A mathematical equation relating low cycle fatigue data to fatigue crack propagation rates

A mathematical equation is derived to predict fatigue crack growth rates on the basis of a J integral analysis from the fatigue fracture behaviour of low cycle fatigue samples. According to this equation, the fatigue crack propagation curves can be predicted if low cycle fatigue data and an initial microcrack size are available. The results obtained from this study show that the predicted fatigue crack propagation rates for Ti-24V, Ti-6Al-4V and Al-6Zn-2Mg alloys are very close to experimental values.     

Mechanics and synergetics of the selfsimilar growth of a fatigue crack

As was shown by T. Yokobori, it is important to combine the fracture mechanics approach with analysis of the fracture mechanism. Analyses parameters controlling boundaries of the selfsimilar growth of a fatigue crack and the relation between threshold characteristics of fracture toughness, corresponding to the change of fracture mechanism (bifurcation points) were carried. The analysis conducted on steels, titanium and aluminium alloys shows that bifurcation points in the fatigue crack growth are highly informative. Their recognition can be instrumental in establishing the relationship between characteristics of cyclic and static fracture toughness.     

Investigating environmental effects on small fatigue crack growth in Ti–6242S using combined ultrasonic fatigue and scanning electron microscopy

In situ ultrasonic fatigue with a cyclic frequency of 20 kHz was employed in an environmental scanning electron microscope (ESEM) to characterize fatigue crack formation and growth in the near alpha titanium alloy Ti–6242S. The role of environment on small fatigue crack initiation and growth was investigated in vacuum and in variable pressures of saturated water vapor, as well as in laboratory air. Small crack growth behavior from cracks initiated at FIB-produced micro-notches indicated a significant environmental dependence, with fatigue crack growth rates increasing with increasing partial pressures of water vapor. Environment also influenced crack initiation lifetime in that cracks initiated earlier in laboratory air than in vacuum or saturated water vapor environments. Transgranular, crystallographic crack growth was observed in each environment, with the crack path in primary α grains producing facets parallel to basal planes when crack size was small. Small crack growth resistance had a marked sensitivity to microstructural features, such as α/α grain boundaries with high misorientation and α/α + β boundaries. These initial investigations demonstrate the usefulness of in situ ultrasonic fatigue instrumentation (UF-SEM) as a new tool for the characterization of environmental and microstructural influences on very high cycle fatigue (VHCF) behavior.     

A cumulative model of fatigue crack growth

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 by means of the local stress/strain at the crack tip. The local stress and strain calculations are based on the general solutions given by Hutchinson, Rice and Rosengren. It is assumed that a small highly strained area existing at the crack tip is responsible for the fatigue crack growth. It is also assumed that the fatigue crack growth rate depends mainly on the width, x¹, of the highly strained zone and on the strain range, $\text{Δ?}{}^1$, within the zone. A relationship between stress intensity factor K and the local strain and stress has been developed. It is possible to calculate the local strain for a variety of crack problems. Then, the number of cycles N¹ required for material failure inside the highly strained zone is calculated. The fatigue crack growth rate is calculated as the ratio $\text{x}{}^1\text{N}{}^1$.The calculated fatigue crack growth rates were compared to the experimental ones. Two alloys steels and two aluminium alloys were analyzed. Good agreement between experimental and theoretical results is obtained.     

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.     

On the influence of rubbing fracture surfaces on fatigue crack propagation in mode III

Fatigue crack growth has been studied under fully reversed torsional loading (R = ?1) using AISI 4340 steel, quenched and tempered at 200°, 400° and 650°C. Only at high stress intensity ranges and short crack lengths are all specimens characterized by a microscopically flat Mode III (anti-plane shear) fracture surface. At lower stress intensities and larger crack lengths, fracture surfaces show a local hill-and-valley morphology with Mode I, 45° branch cracks. Since such surfaces are in sliding contact, friction, abrasion and mutual support of parts of the surface can occur readily during Mode III crack advance. Without significant axial loads superimposed on the torsional loading to minimize this interference, Mode III crack growth rates cannot be uniquely characterized by driving force parameters, such as ΔK_III and ΔCTD_III, computed from applied loads and crack length values. However, for short crack lengths (?0.4 mm), where such crack surface interference is minimal in this steel, it is found that the crack growth rate per cycle in Mode III is only a factor of four smaller than equivalent behaviour in Mode I, for the 650°C temper at $\text{ΔK}{}_{\mathrm{III}}\text{= 45 MPa m}\text{1}\text{2}$.     

Surface crack and cracks networks in biaxial fatigue

Semi-elliptical fatigue crack growth in 304 L stainless steel, under biaxial loading, was investigated. Compared to those of through-cracks under uniaxial loading, the growth rate of surface cracks is increased by a non-singular compressive stress and reduced by a tensile stress, when R = 0. Plasticity-induced crack closure under biaxial loading was investigated through 3D finite element simulations with node release. Roughness and phase-transformation-induced closure effects were also discussed. The interactions in two-directional crack networks under biaxial tension were investigated numerically. It appears that the presence of orthogonal cracks should not be ignored. The beneficial influence of interaction-induced mode-mixities was highlighted.     

System for automated fatigue crack growth testing under random loading

Procedures have been developed for computer-controlled crack propagation testing under random load sequences. They include certain features which are not available in conventional systems, but which appear essential for random load testing. These include the capability to simulate any desired K-function on standard laboratory specimens and continuous on-line rainflow analysis of the test load sequence to exclude cycles falling below given values of threshold stress intensity, stress level or range. The system also includes a procedure for automated crack-opening displacement based crack opening/closing load level measurement. Experimental studies on AlCu alloy sheet material point to a requirement for development of standards for spectrum loading crack growth testing.     

Relation between fatigue threshold and fatigue limit for surface-rolled specimens

After cylinder notch fatigue specimens of 40 CrNiMo steel were rolled, their fatigue limit increased by 41%. The rolled specimens did not fracture, even though they had been loaded for 10⁷ cycles under fatigue limit stress, but a non-propagating fatigue crack was generated. Thus the value of the fatigue limit depends on the fatigue threshold value ΔK_th of the metal of the rolled layer. Plastic deformation increased ΔK_th in these experiments. It can be inferred that ΔK_th of the rolled layer increases from the occurrence of plastic deformation and microvoids on the layer. Calculation of the effect of residual stress in the crack wake on the stress intensity factor ΔK indicates that residual compression stress decreases ΔK by 21.5 MPa √M. It was calculated that rolling induced both the length of the non-propagating crack and the increase of fatigue limit. The calculated values are in accord with experiment. Analysis and calculations indicate that the non-propagating crack is generated on the rolled layer. Thus the fatigue limit is improved because rolling produces residual compression stress in the layer (which decreases the stress intensity factor), and increases ΔK_th of the layer.     

Cryogenic temperature near-threshold fatigue crack growth rate data for JBK-75 stainless steel

An important structural component of the Westinghouse Large Coil Programme superconducting magnet is the JBK-75 (modified A-286) stainless steel conductor sheath. Because the presence of pre-existing cracks or flaws in the conductor sheath is a potential possibility, the structural reliability of the conductor sheath would be enhanced if a threshold level of stress intensity range (ΔK_th) was established below which fatigue crack growth would not occur. Consequently, near-threshold fatigue growth rate data were generated at two load ratios on JBK-75 stainless steel at room and cryogenic temperatures. No load ratio effect on near-threshold fatigue crack growth rate was observed at cryogenic temperatures.     

Characterization of a fracture specimen for crack growth in epoxy due to thermal fatigue

Finite element simulations are carried out to characterize a new fracture specimen, consisting of an outer circular epoxy ring bonded to an inner circular invar plate for accelerated thermal fatigue testing. Radial cracks are introduced in the epoxy ring. The growth of these radial cracks is correlated to the applied energy release rate G. We studied the dependence of G on the crack length, the specimen geometry and the elastic modulus. For short cracks, G is obtained in closed form. Analysis is carried out to determine the critical thermal buckling load the specimen can withstand. Experimental results show that the fatigue crack growth rate per thermal cycle da/dN is given by da/dN = 0.51(ΔG)^0.38 for cycling between 4 and 100 °C but by da/dN = 0.25(ΔG)^0.24 for cycling between 20 and 85 °C, where ΔG is the difference of the energy release rate between the highest and lowest temperatures during a thermal cycle. More severe thermal cycles produce considerably larger fatigue crack growth rates than less severe ones at the same ΔG. This result also implies that isothermal fatigue tests will probably be inadequate to predict thermal fatigue crack growth in epoxies.     

A micromechanical cyclic void growth model for ultra-low cycle fatigue

The influence of stress triaxiality and Lode parameter on microvoid growth phase of ductile fracture under ultra-low cycle fatigue (ULCF) (N_f < 100, N_f = cycles to failure) loading is investigated using micromechanical analyses. A new micromechanical cyclic void growth model (MM-CVGM) to predict the ULCF life of ASTM A992 steels is presented. The MM-CVGM is calibrated and validated from the experiments conducted on axisymmetrically notched specimens. Number of cycles to failure (N_f) and the fracture initiation locations predicted by the model closely matched the experimental observations.     

Crack growth behavior of 7075-T6 under biaxial tension–tension fatigue

Crack growth behavior of aluminum alloy 7075-T6 was investigated under in-plane biaxial tension–tension fatigue with stress ratio of 0.5. Two biaxiality ratios, λ (=1 and 1.5) were used. Cruciform specimens with a center hole, having a notch at 45° to the specimen’s arms, were tested in a biaxial fatigue test machine. Crack initiated and propagated coplanar with the notch for λ = 1 in L–T orientation, while it was non-coplanar for λ = 1.5 between L–T and T–L orientations. Uniaxial fatigue crack growth tests in L–T and T–L orientations were also conducted. Crack growth rate in region II was practically the same for biaxial fatigue with λ = 1 in L–T orientation and for the uniaxial fatigue in L–T or T–L orientations, while it was faster for biaxial fatigue with λ = 1.5 at a given crack driving force. However, fatigue damage mechanisms were quite different in each case. In region I, crack driving force at a given crack growth rate was smallest for biaxial fatigue with λ = 1.5 and for uniaxial fatigue in T–L orientation, followed by biaxial fatigue with λ = 1 and uniaxial fatigue in L–T orientation in ascending order at a given crack growth rate.     

Comparison of fatigue failure criterion in flexural fatigue test

This study compares traditional stiffness and energy based fatigue failure criteria with the fatigue failure criterion based on the viscoelastic continuum damage (VECD) approach. In traditional approach, fatigue failure is defined as the number of cycles at which the stiffness of a material reduces by 50% (N_f50). In energy based approach, fatigue failure is defined by the number of cycles at the maximum energy ratio or Rowe’s maximum stiffness defined by stiffness multiplied by the corresponding number of the cycle (E * N). In VECD approach, fatigue failure is defined by the number of loading cycles at the inflection point of the normalized pseudostiffness (C) versus damage variable (S) curve. It is shown that a correlation exits between traditional criteria and VECD criteria. It is shown that maximum energy ratio or Rowe’s maximum stiffness based fatigue life is higher than the traditional fatigue life (N_f50). This indicates the traditional approach is conservative. A strong correlation of fatigue was observed between the VECD fatigue criterion and energy ratio based fatigue criteria. However, the fatigue life by VECD approach is always less than the fatigue life by energy ratio or Rowe’s maximum stiffness.     

Total fatigue life prediction for Ti-alloys airframe structure based on durability and damage-tolerant design concept

Based on the concept of the damage-tolerance and durability design, the total fatigue life of titanium alloys is divided into three phases: crack initiation (0–0.3 mm), short crack growth (0.3–2 mm) and long crack growth (2 mm–a_C). Among these three phases, different prediction models are accepted due to different failure mechanisms. A computer program was developed to predict the total fatigue life of the titanium alloy structure. Fatigue testing is also conducted for two types of ELI grade titanium alloy to verify the prediction models. The predicted fatigue life agrees well with experimental results.     

On the relationship between fatigue limit,threshold and microstructure of a low-carbon Cr-Ni steel

The relationship between the fatigue limit stress range, Δσ_w, the threshold stress intensity factor, ΔK_th, and microstructure of low-carbon 12CrNi3A steel has been investigated. Non-propagating microcracks were observed on the surface of smooth specimens which has been subjected to at least 5 × 10⁶ cycles at the fatigue limit stress. The size of the cracks depended on the characteristic sizes of the microstructure of the material. Scanning electron microscopy showed that the fractographic characteristics in the near-threshold region of fatigue macrocrack growth were similar to those in the fatigue microcrack initiation region. This implies that the fatigue limit and fatigue threshold of the material have a similar physical meaning, both signifying the resistance of the material to the propagation of fatigue cracks. The relationship ΔK_th = 1.12Δσ_W √πα was shown to be valid, where a is a material parameter relating to microstructure, rather than to the length of a macrocrack. The results also showed that the value of a depends on the material and microstructure, and that both Δσ_W and ΔK_th will change if the microstructural characteristics of the material change.     

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.     

A model for fatigue crack growth in a threshold region

The prediction of fatigue crack growth at very low ΔK values, and in particular for the threshold region, is important in design and in many engineering applications. A simple model for cyclic crack propagation in ductile materials is discussed and the expression

$\text{da}\text{dN}\text{=}\text{2}{}^{\mathrm{1+n}}\text{(1?2v)(ΔK}{}^2{}_{\mathrm{eff}}\text{?ΔK}{}^2{}_{\mathrm{c,eff}}\text{)}\text{4(1+n)π σ}{}^{\mathrm{1?n}}{}_{\mathrm{yc}}\text{E}{}^{\mathrm{1+n}}\text{?}{}^{\mathrm{1+n}}{}_{\mathrm{f}}$

developed. Here, n is the cyclic strain hardening exponent, σ_yc is cyclic yield, and ε_f is the true fracture strain. The model is successfully used in the analysis of fatigue data BS 4360-50D steel.     

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.