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Crack Tip Opening Displacement
Crack tip opening displacement (CTOD) or \delta_\text is the distance between the opposite faces of a crack tip at the 90° intercept position. The position behind the crack tip at which the distance is measured is arbitrary but commonly used is the point where two 45° lines, starting at the crack tip, intersect the crack faces. The parameter is used in fracture mechanics to characterize the loading on a crack and can be related to other crack tip loading parameters such as the stress intensity factor K and the elastic-plastic J-integral. For plane stress conditions, the CTOD can be written as: \delta_\text = \left(\frac\right)\ln\left sec\left(\frac\right)\right/math> where \sigma_\text is the yield stress, a is the crack length, E is the Young's modulus , and \sigma^\infty is the remote applied stress. Under fatigue loading, the range of movement of the crack tip during a loading cycle \Delta\delta_\text can be used for determining the rate of fatigue growth using a crack gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crack Tip Opening Displacement
Crack tip opening displacement (CTOD) or \delta_\text is the distance between the opposite faces of a crack tip at the 90° intercept position. The position behind the crack tip at which the distance is measured is arbitrary but commonly used is the point where two 45° lines, starting at the crack tip, intersect the crack faces. The parameter is used in fracture mechanics to characterize the loading on a crack and can be related to other crack tip loading parameters such as the stress intensity factor K and the elastic-plastic J-integral. For plane stress conditions, the CTOD can be written as: \delta_\text = \left(\frac\right)\ln\left sec\left(\frac\right)\right/math> where \sigma_\text is the yield stress, a is the crack length, E is the Young's modulus , and \sigma^\infty is the remote applied stress. Under fatigue loading, the range of movement of the crack tip during a loading cycle \Delta\delta_\text can be used for determining the rate of fatigue growth using a crack gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fracture
Fracture is the separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially, it is called a shear crack, slip band or dislocation. Brittle fractures occur with no apparent deformation before fracture. Ductile fractures occur after visible deformation. Fracture strength, or breaking strength, is the stress when a specimen fails or fractures. The detailed understanding of how a fracture occurs and develops in materials is the object of fracture mechanics. Strength Fracture strength, also known as breaking strength, is the stress at which a specimen fails via fracture. This is usually determined for a given specimen by a tensile test, which charts the stress–strain cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fracture Mechanics
Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. Theoretically, the stress ahead of a sharp crack tip becomes infinite and cannot be used to describe the state around a crack. Fracture mechanics is used to characterise the loads on a crack, typically using a single parameter to describe the complete loading state at the crack tip. A number of different parameters have been developed. When the plastic zone at the tip of the crack is small relative to the crack length the stress state at the crack tip is the result of elastic forces within the material and is termed linear elastic fracture mechanics (LEFM) and can be characterised using the stress intensity factor K. Although the load on a crack can be arbitrary, in 1957 G. Irwin foun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stress Intensity Factor
In fracture mechanics, the stress intensity factor () is used to predict the stress state ("stress intensity") near the tip of a crack or notch caused by a remote load or residual stresses. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials, and is a critical technique in the discipline of damage tolerance. The concept can also be applied to materials that exhibit ''small-scale yielding'' at a crack tip. The magnitude of depends on specimen geometry, the size and location of the crack or notch, and the magnitude and the distribution of loads on the material. It can be written as: :K = \sigma \sqrt \, f(a/W) where f(a/W) is a specimen geometry dependent function of the crack length, , and the specimen width, , and is the applied stress. Linear elastic theory predicts that the stress distribution (\sigma_) near the crack tip, in polar coordinates (r,\theta) with or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
J-integral
The J-integral represents a way to calculate the strain energy release rate, or work (energy) per unit fracture surface area, in a material. The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov and independently in 1968 by James R. Rice,J. R. Rice, ''A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks'', Journal of Applied Mechanics, 35, 1968, pp. 379–386. who showed that an energetic contour path integral (called ''J'') was independent of the path around a crack. Experimental methods were developed using the integral that allowed the measurement of critical fracture properties in sample sizes that are too small for Linear Elastic Fracture Mechanics (LEFM) to be valid. Lee, R. F., & Donovan, J. A. (1987). J-integral and crack opening displacement as crack initiation criteria in natural rubber in pure shear and tensile specimens. Rubber chemistry and technology, 60(4), 674–688/ref> These experiments ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane Stress
In continuum mechanics, a material is said to be under plane stress if the stress vector is zero across a particular plane. When that situation occurs over an entire element of a structure, as is often the case for thin plates, the stress analysis is considerably simplified, as the stress state can be represented by a tensor of dimension 2 (representable as a 2×2 matrix rather than 3×3). A related notion, plane strain, is often applicable to very thick members. Plane stress typically occurs in thin flat plates that are acted upon only by load forces that are parallel to them. In certain situations, a gently curved thin plate may also be assumed to have plane stress for the purpose of stress analysis. This is the case, for example, of a thin-walled cylinder filled with a fluid under pressure. In such cases, stress components perpendicular to the plate are negligible compared to those parallel to it. In other situations, however, the bending stress of a thin plate cannot be ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yield (engineering)
In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation. The yield strength or yield stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable load in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation. In some materials, such as aluminium, there is a gradual onset of non-linear behavior, making the precise yield point difficult to determine. In such a case, the offset yiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Young's Modulus
Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied lengthwise. It quantifies the relationship between tensile/compressive stress \sigma (force per unit area) and axial strain \varepsilon (proportional deformation) in the linear elastic region of a material and is determined using the formula: E = \frac Young's moduli are typically so large that they are expressed not in pascals but in gigapascals (GPa). Example: * Silly Putty (increasing pressure: length increases quickly, meaning tiny E) * Aluminum (increasing pressure: length increases slowly, meaning high E) Higher Young's modulus corresponds to greater (lengthwise) stiffness. Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler. The first experime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fatigue (material)
In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of the fracture surface. The crack will continue to grow until it reaches a critical size, which occurs when the stress intensity factor of the crack exceeds the fracture toughness of the material, producing rapid propagation and typically complete fracture of the structure. Fatigue has traditionally been associated with the failure of metal components which led to the term metal fatigue. In the nineteenth century, the sudden failing of metal railway axles was thought to be caused by the metal ''crystallising'' because of the brittle appearance of the fracture surface, but this has since been disproved. Most materials, such as composites, plastics and ceramics, seem to experience some sort of fatigue-related failure. To aid in predicting t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crack Growth Equation
A crack growth equation is used for calculating the size of a fatigue crack growing from cyclic loads. The growth of fatigue cracks can result in catastrophic failure, particularly in the case of aircraft. A crack growth equation can be used to ensure safety, both in the design phase and during operation, by predicting the size of cracks. In critical structure, loads can be recorded and used to predict the size of cracks to ensure maintenance or retirement occurs prior to any of the cracks failing. ''Fatigue life'' can be divided into an initiation period and a crack growth period. Crack growth equations are used to predict the crack size starting from a given initial flaw and are typically based on experimental data obtained from constant amplitude fatigue tests. One of the earliest crack growth equations based on the stress intensity factor range of a load cycle (\Delta K) is the Paris–Erdogan equation. : = C(\Delta K)^m where a is the crack length and a/N is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Cottrell
Sir Alan Howard Cottrell, FRS (17 July 1919 – 15 February 2012) was an English metallurgist and physicist. He was also former Chief Scientific Advisor to the UK Government and vice-chancellor of Cambridge University 1977–1979. Early life Cottrell was educated at Moseley Grammar School and the University of Birmingham, where he gained a Bachelor of Science degree in 1939 and a PhD for research on welding in 1942. Career Cottrell joined the staff as a lecturer at Birmingham, being made professor in 1949, and transforming the teaching of the department by emphasising modern concepts of solid state physics.History of Metallurgy at Birmingham Engineering at Birmingham University In 1955 he moved to [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Rankine Irwin
George Rankin Irwin (February 26, 1907 – October 9, 1998) was an American scientist in the field of fracture mechanics and strength of materials. He was internationally known for his study of fracture of materials. Early life and education George R. Irwin was born in El Paso, Texas. His family moved to Springfield, Illinois where he went to school. He attended Knox College in Galesburg, Illinois and earned an A.B. degree in English in 1930. After an additional year studying physics, he transferred to the University of Illinois at Urbana-Champaign where he studied from 1931 to 1935. He received his Ph.D. from the University of Illinois in 1937; his thesis was on the mass ratio of lithium isotopes. Career In 1937 he joined the US Naval Research Laboratory (NRL) in Washington D.C. where he worked until 1967. There he worked on ballistics, specifically on the mechanics of projectiles penetrating targets. Here he developed methods for determining the penetration force that a p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
