Effects of dissolved oxygen on corrosion fatigue cracking of Alloy 690(TT) in pressurized water reactor environments

Alloy 690(TT) is widely used for steam generator tubes in pressurized water reactor (PWRs), where it is susceptible to corrosion fatigue. In this study, the effects of dissolved oxygen on the corrosion fatigue cracking behavior of Alloy 690(TT) in simulated PWR environments were investigated under small scale yielding conditions. Dissolved oxygen, combined with the monotonic plastic zone size (r_p), had a significant influence on out-of-plane cracking of corrosion fatigue crack and environment factor (F_en).     

Fatigue crack growth retardation under constant amplitude and variable mean stress

Fatigue crack growth retardation under stress spectra with constant amplitude and variable mean stress, respectively, was studied. Flat specimens with a central through crack were tested under tension-tension load. The specimens were made with low alloy steel 4 mm thick, with yield strength of 625 Mpa and ultimate tensile strength of 784 MPa. Overload affected crack length increments Δa¹ were studied. The best correlation was obtained between monotonic plane stress plastic zone size 2r_y and Δa¹. The cyclic plastic zone size 2r_pc correlated with crack length increment of minimum crack growth rate after overload. Forman's equation and Willenborg's model of fatigue crack growth retardation were used for theoretical prediction of fatigue crack propagation life. The best agreement between theoretical and experimental results was also obtained using monotonic plastic zone size instead of monotonic plastic zone radius or cyclic plastic zone size. The agreement is reasonably good, even though in the case of one spectrum, cracks were arrested for several thousand cycles.     

On improved crack tip plastic zone estimates based on T‐stress and on complete stress fields

Cracked ductile structures yield locally to form a plastic zone (pz) around their crack tips, which size and shape controls their structural behaviour. Classical pz estimates are based solely on stress intensity factors (SIF), but their precision is limited to very low σ_n/S_Y nominal stress to yield strength ratios. T‐stresses are frequently used to correct SIF‐based pz estimates, but both SIF and SIF plus T‐stress pz estimates are based on truncated linear elastic (LE) stress fields that do not satisfy boundary conditions. Using Griffith's plate complete LE stress field to avoid such truncated pz estimates, the influence of its Williams’ series terms on pz estimation is evaluated, showing that T‐stress improvements are limited to medium σ_n/S_Y values. Then, corrections are proposed to introduce equilibrium requirements into LE pz estimates. Finally, these improved estimates are compared with pz calculated numerically by an elastic–plastic finite element analysis.     

ELEVATED TEMPERATURE FATIGUE IN Ni3Al-BASED ALLOYS

Both high-cycle and low-cycle fatigue properties of hot-extruded powders of a Ni₃Al-based alloy, IC218, have been evaluated. High cycle fatigue measurements were performed under stress controlled conditions at temperatures ranging from 25°C to 850°C. Tests were made in both laboratory air and vacuum environments. Low cycle fatigue tests were conducted under total strain control in a laboratory air environment at 650°C. In high cycle fatigue, high ratios of the fatigue limit (Δσ at 10⁶ cycles) to monotonic yield strength (σ_ys), of approximately Δσ/σ_ys～1, were obtained in the powder extruded IC218 alloy for temperatures ranging from 25°C to 650°C. In low cycle fatigue, a substantial decrease in fatigue life occurred at 650°C, compared to results obtained previously at 25°C. High cycle fatigue performance at low stress/strain amplitudes is better than expected when compared to precipitation strengthened superalloys. The improved performance is explained in terms of the cyclic hardening behavior of the alloy.     

Influence of the cyclic plastic zone size on the propagation of the fatigue crack in case of 12NC6 steel

Under cyclic loading, the plasticized zone becomes complicated; it contains in particular a second plasticized zone, resulting from the local compression which occurs at the time of the closing of the crack to each cycle. The two plastic zones, monotonous (r_m) and cyclic (r_c), are proportional to (K_max/R_e)² et (ΔK/R_e)², respectively. The objective of this work is to study the evolution of the fatigue crack grown rate (FCGR) and the influence of the plastic zone size (r_c), which represents the seat of the residual stresses, on this evolution in the case of 12NC6 steel. Generally, the plastic zone size increases with the crack advance. The FCGR can be correlated with the energy absorptive in these plastic zones.     

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).     

Plastic zone size estimation under cyclic loadings using in situ optical microscopy fatigue testing

An in situ optical microscopy fatigue testing is proposed in this paper to investigate the forward and reversed plastic zone size under cyclic loadings for Al‐7075‐T6. This experimental study is used to verify the hypotheses in a recently developed small time scale formulation of fatigue crack growth. During the testing, the entire cyclic loading cycle is divided into a certain number of steps. Images of the crack tip are taken at each step. The full strain field around the crack tip is determined using the digital image correlation (DIC) technique. The plastic zone size is obtained by combining the DIC results and the material constitutive relationship. Experimental measurements from the proposed study are compared with theoretical predictions. It is observed that the crack closure has a large effect on the reversed plastic zone size. The plastic zone size remains almost constant when the unloading path is below a certain stress level, which is one of the hypotheses used in a previous crack growth model. Discussions are given for the modelling of plastic zone size variation under cyclic loadings and several conclusions are drawn based on the current investigation.     

The plastic zone and growth of fatigue cracks in magnesium MA12 alloy at room and low temperatures

The plastic zone formed at the fatigue crack tip and the fracture topography in MA12 magnesium alloy samples, tested at 293 and 140 K in air and in vacuum, were analysed. It was found that the plastic zone formed in vacuum is characterized by a greater size ($\text{h}$) and degree of plastic strain that in air, and the crack growth rate ($\text{d}\text{l/}\text{d}\text{N}$) is lower. Temperature reduction leads to a decrease in $\text{h}$, while $\text{d}\text{l/}\text{d}\text{N}$ and the fracture mechanism are affected by temperature ambiguously, depending on the alloy microstructure and the $\text{K}{}_{\mathrm{<mtext>max</mtext>}}$ value. It was established that the size of the plastic zone can be described by the equation:

$\text{h=A}\text{(}\text{K}{}_{\max }\text{σ}{}_{\mathrm{0.2ps}}\text{)}{}^2$

where $\text{A}$ is a coefficient dependent on the alloy structural state, environment and test temperature. Evaluation of the cyclic plastic zone size at $\text{K}{}_{\mathrm{<mtext>max</mtext>}}$, corresponding to the transition from a low temperature region to a ‘Paris’ region, showed that this transition occurred when the cyclic plastic zon reached the structural parameter of the material.     

Monotonic and cyclic crack tip plasticity

Monotonic and cyclic plastic zone sizes were measured in a medium strength ferrite-pearlite steel (BM 45) tested in fatigue at 25 Hz at room temperature. Two methods were applied: microhardness and the recently developed ‘fatigue in compression’ technique. The results obtained are discussed in terms of accuracy and reliability.The retardation effect due to overloads was also studied in the same material and is illustrated experimentally as a $\text{d}\text{a}\text{d}\text{N}$ vs ΔK curve. This effect emphasizes the importance of an accurate evaluation of both the size and shape of the overall plastic zone. The shape and dimensions of the cyclic plastic zones seem to indicate that in ductile metals the steady state of fatigue crack growth occurs under plane strain conditions.     

Characterization of the nonlinear fracture resistance parameters for an aviation GTE turbine disc

The effects of crack growth rate model formulation, based on the elastic‐plastic and undamaged/damaged creep crack tip fields on the behaviour of low‐cycle fatigue and creep fracture resistance parameter behaviour, are represented by numerical calculations. The crack growth rate models include the fracture process zone size and damage parameters. An aviation gas turbine engine (GTE) rotating turbine disc is the focus of this innovative application of basic analytical and numerical solutions. For the GTE turbine disc, the constraint parameters, local fracture process zone sizes, and nonlinear plastic (K_p) and creep (K_cr) stress intensity factors are calculated by finite element analysis to characterize the fracture resistance along the semielliptical crack front as a function of the flaw aspect ratio, operation temperature, and disc rotation speed. Predictions of the creep‐fatigue crack growth rate and residual lifetime are given for different combinations of operation loading conditions and damage of the GTE turbine disc.     

Crack growth prediction and non-linear analysis for an elasto-plastic solid

In this paper, a variable radius for the plastic zone is introduced and a maximum principal stress criterion is proposed for the prediction of crack initiation and growth. It is assumed that the direction of crack initiation coincides with the direction of the maximum principal stress. The von Mises yield criterion is applied to define the plastic zone, instead of assuming a plastic zone with a constant distance r from the crack tip. An improvement is made to this fracture criterion, and the criterion is extended to study the crack growth characteristics of mixed mode cracks. Based on the concept of frictional stress intensity factor, k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The proposed crack growth model is discussed by comparing the experimental results with those obtained using the maximum principal stress criterion.     

RETROSPECTIVE VIEW ON THE ROLE OF THE PLASTIC ZONE AT A FATIGUE CRACK TIP

A brief review is presented concerning the history of the development of links between the cyclic plastic zone at a fatigue crack tip, the fracture process zone and the occurrence of fatigue striations; a development in which Regis Pelloux played a pivotal role.     

Acoustic emission behaviour during stage II fatigue crack growth in an AISI type 316 austenitic stainless steel

Acoustic emission (AE) behaviour during fatigue crack growth (FCG) in a ductile AISI type 316 austenitic stainless steel is reported. The two substages in the stage II Paris regime of FCG could be distinguished by a change in the rate of acoustic activity with increase in crack growth rate. The transition point in the cumulative ringdown count plot coincides with that in the da/dn plot. The AE activity increases with increase in ΔK during stage IIa and decreases during stage IIb. The major source of AE during stage IIa is found to be the plastic deformation within the cyclic plastic zone (CPZ) as compared to the phenomena such as monotonic plastic zone (MPZ) expansion, ductile crack growth, crack closure, etc. The increase in AE activity with increase in ΔK during stage IIa is attributed to the increase in the size of the CPZ which is generated and developed only under plane strain conditions. The decrease in AE activity during stage IIb is attributed to the decrease in the size of the CPZ under plane stress condition. The high acoustic activity during the substage IIa is attributed to irreversible cyclic plasticity with extensive multiplication and rearrangement of dislocations taking place within the CPZ. The AE activity is found to strongly depend on the optimum combination of the volume of the CPZ, average plastic strain range and the number of cycles before each crack extension. Based on this, an empirical relationship between the cumulative RDC and ΔK has been proposed and is found to agree well with experimentally observed values.     

Finite-element analysis of fatigue crack closure under plane strain conditions: stabilization behaviour and mesh size effect

An elastic–plastic finite‐element analysis of fatigue crack closure is performed for plane strain conditions. The stabilization behaviour of crack opening level and the effect of mesh size on the crack opening stress are investigated. It has been well reported that the crack opening level under plane stress conditions becomes stable after the crack advances beyond the initial monotonic plastic zone. In order to obtain a stabilized crack opening level for plane strain conditions, the crack must be advanced through approximately four times the initial monotonic plastic zone. The crack opening load tends to increase with the decrease of mesh size. The mesh size nearly equal to the theoretical plane strain cyclic plastic zone size may provide reasonable numerical results comparable with experimental crack opening data. The crack opening behaviour is influenced by the crack growth increment and discontinuous opening behaviour is observed.     

On the evaluation of monotonic and cyclic plastic zones

This paper reviews and compares the various approaches for finding monotonic and cyclic plastic zone sizes for elastic-perfectly plastic and strain hardening materials. All through the analysis Ramberg-Osgood relationship has been used representing the monotonic and cyclic stress-strain curves. The results for elastic-perfectly plastic materials are compared with those available using finite-element technique. The ratio of monotonic plastic zone sizes strain hardening and elastic perfectly plastic materials are found to be related to the Ramberg-Osgood index $\text{n}$.The values of cyclic plastic zone size are found to depend upon factors like crack opening stress, material properties and specimen geometry. The cyclic plastic zone size obtained in this paper compare well with those given by Antolovich.     

Effect of crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔK_eff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.     

Geometrical relationships between side necking and plastic zone size near a crack tip in ductile metals. Part I: Modified boundary layer solutions

The plastic zone size is regarded as the measure of a material's resistance, and it also determines the fracture behaviour. Recently, stereo digital speckle photography (SDSP) has been found to be useful for measuring in-situ the side necking developed on the lateral surfaces of a specimen during a standard fracture test procedure for J_IC . Because plastic deformation occurs without any volume change, the in-plane plastic zone developed around a crack tip should be accompanied by out-of-plane deformation, that is, side necking. With the aid of the new measurement technique, side necking is expected to act as a gauge for indicating the plastic zone size. As a preliminary study, the geometrical relationships between side necking and the plastic zone size near a crack tip in ductile metals are explored by using a finite element model with modified boundary conditions. As parameters representing the geometrical similarity between side necking and the plastic zone, the shapes of each region, the distances from the crack tip to the boundaries of each region, r_p and r_s and the areas of each region, A_p and A_s are examined for their sensitivities to variables such as mode mixity, hardening exponent and so on. Among them, the areas, A_p and A_s seem to be the best for application because an excellent linearity between them is maintained in a wide range of mode mixity and load level regardless of the hardening exponent, specimen thickness and yield stress.     

Crack deflection in the nonlinear zone of ultra-high-strength steel fatigue crack growth curve

The fatigue crack growth rate (FCGR) of 10Ni5CrMoV steel under variable load ratios was investigated. The microscopic observations of growth direction and microstructural analysis were conducted by means of electron backscatter diffraction and transmission electron microscopy. The results showed that FCGR of 10CrNi5MoV steel increased with the increasing load ratio in the mid-growth rate regime; however, it did not completely conform to the Paris Formula. A nonlinear zone existed in the logarithmic coordinate system of the FCGR curve and was unaffected by load ratio. The main impact factors for the appearance of the nonlinear zone were grain size and the size of the plastic zone surrounded fatigue cracks. In the nonlinear zone of the FCGR curve, an apparent crack deflection phenomenon occurred.     

A new method of plastic zone size determined based on maximum crack opening displacement

This paper presents a new method to determine the crack-tip plastic zone size (R_y) in the center cracked plate in tension. The maximum crack opening displacement (MCOD) is used to estimate R_y in this method. Based on the series of calculation results by finite element analysis, the explicit expression for the crack-tip plastic zone size versus MCOD is fitted by least square method. The expression enables to eliminate the influences of the yield stress of material, crack geometry, plate sizes and transverse stress. Therefore, the presented method of R_y determined by MCOD is suitable to any center crack finite plate of any material under uniaxial or biaxial tension.     

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.