Crack closure load measurements for microcracks developed during the fatigue of Al 2219-T851

A compliance technique is utilized to determine the closure load for surface microcracks of one grain size and smaller produced by fully reversed loading fatigue of Al 2219-T851. Specimens are fatigued in flexure in air at 5, 18, and 45 pct relative humidities. Scanning electron microscopy is then utilized to measure crack compliance for selected microcracks and crack closure load is inferred from the break point in the linear relationship between crack opening and applied stress. For zero applied load the microcracks are found to be partially opened and a linear relationship is found between the closure load measured for the microcracks and the zero load crack opening normalized to crack length. This relationship holds regardless of the ambient humidity during fatigue, although there are significant changes in the zero load crack openings developed with humidity. An empirical relationship between the irregularity of the microcrack propagation path as affected by humidity and crack opening at zero load is also identified, which can be used to estimate crack closure load from crack dimensional parameters measured at the specimen surface.     

A comparison of microcrack closure load development for stage I and II cracking events for Al 7075-T651

Closure stress measurements for both Stage I and II surface microcracks of lengths comparable to grain size are made using a compliance technique for Al 7075-T651 specimens fatigued in air at 30 pct relative humidity. As previously reported for Stage II cracking in Al 2219-T851, residual crack openings are observed for zero load which can be empirically related to the crack closure stress. This functional dependence is subsequently used to calculate closure stress values for both Stage I and II events for microcracks in Al 7075-T651 on the basis of residual crack opening values. Stage I crack interaction with grain boundaries is found to induce closure stresses close to the maximum applied stress, explaining the effective crack retardation of Stage I cracks by grain boundaries observed for Al 7075. In these cases the closure load is found to slowly fall as cracking continues by a Stage II mode into a second grain. For Stage n cracking it is possible to estimate the closure load from the cracking path as observed from the surface.     

Crack closure load development for surface microcracks in Al 2219-T851

The development of crack closure load with increasing crack length for noncrystallographic transgranular surface microcracks produced by cyclic fatigue of Al 2219-T851 is studied for two environmental relative humidities (5 and 30 pct). Closure loads are found to be initially low for short cracks and increase with subsequent crack propagation. The increase in closure with crack length is faster if the humidity is low or if the initiation crack size is large, as determined by the size of the surface intermetallic particle initiation site. At 30 pct humidity it is possible to associate the closure load increase observed to a decreasing crack planarity with increasing crack length.     

Fatigue crack initiation and early propagation in Al 2219-T851

Fatigue crack initiation in Al 2219-T851 for fully reversed loading(R = σ/σ_max =?1) parallel to the material rolling direction is found to occur at intermetallic inclusions at the specimen surface. The inclusions are not involved in crack initiation for fatigue perpendicular to the rolling direction, and for this orientation crack initiation is at grain boundaries and specimens have an increased fatigue life. Except for fatigue at low peak stress, multiple numbers of microcracks are formed and for selected failed specimens the number of cracks has been determined as a function of crack length. Such crack length distribution measurements show that there is significant retardation of microcracks by interaction with grain boundaries. Furthermore it is found that the coalescence of microcracks provides a mechanism for cracking to “jump“ grain boundaries and reduce fatigue lifetime. The effect of relative humidity on this process is to increase the observed mean crack length, and decrease the number of crack initiations apparently due to weakening of the matrix-intermetallic interface at potential initiation sites. The overall result is that no significant dependence of fatigue life on relative humidity is found.     

Fatigue crack initiation and early propagation in Al 2219-T851

Fatigue crack initiation in Al 2219-T851 for fully reversed loading(R = σ/σ_max =−1) parallel to the material rolling direction is found to occur at intermetallic inclusions at the specimen surface. The inclusions are not involved in crack initiation for fatigue perpendicular to the rolling direction, and for this orientation crack initiation is at grain boundaries and specimens have an increased fatigue life. Except for fatigue at low peak stress, multiple numbers of microcracks are formed and for selected failed specimens the number of cracks has been determined as a function of crack length. Such crack length distribution measurements show that there is significant retardation of microcracks by interaction with grain boundaries. Furthermore it is found that the coalescence of microcracks provides a mechanism for cracking to “jump“ grain boundaries and reduce fatigue lifetime. The effect of relative humidity on this process is to increase the observed mean crack length, and decrease the number of crack initiations apparently due to weakening of the matrix-intermetallic interface at potential initiation sites. The overall result is that no significant dependence of fatigue life on relative humidity is found. Formerly with the Science Center, Rock-well International     

Analytical Method for Pullout of Anchor from Anchor–Mortar–Concrete Anchorage System due to Shear Failure of Mortar

Depending on the relevant material properties, failure of grouted anchors can take forms of pullout of concrete cones, debonding at either anchor–grout or grout–concrete interface, fracture of anchor and combination of some of these failure modes. Further, if the thickness of the grout layer is thin enough, the shear strength of the grout is relatively low or the anchor is in the form of a steel bar with ribs or spirals, the grout would be sheared off so that the anchor is pulled out. The present study presents an analytical method for the last scenario, i.e., anchor pullout from an anchor–mortar–concrete anchorage due to shear failure of mortar. Two different boundary conditions are considered: fixed bottom surface of concrete as Boundary 1, and top surface of concrete with uniform distributed force as Boundary 2. A shear-lag model was introduced to analyze the behaviors of the mortar and the interfacial properties of both the anchor–mortar and the mortar–concrete interfaces were also considered. Based on the deformation compatibilities of the interfaces and the mortar layer, the distributions of the tensile stresses in the anchor and shear stresses in the mortar along the embedment length were obtained analytically during different loading stages for both Boundaries 1 and 2. Moreover, the probabilities and sequences of shear cracks induced by the mortar failure were determined according to the boundary conditions and the comparison between the shear stresses at the loading and nonloading ends. Double shear crack propagation from both ends with different crack lengths was then investigated. Besides, the pullout load was expressed as a function of the shear crack lengths. Then the maximum load and the corresponding critical crack lengths were obtained by using the theories of extremum. Finally, a series of material, structural, and interfacial parameters were adopted to study their influences on the calculated results using the proposed method, including the critical crack lengths, initial cracking load and maximum pullout load. It was found that the initial cracking and maximum loads in Boundary 1 are larger than those in Boundary 2. However, as the longitudinal rigidity of the concrete increases, the values of the maximum pullout loads in both of the boundary conditions approach each other. It was also found that there exists an effective bonding length, beyond which the critical crack length and maximum pullout load are no longer increased.     

The noncontinuum crack tip deformation behavior of surface microcracks

The crack tip opening displacement (CTOD) of small surface fatigue cracks (lengths of the grain size) in Al 2219-T851 depends upon the location of a crack relative to the grain boundaries. Both CTOD and crack tip closure stress are greatest when the crack tip is a large distance from the next grain boundary in the direction of crack propagation. Contrary to behavioral trends predicted by continuum fracture mechanics, crack length has no detectable effect on the contribution of plastic deformation to CTOD. It is apparent from these observations that the region of significant plastic deformation is confined by the grain boundaries, resulting in a plastic zone size that is insensitive to crack length and to external load.     

The application of fractography to demonstrate the presence of crack tip residual stresses during programmed fatigue crack propagation in mild steel

Constant amplitude and programmed loading fatigue crack propagation tests were carried out on a low carbon steel in three point bending. The Palmgren-Miner summation(Σ _Nⁿ) was found to be consistent and always slightly greater than unity irrespective of the load program. It is suggested that this effect is caused by crack tip compressive stresses opposing propagation. Fracture surface observations using a scanning electron microscope showed changes in fracture mode immediately after a load drop from which it was possible to make estimates of the levels of residual stress present.     

The application of fractography to demonstrate the presence of crack tip residual stresses during programmed fatigue crack propagation in mild steel

Constant amplitude and programmed loading fatigue crack propagation tests were carried out on a low carbon steel in three point bending. The Palmgren-Miner summation(Σ _N ⁿ ) was found to be consistent and always slightly greater than unity irrespective of the load program. It is suggested that this effect is caused by crack tip compressive stresses opposing propagation. Fracture surface observations using a scanning electron microscope showed changes in fracture mode immediately after a load drop from which it was possible to make estimates of the levels of residual stress present.      

The plastic zone and residual stress near a notch and a fatigue crack in HSLA steel

The plastic zone and residual stress around a notch under load and with the load removed, and around a fatigue crack (at the same stress intensity factor as for the notch) have been examined, with automated X-ray techniques and a microbeam. There is good agreement between the measured plastic zone size and Hutchinson's theory for a work hardening material. Residual stresses exist well behind the tip, and vary with depth, so that measurements of crack closure on a surface may not be directly related to closure stress (which samples the bulk). Instabilities in the dislocation arrangement can be detected by comparing X-ray line broadening of bulk specimens under load, and with the load removed. formerly Research Assistant, Department of Materials Science and Engineering, The Technological Institute, Northwestern University, Evanston, IL     

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.     

The influence of crack tip plasticity in the growth of small fatigue cracks

In order to rationalize observed differences in the growth behavior of large and small cracks, local crack tip opening micromechanics have been characterized for both crack size regimes in a high strength aluminum alloy. It is found that crack tip opening displacement, crack tip opening load, and crack opening mode all differ widely for large and small cracks at equivalent cyclic stress intensities (ΔK). High crack tip opening displacements and relatively low, approximately constant, crack opening loads for microcracks account both for their rapid rate of growth relative to large cracks and the absence of a microcrack threshold stress intensity. Crack tip plastic zone sizes also were measured, and it was found that the ratio of plastic zone size to crack length for small cracks is ∼ 1.0, while for large cracks the same ratio is ≪ 1. Simple empirical corrections to ΔK are found inadequate to correlate the growth of large and small cracks. It is concluded that for small cracks, linear elastic fracture mechanics similitude does not apply, and that an alternative crack driving force must be formulated.     

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.     

Mechanisms of Slow Fatigue Crack Growth in High Strength Aluminum Alloys: Role of Microstructure and Environment

The role of microstructure and environment in influencing ultra-low fatigue crack propagation rates has been investigated in 7075 aluminum alloy heat-treated to underaged, peak-aged, and overaged conditions and tested over a range of load ratios. Threshold stress intensity range, ΔK₀, values were found to decrease monotonically with increasing load ratio for all three heat treatments fatigue tested in 95 pct relative humidity air, with ΔK ₀ decreasing at all load ratios with increased extent of aging. Comparison of the near-threshold fatigue behavior obtained in humid air with the data forvacuo, however, showed that the presence of moisture leads to a larger reduction in ΔK₀ for the underaged microstructure than the overaged condition, at all load ratios. An examination of the nature of crack morphology and scanning Auger/SIMS analyses of near-threshold fracture surfaces revealed that although the crack path in the underaged structure was highly serrated and nonlinear, crack face oxidation products were much thicker in the overaged condition. The apparent differences in slow fatigue crack growth resistance of the three aging conditions are ascribed to a complex interaction among three mechanisms: the embrittling effect of moisture resulting in conventional corrosion fatigue processes, the role of microstructure and slip mode in inducing crack deflection, and crack closure arising from a combination of environmental and microstructural contributions.     

Effects of crack aspect ratio on the behavior of small surface cracks in fatigue: Part I. Simulation

A simple simulation of alternate growth of a small surface crack in the surface and depth directions was performed to illustrate the changes in crack aspect ratio, induced by grain boundaries, as a function of crack size. It is shown that at small crack sizes, large variations in aspect ratio, a/c (a is the crack depth and c is the half-surface length), occur, due to local crack front perturbations induced by grains that are oriented for crack growth. At these crack sizes, the assumption of a semicircular crack shape (a/c=1.0) was found to cause errors in stress intensity range (ΔK) calculations. This, in turn, led to significant scatter or “anomaly” in small crack growth rates relative to large cracks. At large crack sizes, the effects of local crack front perturbations on crack aspect ratio and ΔK were found to be insignificant. As a result, the scatter in crack growth data was found to decrease to a negligible level at large crack sizes. It is suggested that the limiting crack size above which the small crack behaves as a large crack, l ₂=10d (d = grain size), proposed by Taylor and Knott, is related to the crack size above which the effects due to aspect ratio variations are small.     

Fatigue crack propagation under varied mean stress conditions

Measurements of fatigue crack growth rates in copper monocrystalline and polycrystalline sheet specimens have been made at 295 K and 77 K to determine mean stress effects on growth rates. When load conditions remained unchanged throughout the period of crack growth, the rate of fatigue crack growth is independent of the level of mean stress and depends only on the cyclic stress amplitude. When the mean stress is changed during the crack growth period, a reduction of mean stress under plane strain conditions causes complete cessation of growth. A similar effect was not observed in plane stress crack growth, presumably due to reduced elastic constraint in narrow specimens containing large cracks. No change in growth rates occurs if the mean load is increased. In the event of crack growth stoppage, either restoration of the full previous mean load or crack re-nucleation under continued cycling at the reduced load levels is sufficient to restore the prior growth rate. A simple model is adapted to explain these observations which emphasizes the interaction of the growth rate with compressive residual stresses generated at the tip of the propagating crack. R. A. Yeske, formerly Research Assistant at Materials Science Department, Northwestern University, Evanston, III. This paper is based on a portion of a thesis submitted by R. A. Yeske in partial fulfillment of the requirements of the degree of Doctor of Philosophy at Northwestern University.     

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.     

Crack Propagation in Flexural Fatigue of Concrete

In this paper the behavior of concrete subjected to flexural fatigue loading is studied. Notched concrete beams were tested in a three-point bending configuration. Specimens were subjected to quasi-static cyclic and constant amplitude fatigue loading. The cyclic tests were performed by unloading the specimen at different points in the postpeak part of the quasi-static loading response. Low cycle, high amplitude fatigue tests were performed to failure using four different load ranges. The crack mouth opening displacement was continuously monitored throughout the loading process. Crack propagation caused by quasi-static and fatigue loads is described in terms of fracture mechanics. It is shown that the crack propagation in the postpeak part of the quasi-static load response is predicted using the critical value of the mode I stress intensity factor (KIC). The ultimate deformation of the specimen during the fatigue test is compared with that from the quasi-static test; it is demonstrated that the quasi-static deformation is insufficient as a fatigue failure criterion. It is observed that crack growth owing to constant-amplitude fatigue loading comprises two phases: a deceleration stage when there is a decrease in crack growth rate with increasing crack length, followed by an acceleration stage where the rate of crack growth increases at a steady rate. The crack length where the rate of crack growth changes from deceleration to acceleration is shown to be equal to the crack length at the peak load of the quasi-static response. Analytical expressions for crack growth in the deceleration and acceleration stages are developed, wherein the expressions for crack growth rate in the deceleration stage are developed using the R-curve concept, and the acceleration stage is shown to follow the Paris law. It is observed that the crack length at failure for constant amplitude fatigue loading is comparable to that of the corresponding load in the postpeak part of the quasi-static response. Finally, a fracture-based fatigue failure criterion is proposed.     

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.     

Effects of crack aspect ratio on the behavior of small surface cracks in fatigue: Part II. Experiments on a titanium (Ti-8Al) alloy

The continuous variations in crack shape or aspect ratio, a/c (a is the crack depth and c is the halfsurface length), of small surface cracks, induced by grain boundaries, have been investigated during the fatigue crack growth of small cracks in a titanium (Ti-8Al) alloy. The significance of the aspect ratio variations in explaining the “anomalous” small-crack behavior was evaluated. The aspect ratio data were determined from the measurements of crack compliance, made using a laser interferometric system, and the measurements of surface crack length (2c), made using a photomicroscopic system. The variations in aspect ratio were found to be large at small crack sizes of the order of a few grain diameters. The experimental a/c data were compared with the patterns of crack aspect ratio variation, obtained from the oretical simulations. The simulated data were generated by assuming alternate crack propagation at the surface and at the depth, the details of which are presented in Part I of the study accompanying this article. A good agreement was found between the simulated and the experimentally observed variations. After incorporating the a/c variations in ΔK calculations, the scatter in the growth data of small cracks was significantly reduced and was found to be of the same order as in large cracks. Additionally, it is shown in this study that the conventional methods of analysis of small-crack data, performed with an assumption of a/c=1, can result in significant errors in ΔK calculation and an increased level of scatter in small-crack growth data. Small cracks also were found to exhibit low closure levels relative to large cracks. The results of the study strongly indicate that characteristics of small cracks, often referred to as anomalous, are due to the assumption of a/c=1 in situations of large variations in aspect ratio, the use of conventional methods of data analysis, and the lower levels of crack closure found naturally in small cracks.