Introduction to Fracture Mechanics
Keywords: crack growth; brittle fractures; stress; materials; flaw size; linear elastic fracture
One of the earliest recorded studies of the failure of materials was in 15th century, with Leonardo da Vinci testing the strength of wire. In the 19th century, fracture theories based on crack growth were proposed by Cauchy and other French mathematicians (1), and later in the early 1900s, Griffith (2) made a quantitative connection between strength and crack size.
For many years, brittle fractures (A) were not well understood, until WWII, when numerous cargo and military ships had failed in service. Although design and metallurgical measures were taken to reduce geometric discontinuities, material failures continued to occur. Following the war, Irwin (3) published a number of papers on theory of fracture mechanics, and in the 1950’s Shank (4) and Parker (5) reviewed numerous historical failures. One of the most famous tank failures occurred in Boston in 1919 – when a large tank of molasses had suddenly failed, causing several deaths and enormous property damage.
Fracture Mechanics studies the interrelation among materials, design, fabrication and loading. The three primary factors of fracture mechanics (stress, materials and flaw size) must be considered for proper engineering design for all design loading conditions.
Material Toughness (Kc, K1c, K1d). Can be defined as the ability to carry a load or deform plastically in the presence of a notch.
Crack Size (a) Brittle fractures initiate from various types of discontinuities, which can vary from extremely small cracks to larger weld or fatigue cracks.
Stress Level (∂) Tensile stress (nominal, residual or both) are necessary for brittle fractures to occur.
Linear Elastic Fracture Mechanics is an analytical procedure that relates the stress field magnitude and distribution in the vicinity of a crack tip to the nominal stress applied to the structure; to the size, shape and orientation of the crack; and to the material properties.
(A) Brittle fracture is the type of catastrophic failure in structures that usually occurs without prior plastic deformation and at extremely high speeds
(1) Bell, E.T. “Men of Mathematics” Simon & Schuster NY (1937)
(2) Griffith, A.A. “The Phenomena of Rupture and Flow in Solids” Philosophical Transactions of the Royal Society of London, A221, pp. 163-197 (1921); and “The Theory of Rupture” Proceedings of the First International Conference of Applied Mechanics, Delft (1924)
(3) Irwin, G.R. “Fracture Dynamics” Fracturing of Metals, American Society for Metals, Cleveland pp. 147-166 (1948)
(4) Shank. M.E. “A Critical Review of Brittle Failure in Carbon Plate Steel Structures Other Than Ships” Ship Structure Committee Report, Serial No. SS-65, National Academy of Sciences – National Research Council, Washington, DC (1953) (Also reprinted as a Welding Research Council Bulletin No. 17)
(5) Parker, E.R. “Brittle Behavior of Engineering Structures” prepared for the Ship Structure Committee under the General Direction of the Committee on Ship Steel – National Academy of Sciences, National Research Council, John Wiley, NY (1957)
(6) Kanninen, M.F., Popelar, C.H. “Advanced Fracture Mechanics” Oxford University Press, NY (1985)
(7) Barsom, J.M., Rolfe, S.T. “Fracture & Fatigue Control in Structures – Applications of Fracture Mechanics” 2nd Ed., Prentice-Hall, NJ (1987)
Fracture Mechanics Resources
Bill O’Donnell, Sr. has published more than 100 papers in professional journals in the areas of stress analysis methods, fracture, creep rupture, buckling and corrosion fatigue life evaluation methods.
O’Donnell Consulting performs design, analysis and troubleshooting including corrosion fatigue, flaw sensitivity, crack propagation, creep rupture and brittle fracture analyses.