To better design structures and machines, understanding of flaws and failures is essential. The body of this work has addressed numerous facets of fatigue crack propagation. The affect of crack closure, testing errors, and data scatter are a few important components of crack growth developed and investigated. It was found that the widely accepted compliance-offset technique for closure measurement may be sensitive to increases in load ratio. Opening load uncertainty was calculated to be on the order of 5%. The application of practical regression techniques and the use of DKeff were used to characterize closureree crack growth data to develop a single intrinsic da/dN curve. The best form of regression was found to be a multi-linear fit. A strip-yield model requiring the intrinsic curve was used to successfully predict crack growth at other load ratios. Uncertainties with a strong dependence on crack mouth displacement were found for da/dN, DK, and a.To better design structures and machines, understanding of flaws and failures is essential. The body of this work has addressed numerous facets of fatigue crack propagation. The affect of crack closure, testing errors, and data scatter are a few important components of crack growth developed and investigated. It was found that the widely accepted compliance-offset technique for closure measurement may be sensitive to increases in load ratio. Opening load uncertainty was calculated to be on the order of 5%. The application of practical regression techniques and the use of DKeff were used to characterize closureree crack growth data to develop a single intrinsic da/dN curve. The best form of regression was found to be a multi-linear fit. A strip-yield model requiring the intrinsic curve was used to successfully predict crack growth at other load ratios. Uncertainties with a strong dependence on crack mouth displacement were found for da/dN, deltaK, and a.

From its discovery, crack closure was recognized as a key aspect in understanding the fatigue crack growth process. Considering the condition of plane stress, a vast amount of research has been conducted experimentally, analytically, and numerically to understand the complex process of fatigue crack growth and crack closure. Nonzero crack opening stress values are routinely observed, and it seems that there is a general agreement regarding the incidence of the phenomenon under plane stress. However, investigations regarding crack closure under plane strain conditions are less abundant. Moreover, the existence of crack closure under the plane strain state of the stress has been questioned. The importance of accurate measurements of closure to predict adequately fatigue crack growth rates should not be underestimated. Models employed to predict fatigue crack growth rates rely on plasticity-induced crack closure concepts, and the validity of plasticity-induced crack closure depends on crack closure measurements. Crack closure measurements can be performed with Elber’s Method, the ASTM standard(Compliance offset method), or it may be done alternatively by the compliance ratio (CR) or the adjusted compliance ratio method (ACR). In this research, a small scale yielding two-parameter modified boundary layer analysis is performed to study the occurrence of plasticity-induced fatigue crack closure under constant amplitude loading and plane strain conditions. A wide range of T-stresses and KI levels are considered in the finite element analysis with the purpose of exploring the behavior of the crack opening stress. Crack closure was observed for some values of T-stress. Other values of T-stress resulted in an absence of closure under steady state conditions. In addition, an elastic-plastic finite element model was used to simulate a growing fatigue crack with WARP3D software. The computed displacements were used to determine the effective stress intensity factor range ΔKeff with the ASTM standard compliance offset approach, the (CR) method, and the (ACR) method. Finally, measurement location effects on ACR and the ability of ACR method to remove residuals stresses were investigated.

The work in this thesis is concerned with the mechanics of the initiation and growth of small fatigue cracks from notches under service load histories. Fatigue life estimates for components subjected to variable amplitude service loading are usually based on the same constant amplitude strain-life data used for constant amplitude fatigue life predictions. The resulting fatigue life estimates although they are accurate for constant amplitude fatigue, are always non conservative for variable amplitude load histories. Similarly fatigue life predictions based on small crack growth calculations for cracks growing from flaws in notches are non conservative when constant amplitude crack growth data are used. These non conservative predictions have, in both cases, been shown to be due to severe reductions in fatigue crack closure arising from large (overload or underload) cycles in a typical service load history. Smaller load cycles following a large near yield stress overload or underload cycle experience a much lower crack opening stress than that experienced by the same cycles in the reference constant amplitude fatigue tests used to produce design data. This reduced crack opening stress results in the crack remaining open for a larger fraction of the stress-strain cycle and thus an increase in the effective portion of the stress-strain cycle. The effective strain range is increased and the fatigue damage for the small cycles is greater than that calculated resulting in a non conservative fatigue life prediction. Previous work at Waterloo introduced parameters based on effective strain-life fatigue data and effective stress intensity versus crack growth rate data. Fatigue life calculations using these parameters combined with experimentally derived crack opening stress estimates give accurate fatigue life predictions for notched components subjected to variable amplitude service load histories. Information concerning steady state crack closure stresses, effective strain-life data, and effective stress intensity versus small crack growth rate data, are all obtained from relatively simple and inexpensive fatigue tests of smooth specimens in which periodic underloads are inserted into an otherwise constant amplitude load history. The data required to calibrate a variable amplitude fatigue crack closure model however, come from time consuming measurements of the return of crack closure levels for small cracks to a steady state level following an underload (large cracks for which crack closure measurements are easier to make cannot be used because at the high stress levels in notches under service loads a test specimen used would fracture). For low and moderately high hardness levels in metals crack growth and crack opening stress measurements have been made using a 900x optical microscope for the small crack length at which a test specimen can resist the high stress levels encountered when small cracks grow from notches. For very hard metals the crack sizes may be so small that the measurements must be made using a confocal scanning laser microscope. In this case the specimen must be removed from the test machine for each measurement and the time to acquire data is only practical for an extended research project. The parameters for the crack closure model relating to steady state crack closure levels vary with material cyclic deformation resistance which in turn increases with hardness. One previous investigation found that the steady state crack opening level was lower and the recovery to a steady state crack opening stress level after an underload was more rapid for a hard than for a soft metal. This observation can be explained by the dependence of the crack tip plastic zone size that determines crack tip deformation and closure level on metal hardness and yield strength. Further information regarding this hypothesis has been obtained in this thesis by testing three different steels of varying hardness levels (6 HRC, 35 HRC, and 60 HRC) including a very hard carburized steel having a hardness level (60 HRC) for which no crack opening stress data for small cracks had yet been obtained. This thesis introduced a new test procedure for obtaining data on the return of crack opening stress to a steady state level following an underload. Smooth specimens were tested under load histories with intermittent underload cycles. The frequency of occurrence of the underloads was varied and the changes in fatigue life observed. The changes in damage per block (the block consisted of an underload cycle followed by intermittent small cycles) were used to determine the value of the closure model parameter governing the recovery of the crack opening stress to its steady state level. Concurrent tests were carried out in which the crack opening stress recovery was measured directly on crack growth specimens using optical microscope measurements. These tests on metals ranging in hardness from soft to very hard were used to assess whether the new technique would produce good data for crack opening stress changes after underloads for all hardness levels. The results were also used to correlate crack closure model parameters with mechanical properties. This together with the steady state crack opening stress, effective strain-life data and the effective intensity versus crack growth rate data obtained from smooth specimen tests devised by previous researchers provided all the data required to calibrate the two models proposed in this investigation to perform strain-life and small crack growth fatigue analysis.

The work in this thesis is concerned with the mechanics of the initiation and growth of small fatigue cracks from notches under service load histories. Fatigue life estimates for components subjected to variable amplitude service loading are usually based on the same constant amplitude strain-life data used for constant amplitude fatigue life predictions. The resulting fatigue life estimates although they are accurate for constant amplitude fatigue, are always non conservative for variable amplitude load histories. Similarly fatigue life predictions based on small crack growth calculations for cracks growing from flaws in notches are non conservative when constant amplitude crack growth data are used. These non conservative predictions have, in both cases, been shown to be due to severe reductions in fatigue crack closure arising from large (overload or underload) cycles in a typical service load history. Smaller load cycles following a large near yield stress overload or underload cycle experience a much lower crack opening stress than that experienced by the same cycles in the reference constant amplitude fatigue tests used to produce design data. This reduced crack opening stress results in the crack remaining open for a larger fraction of the stress-strain cycle and thus an increase in the effective portion of the stress-strain cycle. The effective strain range is increased and the fatigue damage for the small cycles is greater than that calculated resulting in a non conservative fatigue life prediction. Previous work at Waterloo introduced parameters based on effective strain-life fatigue data and effective stress intensity versus crack growth rate data. Fatigue life calculations using these parameters combined with experimentally derived crack opening stress estimates give accurate fatigue life predictions for notched components subjected to variable amplitude service load histories. Information concerning steady state crack closure stresses, effective strain-life data, and effective stress intensity versus small crack growth rate data, are all obtained from relatively simple and inexpensive fatigue tests of smooth specimens in which periodic underloads are inserted into an otherwise constant amplitude load history. The data required to calibrate a variable amplitude fatigue crack closure model however, come from time consuming measurements of the return of crack closure levels for small cracks to a steady state level following an underload (large cracks for which crack closure measurements are easier to make cannot be used because at the high stress levels in notches under service loads a test specimen used would fracture). For low and moderately high hardness levels in metals crack growth and crack opening stress measurements have been made using a 900x optical microscope for the small crack length at which a test specimen can resist the high stress levels encountered when small cracks grow from notches. For very hard metals the crack sizes may be so small that the measurements must be made using a confocal scanning laser microscope. In this case the specimen must be removed from the test machine for each measurement and the time to acquire data is only practical for an extended research project. The parameters for the crack closure model relating to steady state crack closure levels vary with material cyclic deformation resistance which in turn increases with hardness. One previous investigation found that the steady state crack opening level was lower and the recovery to a steady state crack opening stress level after an underload was more rapid for a hard than for a soft metal. This observation can be explained by the dependence of the crack tip plastic zone size that determines crack tip deformation and closure level on metal hardness and yield strength. Further information regarding this hypothesis has been obtained in this thesis by testing three different steels of varying hardness levels (6 HRC, 35 HRC, and 60 HRC) including a very hard carburized steel having a hardness level (60 HRC) for which no crack opening stress data for small cracks had yet been obtained. This thesis introduced a new test procedure for obtaining data on the return of crack opening stress to a steady state level following an underload. Smooth specimens were tested under load histories with intermittent underload cycles. The frequency of occurrence of the underloads was varied and the changes in fatigue life observed. The changes in damage per block (the block consisted of an underload cycle followed by intermittent small cycles) were used to determine the value of the closure model parameter governing the recovery of the crack opening stress to its steady state level. Concurrent tests were carried out in which the crack opening stress recovery was measured directly on crack growth specimens using optical microscope measurements. These tests on metals ranging in hardness from soft to very hard were used to assess whether the new technique would produce good data for crack opening stress changes after underloads for all hardness levels. The results were also used to correlate crack closure model parameters with mechanical properties. This together with the steady state crack opening stress, effective strain-life data and the effective intensity versus crack growth rate data obtained from smooth specimen tests devised by previous researchers provided all the data required to calibrate the two models proposed in this investigation to perform strain-life and small crack growth fatigue analysis.

A titanium alloy (Ti-6Al-4V STOA) plate material was provided by the University of Dayton Research Institute from a previous U.S. Air Force high-cycle fatigue study. Fatigue-crack-growth tests on compact, C(T), specimens have been previously performed at Mississippi State University on the same material over a wide range in rates from threshold to near fracture for several load ratios (R = Pmin/Pmax). These tests used the compression pre-cracking method to generate fatigue-crack-growth-rate data in the near-threshold regime. Current load-reduction procedures were found to give elevated thresholds compared to compression pre-cracking methods. A crack-closure model was then used to determine crackront constraint and a plasticity-corrected effective stress-intensityactor-range relation over a wide range in rates and load ratios. Some engineering estimates were made for extremely slow rates (small-crack behavior), below the commonly defined threshold rate. Single-edge-notch-bend, SEN(B), fatigue specimens were machined from titanium alloy plates and were fatigue tested at two constant-amplitude load ratios (R = 0.1 and 0.5) and a modified Cold-Turbistan engine spectrum. Calculated fatigue lives from FASTRAN, a fatigue-life-prediction code, using small-crack theory with an equivalent-initiallaw-size (semi-circular surface flaw) of 9 µm in radius at the center of the semi-circular edge notch fit the constant-amplitude test data fairly well, but underpredicted the spectrum loading results by about a factor of 2 to 3. Life predictions made with linear-cumulative damage (LCD) calculations agreed fairly well with the spectrum tests.

Yes / Formation of cracks represents one of the major causes of concrete deterioration, which can lead to durability and safety issues. In this work, a novel crack closure system is developed, using polyethylene terephthalate (PET) polymer fibres embedded in a mortar mix. The PET polymer has shape memory properties and shrinks upon thermal activation, if free to do so, or otherwise exerts shrinkage restraint forces. A single knot was manufactured at each end of the PET fibres to provide mechanical anchorage into the mortar matrix. Mortar samples with embedded knotted fibres were pre-cracked and subsequently placed in an oven to thermally activate the polymers and induce the shrinkage mechanism into the fibres. Crack closure was measured in the range 45–100%, depending on the geometry, dimension and distribution of the fibres, and the size of the initial crack. / This work is supported by UKRI-EPSRC (Grant No. EP/P02081X/1, Resilient Materials 4 Life, RM4L).

Elastic-plastic finite element analyses were performed to predict the crack opening level profiles in semi-elliptical surface cracks. A script was written to use the commercial finite element code ANSYS to predict opening levels in cracked geometries. The functionality of the scripts was verified by comparing predicted opening levels in two and three-dimensional center-cracked geometries to experimental results. In addition, a parameter study was performed in which various aspects of the modeling routine were modified. This included a mesh refinement study as well as a study into the effect of a strain hardening material. The main focus of the current research, however, is to compare finite element predicted opening levels with published opening levels determined experimentally. Due to the complexities and long run-times involved with these models, no attempt was made at growing the cracks from initial length to final length. Instead, discrete crack lengths at which experimental opening levels were published were instead used. Also, no attempt was made to predict the crack aspect ratio evolution. The finite element predicted opening levels were in all cases significantly lower than those reported experimentally, however, similar trends in both crack opening level profile along the crack front, and opening level variations with crack growth were shown.

The integrity of nearly all engineering structures are threatened by the presence of cracks. Structural failure occurs if a crack larger than a critical size exists. Although most well designed structures initially contain no critical cracks, subcritical cracks can grow to failure under fatigue loading, called fatigue crack growth (FCG). Because it is impossible or impractical to prevent subcritical crack growth in most applications, a damage tolerant design philosophy was developed for crack sensitive structures. Design engineers have taken advantage of the FCG threshold concept to design for long fatigue lives. FCG threshold (DKth) is a value of DK (crack-tip loading), below which no significant FCG occurs. Cracks are tolerated if DK is less than DKth. However, FCG threshold is not constant. Many variables influence DKth including microstructure, environment, and load ratio. The current research focuses on load ratio effects on DKth and threshold FCG. Two categories of load ratio effects are studied here: extrinsic and intrinsic. Extrinsic load ratio effects operate in the crack wake and include fatigue crack closure mechanisms. Intrinsic load ratio effects operate in the crack-tip process zone and include microcracking and void production. To gain a better understanding of threshold FCG load ratio effects (1) a fatigue crack closure model is developed to consider the most likely closure mechanisms at threshold, simultaneously, and (2) intrinsic load ratio mechanisms are identified and modeled. An analytical fatigue crack closure model is developed that includes the three closure mechanisms considered most important at threshold (PICC, RICC, and OICC). Crack meandering and a limited amount of mixed-mode loading are also considered. The rough crack geometry, approximated as a two-dimensional sawtooth wave, results in a mixed-mode crack-tip stress state. Dislocation and continuum mechanics concepts are used to determine mixed-mode crack face displacements. Plasticity induced crack closure is included by modifying an existing analytical model, and an oxide layer in the crack mouth is modeled as a uniform layer. Finite element results were used to verify the analytical solutions for crack-tip stress intensity factor and crack face displacements. These results indicate that closure for rough cracks can occur at two locations: (1) at the crack-tip, and (2) at the asperity nearest the crack-tip. Both tip contact and asperity contact must be considered for rough cracks. Tip contact is more likely for high Kmax levels, thick oxide layers, and shallow asperity angles, a. Model results indicate that closure mechanisms combine in a synergistic manner. That is, when multiple closure mechanisms are active, the total closure level is greater than the sum of individual mechanisms acting alone. To better understand fatigue crack closure where multiple closure mechanisms are active (i.e. FCG threshold), these interactions must be considered. Model results are well supported by experimental data over a wide range of DK, including FCG threshold. Closure-free load ratio effects were studied for aluminum alloys 2024, 7050, and 8009. Alloys 7050 and 8009 were selected because load ratio effects at FCG threshold are not entirely explained by fatigue crack closure. It is believed that closure-free load ratio mechanisms occur in these alloys. Aluminum alloy 2024 was selected for study because it is relatively well behaved, meandering most load ratio effects are explained by fatigue crack closure. A series of constant Kmax threshold tests on aluminum alloys were conducted to eliminate fatigue crack closure at threshold. Even in the absence of fatigue crack closure load ratio (Kmax) effects persist, and are correlated with increased crack-tip damage (i.e. voids) seen on the fatigue crack surfaces. Accelerated FCG was observed during constant Kmax threshold testing of 8009 aluminum. A distinct transition is seen the FCG data and is correlated with a dramatic increase in void production seen along the crack faces. Void production in 8009 aluminum is limited to the specimen interior (plane-strain conditions), promoting crack tunneling. At higher values of Kmax (+_ 22.0 MPaà m), where plane-stress conditions dominate, a transition to slant cracking occurs at threshold. The transition to slant cracking produces an apparent increase in FCG rate with decreasing DK. This unstable threshold behavior is related to constraint conditions. Finally, a model is developed to predict the accelerated FCG rates, at higher Kmax levels, in terms of crack-tip damage. The effect of humidity (in laboratory air) on threshold FCG was studied to ensure that environmental effects at threshold were separated from load ratio effects. Although changes in humidity were shown to strongly affect threshold FCG rates, this influence was small for ambient humidity levels (relative humidity between 30% and 70%). Transient FCG behavior, following an abrupt change in humidity level, indicated environmental damage accumulated in the crack-tip monotonic plastic zone. Previous research implies that hydrogen (a component of water vapor) is the likely cause of this environmental damage. Analysis suggests that bulk diffusion is not a likely hydrogen transport mechanism in the crack-tip monotonic plastic zone. Rather, dislocation-assisted diffusion is presented as the likely hydrogen transport mechanism. Finally, the (extrinsic) fatigue crack closure model and the (intrinsic) crack-tip damage model are put in the context of a comprehensive threshold model. The ultimate goal of the comprehensive threshold model is to predict fatigue lives of cyclically loaded engineering components from (small) crack nucleation, through FCG, and including failure. The models developed in this dissertation provide a basis for a more complete evaluation of threshold FCG and fatigue life prediction. The research described in this dissertation was performed at NASA-Langley Research Center in Hampton, Virginia. Funding was provided through the NASA GSRP program (Graduate Student Researcher Program, grant number NGT-1-52174). / Ph. D.

No description available.

The application of fracture mechanics to engineering design has provided significant advances in understanding of the causes and mechanisms of failure and crack growth. Despite this, there are still some aspects that remain incompletely understood, such as the crack closure/crack shielding effect. The presence of crack closure/shielding acts to reduce . The mechanisms of crack closure/shielding are complicated, and have not been fully understood. This work focuses on the plasticity-induced crack tip shielding mechanism and presents a novel approach to characterise the elastic stress fields under the influence of the plastic enclave surrounding the crack tip. The model is successfully applied to determine the four stress parameters experimentally using full-field photoelastic stress analysis on polycarbonate CT specimens, following studies of the effect of the crack tip position and the valid data collection zone giving the best fit between the model predictions and the experimental data. The predicted values from the model demonstrate good data repeatability, and exhibit sensible trends as a function of crack length and load ratio that are interpretable in terms of physically meaningful changes to the plastic enclave. In addition, the model is proven to describe the stress field around a crack more accurately than classic Williams‟ stress solution. The model is also extended to AL 2024-T3 specimens using a full-field displacement measurement technique, digital image correlation. Using the Sobel edge detection method to identify the crack tip from the displacement fields with a rectangular shaped data collection zone employed in the current study, reasonable trends were again demonstrated in the experimental results as a function of crack length.