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Fracture Mechanics

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Fracture Mechanics Fracture Mechanics Historical Prospective Historical Prospective Presented by Calvin M. Stewart, PhD MECH 5390-6390 Fall 2020 Outline • Societal Aspects • Historical Prospective • Recent Advances YouTube Videos https://www.youtube.com/playlist?list=PLvC7PjgHRlu6L1tgLEpOXabSpr5uhhsWY Societal Aspects Prospective and Connotation Perspectives of Fracture Connotation of Fracture • Society’s perspective of fracture is that the cracked object(s) is • preventable • harmful • irreparable Historical Prospective Arrowheads, Stone Cutting, Materials, the Industrial Revolution onwards Arrowhead Making • Fracture Mechanics has been exploited by humans from time immemorable. • The earliest humans exploited fracture mechanics to craft Arrowheads from brittle rock materials. • The earliest evidence is 64,000 years ago from Sibudu Cave in South Africa Stone Cutting • Egyptians became masters of fracture mechanics exploiting the brittle fracture of rocks to construct massive structures. (3000 BC>) Giza pyramid complex One of the Seven Wonders of the Ancient World • Knowledge from the Ancient Africa spread into Europe through war, conflict and conquest, resulting in many of the structures admired by West Society such as the roman Colosseum Materials • The primary construction materials prior to the nineteenth century were timber, stone, brick and mortar; only the latter three materials were usually practical for large structures such as cathedrals, because trees of sufficient size for support beams were rare. • Consequently, pre-Industrial Revolution structures were usually designed to be loaded in compression. Industrial Revolution • With the Industrial Revolution came mass production of iron and steel. • These ductile materials removed the earlier restrictions on tensile designs. • Occasionally, steel structures in tensile failed well below the anticipate tensile strength. • Failures in railway equipment, boilers, and tanks due to a lack of understanding the Fracture Mechanics Contributors to Fracture In the nineteenth century, the quantitative connection between fracture stress and flaw size started to be explored. Rankine Griffith Paris Rice Saxena (1842) (1920s) (1961) (1960s) (1990) Inglis Irwin Wells Nikbin (1913) (1950s) (1961) (1976) Versailles train crash On May 8th, 1842 a train returning to Paris derailed at Meudon after the leading locomotive broke an axle, and the carriages behind piled into it and caught fire. It was the first French railway accident and the deadliest in the world at the time, causing between 52 and 200 deaths. Versailles train crash • Caused by fatigue failure of a locomotive axle at a sharp cornered shoulder • Notes: • Occurred on May 8th, 1842 • Carriages behind piled into the wrecked engines and caught fire • Problem solved with better axles designs William John Macquorn Rankine • Worked with railroad axles and other stress concentrations • Participated in studies following the Versailles accident • Recognized the distinctions between fatigue cracks from other cracks • Recognized the importance of stress concentrations in his investigation of railroad axle failures W. J. M. Rankine (1820-1872) SCF = MAX NOM ASTM formed • In 1898, Charles Benjamin Dudley investigated problems with the chemistry of materials used by the Pennsylvania Railroad • He later went on to found the ASTM, a committee-based organization focused on industrial progress • Much later, the committee on fracture was formed in the 1950’s Sir Charles Edward (C.E.) Inglis • In 1913, Inglis considered the fracture behavior of thin glass plates with elliptical holes. • Derived the distribution of elastic stress field in the front of the elliptical notch • Determined that the ratio of dimensions a to b plays a great role in determining the stress at point A. C.E. Inglis (1875-1952) H.M. Westergaard • Using a complex variables approach derived the stress distribution in front of an atomically sharp crack, the worst case, recognizing the stress singularity at the crack tip 퐾 휎푖푗 = 푓푖푗 휃 2휋푟 Westergaard (1888-1950) Alan Arnold Griffith • In 1920s, he extended the work of Inglis to the unstable propagation of a crack in linear-elastic brittle solids. • Invoking the first law of thermodynamics, he found that A flaw becomes unstable, and thus fracture occurs, when the strain energy change that results from an increment of crack growth is sufficient to overcome the surface energy of the material. • Origins of the Energy Approach!!! GG c • Only applicable to Brittle Solids, Not Ductile Metals A. A. Griffith (1893-1963) WWII Liberty Ships The S.S. Schenechtady as she appeared on the morning of Jan. 17, 1943, after suddenly and unexpectedly cracking in half for no apparent reason while moored at the fitting dock at Swan Island. (Image: U.S. GPO) During World War II many brittle fractures in welded tankers and Liberty ships motivated substantial efforts concerning preexisting defects and cracks and the influence of stress concentrations. WWII Liberty Ships • Early ships suffered hull and deck cracks • Number of ships that broke in half: 19 • Failure mechanism due to brittle crack growth at stress concentration • Temperature of the Steel submerged in water fell below the Brittle to Ductile Transition Temperature Liberty Ship Schenectady in the port of Portland fractured from deck to keel. George Rankin Irwin • Born in El Paso, Texas • The fracture mechanics research group at the Naval Research Laboratory was led by Dr. Irwin • In 1948, Irwin extended the work of Griffith by extending theories to ductile materials by including the energy dissipated by local plastic flow • In 1956, developed the energy release rate concept and leveraged Westergaards solution to identify the Stress Intensity Factors KK c Irwin (1907-1998) Ushering the Era of Modern Fracture Mechanics • In 1945, independently proposed the same modification to Griffith’s theory as Orowan • Generalized the Griffith’s theory for cracked bodies of arbitrary shape and loading for Mode I cracks • In 1956, used Westergaard’s analysis to introduce the concept of stress intensity parameter, K, as the amplitude of the crack tip stress field • In 1957, derived the relationship between the Griffith’s Crack Extension Force and K establishing K based Fracture Mechanics on a very firm footing • Estimated the size of the plastic zone and proposed a method to account for small-scale- yielding (SSY) • Derived the relationship between crack tip opening George R. Irwin (1907-1998) displacement and K • ASTM and ICF have medals named after Dr. Irwin • De Havilland Comet • The Comet, the first jet propelled passenger airplane, started service in May 1952 after more than 300 hours of flight tests. • Three plane crashes caused by repeated pressurization of the metallic fuselage skin at sharp corners near windows De Havilland Comet • After exhaustive investigations it was concluded that the accidents were caused by fatigue failure of the pressurized cabin. • All Comet aircraft of this type were taken out of service and additional attention was focused on airframe fatigue design. • Shortly after this, the first emphasis on fail-safe design in aircraft rather than safe-life gathered momentum in the USA. This would place much more attention on maintenance and inspection. Alan Arthur Wells • In 1956, Wells used fracture mechanics to show that the fuselage failures in several Comet jet aircraft resulted from fatigue cracks reaching a critical size. • In 1961, in parrallel with Irwin, Dugdale, and Barenblatt, developed a correction for crack tip plasticity • First proposed using Crack Tip Open Displacement (CTOD) as an alternative fracture criterion when significant plasticity proceeds failure. Wells (1924-2005) Paul C. Paris • In 1955 with working as a faculty associate for Boeing he investigated the “De Havilland Comet” Failures • In 1961, Discovered that the Fatigue Crack Growth Rate is related to the stress intensity factor range • Resulted in Paris Law da m =CK( ) dN Paul C Paris (1930-2017) Paul C. Paris • Extended the use of K, ∆K, for characterizing Fatigue Crack Growth, known as the Paris-Law • Proposed the concept of threshold value of ∆K and the effects of load ratio, R. • Envisioned the relationship between K and the environment assisted rate of crack growth • Led the adoption of damage tolerant approach to design in aerospace and power generation industries • Collaborated with George Irwin and Hiroshi Tada to produce the first compendium of K solutions • Made seminal contributions to the development of elastic-plastic fracture mechanics • ICF established the Paul Paris Gold Medal to memorialize his contributions and impact on the field ASTM Committees • ASTM Committee E-24 on Fracture testing was formed in 1964. This committee has contributed significantly to the field of fracture mechanics and fatigue crack growth. • ASTM Committee E08 on Fatigue and Fracture was formed in 1993 as a result of a merger between Committees E09 and E24. E08 meets twice a year, in May and November, with about 75 members attending two days of technical meetings and one or two days of workshops and symposia. The Committee has approximately 500 members and has jurisdiction of 32 standards, published in the Annual Book of ASTM Standards, Volume 3.01. ASTM Test Methods for LEFM Test Method and Year of First Leaders Publication of Select Standards ASTM E-399 (1964): Measurement Edward T. Wessel, William Brown, of Plane Strain Fracture Toughness John Srawley, George Irwin, Paul Paris, J.G. Kaufman ASTM E-561 (1968): Measurement Donald
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