Crack tip closure and environmental crack propagation

Crack propagation rate, da/dN, and crack tip closure stress, σ_cc, in part-through crack fatigue specimens of aluminum alloys are drastically affected by gaseous environments. The present studies indicate that the crack closure reflects the influence of the environment on the plastic deformation at the crack tip, and, therefore, on the crack propagation rates. Postulating that da/dN is mainly determined by $\text{ΔK}{}_{\mathrm{eff}}\text{∝ (σ}{}_{\max }\text{?σ}{}_{\mathrm{cc}}\text{)}$ (instead of $\text{ΔK ∝ (σ}{}_{\max }\text{?σ}{}_{\min }\text{)}$, as is done traditionally) leads to the relationship $\text{da/dN = A(ΔK}{}_{\mathrm{eff}}\text{)}{}^{\mathrm{n}}$ in which $\text{A}$ and $\text{n}$ are virtually independent of the gaseous environment. The exponents are $\text{n ≈ 3.3}$ for Al 7075 T651 and $\text{n ≈ 3.1}$ for Al 2024 T351, respectively.     

Some problems in experimental fracture mechanics

A standard procedure for the determination of fracture toughness K_IC is discussed. The insufficiency of the existing K_ic determination confidence criteria is stressed and the following criteria are proposed instead: φ_max ? 1.5%; $\text{σ}{}_{\mathrm{fr}}{}^{\mathrm{net}}\text{σ}{}_{\mathrm{0.2\; ?\; 0.8}}$, in conjunction with the old criterion $\text{P}{}_{\max }\text{P}{}_{\mathrm{Q}}\text{? 1.1}$. Determination of K_IC from P_max should be used instead of from P_Q.A method for the determination of a point on the “force-displacement” diagram corresponding to crack growth initiation is set forth. The method is based on specimen compliance tests under repeated load-relief cycles. The crack growth initiation point is used to determine both the critical crack opening and plane strain fracture toughness. The indefinite effect of the growing crack (in the ease of crack opening or Cherepanov-Rice integral calculations) is thereby eliminated. Necessity is emphasized to determine the share of the J-integral which contributes to fracture process. A method for plotting the elastic displacement diagram is proposed which allows on the basis of preliminary estimates to determine fracture toughness of small-sized specimens without using special setups. The area ratio between the plastic and elastic strain diagrams is proposed to be adopted as fracture type criterion. Certain experiments to determine crack resistance of material specimens are described and discussed.     

Studies on crack growth rate under high temperature creep,fatigue and creep-fatigue interaction—II: On the role of fracture mechanics parameter aeffσg

For high temperature creep, fatigue and creep-fatigue interaction, several authors have recently attempted to express crack growth rate in terms of stress intensity factor $\text{K}{}_{\mathrm{I}}\text{= α}\text{aσ}{}_{\mathrm{g}}$, where a is the equivalent crack length as the sum of the initial notch length a₀ and the actual crack length $\text{a}{}^1$, that is, $\text{a = a}{}_0\text{+ a}{}^1$. On the other hand, it has been shown by Yokobori and Konosu that under the large scale yielding condition, the local stress distribution near the notch tip is given by the fracture mechanics parameter of $\text{aσ}{}_{\mathrm{g}}\text{?(σ}{}_{\mathrm{g}}$), where a is the cycloidal notch length, σ_g is the gross section stress and $\text{?(σ}{}_{\mathrm{g}}$) is a function of σ_g. Furthermore, when the crack growth from the initial notch is concerned, it is more reasonable to use the effective crack length a_eff taking into account of the effect of the initial notch instead of the equivalent crack length a. Thus we believe mathematical formula for the crack growth rate under high temperature creep, fatigue and creep-fatigue interaction conditions may be expressed at least in principle as function of $\text{a}{}_{\mathrm{eff}}\text{σ}{}_{\mathrm{g}}\text{, σ}{}_{\mathrm{g}}$ and temperature.In the present paper, the geometrical change of notch shape from the instant of load application was continuously observed during the tests without interruption under high temperature creep, fatigue and creep-fatigue interaction conditions. Also, the effective crack length a_eff was calculated by the finite element method for the accurate estimation of local stress distribution near the tip of the crack initiated from the initial notch root. Furthermore, experimental data on crack growth rates previously obtained are analysed in terms of the parameter of $\text{a}{}_{\mathrm{eff}}\text{σ}{}_{\mathrm{g}}$ with gross section stresses and temperatures as parameters, respectively.     

The effects of load ratio on environmentally assisted fatigue crack growth

A modification to the model of Weir et al. for surface reaction and transport controlled fatigue crack growth has been developed to explicitly account for the effect of load ratio on environmentally assisted fatigue crack growth. Load ratio was found to affect principally gas transport to the crack tip, and therefore affected only transport controlled crack growth response. Experimental verification of the modified model was made by studying the room temperature fatigue crack growth responses at different load ratios for a 2219-T851 aluminum alloy exposed to water vapor.The results show that the effects of load ratio can be attributed to two different sources—one relating to its effect on local deformation at the crack tip and is reflected through the mechanical component, (d$\text{a}$/d$\text{N}$)₀ and the other on its role in modifying environmental effect and is manifested through the corrosion fatigue component, $\text{(da/dN)}{}_{\mathrm{cf}}$ Furthermore, the results show that the saturation value of corrosion fatigue component, $\text{(da/dN)}{}_{\mathrm{cf,s}}$, is essentially independent of $\text{R}$, and that the exposure needed to produce “saturation response” ($\text{P}{}_0\text{/2f)}{}_{\mathrm{s}}$, as a function of load ratio can be predicted from the modified model. The modified model, therefore, allows one to predict the corrosion fatigue crack growth response for any load ratio on the basis of measurements made at a single load ratio, provided that the values of ($\text{da/dN}$), are known.     

Crack closure in 2219-T851 aluminum alloy

The effects of specimen thickness, stress ratio ($\text{R}$) and maximum stress intensity factor ($\text{K}{}_{\max }$) on crack closure (or opening) were studied using a 2219-T851 aluminum alloy. The crack length and the occurrence of crack closure were measured by an electrical potential method. The experimental work was carried out within the framework of linear-elastic fracture mechanics.The experimental results show that the onset of crack closure (or opening) dependes on $\text{R, K}{}_{\mathrm{<mtext>max</mtext>}}$), and specimen thickness. In terms of the “effective stress intensity range ratio” ($\text{U}$), as defined by Elber, the results show that $\text{U}$ tends to increase for increasing $\text{R}$, decrease for increasing $\text{K}{}_{\max }$, and decrease with increasing specimen thickness. From these trends, it is shown that the “effective stress intensity range” ($\text{ΔK}{}_{\mathrm{<mtext>eff</mtext>}}$) does not always increase with increasing stress intensity range ($\text{ΔK}$).The experimental results show that crack closure cannot fully account for the effects of stress ratio, specimen thickness and $\text{K}{}_{\max }$ on fatigue crack growth. The use of $\text{ΔK}{}_{\mathrm{<mtext>eff</mtext>}}$ as a parameter for characterizing the mechanical driving force for fatigue crack growth is questioned.     

Crack closure studies under constant amplitude loading

Crack closure experiments were performed on 6063-T6 Al-alloy using a COD-gauge for various load ranges and stress ratios. Experimental results show that for a given stress ratio, $\text{R}$, the crack closure load goes on decreasing as crack length increases (or $\text{K}{}_{\max }$ increases) and reaches even below minimum load level at higher values of stress ratios. On the basis of these experimental results, a model for effective stress intensity range ratio $\text{U}$, which is found to be a function of stress ratio $\text{R}$ and $\text{k}{}_{\max }$, is developed.     

Effect of some aircraft loading program modifications on the fatigue life of open hole specimens

Flight simulation and program tests were performed with different 2024-T3 sheet specimens containing a central hole. The effect of the peak-load frequency on the damage sum and flight number was investigated. Gust spectrum test results were compared with those of other authors. For sufficiently close spectra with similar log-linear gust load distribution but different GAG cycle distribution, the relative Miner rule yielded satisfactory results. In the case of truncation levels $\text{S}{}_{\max }\text{= 1.84σ}{}_{\mathrm{m}}$ and $\text{S}{}_{\max }\text{= 1.685σ}{}_{\mathrm{m}}$, the investigated change of the frequency of stress cycles at the highest loading level (for cycle numbers smaller than those following from the log-linear gust distribution) had a weak effect on the damage sum, while the effect of decrease of the frequency of the lowest stress amplitude $\text{σ}{}_{\mathrm{a}}\text{= 0.222σ}{}_{\mathrm{m}}$ (MiniTWIST instead of TWIST) was considerable in some cases. It was found that in particular loading program cases, rare load peaks may have not only a beneficial but also a detrimental effect on the number of simulated flights. Truncation had a detrimental effect but the increase of the number of overload peaks above the number of cycles at the truncation level associated with the log-linear gust distribution had also a detrimental effect.     

Dynamic stress distribution around the tip of a running crack

The stress distribution is obtained around the tip of a crack running in a brittle material. The stresses are written as the sum of the associated static solution and the wave-effect terms which depend upon the crack speed. The results obtained clearly reduce to the associated static solutions if the crack speed vanishes.Near the tip of the crack, the dynamic stress-intensity factor for the circumferential stress, $\text{σ}{}_{\mathrm{\theta \theta }}$, is written as the product of the associated static stress-intensity factor and the dynamic correction factor which is a nondimensional function of the crack speed, $\text{V}$, the angle from the crack plane, θ, and Poisson's ratio, ν. The value of the correction factor is computed for various values of $\text{V}$ and θ at $\text{ν = 0.25}$. It is shown that the maximum tensile value of $\text{σ}{}_{\mathrm{\theta \theta }}$, occurs on the crack plane for $\text{V}$ less than 0.7 time shear wave speed, $\text{c}{}_2$, and suddenly shifts to the plane of $\text{θ = 55°}$ for $\text{V}$ slightly larger than 0.7 $\text{c}{}_2$. For $\text{V > 0.7}$$\text{c}{}_2$, the angle θ for the maximum $\text{σ}{}_{\mathrm{\theta \theta }}$, θ being larger than 55°, varies continuously with the crack speed, $\text{V}$. The results obtained are used to discuss the growth of branching crack.     

Fracture behaviour of dynamically loaded ship building plate material

The fracture toughness values of ship building mild steel measured over a temperature range ? 196°C to 28°C and crack tip strain rates ranging from 10^?5/sec to 10^?1/sec are examined in the light of the models recently proposed by Malkin and Tetelman. The effect of a change in inclusion morphology brought about by electroslag refining on the fracture toughness of the steel is also evaluated. It is found that the stress-induced fracture criterion ofthe model applies for the case where the ratio $\text{σ}{}^1{}_{\mathrm{f}}\text{σ}{}_{\mathrm{YS}}\text{? 3.94}$. This ratio is independent of the strain rate. In the strain induced fracture region of the model, the critical strain near the crack tip, ?_f(Rβ) is a function of the yield stress irrespective of temperature and strain rate. Electroslag refining reduces significantly the size and volume fraction of the inclusions and changes their shape from prolate ellipsoid to spherical. Apparently the electroslag refining does not improve fracture toughness significantly if the fracture toughness of the as received material measured with the major axis of the inclusions perpendicular to the crack front, is taken as a basis of comparison.     

Organizational scheme for corrosion-fatigue crack propagation data

A model, proposed earlier, is modified in an attempt to explain a number of curious behaviors of corrosion-fatigue crack propagation (CFCP). The behaviors include effects of load ratio R in air and salt water vs vacuum, and effects of loading frequency at fixed R in these environments. Assumptions of the modeling are reviewed in detail in view of earlier objections to them. The ingredients of CFCP per this model: Poisson contraction, strain hardening, ligament surface attack/annihilation, and stress relaxation are developed and related to conditions of the crack tip locale. In the modeling, a parameter G, for growth rate factor, is developed solely as a function of the form of the ordinary or of the cyclic stress-strain curve. Previous work had developed a G₁ for the ordinary curve, to be associated with the surface attack effect as in stress-corrosion cracking, and one G₂ for the cyclic curve, to be associated with the stress relaxation effect as in fatigue crack propagation (FCP). A hybrid $\text{G}{}_{\mathrm{<mtext>2</mtext><mtext>1</mtext>}}$ is developed, combining attributes of both, which seems to successfully describe the corrosion induced augmentation of G₂. Parametric curves of $\text{G}{}_{\mathrm{<mtext>2</mtext><mtext>1</mtext>}}\text{(+G}{}_2\text{)}$ correspond well with stage II frequency-dependent growth in CFCP. However, alone they do not explain the frequency-wise stage II threshold shift nor the frequency-independent air-environment FCP rate. It is found that these trends can be represented by loci of constant plastic strain rate, due to crack loading and propagation, relative to the surface annihilation rate. Such loci are determined by comparing growth rate factor maps with strain rate maps, using parametric curves of equal geometric-series spacing. Maps of this sort are used to analyze about a dozen cases of CFCP including two titanium alloys and three steels, with one of the steels of four different tempers. Stress-strain curves of the low strength steels are processed to remove the Lüder band effect to facilitate the modeling. The scheme for data organization involves a representation of indexes of the two kinds of parametric curves fitting the data, and the process zone size implied by the fitting. Model predication of load-ratio effects on the fatigue crack growth threshold is in good correspondence with literature data. Comparison of estimated process zone sizes with literature data of microstructural and fractographic size measurements is encouraging.     

On the cyclic behavior of cast and extruded aluminum alloys. Part A: Fatigue crack propagation

The fatigue crack propagation (FCP) response of a cast and extruded aluminum alloy was examined as a function of mean stress and specimen orientation. The extruded alloy was tested in both the longitudinal and transverse orientation and no difference in FCP response was noted. FCP tests were conducted at R ratios of 0.1, 0.5, 0.65 and 0.8. In the threshold regime, it was seen that as R ratio increased, $\text{Δ}\text{K}{}_{\mathrm{TH}}$ decreased. In addition, ΔK_TH values determined for the cast alloy were superior to those determined for the extruded alloy at all R ratios examined. The threshold regime was also shown to be K_MAX rather than $\text{Δ}\text{K}$ dependent. At intermediate ΔK levels, a mean stress effect was seen for both alloys at R ratios less than 0.5. Crack closure was monitored during testing so that ΔK_EFF values could be determined. $\text{Δ}\text{K}{}_{\mathrm{EFF}}$ was seen to explain mean stress effects at intermediate $\text{Δ}\text{K}$ levels.     

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.     

Fatigue crack propagation in steels

From previous investigations of the mechanisms of both fracture and fatigue crack propagation, the static fracture model proposed by Lal and Weiss may be thought as reasonable for describing fatigue crack propagation in metals at both low and intermediate stress intensity factor ranges $\text{ΔK}$. Recent progress in fatigue crack propagation indicates that it is not only possible, but also necessary, to modify this static fracture model. Based on the modified static fracture model, the effective stress intensity factor range $\text{ΔK}{}_{\mathrm{eff}}$, which is defined as the difference between $\text{ΔK}$ and the fatigue crack propagation threshold value $\text{Δ}{}_{\mathrm{th}}$, is taken as the governing parameter for fatigue crack propagation. Utilising the estimates of the theoretical strengths of metals employed in industry, a new expression for fatigue crack propagation, which may be predicted from the tensile properties of the metals, has been derived. The correlation between the fatigue crack propagation rate and the tensile properties is thus revealed. The new expression fits the test results of fatigue crack propagation of steels below 10^?3 mm/cycle and indicates well the effect of stress ratio on the fatigue crack propagation rate.     

Effect of mechanical properties of material on rate of fatigue crack propagation

Many experimental and analytical equations on a rate of a fatigue crack propagation have been proposed. However, it seems that they can not fully express its complex behavior. There are still many problems remaining to be solved in order to clarify its mechanism. One of them is to clarify the relation between the rate of the crack propagation and the mechanical properties of material. In this paper, the rate of the crack propagation is analysed to clarify this problem. This analysis is based on the observation results of the fatigue crack propagation behavior previously by the authors. The analytical result is compared with the experimental one to make sure that they agree with each other. The conclusion obtained is; the rate of fatigue crack propagation is expressed by using the stress intensity factors as

$\text{dl}\text{dN}\text{= {}\text{c}\text{[Y}{}^2\text{F}{}^{\mathrm{a}}\text{E}{}^{\mathrm{a(1?n)}}\text{]}\text{} (K}{}_{\max }\text{)}{}^2\text{(K}{}_{\mathrm{a}}\text{)}{}^{\mathrm{a(2?n)}}$

. where C is a constant; E, Young's modulus; F, plastic coefficient; Y, yield stress; K_max and K_a, maximum and amplitude of the stress intensity factor, and α and n, exponents of the Manson-Coffin's law and work-hardening.     

On the cyclic behavior of cast and extruded aluminum alloys. Part B: Fractography

In a prior study [1], the fatigue crack propagation (FCP) response of a cast and an extruded aluminum alloy was examined as a function of mean stress and specimen orientation while crack closure data were collected. In this work, extensive electron fractographic studies were conducted on the previously generated fatigue fracture surfaces using both scanning and transmission electron microscopy. The threshold micromorphology revealed crisp, cleavage-like facets. Striation spacing measurements at intermediate and high $\text{Δ}\text{K}$ levels were obtained to determine microscopic growth rates; these measurements were seen to vary with $\text{R}$ ratio and were best correlated with $\text{ΔK}{}_{\mathrm{EFF}}$ rather than $\text{Δ}\text{K}{}_{\mathrm{APP}}$. Slope changes in the $\text{da/da-}\text{Δ}\text{K}$ plots were identified and attempts made to establish correlations between the associated plastic zone sizes and microstructural dimensions. Of particular note, a stage IIa to IIb transition in the extruded material was found to correspond to a micromechanism change from faceted growth to striated growth when the reversed plastic zone size was similar to the subgrain dimension.     

Some experimental observations on the Poisson's ratio of sea-ice

Measurements were made on the longitudinal and transverse strain of sea-ice beams loaded in flexure. The specimens were tested with stress rates varying from 10 to 600 kPa s^?1 and temperatures ranging from ?5°C to ?40°C. Under these conditions, the effective strain ratio μ increases with increasing temperature and decreasing stress rate. The strong influence of the stress rate, σ, suggests an empirical law of the form: μ = 0.24$\text{(}\text{σ}\text{?}\text{σ}\text{?}{}_1\text{)}{}^{\mathrm{?0.29}}\text{+ μ}{}_{\mathrm{D}}$ where σ is the stress rate (kPa s^?1), $\text{σ}\text{?}{}_1$ is a unit stress ratio (1 kPa s^?1) and μ_D is a dynamic value of Poisson's rate which depends on the temperature.     

Fatigue crack propagation from a crack inclined to the cyclic tensile axis

Cyclic stresses with stress ratio R = 0.65 were applied to sheet specimens of aluminium which have an initial crack inclined to the tensile axis at angles of 30°, 45°, 72° or 90°. The threshold condition for the non-propagation of the initial crack was found to be given by a quadratic form of the ranges of the stress intensity factors of modes I and II. The direction of fatigue crack extension from the inclined crack was roughly perpendicular to the tensile axis at stress ranges just above the threshold value for non-propagation. On the other hand, at stress ranges 1.6 times higher than the threshold values the crack grew in the direction of the initial crack. The rate of crack growth in the initial crack direction was found to be expressed by the following function of stress intensity factor ranges of mode I, K₁, and mode II, K₂: $\text{dc}\text{dN}\text{= C(K}{}_{\mathrm{eff}}\text{)sum}$, where $\text{K}{}_{\mathrm{eff}}\text{= [K}{}_1{}^4\text{+ 8K}{}_2{}^4\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$. This law was derived on the basis of the fatigue crack propagation model proposed by Weertman.