Christensen Failure Criterion
Failure criteria for isotropic materials has been a long standing problem. Despite many historical attempts, there have not been any successful general forms that span the range from ductile to brittle materials. A new failure criterion that aims to do so has been recently developed. The isotropic material failure theory by Christensen has a two property form calibrated by the uniaxial tensile and compressive strengths T and C . It is based upon a sequence of seven related archive journal papers, the first of which was published in 1997. The website describing it in considerable detail was started in 2007, and it was first utilized by eFunda in 2008.
The overall failure criterion is composed of two separate subcriteria representing competitive failure mechanisms. when expressed in principal stress components, it is given by :
- Polynomial Invariants Failure Criterion
- Coordinated Fracture Criterion
The geometric form of (1) is that of a paraboloid in principal stress space. The fracture criterion (2) (applicable only over the partial range 0 ≤ T/C ≤ 1/2 ) cuts slices off the paraboloid, leaving three flattened elliptical surfaces on it. The fracture cutoff is vanishingly small at T/C=1/2 but it grows progressively larger as T/C diminishes.
The organizing principle underlying the theory is that all isotropic materials admit a distinct classification system based upon their T/C ratio. The comprehensive failure criterion (1) and (2) reduces to the Mises criterion at the ductile limit, T/C = 1. At the brittle limit, T/C = 0, it reduces to a form that cannot sustain any tensile components of stress.
Many cases of verification have been examined over the complete range of materials from extremely ductile to extremely brittle types. Also, examples of applications have been given. Related criteria distinguishing ductile from brittle failure behaviors have been derived and interpreted.
- ^ a b Christensen, R. M.,(2010),http://www.failurecriteria.com.
- ^ Christensen, R.M. (1997).Yield Functions/Failure Criteria for Isotropic Materials, Pro. Royal Soc. London, Vol. 453, No. 1962, pp. 1473-1491
- ^ Christensen, R.M. (2007), A Comprehensive Theory of Yielding and Failure for Isotropic Materials, J. Engr. Mater. and Technol., 129, 173-181
- ^ eFunda,(2010),http://www.efunda.com/home.cfm.
- ^ S. K. Ha, K. K. Jin and Y. C. Huang,(2008), Micro-Mechanics of Failure (MMF) for Continuous Fiber Reinforced Composites. Journal of Composite Materials, vol. 42, no. 18, pp. 1873-1895.
Wikimedia Foundation. 2010.
Look at other dictionaries:
Micro-Mechanics of Failure — Figure 1. Hierarchy of micromechanics based analysis procedure for composite structures. Micro Mechanics of Failure (MMF) is a newly proposed methodology, providing a more logical explanation of failure mechanism of continuous f … Wikipedia
performing arts — arts or skills that require public performance, as acting, singing, or dancing. [1945 50] * * * ▪ 2009 Introduction Music Classical. The last vestiges of the Cold War seemed to thaw for a moment on Feb. 26, 2008, when the unfamiliar strains … Universalium
Pedophilia — This article is primarily about the sexual interest in prepubescent children. For the sexual act, see Child sexual abuse. For the primary sexual interest in 11–14 year old pubescents, see Hebephilia. For mid to late adolescents (15 19), see… … Wikipedia
Denmark — /den mahrk/, n. a kingdom in N Europe, on the Jutland peninsula and adjacent islands. 5,268,775; 16,576 sq. mi. (42,930 sq. km). Cap.: Copenhagen. * * * Denmark Introduction Denmark Background: Once the seat of Viking raiders and later a major… … Universalium
Darth Vader — Anakin Skywalker / Darth Vader Star Wars character … Wikipedia
Nichiren — (日蓮) A statue of Nichiren outside Honnoji in the Teramachi District of Kyoto. School Mahayana, Nichiren Personal … Wikipedia
statistics — /steuh tis tiks/, n. 1. (used with a sing. v.) the science that deals with the collection, classification, analysis, and interpretation of numerical facts or data, and that, by use of mathematical theories of probability, imposes order and… … Universalium
Idealism (italian) and after — Italian idealism and after Gentile, Croce and others Giacomo Rinaldi INTRODUCTION The history of twentieth century Italian philosophy is strongly influenced both by the peculiar character of its evolution in the preceding century and by… … History of philosophy
Rheumatoid arthritis — Classification and external resources A hand affected by rheumatoid arthritis ICD 10 M … Wikipedia
Media and Publishing — ▪ 2007 Introduction The Frankfurt Book Fair enjoyed a record number of exhibitors, and the distribution of free newspapers surged. TV broadcasters experimented with ways of engaging their audience via the Internet; mobile TV grew; magazine… … Universalium