Significance of the small crack growth law and its practical application

The effects of microstructure and specimen size on the fatigue crack growth rate of an annealed 0.42 C steel were investigated under uniaxial fatigue loading in air. Although a dramatic fluctuation of crack growth rate was found in the propagation process of microstructurally small cracks, the mean value of crack growth rate can be evaluated by a simple mechanical parameter, σ _a ⁿ l (l, crack length; n, constant), under high stress levels where small-scale yielding conditions are exceeded. This parameter is also effective for cracks larger than 1 to 2 mm under high stress levels, as long as the finite boundary effect of a specimen on the driving force of crack propagation is considered. The crack growth rate of the alloy was described as a function of stress amplitude and crack length in terms of two mechanical parameters, σ _a ⁿ l and ΔK. The applicable conditions of the two parameters were discussed and manifested.     

An analysis of non-propagating fatigue cracks

An analysis for the formation of nonpropagating fatigue cracks at (the base of V-shaped) notch roots, based on the considerations of the extent of the critically stressed region ahead of a notch or a crack tip, and the resulting volumetric strength effect, is developed. Assuming that the minimum local cyclic stress required for crack initiation from a notch root is equal to the unnotched fatigue limit, σ_e, and that the minimum local cyclic stress required for the propagation of the crack is equal to the theoretical strength of the material, σ_e, a model of notch fatigue limit is proposed that shows that nonpropagating cracks should form at the notch base if ρ≤ ρ⁰, a critical root radius, provided the notch is sufficiently deep,i.e. d ≥ ρ₀. The radius ρ₀ is a material constant and can be estimated from known material properties. The estimated values of ρ₀ are in fairly good agreement with available experimental values for steels and pure copper. For stresses near the notch fatigue limit it is suggested that p₀ be regarded as a radius above which notch fatigue limit is essentially initiation controlled and below which essentially propagation controlled. The notch fatigue limit based on complete fracture can then be estimated more accurately with mild as well as sharp notches. D. N. LAL, formerly a Graduate Assistant in Materials Science, Syracuse University     

Study of mechanism of cleavage fracture at low temperature

In this investigation, a series of crack opening displacement (COD) tests were carried out at several low temperatures for C-Mn weld steel. Some of the specimens were loaded until fracture, and the mechanical properties and microscopic parameters on fracture surfaces were measured. Other specimens were unloaded before fracture at different applied loads. The distributions of the elongated cavities and the cleavage microcracks ahead of fatigue crack tips were observed in detail. Based on the experimental results, the combined criterion of a critical strainε _p ≥ ε_c) for initiating a crack nucleus, a critical stress triaxiality(σ _m/σ ≥ t_c) for preventing it from blunting, and a critical normal stress(σ _yy/σ_f) for the cleavage extension was proposed again, and the critical values of ε_p and σ_m/−σ for the C-Mn weld steel were measured. The reason why the minimum COD value could not be zero is explained. The mechanism of generation of the lower limit COD value on the lower shelf of the toughness transition curve is proposed.     

Further study on the mechanism of the ductile-to-brittle fracture transition in C-Mn base and weld steel

In the present study, the crack opening displacement (COD) tests of specimens of C-Mn base and weld steel were carried out in the ductile-brittle transition temperature region. The majority of the specimens were fractured and others were unloaded prior to fracture after ductile fracture initiated and extended. The cavities and cleavage microcracks located in the vicinities of tips of fibrous cracks of the unloaded specimens were observed in detail. The finite element method (FEM) calculations of the stress and strain distribution ahead of the tip of an extending fibrous crack were completed. The mechanism of the ductile-to-brittle fracture transition was further investigated. It was revealed that in the ductile-brittle transition temperature region, the ductile fracture process was independent of temperature. The ductile-to-brittle fracture transition was triggered by initiating a catastrophic extension of a cleavage crack ahead of the fibrous crack tip, which occurred in a condition satisfying a combined criterion composed of three items, i.e., ε _p ≥ ε _pc for initiating a crack nucleus; σ _m √σ ≥ T _c for preventing the crack nucleus from blunting; and σ _yy ≥ σ _f for propagating the crack nucleus. For a specimen in which a fibrous crack occurred and propagated, the critical event for initiating a brittle cleavage fracture was the propagation of a ferrite grain-sized crack into neighboring grains. With extension of a fibrous crack, the behavior of the ductile-to-brittle fracture transition could be analyzed by the effect of the size of an “active zone” on the initiation of the brittle cleavage fracture.     

Fracture behavior of C-Mn steel and weld metal in notched and precracked specimens: Part II. micromechanism of fracture

The microscopic fracture behaviors of a C-Mn steel plate and of two types of weld metal in Charpy V, crack tip opening displacement (COD), and precracked impact specimens have been studied by observations of the size distribution of the cleavage-initiating particles, the morphology of the fibrous crack zones, the microstructure in the region initiating the cleavage crack, and the size distribution of microcracks remaining in the specimens. It has been found that the different values of the microscopic cleavage fracture stress, σ_f, measured in notched and precracked specimens of the same metal result from the change in the critical event (critical length) in the fracture processes. The critical event in the Charpy V-notched specimens at —45 °C to —65 °C is the propagation of a ferrite grain-sized microcrack into the ferrite matrix; however, in the precracked COD specimens at —110 °C, it is the propagation of a second-phase particle-sized microcrack into the neighboring ferrite grain. The change of the critical event is considered to be related to the difference of effective shear stress ahead of a notch root or a crack tip. The different sensitivities to the notch acuity of the base and weld metal result from their micro-structures. Finally, the prerequisite for establishing a correlation between Charpy V and COD tests is analyzed.     

Critical assessment of the local cleavage stress σ ƒ * in notch specimens of C-Mn steel

An elastic-plastic finite element method (FEM) was used to calculate the stress and strain distributions ahead of notches with various root radii in a bending specimen of C-Mn steel with grain sizes of 10 and 30 μm. By accurately measuring the distance of the cleavage initiation site from the root of the notch, the local cleavage stress σ _ƒ ^* was measured. When the notch radius increased from 0.25 to 1.0 mm, the distribution of high stress had a definite variation but the σ _ƒ ^* remained relatively constant. In notch specimens with different root radii, the critical fracture event is identical,i.e., propagation of a ferrite grain-sized crack into the neighboring matrix. Therefore, the σ _ƒ ^* is mainly determined by the length of the critical microcrack, here, the size of ferrite grain instead of the high stress volume for finding an eligible brittle particle. The critical strain for initiating a crack was about 1 pct. The cleavage site ahead of a notch was related to the relative distributions of stress and strain and the random distribution of the weakest grains. The higher fracture load of the fine-grain material can be attributed to its higher value of σ _ƒ ^* /σ_o as compared with the coarse-grain. The σ _ƒ ^* /σ_o is a potential engineering parameter for toughness assessment in notch specimens.     

Effects of loading rate on fracture behavior of low-alloy steel with different grain sizes

Four-point bend (4PB) tests of notched specimens loaded at various loading rates, for low alloy steel with different grain sizes, were done, and the microscopic observation and finite-element method (FEM) calculations were carried out. It was found that for the coarse-grained (CG) microstructure, an appreciable drop in notch toughness with a loading rate of around 60 mm/min appeared, and further increasing the loading rate leads to a slight additional decrease in notch toughness. For the fine-grained (FG) microstructure, the effect of loading rate was not apparent. The change in toughness resulted from a change of the critical event controlling the cleavage fracture with increasing loading rate. For the CG microstructure with a lower cleavage-fracture stress (σ _f ), with an increasing loading rate, the critical event of cleavage fracture can be changed from the propagation of a pearlite colony-sized crack or a ferrite grain-sized crack, through the mixed critical events of crack propagation and crack nucleation, then to crack nucleation. This change deteriorates the toughness. For the FG microstructure with a higher cleavage-fracture stress, the critical event of cleavage fracture is the crack propagation and does not change in the loading-rate range from 120 to 500 mm/min. The measured σ _f values do not change with loading rate, as long as the critical event of cleavage fracture does not change. The higher notch toughness of the FG microstructure arises from its higher σ _f and the critical plastic strain (ε _pc ) for initiating a crack nucleus, and the fracture behavior of this FG steel is not sensitive to loading rate in the range of this work.     

Further study on the scattering of the local fracture stress and allied toughness value

In this investigation, the values and their scatters of the local fracture stressof and the fracture load P_f and allied toughness values of base and weld metals were measured, and the main reasons for scattering were analyzed. The results showed that the scatters in σ _f ^* , in general, were the smallest. Measuring the fracture initiation sites with a scanning electron microscope and calculating the location of maximum stress and the range covered by the 95 pct maximum stress did not reveal a “characteristic distance” with a statistical feature, over which the local fracture stress must be exceeded by normal stress. Instead, a combined criterion of a critical strain for initiating a crack nucleus and a critical value and triaxiality of stress for its propagation must be satisfied. The present study discovered the phenomenon that the fracture initiation site could locate at the left side (shorter distance side) of the location of the maximum stress. The reasons for this phenomenon and for the minimum crack opening displacement (COD) value not being zero even though a characteristic distance did not exist were proposed.     

Fatigue crack propagation in carburized X-2M steel

The growth rates of fatigue cracks propagating through the case and into the core have been studied for carburized X-2M steel (0.14 C, 4.91 Cr, 1.31 Mo, 1.34 W, 0.42 V). Fatigue cracks were propagated at constant stress intensities, ΔK, and also at a constant cyclic peak load, and the crack growth rates were observed to pass through a minimum value as the crack traversed the carburized case. The reduction in the crack propagation rates is ascribed to the compressive stresses which were developed in the case, and a pinched clothespin model is used to make an approximate calculation of the effects of internal stress on the crack propagation rates. We define an effective stress intensity, K_e = K_a + K_i, where K_a is the applied stress intensity, K_i = σ_id _i ^1/2 , σ_i is the internal stress, and d_i is a characteristic distance associated with the depth of the internal stress field. In our work, a value of d_i = 11 mm (0.43 inch) fits the data quite well. A good combination of resistance to fatigue crack propagation in the case and fracture toughness in the core can be achieved in carburized X-2M steel, suggesting that this material will be useful in heavy duty gears and in aircraft gas turbine mainshaft bearings operating under high hoop stresses.     

A notch analysis of fracture approach to fatigue crack propagation

A model of fatigue crack growth is proposed that utilizes the recent developments in notch analysis of fracture and a concept of size effect that results from the changes in the critically stressed volume ahead of a crack tip. Accordingly, the fatigue crack growth mechanism involves local stresses reaching the theoretical cohesive strength and causing brittle fracture of atomic bonds at nominal stresses near the threshold, whereas slip-plane decohesion and plastic blunting and resharpening of the crack tip process may occur at stresses above the threshold range. The model contains three material parameters σFF nF, and ρF, that conveniently extend continuum analysis to situations where inhomogeneity of the material structure can influence the behavior appreciably. The analytical expression from the model was found to correlate fatigue crack growth data reasonably well in the low and intermediate stress ranges in Al 2024-T3, Al 7075-T6 and 250 grade maraging steel. The fracture modes observed are in agreement with the predictions from the model. The same fatigue crack growth model can be extended to estimating the threshold stress intensity factor range, ΔK_o and fatigue notch sensitivity of different materials.     

Mechanism of detrimental effects of carbon content on cleavage fracture toughness of low-alloy steel

The variation in fracture toughness of low-alloy base steels and weld steels with carbon contents of 0.08 and 0.21 wt pct was investigated using notched and precracked specimens tested at low temperatures. The attention is focused on the mechanism associated with detrimental effects on cleavage fracture toughness resulting from increasing carbon content. Analyses reveal that, in the case of constant ferrite grain sizes with increasing carbon content, the yield stress σ _y increases and the local fracture stress σ _f remains constant for notched specimens. For precracked specimens, the σ _y increases, whereas the σ _f decreases. In both cases, the ratio σ _f /σ _y decreases; this ratio is one of the principal factors inducing the deterioration in the cleavage fracture toughness of the higher carbon steels. Analyses also reveal that the critical strain for initiating a crack nucleus, which decreases with increasing carbon content and impurity elements, appears to be another principal factor that has a negative effect on the fracture toughness in both notched and precracked specimens. The results of the fracture toughness measured for weld metal with various grain sizes further support the predominant effect of grain size on the toughness of notched specimens.     

The Effect of Grain Size on Fatigue Growth of Short Cracks

The influence of alloy grain size on growth rates of surface cracks 20 to 500 μm in length was studied in Al 7075-T6 specimens prepared in 12 and 130 μn grain sizes. Grain boundaries temporarily interrupt the propagation of cracks shorter than several grain diameters in length. Linear elastic fracture mechanics is inadequate to describe resulting average growth rates which must instead be characterized as a function of cyclic stress amplitude, σ_a, and alloy grain size as well as stress intensity range, σK. These observations are rationalized using two models, one that relates crack closure stress to alloy grain size, and a second that relates the development of microplasticity in a new grain in the crack path to grain size. In addition, growth rates were found to be faster in fully reversed loading than in tension-tension loading, especially in the large grained material. Evidence is presented to demonstrate that this is a consequence of the fatigue induced development of a compressive residual surface stress during tension-tension loading. These complex effects, and the role of grain size in determining short crack growth, are discussed.     

Fatigue crack propagation in carburized high alloy bearing steels

Fatigue cracks were propagated through carburized cases in M-50NiL (0.1 C,4 Mo, 4 Cr, 1.3 V, 3.5 Ni) and CBS-1000M (0.1 C, 4.5 Mo, 1 Cr, 0.5 V, 3 Ni) steels at constant stress intensity ranges, ΔK, and at a constant cyclic peak load. Residual compressive stresses of the order of 140 MPa (20 Ksi) were developed in the M-50NiL cases, and in tests carried out at constant ΔK values it was observed that the fatigue crack propagation rates,da/dN, slowed significantly. In some tests, at constant peak loads, cracks were stopped in regions with high compressive stresses. The residual stresses in the cases in CBS-1000M steel were predominantly tensile, probably because of the presence of high retained austenite contents, andda/dN was accelerated in these cases. The effects of residual stress on the fatigue crack propagation rates are interpreted in terms of a pinched clothespin model in which the residual stresses introduce an internal stress intensity, K_i where K_i, = σ_id _i ^1/2 (σ_i = internal stress, d_i = characteristic distance associated with the internal stress distribution). The effective stress intensity becomes K_e = K_a + K_i where K_a is the applied stress intensity. Values of K_i were calculated as a function of distance from the surface using experimental measurements of σ_i and a value of d_i = 11 mm (0.43 inch). The resultant values of K_e were taken to be equivalent to effective ΔK values, andda/dN was determined at each point from experimental measurements of fatigue crack propagation obtained separately for the case and core materials. A reasonably good fit was obtained with data for crack growth at a constant ΔK and at a constant cyclic peak load. The carburized case depths were approximately 4 mm, and the possible effects associated with the propagation of short cracks were considered. The major effects were observed at crack lengths of about 2 mm, but the contributions of short crack phenomena were considered to be small in these experiments, since the two steels were at high strength levels, and short cracks would be expected to be of the order of 10 μm. Also, the two other steels behaved differently and in a way which followed the residual stress patterns. Both M-50NiL and CBS-1000M have a high fracture toughness, with K_lc = 50 MPa · m^1/2 (45 Ksi · in^1/2), and the carburized cases exhibit excellent resistance to rolling contact fatigue. Thus, M-50NiL, carburized, may be useful for bearings where high tensile hoop stresses are developed, since fatigue cracks are slowed in the case by the residual compressive stresses, and fracture is resisted by the relatively tough core.     

Microcrack initiation and acoustic emission during fracture toughness tests of A533B steel

The initiation of microcracks at MnS inclusions during fracture toughness tests of ASTM A533B steel compact tension specimen was detected by an 8-channel acoustic emission recording system. The microcracks were located as far as 7 mm ahead of the precrack front with a large spread of 5 mm above and below the plane of the main crack. Most of the microcracks were found to form before they were engulfed by the plastic zone which was determined by a finite element analysis. Assuming that the material is homogeneous and elastic outside the plastic zone, we estimated that microcracks were formed when the normal tensile stress σ_z at each inclusion is in the range of 400 to 800 MPa. The estimated stress value exceeds the uniaxial yield strength, σ_ys = 477 MPa of the material because σ_z near the crack tip could be as large as3σ _ys due to the stress triaxiality under plane strain conditions. Formerly Visiting Scientist in the Department of Theoretical and Applied Mechanics, Cornell University (on leave from Institute of Industrial Science, University of Tokyo, Tokyo, Japan).     

The role of metal plasticity and interfacial strength in the cracking of metal/ceramic laminates

Two models based on elastic-plastic fracture mechanics and fiber bridging are developed to study the role of plastic yielding in metals and the interfacial strength of metal/ceramic laminates. There are two types of damage observed in metal/ceramic laminates: multiple cracking and macroscopic crack propagation. The former occurs around the macroscopic crack tip and thus distributes the damage and enhances the composite's toughness. The present models establish that there exists a critical metal/ceramic layer thickness ratio above which multiple cracking dominates and that this ratio decreases (hence increasing the possibility of multiple cracking) as the ratios of metal yield stress over ceramic strength, metal modulus over ceramic modulus, and metal/ceramic interfacial strength over ceramic strength increase. Good agreement between the present models and experimental results is observed for both damage modes, i.e. multiple cracking vs macroscopic crack propagation, and for critical stress intensity factors. The elastic-plastic fracture mechanics and fiber-bridging models predict that multiple cracking is ensured if the metal layer thickness is 2.5 times larger than the ceramic layer thickness, regardless of the metal/ceramic properties.     

The influence of SiC particulates on fatigue crack propagation in a rapidly solidified Al-Fe-V-Si alloy

The fatigue crack propagation properties of a rapidly solidified aluminum alloy are compared with those of a metal matrix composite (MMC) made of the same base alloy with the addition of 11.5 vol pct SiC particulate. The high-temperature base material, alloy 8009 produced by Allied-Signal, Inc. (Morristown, NJ), is solidified and processed using powder metallurgy techniques; these techniques yield a fine-grained, nonequilibrium microstructure. A direct comparison between the fatigue crack propagation properties of the reinforced and unreinforced materials is possible, because alloy 8009 requires no postprocessing heat treatment. As a consequence, this comparison reflects the influence of the SiC particulate and not differences in microstructure that could arise during processing and aging. The experimental data demonstrate that the SiC-reinforced material exhibits modestly superior fatigue crack propagation properties: slower crack growth rates for a given ΔK, at near-threshold crack growth rates. Even when the data are corrected for crack closure using an effective stress intensity factor, ΔK_eff, the composite exhibits lower crack propagation rates than the unreinforced matrix alloy. Microscopic evidence shows a rougher fracture surface and a more tortuous crack path in the composite than in the base alloy. It is argued that the lower crack growth rates and higher intrinsic threshold stress intensity factor observed in the composite are associated with crack deflection around SiC particles. Formerly Graduate Research Assistant, University of California-Davis     

Near-threshold fatigue crack growth behavior in copper

Near-threshold fatigue crack growth rate data were developed in annealed, quarter-hard, and full-hard copper at various load ratios, (R = σ_min/σ_max). Increasing theR value decreases the resistance to threshold crack growth. At a fixed value ofR, annealed copper has the slowest near-threshold crack propagation rate while full-hard copper has the fastest crack growth rate. Waveform (sine and triangle) and specimen geometry (WOL, CT, and CCT) do not appear to affect the rates of near-threshold crack propagation. The influences of load ratio and material strength on threshold crack growth behavior can be rationalized by crack closure.     

Effect of grain size and texture on the mechanical properties of warm worked cadmium-1.5 Pct zinc alloy

The structural changes occurring during warm working of Cd-1.5 pct Zn alloy and their effect on the subsequent mechanical properties are studied. It is observed that changes in grain size and preferred orientation are important to a large extent in controlling the mechanical strength. The Hall-Petch slope,R decreases in the warm worked material while the friction stress, σ_o increases. The lowerR values are attributed to the development of a {10-1t} texture and the higher σ_o values are interpreted on the basis of changes in the basal texture.     

Effects of tensile prestrain on the notch toughness of low-alloy steel

Tensile prestrains of various levels were applied to blank steel specimens. Four-point bend tests of notched specimens at various temperatures revealed an appreciable drop in the notch toughness of the specimens, which experienced 3 pct tensile prestrain. Further prestrains of up to 20 pct had a negligible effect on the notch toughness despite additional increases in the yield strength. Microscopic analyses combined with finite element method (FEM) calculations revealed that the decrease in toughness resulted from a change of the critical event controlling the cleavage fracture. The increase in yield strength provided by prestraining allowed the normal tensile stress at the notch tip to exceed the local fracture stress σ _f for propagating a just-nucleated microcrack. As a result, for the coarsegrained steel with low σ _f tested presently, the critical event was changed from tensile stress-controlled propagation of a nucleated microcrack to plastic strain-controlled nucleation of the microcrack at the notch tip. A reduction of toughness was induced as a result of this. The increase in yield strength provided by decreasing the test temperature acted in the same way.     

Effect of alloying elements on the structure and properties of Al-Li-Cu cast alloys

The structure and mechanical and service properties of Al-Li-Cu alloys are determined, and the results obtained are used to find the effect of major and additional components on their properties and to design a high-strength heat-treatable cast alloy with a low density. After quenching and maximum-strength aging, this alloy has the following level of mechanical properties (casing in a metal mold): σ_u = 360–370 MPa and δ = 6.0–7.5%.