Page 218 - Mechanics of Asphalt Microstructure and Micromechanics

210 Ch a p t e r S i x

6.6.13 Fatigue Cracking
The fatigue crack growth rate in metals:

da m
CK)
= ( Δ
dN (6-229)
K
Δ= K − K
max min

6.7 General Considerations of Inelasticity
in
By extending equation s = E(e − e ) to include various sources of inelastic deformation,
the unified theories based on internal state variables have been proposed. A systematic
description was presented in Lublinar (1992). It is worthwhile to develop a unified the-
ory to describe plasticity, viscoelasticity, viscoplasticty, and continuum damage me-
chanics in a unified format.

Suggested Readings
This chapter is mainly based on the teaching notes of the author. These notes are pre-
pared following the presentations from several excellent textbooks. More specifically,
hyperelasticity is based on Bower (2010); plasticity is based on Bower (2010) and Lub-
liner (1990); viscoelasticity is based on Findley et al. (1989); continuum damage me-
chanics is based on Lemaitre (1992); fracture mechanics is based on Anderson (1995). If
readers need more backgrounds, please read these books. For convenience and connec-
tions, the symbols adopted in this chapter are consistent with those used in these books.
In recent years, quite a few books have been published to address the fundamentals for
asphalt mechanics. They include Creep Mechanics (Betten, 2005), Mechanics of Fatigue
(Bolotin, 1999), Microcontinuum Field Theories (Eringen, 1999), Fatigue of Materials
(Suresh, 1998), and Deformation and Fracture Mechanics of Engineering Materials
(Hertzberg, 1996). Interested readers should try to read these books.

References
Anderson, T.L. (1995). Fracture Mechanics: Fundamentals and Applications. 2nd Edition.
CRC Press, Moscow.
Betten, J. (2005). Creep Mechanics. Springer, Berlin.
Bolotin, V.V. (1999). Mechanics of Fatigue. CRC Press, Moscow.
Bower, F.A. (2010). Applied Mechanics of Solids. CRC Press, Taylor & Francis Group.
Drucker, D.C. and Prager, W. (1952). Soil mechanics and plastic analysis for limit design. Quar-
terly of Applied Mathematics, Vol.10, No.2, pp.157–165.
Eringen, A.C. (1999). Microcontinuum Field Theories. Springer, New York.
Findley, W.N., Lai, J. and Onaran, K. (1989). Creep and Relaxation of Nonlinear Viscoelastic Ma-
terials, with an Introduction to Linear Viscoelasticity. Dover Publications, Inc., New York.
Gotoh, M., (1977a). A theory of plastic anisotropy based on a yield function of fourth order
(plane stress state)-I. International Journal of Mechanical Sciences, Vol.19, No.9, pp.505–512.