Growth and coalescence of two collinear indentation cracks in glass

Subcritical growth and coalescence of two collinear cracks of different lengths were investigated using small Knoop indentation cracks in glass. Indentation cracks subjected to bending in water showed anomalous crack growth in terms of the stress intensity factor, K_I. The crack growth velocity, dc/dt, was initially high, decreased and thereafter increased with increasing K_I. The effective stress intensity factor, K_I,eff, was calculated by adding a term describing the state of residual stress to explain this anomalous growth. Before crack coalescence, a large crack showed a crack velocity higher than expected from the coalescent crack. The coalescent crack velocity increased with K_I,eff and the slope of dc/dt−K_I,eff curves differed from that for a single crack, depending on the crack length.     

Effect of yield stress and specimen size on the position of fracture toughness peak (FTP) in Ji-a/W curves

Early work showed that there was a fracture toughness peak (FTP) as the fracture toughness changed with crack length/specimen width (a/W). It could be thought of as a “safe crack” for the cracks whose length is smaller than that where the FTP is located. In the present paper, it is indicated that the crack length of FTP isJ_i-a/Wcurves decreases with increasing yield stress of material and specimen size and decreasing test temperature. The reason for the fracture toughness being insensitive to the (a/W) for the ultra-high strength and brittle material is explained.     

Finite element analysis of an interface crack with large crack-tip contact zones

There is considerable ambiguity regarding the limiting values of the strain energy release rate (SERR) components at the tips of a crack lying along the interface between two dissimilar isotropic media. In this paper this aspect is examined using finite element analysis and Modified Crack Closure Integral (MCCI) for a problem in which the material properties are chosen so as to cause a large size crack-tip contact zone. By careful choice of this problem, interpenetration of the crack faces in the crack-tip contact zones is observed for the first time in the finite element analysis. Earlier solutions primarily on remote mode 1 loading reported that SERR components do not converge as the virtual crack extension Δa → 0 and that these components show an oscillatory nature when Δa is less than the contact zone size r_c. In the present work, multipoint constraints are imposed on crack face normal displacements in the contact zone and meaningful results are generated for both remote tension and shear loading cases. The apparent nonconvergence of the SERR components as Δa → 0 can be explained if these components are considered as functions of Δa, and Δa is considered as the actual crack growth step size.     

The use of ΔK when examining microstructural effects on small fatigue crack growth

The behaviour of small fatigue cracks has been studied in the Al---Li---Cu---Mg---Zr alloy 8090. It was found that the crack inclination normal to the surface of the specimen made crack deflections and kinking in the plane of the specimen surface irrelevant to the crack driving force. The low closure levels associated with small fatigue cracks reduce the effect of microstructure on crack growth but this does not affect the ability of ΔK (stress intensity factor range) to detect microstructural influences. The use of ΔJ (J-integral range) as a correlating parameter reduced the differences between the data for long and short fatigue cracks. However, there was no evidence that ΔJ was superior at identifying microstructural effects. Similarly the effect of the higher-order terms on the value of ΔK was found to be minor. It is concluded that the use of ΔK is not likely to bias the microstructural effects and so ΔK may be used when examining microstructural effects on small fatigue crack growth.     

Fatigue crack propagation rate at low ΔK of two aluminum sheet alloys, 2024-T3 and 7075-T6

For transport aircraft with long lifetimes, crack growth data to implement the durability life requirements in the low ΔK range are needed. This is the region comprising most of the lifetime for the cracks of interest, and it is also the region where there is little data available. Crack growth data in the form of da/dN vs ΔK vs R at constant amplitude for two primary aircraft aluminum sheet alloys, 2024-T3 and 7075-T6 (clad) were measured in laboratory air and 140°F in the low da/dN region 10⁻⁸ to 10⁻⁵ in./cycle. Crack growth rates were correlated with stress state and with fractographic features.     

Experimental K-calibration for corner cracks under bending loading

The geometric correction function F in the expression for stress intensity factors has been determined experimentally by a compliance method for bar-shaped specimens of Al-7475-T761 (with a rectangular cross-section) cyclically loaded in bending at R = −1 and room temperature. The experimental method makes it possible to resolve the behaviour of the crack during the tensile and compressive portions of the loading cycle. This leads to the introduction of the initial notch size as an additional correction parameter. The development of the equilibrium shape of the crack during crack growth up to long surface distances has been investigated. These results have been used for the determination of F. A comparison with literature data is presented.     

Fatigue damage in a unidirectional SiC/Al composite due to push-pull and zero-pull loading

Axial fatigue behaviour due to fully reversible and zero-tension cyclic loads on specimens cut from a 5 mm thick panel of a unidirectional SiC/A1 composite has been investigated at room temperature. The panel contained 40 vol.% SiC fibres (SCS-2), sandwiched between 32 layers of A1 6061 foils, which were bonded together by hot-pressing. The loading was always parallel to the fibres. Steady hysteresis loops were observed in the stress-strain plot after about 3 cycles of loading. A plot of S/N curves showed that at load ratio R = 0 the fatigue strength of the composite was about 3 times higher than that of the monolithic matrix metal. At R = −1, however, the fatigue strength of the composite was even lower than that of the matrix metal. At both R = 0 and R = −1, the composite suffered large modulus losses (about 15%) at cycles well before the final failure. At R = 0 the modulus loss involved fibre breakage and matrix cracks, which were transverse as well as parallel to the loading direction, while at R = −1 it involved delamination cracks and barrelling of outer layers. Fractography after the final failure at R = 0 showed secondary cracks and fibre pull-out.     

Statistical investigation of surface fatigue cracks in large-sized turbine rotor shaft steel

Distribution properties of an initiation life N_i and a propagation life N_p of surface cracks, statistical characteristics of a crack growth rate dl/dN, and a relationship between a scatter of the distributions and a gradient a of S-log N curves in rotating bending fatigue tests were investigated for Ni-Cr-Mo-V steel, using for a large-sized turbine rotor shaft. The distributions of N_i and N_p were expressed as Weibull distributions, and the scatter of them for smooth specimens and for lower stress amplitude σ_a tests were larger than those for notched ones and for higher σ_a tests, respectively. The statistical properties of crack propagation rate were almost similar in both smooth and notched specimens. The relationship between the a and a coefficient of variation η for the distributions of N_i, N_p and a final fracture life N_f was expressed as η = c(a)^−b, where c and b are constants.     

Applying strain energy density factor theory to propagation estimating of surface crack in tubular T-joints

The propagation direction of a surface crack in tubular T-joints and the surface crack profile are studied in this paper. By using Photoelasticity and Finite Element method, the distribution of Stress Intensity Factor (SIF) along the front edge of the prefabricated semi-elliptic surface cracks at the hot spots of tubular T-joints is obtained. The results show that the cracks are subjected to mix-mode loading, and the distribution of SIF along the front edge of the crack depends not only on a/T, the ratio of crack depth to the thickness of chord wall, but also largely on shape ratio a/c, the ratio of depth of the crack a to its length c. It can also be predicted that there exists a certain precedent propagation direction for a surface crack with a certain a/c. According to the Strain Energy Density Factor theory the condition of constant strain energy density factor S on the front edge of the crack will be enforced on each point of the prosective crack profile, so that the crack profile can be pre-estimated.     

Small-crack growth and fatigue life predictions for high-strength aluminium alloys. Part II: crack closure and fatigue analyses

Small-crack effects were investigated in two high-strength aluminium alloys: 7075-T6 bare and LC9cs clad aluminium alloys. Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks. In the experimental program, fatigue and small-crack tests were conducted on single-edge-notch tension (SENT) specimens and large-crack tests were conducted on middle-crack tension specimens under constant-amplitude and Mini-TWIST spectrum loading. A pronounced small-crack effect was observed in both materials, especially for the negative stress ratios. For all loading conditions, most of the fatigue life of the SENT specimens was shown to be crack propagation from initial material defects or from the cladding layer. In the analysis program, three-dimensional finite-element and weight-function methods were used to determine stress intensity factors, and to develop equations for surface and corner cracks at the notch in the SENT specimen. (Part I was on the experimental and fracture mechanics analyses and was published in Fatigue Fract. Engng Mater. Struct. 21 , 1289–1306, 1998.) This part focuses on a crack closure and fatigue analysis of the data presented in Part I. A plasticity-induced crack-closure model was used to correlate large-crack growth rate data to develop the baseline effective stress intensity factor range (Δ K _eff ) against rate relations for each material, ignoring the large-crack threshold. The model was then used with the Δ K _eff rate relation and the stress intensity factors for surface or corner cracks to make fatigue life predictions. The initial defect sizes chosen in the fatigue analyses were similar to those that initiated failure in the specimens. Predicted small-crack growth rates and fatigue lives agreed well with experiments.     

STUDY ON FATIGUE THRESHOLD BEHAVIOUR AND FATIGUE CRACK PROPAGATION IN A CAST Co-Cr-Mo ALLOY USED FOR SURGICAL IMPLANTS

Abstract— —Fatigue crack propagation rates (d a /d N ) and fatigue crack thresholds (Δ K _th) have been studied in a cast Co-Cr-Mo alloy used for surgical implants with various grain sizes. Results for materials with average grain sizes of about 400 and 60μm respectively are presented. Threshold values close to 10–15 MPam have been measured with decreasing values observed on increasing the grain size. Similar effects of grain size are found on the crack propagation behaviour at higher growth rates, where a coarse grain size material show a higher crack growth rate than a fine grain size material at the same Δ K levels. The effects of microstructure on fatigue properties of the cast Co-Cr-Mo alloy are caused not only by grain size variation but are also attributed to the microstructural differences: a coarse-grained material with a directionally grown dendritic structure vs a fine-grained material with an equiaxed grain structure.     

THREE-DIMENSIONAL CRACK-SHAPE EFFECTS DURING THE GROWTH OF SMALL SURFACE FATIGUE CRACKS IN A TITANIUM-BASE ALLOY

Abstract— A basic study was performed on the evolution of three-dimensional shapes of small surface fatigue cracks during fatigue, and the effect of this evolution on small-crack growth behavior of a titanium-base alloy. Specifically, the nature and the magnitude of variations in crack aspect ratio, a/c (a is the crack depth and c is the half-surface crack length), during cyclic crack growth and its impact on growth rates have been studied. Experiments were performed on naturally initiated micro-cracks in a microstructure consisting of equiaxed primary-α₂ phase in a Widmanstätten (transformed β) matrix. Several cracks under stress ratio (R) levels of 0.1 and ?1, were studied. A specialized experimental system, consisting of a laser interferometer (to measure precisely the small-crack surface displacements), and a photo microscope (to automatically and continuously photograph the fatigue micro-cracks) was employed in the study. Apparent aspect ratios of surface cracks were calculated from the compliance response and the surface crack length data as a function of fatigue cycles. These data enabled accurate calculations of growth rates at the surface crack tip as well as the tip at depth in the bulk over the entire crack growth period, thus giving an insight into the crack growth process. Measurements of closure levels of small cracks were also performed and were used to partly account for the differences in growth rates. In the comparisons of small-crack growth data with the large-crack data, surface growth rates correlated relatively well with the large-crack data. Growth rates at depth exhibited large variations due to the irregularity of crack fronts at this location, and these rates deviated significantly from the large-crack behavior. Additionally, these growth rates varied between different cracks. An attempt was made to rationalize these observations in terms of the effects of inhomogeneities present in the microstructure.     

Constituent damage mechanisms in metal matrix composites under fatigue loading, and their effects on fatigue life

Load controlled fatigue experiments were performed on 8-ply unidirectional ([0]₈) SCS-6-Ti-15-3 metal matrix composites (MMCs) at different temperatures, and the results were interpreted in terms of the overall three-regime framework of fatigue. The emphasis was on understanding the mechanisms and mechanics of constituent damage evolution, and their effects on fatigue life. Most tests were performed at an R-ratio of 0.1, but limited fully-reversed (R = −1) tests were conducted. In regime 1, damage was fiber failure dominated, but the exact mechanisms were different at room and elevated temperatures. In regime 2, observation of matrix cracks and persistent slip bands provided convincing evidence of matrix dominated damage. Weak fiber-matrix interfaces contributed to crack bridging. However, fiber fracture also played an important role in regime 2; tension-tension and tension-compression tests showed similar lives on a maximum fiber stress basis, although the strain range, which primarily controls matrix crack growth, was almost double for R = −1 compared with R = 0 or 0.1. Good agreement was obtained from the different R-ratio tests, between the MMC and matrix data, and data at room and elevated temperatures, when compared based on the strain range in the tension part of a cycle. Analyses and observations of fiber pull-out lengths and fiber fractures in the matrix crack wake provided evidence of fiber damage; the analyses also helped to explain increased fiber bridging with fiber volume fraction. Issues of fatigue life prediction are briefly discussed.     

Fatigue properties of ultrafine grained low carbon steel produced by equal channel angular pressing

Ultrafine grained low carbon (0.15 wt.% C) steel produced by equal channel angular pressing (ECAP) was tested for investigating fatigue properties, including cyclic softening and crack growth rate. Emphasis was placed on investigating the effect of load ratio on the fatigue crack growth rates of ultrafine grained microstructure. The ECAPed steel exhibited cyclic softening. After the first cycle, the tension and compression peak stresses decreased gradually with the number of cycles. Fatigue crack growth resistance and the threshold of ECAPed ultrafine grained steel were lower than that of an as-received coarse grained steel. This was attributed to a less tortuous crack path. The ECAPed steel exhibited slightly higher crack growth rates and a lower ΔK_th with an increase in R ratio. The R ratio effect on growth rates and ΔK_th was basically indistinguishable at a lower load ratio (R>0.3) compared with other alloys, indicating that the contribution of the crack closure vanished. This was explained by the fact that finer grained materials produce a lower opening load P_op due to a relatively less serrated crack path. Consequently, K_min can reach K_op readily with a smaller increment of load ratio. The crack growth rate curve for the ECAPed ultrafine grained steel exhibited a linear extension to the lower growth rate regime than that for the coarse grained as-received steel. This behavior can be explained by a reverse crack tip plastic zone size (r_p) that is always larger than the grain size.     

Microstructurally-dependent model for predicting the kinetics of physically small and long fatigue crack growth

Based on the proposed concept of the fatigue threshold stress intensity factor ranges, a model has been developed that describes the kinetics of physically small fatigue crack and long fatigue crack growth. The model allows the calculation of the crack growth rate under the regular fully-reversed uniaxial loading from the data on the static characteristics of mechanical properties and the microstructure of the initial material. The crack depth at which the cyclic plastic zone size ahead of the crack tip will exceed the grain size should be considered as a criterion of the small-to-long crack transition. Under high-cycle fatigue conditions physically small fatigue crack growth will be divided into two phases of growth: the first phase is when the crack propagates along the slip planes of individual grains, and the second one is when the crack changes the mechanism of growth and propagates in the plane perpendicular to the loading direction. The model validity has been tested using the experimental data on the growth of the long cracks in specimens of titanium alloy VT3-1 in seven microstructural states and the small cracks in specimens of titanium alloy Ti–6Al–4V and aluminum alloy 2024-T3. Good agreement between the calculated and experimental results is obtained.     

The effect of load ratio on the threshold stresses for fatigue crack growth in medium carbon steels

A study of the effect of load ratio, R, on the low crack growth rates and the threshold stress conditions exhibited by five medium carbon steels has been conducted. It was found that decreased values of R retarded crack growth to an increasing degree as a defined threshold for crack growth was approached, such that this threshold showed a marked dependence on K max rather than ΔK. Comparisons of the five materials showed that the threshold increased as yield strength increased for a given R, but this effect could be normalised in terms of a constant value of the maximum plastic zone size at the crack tip.     

Growth mechanism of stress corrosion cracking in high strength steel

Stress corrosion crack growth rates are measured at sveral stress intensity levels for low-tempered 4340 steel in 0.1N H₂SO₄ solution. The characteristics of the growth rates are divided into three regions of stress intensity factors: Region I near K_1SCC; Region III near unstable fracture toughness, K_1SC; and Region II, which lies between the two. K_1SCC is the value of K at which no crack growth can be detected after 240 hr.

In order to explain these experimental results, the crack initiation analysis reported in a previous paper is extended to the growth rates. A detached crack initiates and grows at the tip of an already existing crack. When the detached crack reaches the tip of the main crack, the process repeats as a new existing crack.

A relationship between crack growth rate, v, and stress intensity factor, K, is obtained as a function of b/a and a = b + d, where b is the distance from the tip of the main crack to the detached crack, and d is the ydrogen atom saturated domain.

The experimental data are in good agreement with the theoretical values in Region II when a = 0.02 mm, b/a = 0.8, c₁/c₀ = 2.8 for 200°C tempered specimens and a = 0.015 mm, b/a = 0.7, c₁/c₀ = 3.0, ρ_b = 0.055 mm for 400°C tempered specimens, where ρ_b is a fictitious notch radius. The plateau part in Region II for 400°C tempered specimens is also successfully explained by the present theory. For Region III, the value of b/a will be almost equal to 1 because v → ∞ for b/a → 1. On the other hand, for Region I, b/a will be zero, since the value of v becomes negligibly small and no crack growth is observable.     

A study of fatigue crack growth of 7075-T651 aluminum alloy

Both standard and non-standard compact specimens were employed to experimentally study the crack growth behavior of 7075-T651 aluminum alloy in ambient air. The effects of the stress ratio (R), overloading, underloading, and high–low sequence loading on fatigue crack growth rate were investigated. Significant R-ratio effect was identified. At the same R-ratio, the influence of specimen geometry on the relationship between crack growth rate and stress intensity factor range was insignificant. A single overload retarded the crack growth rate significantly. A slight acceleration of crack growth rate was identified after a single underload. The crack growth rate resumed after the crack propagated out of the influencing plastic zone created by the overload or underload. A parameter combining the stress intensity factor range and the maximum stress intensity factor can correlate the crack growth at different stress ratios well when the R-ratio ranged from −2 to 0.5. The parameter multiplied by a correction factor can be used to predict the crack growth with the influence of the R-ratio, overloading, underloading, and high–low sequence loading. Wheeler’s model cannot describe the variation of fatigue crack growth with the crack length being in the overload influencing zone. A modified Wheeler’s model based on the evolution of the remaining affected plastic zone was found to predict well the influence of the overload and sequence loading on the crack growth.     

Effect of frequency on ambient temperature fatigue crack growth in a silicon carbide reinforced silicon nitride composite

A detailed study on a silicon nitride reinforced with silicon carbide whiskers has been undertaken on room temperature fatigue during static and dynamic loading at constant ΔK. It is shown that sub-critical crack growth rates are lower when the material experiences sustained far field loading than during cyclic far field loading. The increased crack growth rate during cyclic loading is attributed to a wedging effect within the crack wake causing an increase in the tensile stress and resultant increased micro-cracking ahead of the crack tip. This additional micro-structural damage leads to enhanced sub-critical crack growth rates during cyclic loading. The asperities that are responsible for the wedging effect are attributed to the isolation of small portions of material due to branching of small cracks and by degradation of the bridging SiC whiskers and Si₃N₄ grains within the crack wake.     

Near-tip dynamic fields for a crack advancing in a power-law elastic-plastic material: Modes I, II and III

Near-tip dynamic asymptotic stress fields of a crack advancing in an incompressible power-law elastic-plastic material are presented. It is shown that the stress- and strain-singularity are, respectively, of the order (In(R₀/r))^1/(n−1) and (In(R₀/r))^n/(n−1), where R₀ is a length parameter, r measures distance from the crack tip, and n is the power-law exponent. The angular variations of these fields are identical with those corresponding to dynamic crack growth in an elastic-perfectly-plastic material (Gao and Nemat-Nasser, 1983a,b).