Contact of crack surfaces during fatigue: Part 2. Simulations

A detailed model of the role of asperities in crack closure has been initiated in Part 1 of this article. Crack opening stress is defined as the far-field stress required to overcome the asperity-induced contact stresses along the crack. In this Part 2, the magnitude of crack opening stress is established as a function of roughness (σ ₀); asperity density (N); maximum stress level (S _max/S _y ); shakedown pressure (p ^s ₀/k), which reflects the effect of tangential tractions or friction; R ratio; and crack length. Normalizations permit application to a wide range of materials. The results, for selected levels of asperity density, are consolidated upon comparing the crack opening displacement (COD) with the roughness (σ ₀) over four orders of magnitude. Specifically, a nonlinear relationship between COD/σ ₀ and crack opening stress was established that can be readily used to determine crack opening stress over a broad range of conditions. The model has been utilized to predict crack opening stress levels for several materials, including 0.8 pct C steels, 9Cr-1Mo steels, Ti-4Al, Ti-46Al (γ-aluminide), and Al 2124 alloys. Experimental measurements of crack roughness and asperity density were conducted on titanium aluminide specimens using confocal microscopy, and crack closure predictions were made with the model. The predictions demonstrated very good agreement with the experimentally measured closure levels.     

Fatigue crack growth in a particulate TiB<Subscript>2</Subscript>-reinforced powder metallurgy iron-based composite

Fatigue crack growth behavior has been examined in a particulate titanium diboride (TiB₂)-reinforced iron-based composite that had been produced via a mechanical alloying process. Comparison with equivalent unreinforced material indicated that fatigue crack growth resistance in the composite was superior to monolithic matrix material in the near-threshold regime. The composite exhibited relatively low crack closure levels at threshold, indicative of a high intrinsic (effective) threshold growth resistance compared to the unreinforced iron. The lower closure levels of the composite were consistent with reduced fracture surface asperity sizes, attributable to the reinforcement particles limiting the effective slip distance for stage I-type facet formation. The observed shielding behavior was rationalized in terms of recent finite-element analysis of crack closure in relation to the size of crack wake asperities and the crack-tip plastic zone. The different intrinsic fatigue thresholds of the composite and unreinforced iron were closely consistent with the influences of stiffness and yield strength on cyclic crack-tip opening displacements. Cracks in the composite were generally seen to avoid direct crack-tip-particle interaction.     

Mode I stress intensity factors induced by fracture surface roughness under pure mode III loading: Application to the effect of loading modes on stress corrosion crack growth

A model to estimate the reduction of effective crack tip Mode III stress intensity factors by frictional and asperity interaction of an idealized fracture surface is described. An extension of the model is used to calculate the Mode I stress intensity factors due to the crack tip opening displacement induced by the mismatch of the fracture surface asperities. The results of calculations based on a “reasonable” fracture surface profile are used to analyze experimental studies designed to determine the relative significance of hydrogen embrittlement and crack tip dissolution in stress corrosion crack growth in Al alloys by comparison of Mode I and Mode III stress corrosion cracking (SCC) resistance. It is concluded that a pure Mode III stress state is not possible for cracks with microscopically rough surfaces and that the magnitude of the induced Mode I stress intensity factor is sufficient to cause stress corrosion crack growth.     

Fracture surface interference in shear—I. A model based on experimental surface characterizations

A closed form model for estimating the reduction in Mode II stress intensity factor (SIF) and the induced Mode I SIF resulting from the mismatch of fracture surface asperities during shearing of the fracture surfaces is presented. At a given effective Mode II SIF, discretizations of actual Mode I fracture surfaces are displaced in shear according to the classical √r shear displacement law including crack tip plasticity. The crack faces are then “opened” enough to prevent interpenetration of the shifted surfaces resulting in a single point contact. The induced Mode I SIF is then calculated from the solution for a flat crack, opened by a concentrated normal force assuming a classical √r opening displacement law. The resistance Mode II SIF is found from the corresponding problem with a concentrated tangential force which is proportional to the normal force, and is positive or negative, depending on whether the sliding is uphill or downhill, respectively. The proportionality factor is determined through Coulomb's law of sliding friction applied to the inclined asperity surface at the contact point. The applied Mode II SIF is simply the sum of the effective and the resistance Mode II SIF's. The model predicts large initial resistance to the applied Mode II SIF and an induced Mode I SIF of the same order as the effective Mode II SIF. The secondary structure of the K_IIeff vs K_IIapp curves is directly related to the periodicity of the fracture surface profile. It is suggested that the model should be modified to account for asperity wear and subsequent modification of the fracture surface profile.     

Fatigue crack growth in MAR-M200 single crystals

The effects of crystallographic orientation on the fatigue crack growth behavior of MAR-M200* single crystals were examined. Using compact-tension specimens tested at 20 Hz, fatigue crack growth rates were determined at ambient temperature at minimum stress to maximum stress ratios,R, of 0.1 and 0.5. In most cases, subcritical crack growth occurred either along a single {111} slip plane or a combination of {111} planes. The mode of cracking was generally mixed and contained mode I, II, and III components. Considerable crack deflection and branching were also observed. Some fracture surfaces were found to contain a significant amount of asperities and, in some specimens, black debris. Based on Auger spectroscopic analyses and the fracture surface appearance, it appears that the black debris represented oxides formed due to rubbing of the fracture surfaces. Using stress intensity solutions obtained based on the Boundary-Integral-Equation technique, an effective ΔK was successfully used for correlating the crack growth rate data. The results indicate that the effect of crystallographic orientation on crack growth rate can be explained on the basis of crack deflection, branching, and roughness-induced crack closure. Formerly with Southwest Research Institute     

Effect of crack surface geometry on fatigue crack closure

The geometry of crack faces often plays a critical role in reducing crack extension forces when crack closure occurs during fatigue crack growth. Most previous studies of fatigue crack closure are concerned with mechanical measures of closure as related to the crack growth rate; very little attention has been given to the geometry of the crack surfaces. Our objective is to identify those aspects of crack surface geometry that are important in the closure process, to develop quantitative fractographic techniques to estimate such attributes in a statistically significant and robust manner, and to correlate them to the physical process of crack closure. For this purpose, fatigue crack propagation experiments were performed on a Ni-base superalloy and crack growth rates and crack closure loads were measured. Digital image profilometry and software-based analysis techniques were used for statistically reliable and detailed quantitative characterization of fatigue crack profiles. It is shown that the dimensionless, scale-independent attributes, such as height-to-width ratio of asperities, fractal dimensions, dimensionless roughness parameters,etc., do not represent the aspects of crack geometry that are of primary importance in the crack closure phenomena. Furthermore, it is shown that the scaledependent characteristics, such as average asperity height, do represent the aspects of crack geometry that play an interactive role in the closure process. These observations have implications concerning the validity of geometry-dependent, closure-based models for fatigue crack growth.     

Fatigue crack propagation in aluminum- lithium alloy 2090: Part I. long crack behavior

A study has been made of the mechanics and mechanisms of fatigue crack propagation in a commercial plate of aluminum-lithium alloy 2090-T8E41. In Part I, the crack growth and crack shielding behavior of long (≳5 mm) through-thickness cracks is examined as a function of plate orientation and load ratio, and results compared to traditional high strength aluminum alloys. It is shown that rates of fatigue crack extension in 2090 are, in general, significantly slower (at a given stress intensity range) than in traditional alloys, although behavior is strongly anisotropic. Differences in growth rates of up to 4 orders of magnitude are observed between the L-T, T-L, and T-S orientations, which show the best crack growth resistance, and the S-L, S-T, and L + 45, which show the worst. Such behavior is attributed to the development of significant crack tip shielding (i.e., a reduction in local crack driving force), primarily resulting from the role of the crack path morphology in inducing crack deflection and crack closure from the consequent asperity wedging. Whereas crack advance perpendicular to the rolling plane (e.g., L-T,etc.) involves marked crack path deflection and branching, thereby promoting very high levels of shielding to cause the slowest growth rates, fatigue fractures parallel to the rolling plane (e.g., S-L,etc.) occur by an intergranular, delamination-type separation, with much lower shielding levels to give the fastest growth rates. The implications of such “extrinsic toughening” effects on the fracture and fatigue properties of aluminum-lithium alloys are discussed in detail. R. O. RITCHIE, Professor and Director, Center for Advanced Materials, Lawrence Berkeley Laboratory     

Contacting surfaces: A problem in fatigue and diffusion bonding

Contact between surfaces usually occurs at asperities under compression or at connecting ligaments, depending on how the interface is formed. This paper deals with the nondestructive evaluation of the topology of contact and with the use of this information to predict the effects that loads borne by these contacts have on mechanical properties. Two specific examples are discussed: a fatigue crack and a diffusion bond. Asperity contact along the fracture surface of a fatigue crack partially shields the crack tip from the externally applied driving force. Using information from acoustic experiments, the geometry of the asperities, the contacting stress, and the shielding stress intensity factor have been estimated. Acoustically, a diffusion bonded interface looks very similar to that joining the two sides of a partially closed crack. In this particular case, the acoustically determined geometry of well-bonded ligaments can be verified by fractography of destructively tested samples whose bond strength has also been determined. Models to determine the bond strength from the ligament geometry are being suggested.     

The micromechanics of fatigue crack growth at 25 °C in Ti-6Al-4V reinforced with SCS-6 fibers

Micromechanics parameters for fatigue cracks growing perpendicular to fibers were measured for the center-notched specimen geometry. Fiber displacements, measured through small port holes in the matrix made by electropolishing, were used to determine fiber stresses, which ranged from 1.1 to 4 GPa. Crack opening displacements at maximum load and residual crack opening displacements at minimum load were measured. Matrix was removed along the crack flanks after completion of the tests to reveal the extent and nature of the fiber damage. Analyses were made of these parameters, and it was found possible to link the extent of fiber debonding to residual COD and the shear stress for fiber sliding to COD. Measured experimental parameters were used to compute crack growth rates using a well-known fracture mechanics model for fiber bridging tailored to these experiments.     

钢轨表面疲劳裂纹扩展机制

 针对轮轨接触疲劳问题,基于Hertz接触理论与库伦摩擦定律,建立含表面裂纹的轮轨接触疲劳计算模型,并对加载位置、轴重、摩擦因数等因素对裂纹扩展速率的影响进行研究。结果表明,轮轨滚动接触的表面裂纹为I-II型裂纹,且以II型扩展为主,其最容易发生断裂的位置在接触斑边缘。轴重和摩擦力是影响轮轨接触疲劳的两个重要因素;随着轴重的增加,应力强度因子[KI、][KII]均呈增加趋势,20 t相对于10 t分别增加359%和185%;随着摩擦因数的增加,应力强度因子[KI、][KII]均呈增加趋势,0.3的摩擦因数相对于无摩擦分别增加了108.7%和119.3%,表明摩擦力的存在明显加剧了裂纹扩展速率。在钢轨涂油养护时,应优先选用固体润滑剂。     

The effect of residual stress on the fatigue crack growth behavior of Al-Si-Mg cast alloys—Mechanisms and corrective mathematical models

The fatigue crack growth (FCG) behavior of various types of alloys is significantly affected by the presence of residual stress induced by manufacturing and post-manufacturing processes. There is a qualitative understanding of the effects of residual stress on fatigue behavior, but the effects are not comprehensively quantified or accounted for. The difficulty in quantifying these effects is largely due to the complexity of residual-stress measurements (especially considering that parts produced in similar conditions can have different residual-stress levels) and the lack of mathematical models able to convert experimental data with residual stress into residual-stress-free data. This article provides experimental, testing, and mathematical techniques to account for residual-stress effects on crack growth rate data, together with two methods for eliminating residual stresses in crack growth test specimens. Fracture-mechanics concepts are used to calculate, in simple and convenient ways, stress-intensity factors caused by residual stresses. The method is advantageous, considering that stress-intensity factors are determined before the actual test is conducted. Further on, residual-stress-intensity factors are used to predict the residual-stress distribution in compact tension (CT) specimens prior to testing. Five cast Al-Si-Mg alloys with three Si levels (in unmodified (UM) as well as Sr-modified (M) conditions) were analyzed both with and without residual stress. Fatigue cracks are grown under both constant stress ratio, R=0.1, and constant maximum stress-intensity factor, K _max = const., conditions. The mechanisms involved in crack growth through residual-stress fields are presented.     

Effects of Processing Residual Stresses on Fatigue Crack Growth Behavior of Structural Materials: Experimental Approaches and Microstructural Mechanisms

Fatigue crack growth mechanisms of long cracks through fields with low and high residual stresses were investigated for a common structural aluminum alloy, 6061-T61. Bulk processing residual stresses were introduced in the material by quenching during heat treatment. Compact tension (CT) specimens were fatigue crack growth (FCG) tested at varying stress ratios to capture the closure and K _max effects. The changes in fatigue crack growth mechanisms at the microstructural scale are correlated to closure, stress ratio, and plasticity, which are all dependent on residual stress. A dual-parameter ΔK–K _max approach, which includes corrections for crack closure and residual stresses, is used uniquely to connect fatigue crack growth mechanisms at the microstructural scale with changes in crack growth rates at various stress ratios for low- and high-residual-stress conditions. The methods and tools proposed in this study can be used to optimize existing materials and processes as well as to develop new materials and processes for FCG limited structural applications.     

The Small Fatigue Crack Growth Behavior of an AM60 Magnesium Alloy

The effects of thermomechanical processing and subsequent heat treatment on the small fatigue crack growth (FCG) behavior of an AM60 (Mg-6.29Al-0.28Mn wt pct) alloy were evaluated. The effects of mechanical loading parameters, such as maximum stress and load-ratio, on the small FCG behavior were also determined. Maximum stress did not appear to affect the crack propagation rate of small cracks in the stress and crack size ranges considered. Materials with different microstructures and yield stresses, introduced by different processing conditions, showed similar crack growth rates at equivalent stress intensity factor ranges. The effect of load ratio on small crack growth rates was recorded. Fracture surface characterization suggested that the fatigue crack propagation mechanism was a mixture of transgranular and intergranular cracking. Porosity and other material defects played respective important roles in determining the fatigue crack initiation and propagation behavior.     

Growth of small fatigue cracks in PH 13-8 Mo stainless steel

The growth of small fatigue cracks in PH 13-8 Mo (H1050) stainless steel under constant amplitude loading at different mean stresses (R=0.1 and −1) under generally high cycle fatigue conditions was investigated. Small cracks were allowed to initiate naturally at the root of a single edge notch specimen and were monitored using a surface replicating technique. It was found that the initiation and growth of surface cracks up to 100 μm encompassed 70 to 90 pct of the total fatigue life at stress amplitudes just above the fatigue limit. Cracks of length less than 100 μm were subject to strong influences of the microstructure and exhibited stage I (shear-dominated) growth, which was manifested in oscillatory crack growth rates. The oscillations diminished as the crack transitioned to stage II growth. The higher stress ratio (R=0.1) resulted in a more rapid transition from stage I to stage II growth in comparison to R=−1. After transitioning to stage II, the crack growth could be well characterized by conventional long crack tools even when the crack was still physically small. The small crack growth behavior is shown to be similar to that of a quenched and tempered AISI 4340 steel having a comparable strength.     

Effect of oxidation kinetics on the near threshold fatigue crack growth behavior of a nickel base superalloy

The influence of oxidation kinetics on the near threshold fatigue crack growth behavior of a nickel base precipitation hardened superalloy was studied in air from 427° to 649 °C. The tests were conducted at 100 Hz and at load ratios of 0.1 and 0.5. The threshold ΔK values were found to increase with temperature. This behavior is attributed to oxide deposits that form on the freshly created fracture surfaces which enhance crack closure. As determined from secondary ion mass spectrometry, the oxide thickness was uniform over the crack length and was of the order of the maximum crack tip opening displacement at threshold. Oxidation kinetics were important in thickening the oxide on the fracture surfaces at elevated temperatures, whereas at room temperature, the oxide deposits at near threshold fatigue crack growth rates and at low load ratios were thickened by an oxide fretting mechanism. The effect of fracture surface roughness-induced crack closure on the near threshold fatigue crack growth behavior is also discussed. Formerly with General Electric Company, Advanced Nuclear Technology Operation, Sunnyvale, CA 94086.     

Failure Diagram and Chemical Driving Forces for Subcritical Crack Growth

Kitagawa-Takahashi diagram that is modified for fatigue is now extended to the subcritical crack growth behavior under stress-corrosion crack growth. The analogy with the fatigue helps us to identify several regimes of interest from both the point of understanding of the material behavior as well as quantification of the failure process for structural design of components that are subjected to stress-corrosion and corrosion fatigue crack growths and failure. In particular, the diagram provides a means of defining the mechanical equivalent of chemical stress concentration factor and the chemical crack-tip driving forces to crack growth or its arrest. In addition, threshold stresses, crack arrest, and nonpropagating crack growth conditions can be defined, which help in developing sound design methodology against stress corrosion and corrosion fatigue. Chemical crack driving forces under corrosion fatigue can be similarly defined using the inert behavior as a reference.     

The effects of residual macrostresses and microstresses on fatigue crack propagation

The effects of residual microstresses and tensile residual macrostresses on fatigue crack propagation (FCP) are examined in a high-carbon steel. Phase-specific diffraction measurements show that uniaxial deformation and radial cold expansion produce predominantly microstress and tensile macrostress fields, respectively. Microstresses are found to have little effect on FCP rates, while tensile macrostresses increase crack growth rates in a manner that depends systematically on ΔK. The increases are partly attributed to crack closure, which was found to be appreciable near the surface of control samples but absent in the presence of tensile residual stresses. Both the ΔK dependence and absence of microstress effects were explored by X-ray microbeam measurements around propagating fatigue cracks and found to stem from fading and/or redistribution of residual macrostresses and microstresses during fatigue crack growth.     

Three-Orthogonal-Direction Stress Mapping around a Fatigue-Crack Tip Using Neutron Diffraction

Quantitative determination of the stress fields around the crack tip is a challenging and important subject to understand the fatigue crack-growth mechanism. In the current study, we measured the distribution of residual stresses and the evolution of the stress fields around a fatigue crack tip subjected to the constant-amplitude cyclic loading in a 304L stainless steel compact-tension (CT) specimen. The three orthogonal stress components (i.e., crack growth, crack opening, and through thickness) of the CT specimen were determined as a function of distance from the crack tip with 1-mm spatial resolution along the crack-propagation direction. In-situ neutron-diffraction results show that the enlarged tensile stresses were developed during loading along the through-thickness direction at a localized volume close to the crack tip, resulting in the lattice expansion in all three orthogonal directions during P _max. The current study suggests that the atypical plane strainlike behavior observed at the midthickness position might be the reason for the mechanism of the faster crack-growth rate inside the interior than that near the surface.     

Failure Diagram for Chemically Assisted Crack Growth

A failure diagram that combines the thresholds for failure of a smooth specimen to that of a fracture mechanics specimen, similar to the modified Kitagawa diagram in fatigue, is presented. For a given material/environment system, the diagram defines conditions under which a crack initiated at the threshold stress in a smooth specimen becomes a propagating crack, by satisfying the threshold stress intensity of a long crack. In analogy with fatigue, it is shown that internal stresses or local stress concentrations are required to provide the necessary mechanical crack tip driving forces, on one hand, and reaction/transportation kinetics to provide the chemical potential gradients, on the other. Together, they help in the initiation and propagation of the cracks. The chemical driving forces can be expressed as equivalent mechanical stresses using the failure diagram. Both internal stresses and their gradients, in conjunction with the chemical driving forces, have to meet the minimum magnitude and the minimum gradients to sustain the growth of a microcrack formed. Otherwise, nonpropagating conditions will prevail or a crack formed will remain dormant. It is shown that the processes underlying the crack nucleation in a smooth specimen and the crack growth of a fracture mechanics specimen are essentially the same. Both require building up of internal stresses by local plasticity. The process involves intermittent crack tip blunting and microcrack nucleation until the crack becomes unstable under the applied stress.