Effect of impact modification on slow crack growth in poly(vinyl chloride)

The effect of impact modification on slow crack growth in a poly(vinyl chloride) (PVC) compound was examined in order to test a methodology for predicting long-term creep fracture from short-term tension-tension fatigue tests. In all cases the crack propagated in a stepwise manner through a crack tip craze zone. Step length was analyzed in terms of the Dugdale model for a crack tip plastic zone. The overall crack growth rate in fatigue and creep followed the conventional Paris power law with the same power 2.7, da/dt = A _f K _I ^2.7 and da/dt = BK _I ^2.7,respectively. The effects of frequency, temperature, and R-ratio (the ratio of the minimum to maximum stress intensity factor in the fatigue loading cycle) on the Paris prefactor were determined. Crack growth rate was modeled as the product of a creep contribution that depended only on the maximum stress intensity factor and a fatigue contribution that depended on strain rate da/dt = B _f K _I,max ^2.7 (1 + C , where C is a coefficient defining the strain rate sensitivity. A linear correlation allowed for extrapolation of the creep prefactor B _f from fatigue data. Impact modification decreased B _f but had no effect on C.     

A French guideline for defect assessment and leak before break analysis

A large program was launched in France in order to develop defect assessment procedures and leak-before-break methods (LBB) applicable for the design and for operating FBR plants. As a result of the collaboration between CEA, EdF and Novatome, a French guideline A16 has been produced as a first step in order to produce further documents in RCC-MR for design and for in-service inspection. This paper presents the main items developed in this guide considering low and high temperature: ? fatigue or creep-fatigue crack initiation based on the σ_d approach calculating stress and strain at a distance d=50 μm from the crack tip.

? fatigue crack growth based on da/dN-δK_eff relationship with a δK_eff derived from a simplified estimation of δJ by reference stress.

? creep-fatigue crack growth adding the fatigue crack growth and the creep crack growth during the hold time derived from a simplified evaluation of C*,

? ductile tearing based on simplified estimation of J (reference stress method) and plastic collapse of the ligament with and without holdtime,

? leak-before-break procedure.

Some detailed examples explaining the use of this A16 guide are presented.     

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).     

Calculating crack growth from small discontinuities in 7050-T7451 under combat aircraft spectra

This paper supplements previous work which showed that the crack growth rate in a large range of metallic materials fitted a variant of the Hartman–Schijve equation where da/dN is a function of (ΔK − ΔK_thr)^α, where ΔK_thr is a parameter that reflects the apparent fatigue stress intensity threshold of the material, and α is approximately 2. For the case of 7050-T7451 aluminium alloy the same equation is shown to fit both long and short crack growth data once the appropriate ΔK_thr is chosen for each specific data set. This equation is used here to produce accurate predictions of the fatigue crack growth in 7050-T7451 aluminium alloy specimens with both a low and high stress concentration subjected to two combat aircraft loading spectra. Thus, it is postulated that if long crack data are fitted to the variant of the Hartman–Schijve equation then accurate predictions can be made in the short crack regime for a wide range of materials.     

Effects of various environments on fatigue crack growth in Laser formed and IM Ti–6Al–4V alloys

The fatigue crack growth behaviors of Laser formed and ingot metallurgy (IM) Ti–6Al–4V alloys were studied in three environments: vacuum, air and 3.5% NaCl solution. Taking the Unified Fatigue Damage Approach, the fatigue crack growth data were analyzed with two intrinsic parameters, stress intensity amplitude ΔK and maximum stress intensity K_max, and their limiting values ΔK^* and . Fatigue crack growth rates da/dN were found increase with stress ratio R, highest in 3.5% NaCl solution, somewhat less in air and lowest in vacuum, and higher in IM alloy than in Laser formed one. In 3.5% NaCl solution, stress corrosion cracking (SCC) was superimposed on fatigue at R=0.9 for where K_max>K_ISCC, the threshold stress intensity for SCC. This and environment-assisted fatigue crack growth were evidenced by the deviation in fatigue crack growth trajectory (ΔK^* vs. curve) from the pure fatigue line where . Furthermore, the fractographic features, identified along the trajectory path, reflected the fatigue crack growth behaviors of both alloys in a given environment.     

Propagation of “small fatigue crack” initiated from notch-root

Recently, early stage of initiated fatigue crack propagation, so-called, “small crack” propagation behavior from notch-root is becoming more and more important for the developement of improved prediction of fatigue life of structural components. In the present paper, fine-grid-method which was already presented in the previous paper was applied to this problem. Special attention was given to the crack-tip strain changes of “small crack” engulfed in the plastic field of the notch. The relationship between fatigue crack propagation rate, $\text{da}\text{dN}$, and stress intensity factor range, ΔK, as well as local crack-tip strain range, Δ?^T, which was previously proposed by the authors were investigated.     

Parameter representation of fatigue crack growth

From the study of the crack propagation data in fatigue, a parameter in the form P = mlogδK + C has been suggested, where the slope m and the intercept C are functions of the variables like stress ratio R, frequency w, and temperature T. Case studies where data are available for various stress ratios have been made and a Master Curve connecting the crack propagation rate da/dN and the parameter P has been obtained. Experimental data for various values of δK and R have been found to agree well with the theoretical prediction.     

Correlation of fatigue and creep crack growth in poly(vinyl chloride)

Slow crack growth in PVC pipe was studied in order to develop a methodology for predicting long-term creep fracture from short-term tension-tension fatigue tests. In all cases, the crack propagated continuously through a crack-tip craze. In fatigue, the density of drawn craze fibrils gradually increased with decreased frequency and increased temperature. At the lowest frequency, 0.01 Hz, the fibril density in fatigue approached that in creep. The kinetics of fatigue and creep crack growth followed the conventional Paris law formulations with the same exponent 2.7, da/dt = A _f K _I ^2.7, da/dt = BK _I ^2.7, respectively. The effects of frequency, temperature and R-ratio (the ratio of minimum to maximum stress intensity factor in the fatigue loading cycle) on the Paris law prefactors were characterized. Comparison of frequency and R-ratio tests revealed that the fatigue contribution depended on strain rate. Therefore, at each temperature, crack growth rate was modeled as the product of a creep contribution that depended only on the maximum stress intensity factor and a fatigue contribution that depended on strain rate: (da/dt) = BK _I,max ^2.7 (1 + C), where B is the prefactor in the Paris law for creep and C is a coefficient defining the strain rate sensitivity. A linear correlation allowed extrapolation of the creep prefactor (B) from fatigue data. The extrapolated values were systematically higher than the values measured directly from creep and only converged at T _g . The difference was attributed to damage of the craze fibrils during crack closure upon unloading in the fatigue cycle.     

Predicting fracture and fatigue crack growth properties using tensile properties

The safe-life assessment of components requires information such as the plane stress (K_c), plane strain (K_Ic), part-through fracture toughness (K_Ie), and the fatigue crack growth rate properties. A proposed parametric/theoretical approach, based on an extended Griffith theory is used to derive fracture toughness properties and generate fatigue crack growth rate data for a range of alloys. The simplicity of the concept is based on the use of basic, and in most cases available, uniaxial stress-strain material properties data to derive material fracture toughness values. However since the methodology is in part based on an empirical relationship a wide ranging validation with actual data is required. This paper uses steel, aluminum and titanium based alloys from a pedigree database to quantify material properties sensitivity to the predictions for K_Ic and K_c and the subsequent estimation of ΔK_th threshold and the Paris constants, C and n values. A sensitivity analysis using experimental scatter bounds show the range of da/dN predictions can be achieved. It is found K_Ic/ΔK_th ratios designated as α has a range of 5-25 irrespective of tensile ductility, ε_f, and is insensitive to it. The value of ΔK_th for all the alloys considered was found to be proportional to the final elongation, ε_f, and an empirical relationship describing ΔK_th as a function of ε_f was established. Furthermore it is suggested that, with the knowledge of appropriate tensile properties and the estimated range of K_Ic/ΔK_th ratios for the different alloys applying this method could be an appropriate tool that can be used to conservatively predict fracture and fatigue in similar alloy categories. Thus helping to reduce costs and optimize the number of experimental tests needed for alloy characterizations.     

Fatigue crack growth of a metastable austenitic stainless steel

The fatigue crack growth behavior of an austenitic metastable stainless steel AISI 301LN in the Paris region is investigated in this work. The fatigue crack growth rate curves are evaluated in terms of different parameters such as the range of stress intensity factor ΔK, the effective stress intensity factor ΔK_eff, and the two driving force parameter proposed by Kujawski K¹.The finite element method is used to calculate the stress intensity factor of the specimens used in this investigation. The new stress intensity factor solution has been proved to be an alternative to explain contradictory results found in the literature.Fatigue crack propagation tests have been carried out on thin sheets with two different microstructural conditions and different load ratios. The influence of microstructural and mechanical variables has been analyzed using different mechanisms proposed in the literature. The influence of the compressive residual stress induced by the martensitic transformation is determined by using a model based on the proposal of McMeeking et al. The analyses demonstrate the necessity of including K_max as a true driving force for the fatigue crack growth. A combined parameter is proposed to explain the effects of different variables on the fatigue crack growth rate curves. It is found that along with residual stresses, the microcracks and microvoids are other factor affecting the fatigue crack growth rate in the steel studied.     

Cyclic fatigue crack growth tests on disc specimens

A ring has been designed and built in which four disc specimens containing bore cracks were subjected to fatigue conditions by continuous cycling between variable upper and lower speed limits. The behaviour of the individual cracks was found to be inconsistent. While in the majority of cases the crack growth rate was always less than that predicted by the expression da/dN = C(ΔK)ⁿ, where C and n constants which were found from crack growth tests on standard fracture toughness specimens, an important exception was found in which a pair of cracks grew slowly over a large number of cycles before growing at a very much faster rate than that predicted. Some cracks grew much more slowly than predicted and some did not grow at all, even though minimum values of ΔK were always greater than threshold values. The circumstances which govern the different types of crack growth rate behaviour are examined using finite element analysis. It appears that, for a given specimen geometry and rotational speed, the controlling influences are the number and relative lengths of the bore cracks.     

On fatigue lives of diecast and extruded Mg alloys

In this study, fatigue tests were carried out on both diecast and extruded Mg alloys to study their distributions of fatigue lives under constant stress amplitudes. During the fatigue process of the diecast Mg alloy, cracks initiated from the casting defects inside of the specimen, and then propagated prior to final failure of the specimen. While in the extruded Mg alloy, cracks initiated from the inclusions located on the specimen surface. With assuming the above defects as the initial cracks, the initial maximum stress intensity factors K_imax were evaluated. There are common relations between the initial maximum stress intensity factors K_imax and fatigue lives N_f, regardless of the stress amplitudes for the both Mg alloys at the constant R ratio of −1. The lower K_imax, the longer N_f becomes. Integrating the fatigue crack propagation law from the initial maximum stress intensity factor K_imax to the fatigue fracture toughness K_fc, the relations K_imax vs. N_f can be successfully evaluated.Distributions of fatigue lives at the constant stress amplitudes can be represented by the Weibull distributions. Dispersion in the fatigue lives becomes larger at the lower stress amplitude as compared with those at the higher stress amplitudes. This trend is observed commonly for both diecast and extruded Mg alloys.     

Inclusion-controlled high cycle fatigue behavior of a high V alloyed powder metallurgy cold-working tool steel

Axial loading fatigue tests were carried out to study the influence of inclusion on high cycle fatigue behavior of a high V alloyed powder metallurgy cold-working tool steel (AISI 11). The fatigue strength of 1538 MPa with endurance life of 10⁷ cycles were obtained by stair-case method. The fatigue specimens were also subjected to a constant maximum stress of 1650 MPa to investigate the relationship among inclusion origin size (10-30 μm), fish-eye size (70-130 μm) and fatigue life (10⁵-10⁷ cycles). The fatigue life was found to be dependent on the inclusion size and the crack propagating length. A compressive residual stress of 300-450 MPa turned out to be present at the specimen surface, and finally induced the interior failure mode. Further investigation into the correlation between stress intensity factors of inclusion origin and corresponding stages of fatigue crack growth and fatigue life revealed that the high cycle fatigue behavior was controlled by crack propagation. According to the fractographic investigation, two distinct zones were observed in fish-eye, representing Paris-Law and fast fatigue crack growth stage, respectively. Threshold stress intensity for crack propagation of 3.9 MPa√m was obtained from the well correlated line on the ΔK_I-log N_? graph. The fracture toughness can also be estimated by the mean value of stress intensity factor ranges for fish-eye.