A MODEL RELATING LOW CYCLE FATIGUE PROPERTIES AND MICROSTRUCTURE TO FATIGUE CRACK PROPAGATION RATES

Abstract— The fatigue crack propagation rate is related to the cyclic flow stress and the cyclic ductility of materials by means of a ductility exhaustion mechanism. The da/dN vs. ΔK relationship is derived from the assumption that an elemental crack extension occurs when the sum of the fractional fatigue life of an element at various cycles equals unity. A comparison of predicted crack growth curves with those obtained experimentally for representative alloys shows good agreement. The threshold ΔK behavior has been explained in terms of the existence of a threshold plastic strain amplitude.     

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.     

Vacuum effects on fatigue crack growth in submicrometre‐thick freestanding copper films

To clarify vacuum effects on fatigue crack growth in freestanding metallic thin films, experiments were conducted on approximately 500‐nm‐thick copper films inside a field emission scanning electron microscope. Fatigue crack growth accompanied by intrusion/extrusion formation occurred in vacuum, and da/dN was smaller than in air in the middle‐ΔK region (ΔK ≈ 1.7‐3.1 MPam^1/2). Conversely, in the low‐ΔK region (ΔK ? 1.7 MPam^1/2), da/dN was larger in vacuum than in air. Further, fatigue crack growth in vacuum occurred below the fatigue threshold in air (ΔK_th,air). A nonpropagating crack after reaching ΔK_th,air continued to propagate in vacuum when the environment changed from air to vacuum. This indicates that fatigue crack growth resistance is smaller in vacuum than in air under the same effective driving force. The fatigue damage area near the crack paths in vacuum in the low‐ΔK region became wider, suggesting that the nucleation of fatigue damage was enhanced in vacuum.     

A cumulative model of fatigue crack growth and the crack closure effect

A model of fatigue crack growth based on an analysis of elastic/plastic stress and strain at the crack tip is presented. It is shown that the fatigue crack growth rate can be calculated using the local stress/strain at the crack tip by assuming that a small highly strained area $\text{x}{}^1$, existing at the crack tip, is responsible for the fatigue crack growth, and that the fatigue crack growth may be regarded as the cumulation of successive crack re-initiations over a distance $\text{x}{}^1$. It is shown that crack closure can be modelled using the effective contact zone g behind the crack tip. The model allows the fatigue crack growth rate over the near threshold and linear ranges of the general da/dN versus ΔK curve to be calculated. The fatigue crack growth retardation due to overload and fatigue crack arrest can also be analysed in terms of g and $\text{x}{}^1$.Calculated fatigue crack growth rates are compared with experimental ones for low and high strength steel.     

Time derivative equations for mode I fatigue crack growth in metals

Predicting fatigue crack growth in metals remains a difficult task since the available models based on the Paris law are cycle-derivative equations (da/dN), while service loads are often far from being cyclic. This imposes a cycle-reconstruction of the load sequence, which significantly modifies the load history in the signal. The main objective of this paper is therefore to propose a set of time-derivative equations for fatigue crack growth in order to avoid any cycle reconstruction. The model is based on the thermodynamics of dissipative processes. Its main originality lies in the introduction of a supplementary state variable for the crack, which allows describing continuously the state of the crack throughout any complex load sequence. The state of the crack is considered to be fully characterized at the global scale by its length a, its plastic blunting ρ, and its elastic opening. In the equations, special attention is paid to the elastic energy stored inside the crack tip plastic zone, since, in practice, residual stresses at the crack tip are known to considerably influence fatigue crack growth. The model consists finally in two laws: a crack propagation law, which is a relationship between dρ/dt and da/dt and which observes the inequality stemming from the inequality of Clausius Duhem, and an elastic–plastic constitutive behaviour for the cracked structure, which provides dρ/dt versus load and which stems from the energy balance equation. The model was implemented and tested. It successfully reproduces the main features of fatigue crack growth as reported in the literature, such as the Paris law, the stress ratio effect, and the overload retardation effect.     

Interfacial fatigue crack growth in foam core sandwich structures

This paper deals with the experimental measurement of face/core interfacial fatigue crack growth rates in foam core sandwich beams. The so-called ‘cracked sandwich beam’ specimen is used, slightly modified, which is a sandwich beam that has a simulated face/core interface crack. The specimen is precracked so that a more realistic crack front is created prior to fatigue growth measurements. The crack is then propagated along the interface, in the core material, during fatigue loading, as is assumed to occur in a real sandwich structure. The crack growth is stable even under constant amplitude testing. Stress intensity factors are obtained from the FEM which, combined with the experimental data, result in standard da/dN versus ΔK curves for which classical Paris’ law constants can be extracted. The experiments to determine stress intensity factor threshold values are performed using a manual load-shedding technique.     

A model of corrosion fatigue crack growth in ship and offshore steels

A model describing corrosion fatigue crack growth rate da/dN has been proposed. The crack growth rate is assumed to be proportional to current flowing through the electrolyte within the crack during a loading cycle. The Shoji formula for the crack tip strain rate has been assumed in the model. The obtained formula for the corrosion fatigue crack growth rate is formally similar to the author's empirical formulae established previously. The different effects of ΔK and the fatigue loading frequency f on da/dN, in region I as compared to region II of the corrosion fatigue crack growth rate characteristics can be described by a change of one parameter only: the crack tip repassivation rate exponent.     

Influence of effective stress intensity factor range on mixed mode fatigue crack propagation

ABSTRACT The behaviour of fatigue crack propagation of rectangular spheroidal graphite cast iron plates, each consisting of an inclined semi‐elliptical crack, subjected to axial loading was investigated both experimentally and theoretically. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. In the present investigation, the growth of the fatigue crack was monitored using the AC potential drop technique, and a series of modification factors, which allow accurate sizing of such defects, is recommended. The rate of fatigue crack propagation db/dN is postulated to be a function of the effective strain energy density factor range, ΔS_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The mixed mode crack growth criterion is discussed by comparing the experimental results with those obtained using the maximum stress and minimum strain energy density criteria. The threshold condition for nongrowth of the initial crack is established based on the experimental data.     

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.     

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.     

Fracture mechanics of surface fatigue crack growth by ductile striation space measurement in notched Waspaloy

Ductile striation space (DSS), a parameter to predict actual cracks in both direction of length and depth, is proposed for the surface fatigue crack behaviors on notched Waspaloy. Three different lengths (1, 2 and 4 mm) of artificial notches are formed as the initial surface crack for an applied maximum stress of 1,103 MPa at the stress ratio R of 0.05. These notches are similar with the appearance of the surface cracks found from the survey of compressor disk. The results show that, all initial crack sites in the depth direction started from the multiple origination sites. The DSS parameter was clearly confirmed, and it also proves the high effectiveness of the measurement in the range of the stress intensity factors for acquiring the crack growth rate on the fractured surface. The surface cracks on Waspaloy at room temperature in an atmosphere perfectly follow the relation of ΔK versus da/dN and db/dN, even though there are, respectively, earlier and later timing differences on the initiation of cracks for the notch sizes of 1 and 4 mm. The results of ΔK versus da/dN and db/dN relations show a similar slope for three different kinds of notches.     

Three-dimensional finite element simulations of microstructurally small fatigue crack growth in 7075 aluminium alloy

Three‐dimensional finite element simulations were performed to study the growth of microstructurally small fatigue cracks in aluminium alloy 7075‐T651. Fatigue crack propagation through five different crystallographic orientations was simulated using crystal plasticity theory, and plasticity‐induced crack opening stresses were calculated. The computed crack opening stresses were used to construct small crack da/dN‐ΔK diagrams. The generated da/dN‐ΔK curves compared well with experimental small crack data from the literature. The variance observed among the da/dN‐ΔK results, which occurred as a consequence of the different crystallographic orientations employed, was found to be of the same order of magnitude as commonly observed variability in small fatigue crack growth data. This suggests that grain orientation is a major contributor to observed small fatigue crack data scatter.     

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.     

Microstructure variation effects on room temperature fatigue threshold and crack propagation in Udimet 720Li Ni-base superalloy

An assessment of the effects of microstructure on room temperature fatigue threshold and crack propagation behaviour has been carried out on microstructural variants of U720Li, i.e. as‐received U720Li, U720Li‐LG (large grain variant) and U720Li‐LP (large intragranular coherent γ′ variant). Fatigue tests were carried out at room temperature using a 20 Hz sinusoidal cycling waveform at an R‐ratio = 0.1 on 12.5 mm × 12.5 mm square cross‐section SENB specimens with a 60° starter notch. U720Li‐LG showed the highest threshold ΔK (ΔK_th), whilst U720Li‐LP showed the lowest ΔK_th value. U720Li‐LP also showed higher crack growth rates in the near‐threshold regime and at high ΔK (although at higher ΔK levels the difference was less marked). Crack growth rates of U720Li and U720Li‐LG were relatively similar both in the near‐threshold regime and at high ΔK. The materials showed crystallographic stage I type crack growth in the near‐threshold regime, with U720Li showing distinct crystallographic facets on the fracture surface, while U720Li‐LG and U720Li‐LP showed mostly microfacets and a lower proportion of large facets. At high ΔK, crack growth in the materials becomes flat and featureless indicative of stage II type crack growth. The observed fatigue behaviour, which is an effect of the combined contributions of intrinsic and extrinsic crack growth resistances, is rationalized in terms of the microstructural characteristics of the materials. Enhanced room temperature fatigue threshold and near‐threshold long crack growth resistance are seen for materials with larger grain size and higher degree of planar slip which may be related to increased extrinsic crack growth resistance contributions from crack tip shielding and roughness‐induced crack closure. Differences in the deformation behaviour, either homogeneous or heterogeneous due to microstructural variation in this set of materials may provide approximately equivalent intrinsic crack growth resistance contributions at room temperature.     

Time-derivative equations for fatigue crack growth in metals

Predicting fatigue crack growth in metals remains a difficult task because available models are based on cycle-derivative equations, such as the Paris law, while service loads are often far from being cyclic. The main objective of this paper is therefore to propose a set of time-derivative equations for fatigue crack growth. The model is based on the thermodynamics of dissipative processes. For this purpose, three global state variables are introduced in order to characterize the state of the crackthe crack length a, the plastic blunting at crack tip and the intensity of crack opening C. Thermodynamics counterparts are introduced for each variable. Special attention is paid to the elastic energy stored inside the crack tip plastic zone, because, in practice, residual stresses at crack tip are known to considerably influence fatigue crack growth. The stored energy is included in the energy balance equation, and this leads to the appearance of a kinematics hardening term in the yield criterion for the cracked structure. No dissipation is associated with crack opening, but to crack growth and to crack tip blunting. Finally, the model consists in two laws: a crack propagation law, which is a relationship between d dt and da/dt and which observes the inequality stemmed from the second principle, and an elastic-plastic constitutive behaviour for the cracked structure, which provides d dt versus applied-load. The model was implemented and tested. It reproduces successfully the main features of fatigue crack growth as reported in the literature, such as the Paris law, the stress-ratio effect and the overload retardation effect.     

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.     

Multiaxial small fatigue crack growth in metals

Observations related to the formation and growth of small cracks ranging from subgrain dimension up to the order of 1 mm are summarized for amplitudes ranging from low cycle fatigue (LCF) to high cycle fatigue (HCF) conditions for polycrystalline metals. Further efforts to improve the accuracy of life estimation which address LCF, HCF and LCF–HCF interactions must consider various factors that are not presently addressed by conventional elastic–plastic fracture mechanics (EPFM) or linear elastic fracture mechanics (LEFM) approaches based on long, self-similar cracks in homogeneous, isotropic materials, nor by conventional HCF design tools such as the ε–N curve, the S–N curve, modified Goodman diagram and fatigue limit.Development of microstructure-sensitive fatigue crack propagation relations relies on deeper understanding of small crack behavior, including (a) interactions with microstructure and lack of constraint for microstructurally small cracks, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) local mode mixity effects on small crack growth. The basic technology is not yet sufficiently advanced in these areas to implement robust damage tolerant design for HCF. This paper introduces an engineering model which approximates the results of slip transfer calculations related to crack blockage by microstructure barriers; the model is consistent with critical plane concepts for Stage I growth of small cracks, standard cyclic stress–strain and strain–life equations above threshold, and the Kitagawa diagram for HCF threshold behaviors. It is able to correlate the most relevant trends of small crack growth behavior, including crack arrest at the fatigue limit, load sequence effects, and stress state effects.     

Simulating small crack growth behaviour using crystal plasticity theory and finite element analysis

Predictions of small crack growth under cyclic loading in aluminium alloy 7075 are performed using finite element analysis (FEA), and results are compared with published experimental data. A double‐slip crystal plasticity model is implemented within the analyses to enable the anisotropic nature of individual grains to be approximated. Small edge‐cracks in a single grain with a starting length of 6 μm are incrementally grown following a node‐release scheme. Crack‐tip opening displacements (CTOD) and crack opening stresses are calculated during the simulated crack growth, and da/dN against ΔK diagrams are computed. Interactions between the crack tip and a grain boundary are also considered. The computations are shown to accurately capture the magnitude and the variability normally observed in small crack fatigue data.     

Identification of fatigue crack growth mechanisms in IN100 superalloy as a function of temperature and frequency

A study is undertaken to investigate the fatigue crack growth rate properties of polycrystalline IN100 through the identification of crack growth mechanisms as a function of temperature, frequency and ΔK. An additional goal is to determine the stress free activation energy of IN100. Constant amplitude, load controlled tests are performed at room temperature (22 °C), 316 °C, 482 °C and 649 °C under two different loading frequencies of 20 and 0.33 Hz. These specimens are then analysed via scanning electron microscopy (SEM) to determine failure mechanisms. SEM shows that, as temperature increased from room temperature to 649 °C, the fracture mechanism transitions from transgranular to intergranular. The fracture mechanism is shown to transition from intergranular to transgranular at elevated temperatures as da/dN increases as a result of growing ΔK. Scanning electron microscopy shows that, as frequency decreases from 20 to 0.33 Hz at 649 °C, the fracture mechanism transitions from transgranular to intergranular.     

Very high cycle fatigue properties of high‐strength spring steel 60SiCrV7

The very high cycle fatigue properties of spring steel 60SiCrV7 for automotive suspension system with different hydrogen contents were studied by using ultrasonic fatigue testing and fatigue crack growth testing. The results show that the S–N curves exhibit continuous drop of fatigue lives and no obvious horizontal line exists. Similar fracture surface features were observed for all the specimens that failed mainly from internal inclusions with surrounding granular bright facet (GBF). Fatigue strength decreases remarkably with increasing hydrogen content. The applied stress intensity factor range at the periphery of GBF ΔK_GBF is approximately proportional to 1/3 power of the square of GBF area. The average values of ΔK_GBF for uncharged specimens are close to crack growth threshold ΔK_th, which indicates that ΔK_GBF could be regarded as the threshold value governing the beginning of stable fatigue crack propagation. The increase of hydrogen content tends to reduce ΔK_GBF.