Page 108 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C02.fm Page 88 Thursday, April 14, 2005 6:28 PM

88 Fracture Mechanics: Fundamentals and Applications

FIGURE 2.60 Interaction between two identical parallel through-wall cracks in an infinite plate. Taken from
Murakami, Y., Stress Intensity Factors Handbook. Pergamon Press, New York, 1987.

APPENDIX 2: MATHEMATICAL FOUNDATIONS OF LINEAR
ELASTIC FRACTURE MECHANICS

A2.1 PLANE ELASTICITY

This section catalogs the governing equations from which linear fracture mechanics is derived. The
reader is encouraged to review the basis of these relationships by consulting one of the many
textbooks on elasticity theory. 4
The equations that follow are simplifications of more general relationships in elasticity and are
subject to the following restrictions:

• Two-dimensional stress state (plane stress or plane strain)
• Isotropic material
• Quasistatic, isothermal deformation
• Absence of body forces from the problem (In problems where body forces are present,
a solution can first be obtained in the absence of body forces, and then modified by
superimposing the body forces.)

Imposing these restrictions simplifies crack problems considerably, and permits closed-form solu-
tions in many cases.

4 This appendix is intended only for more advanced readers, who have at least taken one graduate-level course in the theory
of elasticity.