The retardation phenomenon of fatigue crack growth in HT80 steel

The fatigue crack growth behavior resulting from single and multiple applications of overload was investigated for HT80 steel. A peak load was found to cause retardation of the crack growth rate, which becomes stronger with increasing the peak/baseline stress ratio or with decreasing baseline stress intensity. Multiple overloads resulted in additional retardation. These experimental data were explained according to a new model based on crack closure conception, being correlated with the residual plastic zone size ahead of crack tip induced by the peak overload(s). The proposed formulation of retardation was expressed simply as a function of peak/baseline stress ratio, $\text{r}$, and two material parameters, $\text{m}$ and β. $\text{m}$ the exponent parameter in Paris equation and β is the ratio of crack distance at the maximum retardation to the residual plastic zone size. The retardation was predicted to increase with increasing $\text{r}$ and $\text{m}$ and with decreasing β. It was suggested that the parameter, β, reflects the change in the morphology of crack tip resulted from the application of overload, which determines the shape of the curve for retarded crack growth rate vs crack distance.     

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.     

Mechanics of fatigue crack propagation by crack-tip plastic blunting

The power relation between the fatigue crack propagation rate $\text{d}\text{a/}\text{d}\text{N}$ and the $\text{J}$ integral range $\text{ΔJ}$ was obtained for OFHC copper, 0.04%C steel and stainless steel (Type 304). The physical meaning of the relation was investigated based on the observation of the crack opening behavior and fractography. The striations, whose spacing was equal to $\text{d}\text{a/}\text{d}\text{N}$, confirm crack-tip blunting as being an operating mechanism for crack growth. $\text{d}\text{a/}\text{d}\text{N}$ was expressed as a power function of the crack-tip opening displacement (Δ CTOD), $\text{d}\text{a/}\text{d}\text{N = A(Δ}\text{CTOD}\text{)}{}^{\mathrm{p}}$, where $\text{p}$ was larger than one. The major portion of Δ CTOD contributes to crack growth at high rates, while a considerable fraction of Δ CTOD occurs behind the crack tip at low rates. Δ CTOD is correlated to $\text{ΔJ}$ divided by the yield strength σ'_Y through the equation,$\text{Δ}\text{CTOD}\text{= B(ΔJ/σ}{}_{\mathrm{Y}}\text{′)}{}^{\mathrm{q}}$, where $\text{q}$ is nearly equal to one for 0.04%C steel and is larger than one for copper. The variation of $\text{q}$ with material was explained based on the observed distribution of the crack opening displacement. The final equation for fatigue crack growth is given as $\text{d}\text{a/}\text{d}$N = A · B^p(ΔJ/σ_Y′)^pq. When the shape of the crack tip opening is geometrically similar, both $\text{p}$ and $\text{q}$ are one. For a general case, both are larger than one, yielding the exponent of the $\text{d}\text{a/}\text{d}\text{N-ΔJ}$ relation deviating from 1 up to 2.3.     

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.     

Effect of specimen thickness on the crack propagation and crack branching in delayed failure

The crack propagation and crack branching behaviors in delayed failure have been investigated on the specimens with various thickness ($\text{B = 1.5–10}\text{mm}$).The crack propagation velocity reveals a maximum value at a medium specimen thickness ($\text{B = 5}\text{mm}$). This fact can be understood by assuming the compound effect of two factors that the triaxiality of stress at crack tip as a driving force for hydrogen diffusion increases with increase of specimen thickness $\text{B}$, and that the invasion of hydrogen atoms from specimen surface increases with decrease of $\text{B}$.The stress intensity factor at crack branching, $\text{K}{}_{\mathrm{IB}}$, increases with decrease of specimen thickness $\text{B}$, and when B is 1.5 mm, the specimen fractures without showing the crack branching. The latter fact can be explained by connecting the necessary and sufficient conditions for crack branching with the decrease in height of plastic region at the crack tip in thin specimens.     

Compressive maximum shear crack initiation and propagation

A maximum shear crack γ (a Mode II shear crack along the maximum shear direction associated with the crack tip shear displacement) was produced successfully in a so-called compressive maximum shear (CMS) specimen. This specimen was specificially designed to produce a compressive maximum shear failure which is one of two mechanisms widely believed to be responsible for limiting bearing fatigue life in rolling contact. The fracture initiation stress (or crack nucleation stress) σ_c and the upward crack propagation rate (toward the loading surface) $\text{dli}\text{dσi}$ per unit cyclic compressive stress increment were determined for the 52100 steel. These parameters were measured at two cleanness levels (DE and CEVM) [DE: basic electric arc furnace melted plus vacuum degassed. CEVM: Consumable electrode vacuum melted] and two tempered hardness levels, RC61 and 51. The possibility of determining K₁₁ for ith cycle was also elucidated. The formation of tail cracks and parallel multiple cracks as fine structure of CMS cracks can be well expounded by the concept of restoring tensile stresses and the residual shear stress relaxation at the CMS crack tip. The fracture mechanism advanced here can explain the formation of similar tail cracks and parallel multiple cracks frequently observed along the inclined shear cracks existing in the subsurface regions of rolling     

Cyclic analysis of a propagating crack and its correlation with fatigue crack growth

Stress and strain field of a propagating fatigue crack and the resulting crack opening and closing behavior were analysed. It was found that a propagating fatigue crack was closed at tensile external loads due to the cyclically induced residual stresses. Strain range value $\text{Δ?}{}_{\mathrm{y}}$ in the vicinity of the crack tip was found to be closely related with the effective stress intensity factor range $\text{ΔK}{}_{\mathrm{eff}}$ which was determined on the basts of the analytical crack opening and closing behavior at its tip. Application of this analysis to the non-propagating fatigue crack problem and the fatigue crack propagation problems under variable stress amplitude conditions revealed that both $\text{Δ?}{}_{\mathrm{y}}$ and $\text{ΔK}{}_{\mathrm{eff}}$ were essential parameters governing fatigue crack growth rate.     

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.     

Elastodynamic near-tip fields for a rapidly propagating interface crack

The elastodynamic stress field near a crack tip rapidly propagating along the interface between two dissimilar isotropic elastic solids is investigated. Both anti-plane and in-plane motions are considered. The anti-plane displacements and the in-plane displacement potentials are sought in the separated forms $\text{r}{}^{\mathrm{q}}\text{F(θ)}$, $\text{r}$ and θ being polar coordinates centered at the moving tip. The mathematical statement of the problem reduces to a second-order linear ordinary differential equation in θ, which can be solved analytically. Formulation of the boundary and interface conditions leads to an eigenvalue problem for the singularity exponent $\text{q}$. For the in-plane problem, root $\text{q}$ is found to be complex. Thus, the stresses exhibit violent oscillations within a small region around the crack tip, and the solutions have physical significance only outside this region. The angular stress distributions are plotted for various crack speeds, and it is found that at a high enough speeds the direction θ of maximum stress moves out of the interface. This result indicates that a running interface crack may move into one of the adjoining materials.     

Effect of side-grooving on the compliance of the cantilever bend specimen

The precracked cantilever bend specimen, which is normally employed to determine the stress corrosion cracking threshold $\text{K}{}_{\mathrm{Iscc}}$, can also be used to obtain the stress corrosion crack growth rate as a function of stress intensity factor $\text{K}{}_{\mathrm{I}}$. When the crack is obscured, crack growth can be monitored by measuring the crack-opening displacement and converting this to crack length by means of the compliance relationship for the specimen. Compliance relationships were therefore determined for 0.5-in.-thick AISI 4340 steel cantilever bend specimens with net-to-gross thickness ratios of 1.0 (no side grooves), 0.8(shallow side grooves), and 0.6 (deep side grooves). The shallow side grooves had no effect on the crack-opening compliance relationship, while the deep side grooves increased the crack-opening compliance by about 20%.     

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 stress field near the blunt crack tip and the fracture criterion

The asymptotic expansion solution containing two terms for the stress field near the blunt crack tip is obtained. It is proposed that the slit be divided into the ideal crack, blunt crack I, blunt crack II and the notch in accordance with the geometrical structure of the slit tip. Whether the blunt crack can be considered as the ideal crack will depend mainly on the following three factors: $\text{√}\text{2R}{}_0\text{C}$, $\text{√}\text{R}{}_0\text{r}{}_{\mathrm{c}}$ and the profile of the crack. In this paper, the influence of the crack tip radius on the fracture criterion is studied and it is shown that the classical strength theories belong to the unconditional extremum criteria while the S criterion, etc. in fracture mechanics belong to the conditional extremum criteria. A modified maximum tension stress theory is developed, in which the fracture theories of the crack and the notch can be roughly unified.     

An analysis of creep crack propagation on the basis of the plastic singular stress field

In order to gain an insight into creep crack propagation problems a mechanics approach is presented in this paper on the basis of the plastic singular stress field near a crack tip under the Mode III and I steady-state creep conditions, in combination with a generalized creep damage hypothesis. Closed form equations which predict rates of creep crack propagation are obtained analytically. According to this analysis, it is found that $\text{b}{}_1\text{(n + 1)}$ is the index which characterizes the effect of damage accumulation in front of a crack, where n is the creep exponent and b₁ is the exponent involved in the creep damage hypothesis used in this analysis. The tendency of the predicted crack propagation behaviors is consistent with experimental data available in the literature.     

Fatigue crack tip strain loop under single overload in Fe3Si steel

For the problem of the retardation of fatigue crack growth caused by single overload, cyclic strain changes in one cycle of the local crack tip region were investigated by using fine-grid-method. From the application of Crack Tip Strain Loop (C.T.S.Loop), the correlation between effective stress intensity factor range (ΔK_eff^T) defined from the stress range of C.T.S.Loop and crack growth rate ($\text{d}\text{a}\text{d}\text{N}$) was discussed. Moreover, from the strain range of C.T.S.Loop, the correlation between crack-tip strain range (Δ_?^T) and $\text{d}\text{a}\text{d}\text{N}$ was also investigated.     

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.     

Fatigue crack growth under C.O.D. cycling

The possibility of using the parameter crack opening displacement as the basis for describing fatigue crack growth behavior in mild steel has been examined. Results are reported on crack growth rates under constant C.O.D. cycling for both plain and welded mild steel of two thicknesses. They show that a power law relationship exists between the crack tip opening displacement and the crack growth rate which fits both the $\text{1}\text{4}$ and $\text{1}\text{2}$ in thick material. Some preliminary results on welded specimens also fit the same power law. Extension of this relationship to the high cycle growth region also gave a reasonable correlation with experimental results.     

Transient shear waves in a wedge subjected to rapid tearing

The surface of an elastic wedge is subjected to sudden antiplane surface tractions and displacements sufficient to cause tearing. The subsequent crack instability is investigated. The wedge faces subtend an angle κπ with the line of antisymmetry, along which the crack propagates with a constant velocity v. For the externally applied disturbances that are considered here, and for constant crack tip velocities, the particle velocity and $\text{?t}{}_{\mathrm{\theta z}}$ are functions of $\text{r}\text{t}$ and θ only, which allows Chaplygin's transformation and conformai mapping to be used. The theory of analytic functions is then used. For various values of the crack propagation velocity, the dependence of the elastodynamic stress intensity factor, and energy flux into the crack tip, on the wedge angle 2κπ is investigated.     

On crack opening stress level in fatigue by Eddy current technique

Linear elastic fracture mechanics relates fatigue crack growth with the stress intensity factor at the crack tip. Presence of residual deformations at the tip of a fatigue crack reduces the crack tip stress intensification such that effective stress intensity range $\text{ΔK}{}_{\mathrm{e}}\text{= U · ΔK}$. In this paper use of eddy current technique is exhibited to find the values of test value of effective stress range factor $\text{U}{}_{\mathrm{test}}$. A reasonable comparison between computed and experimental results of $\text{U}{}_1$ and $\text{U}{}_{\mathrm{test}}$ on two Al alloys 6061-T6 and 6063-T6 has recommended the Eddy Current Technology for finding out the values of crack opening stress level under given loading conditions.     

A brief survey of the advances of fracture mechanics in china

A brief survey was made of the recent advances of macro-fracture mechanics in China up to December 1979. Topics dealt with included; (1) The stress field near the crack tip and fracture models; (2) The $\text{J-}\text{integral}$; (3) The calculation of the stress intensity factor; (4) Fracture criteria for mixed mode cracks; and (5) Fracture crack propagation.