Effects of microstructure on long and short crack growth in nickel base superalloys

The use of engineering materials in critical applications necessitates the accurate prediction of component lifetime for inspection and renewal purposes. In fatigue limited situations, it is necessary to be able to predict the growth rates of cracks from initiation at a defect through to final fracture. To this end, fatigue crack growth data are presented for different microstructures of typical nickel base superalloys used in gas turbine engines. Crack growth behaviour throughout the life history of the crack, i.e. from the short crack through to the long crack propagation regime, is described for each microstructural condition and discussed in terms of current theories of fatigue crack propagation.

Crystallographic fatigue crack growth in nimonic AP1

Recently a controversy has developed over whether crystallographic crack growth near threshold in nickel-base superalloys occurs along right brace 111 left brace slip planes or right brace 100 left brace planes at room temperature. In this work crack propagation is shown to occur on both right brace 100 left brace and right brace 111 left brace planes. The most common facet plane is right brace 111 left brace and this is the only orientation observed at the lowest stress intensities, but at higher stress intensities occasional right brace 100 left brace facets are also produced. This behavior is compared with similar results in aluminum alloys.

Effects of crack length and shape on the fracture toughness of a high strength steel 300m

The results of fracture toughness tests on a high strength steel 300m are presented. These results show (i) that in the presence of through-thickness cracks the toughness remains constant down to (a/W)-ratios as low as 0.01 and failure loads up to 0.85σy, and (ii) that the material is more resistant to crack growth when the cracks are semi-elliptical in shape, giving a toughness value which is almost 25 per cent higher than the through-thickness one. Three independent stress analyses are used to obtain stress intensity values for the semi-elliptical cracks and additional confirmation of the increase in toughness comes from stretch zone measurements.

Relevance of microstructural influences in the short crack regime to overall fatigue resistance

The behaviour of short fatigue cracks is shown to be relevant only to a limited number of engineering situations. Within these situations, further restrictions on the extent to which metallurgical control can be exerted to improve fatigue crack growth behaviour are identified. The degree of control remaining is discussed in terms of two separate regimes which are described as intrinsic and extrinsic crack growth resistance. These separate effects are highlighted by comparisons both within and between a wide range of alloy systems. The implications of such an analysis are discussed in terms of aerospace applications.

Effects of microstructure, temperature and R-ratio on fatigue crack propagation and threshold behaviour in two Ni-base alloys

Fatigue crack propagation and threshold data for two Ni-base alloys, Astroloy and Nimonic 901, are reported. At room temperature the effect which altering the load ratio (R-ratio) has on fatigue behaviour is strongly dependent on grain size. In the coarse grained microstructures crack growth rates increase and threshold values decrease markedly as R rises from 0. 1 to 0. 8, whereas only small changes in behaviour occur in fine grained material. In Astroloy, when strength level and gamma grain size are kept constant, there is very little effect of processing route and gamma prime distribution on room temperature threshold and crack propagation results. The dominant microstructural effect on this type of fatigue behaviour is the matrix ( gamma ) grain size itself.

Effects of grain size and microstructure on threshold values and near threshold crack growth in powder-formed Ni-base superalloy

Threshold stress intensity values, ranging from ∼6 to 16 MN m −3/2 can be obtained in powder-formed Nimonic AP1 by changing the microstructure. The threshold and low crack growth rate behaviour at room temperature of a number of widely differing API microstructures, with both ‘necklace’ and fully recrystallized grain structures of various sizes and uniform and bimodal γ′-distributions, have been investigated. The results indicate that grain size is an important microstructural parameter which can control threshold behaviour, with the value of threshold stress intensity increasing with increasing grain size, but that the γ′-distribution is also important. In this Ni-base alloy, as in many others, near threshold fatigue crack growth occurs in a crystallographic manner along {111} planes. This is due to the development of a dislocation structure involving persistent slip bands on {111} planes in the plastic zone, caused by the presence of ordered shearable precipitates in the microstructure. However, as the stress intensity range is increased, a striated growth mode takes over. The results presented show that this transition from faceted to striated growth is associated with a sudden increase in crack propagation rate and occurs when the size of the reverse plastic zone at the crack tip becomes equal to the grain size, independent of any other microstructural variables.

Crack initiation in asphalt mixtures under external compressive loads

Crack initiation was studied for asphalt mixtures under external compressive loads. High tensile localized stresses e direction of the external loads. A quantitative crack initiation criterion the edges of compressed air voids lead to the growth of wing cracks in thon was derived using pseudostrain energy balance principle. Bond energy is determined and it increases with aging and loading rate while decreases with temperature. Cohesive and adhesive cracking occur simultaneously and a method was proposed to determine the individual percentage. The crack initiation criterion is simplified and validated through comparing the predicted and measured compressive strength of the asphalt mixtures.

Anisotropic characterization of crack growth in the tertiary flow of asphalt mixtures in compression

Asphalt mixtures exhibit primary, secondary, and tertiary stages in sequence during a rutting deterioration. Many field asphalt pavements are still in service even when the asphalt layer is in the tertiary stage, and rehabilitation is not performed until a significant amount of rutting accompanied by numerous macrocracks is observed. The objective of this study was to provide a mechanistic method to model the anisotropic cracking of the asphalt mixtures in compression during the tertiary stage of rutting. Laboratory tests including nondestructive and destructive tests were performed to obtain the viscoelastic and viscofracture properties of the asphalt mixtures. Each of the measured axial and radial total strains in the destructive tests were decomposed into elastic, plastic, viscoelastic, viscoplastic, and viscofracture strains using the pseudostrain method in an extended elastic-viscoelastic correspondence principle. The viscofracture strains are caused by the crack growth, which is primarily signaled by the increase of phase angle in the tertiary flow. The viscofracture properties are characterized using the anisotropic damage densities (i.e., the ratio of the lost area caused by cracks to the original total area in orthogonal directions). Using the decomposed axial and radial viscofracture strains, the axial and radial damage densities were determined by using a dissipated pseudostrain energy balance principle and a geometric analysis of the cracks, respectively. Anisotropic pseudo J-integral Paris' laws in terms of damage densities were used to characterize the evolution of the cracks in compression. The material constants in the Paris' law are determined and found to be highly correlated. These tests, analysis, and modeling were performed on different asphalt mixtures with two binders, two air void contents, and three aging periods. Consistent results were obtained; for instance, a stiffer asphalt mixture is demonstrated to have a higher modulus, a lower phase angle, a greater flow number, and a larger n1 value (exponent of Paris' law). The calculation of the orientation of cracks demonstrates that the asphalt mixture with 4% air voids has a brittle fracture and a splitting crack mode, whereas the asphalt mixture with 7% air voids tends to have a ductile fracture and a diagonal sliding crack mode. Cracks of the asphalt mixtures in compression are inclined to propagate along the direction of the external compressive load. © 2014 American Society of Civil Engineers.

On a Hypersingular Equation of a Problem, for a Crack in Elastic Media

Mathematics Subject Classification 2010: 45DB05, 45E05, 78A45.

On a 3D-Hypersingular Equation of a Problem for a Crack

MSC 2010: 45DB05, 45E05, 78A45

Crack Theory with Singularities at the Boundary

2002 Mathematics Subject Classification: 35S15, 35J70, 35J40, 38J40

Optimal redistricting under geographical constraints: Why "pack and crack" does not work

We show that optimal partisan redistricting with geographical constraints is a computationally intractable (NP-complete) problem. In particular, even when voter's preferences are deterministic, a solution is generally not obtained by concentrating opponent's supporters in \unwinnable" districts ("packing") and spreading one's own supporters evenly among the other districts in order to produce many slight marginal wins ("cracking").

Crack tip stress study for elastic-perfectly plastic materials with some applications

The problems of plasticity and non-linear fracture mechanics have been generally recognized as the most difficult problems of solid mechanics. The present dissertation is devoted to some problems on the intersection of both plasticity and non-linear fracture mechanics. The crack tip is responsible for the crack growth and therefore is the focus of fracture science. The problem of crack has been studied by an army of outstanding scholars and engineers in this century, but has not, as yet, been solved for many important practical situations. The aim of this investigation is to provide an analytical solution to the problem of plasticity at the crack tip for elastic-perfectly plastic materials and to apply the solution to a classical problem of the mechanics of composite materials.^ In this work, the stresses inside the plastic region near the crack tip in a composite material made of two different elastic-perfectly plastic materials are studied. The problems of an interface crack, a crack impinging an interface at the right angle and at arbitrary angles are examined. The constituent materials are assumed to obey the Huber-Mises yielding condition criterion. The theory of slip lines for plane strain is utilized. For the particular homogeneous case these problems have two solutions: the continuous solution found earlier by Prandtl and modified by Hill and Sokolovsky, and the discontinuous solution found later by Cherepanov. The same type of solutions were discovered in the inhomogeneous problems of the present study. Some reasons to prefer the discontinuous solution are provided. The method is also applied to the analysis of a contact problem and a push-in/pull-out problem to determine the critical load for plasticity in these classical problems of the mechanics of composite materials.^ The results of this dissertation published in three journal articles (two of which are under revision) will also be presented in the Invited Lecture at the 7$\rm\sp{th}$ International Conference on Plasticity (Cancun, Mexico, January 1999). ^

A phenomenology of crack abuse

The aim of this dissertation is to identify, describe, and explain the common experiences defining the crack abuser's life-world. Its method is phenomenological. Using basic cybernetic premises, a neurophysiologically oriented phenomenological framework concerning the constitution of thoughts, memories, and perceptions is first written. The framework is designed to hypothetically represent the neuropathology of crack abuse within a perspective that prescinds and describes the constitution, flow, and interdependence of experience. After the framework is written, the dissertation outlines the neuro-psychopharmacology of crack abuse and delimits crack abusers as a specific group within the more general population of cocaine users. It then represents the neuropathology of crack abuse within its phenomenological framework and uses the first-person accounts of forty-two crack dependents to actualize a phenomenological sketch of the crack abuser's life-world. The ethnographies afford the possibility of writing a “thick” description of the crack abuser's daily life—one that communicates the substance, order, and subjective and cultural dimensions of the dependent's defining experiences. ^ The dissertation's goals are successfully realized. The framework written and the ethnographies recorded and transcribed, the dissertation is able to identify, describe, and to a certain extent explain some of the common experiences defining the crack abusers life-world. The dissertation concludes that the crack abuser's life-world is organized around three primary and four secondary experiences. His primary experiences include: (1) an almost complete, yet fleeting, satisfaction of the ego's innate insufficiency and sublime, erotic-like stimulation of its core, (2) a fundamental inclination and expansion of the uniquely oriented euphoria-dysphoria dynamic that vivifies and orients the flow of consciousness, and (3) a change in the ego's innate structure. His secondary experiences include: (a) a characteristic aiming of projects, actions, and conduct toward the procurement and consumption of crack, (b) a denigration in the hold of legitimations and institutionalizations on the thematic field, (c) a strict alignment and a contraction in the scope of logical types pointing to the salient experiences within the stock of knowledge, and (d) for some crack abusers, ontological insecurity, despair, and exhaustion. ^

Usuários de crack, instituições e modos de subjetivação: estudo das práticas e da eficácia terapêutica em uma comunidade terapêutica religiosa (RN)

This anthropological research has as main goal to grasp the meanings and perceptions - mode of subjectivity - of crack users in relation to the proposals of Therapeutic Communities (TC) of religious character. The work emphasizes the analysis of Therapeutic Communities of Rio Grande do Norte state, studying a particular organization, called Anzóis da Dor. I intend to analyze qualitative data, focusing on an analysis of the discursive content of speeches and the observation of social interaction, which results in an ethnographic text characterized by a dense description. In relation to the dissertation’s specific goals, we seek to present a general overview of the emergence and development of Therapeutic Communities – encompassing general and local considerations - and pointing out to the dynamics of religious healing systems of these institutions, besides the principles that guide them. In methodological terms, I conducted the partial mapping of therapeutic communities located in Rio Grande do Norte state; interviews with Therapeutic Communities coordinators, visits, participant observation in one of these institutions as well as some interviews with crack users and people close to these social agents in relation to the Therapeutic Communities and the treatment offered by them