Failure Surface Graphics in Stress Space

Richard M. Christensen — Mon, 18 May 2009 12:11:20 -0400

A new section has been added to the website on failure criteria for engineering materials. This new work displays many different three-dimensional computer graphics of failure criteria surfaces in stress space. The full range of isotropic materials are covered from ductile metals to brittle ceramics and glasses and beyond. All of these computer generated graphics can be seen at www.failurecriteria.com/failuresurfacegr.html.

The limiting case of ductile behavior is that of the Mises criterion with its cylindrical failure surface representation. A related historical uncertainty has always involved the search for and the identification of the opposite and counter-balancing limiting case, that of the brittle limit. The mathematical form of the present physical theory admits and gives this limiting case at the brittle end of the scale. The corresponding three dimensional graphic form for this limiting case is explicitly shown. In principal stress space the brittle limit failure surface form is composed of a triangular pyramid shape near the origin, which transitions into a paraboloid, with corners between the two competing modes of failure, along with other crucial features.

The entire theory and all of the graphical forms are completely calibrated by only two failure properties, the uniaxial tensile and compressive strengths. The usage of the two uniaxial strengths is far more efficient, effective, and general than are forms combining the shear strength with any other strength measure(s). Many other related matters also are covered at www.FailureCriteria.com.

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Failure Surface Graphics in Stress Space