Page 193 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C004.fm Page 173 Thursday, April 21, 2005 5:38 PM

4 Dynamic and

Time-Dependent Fracture

In certain fracture problems, time is an important variable. At high loading rates, for example,
inertia effects and material rate dependence can be significant. Metals and ceramics also exhibit
rate-dependent deformation (creep) at temperatures that are close to the melting point of the
material. The mechanical behavior of polymers is highly sensitive to strain rate, particularly above
the glass transition temperature. In each of these cases, linear elastic and elastic-plastic fracture
mechanics, which assume quasistatic, rate-independent deformation, are inadequate.
Early fracture mechanics researchers considered dynamic effects, but only for the special case
of linear elastic material behavior. More recently, fracture mechanics has been extended to include
time-dependent material behavior such as viscoplasticity and viscoelasticity. Most of these newer
approaches are based on generalizations of the J contour integral.
This chapter gives an overview of time-dependent fracture mechanics. The treatment of this subject
is far from exhaustive, but should serve as an introduction to a complex and rapidly developing field.
The reader is encouraged to consult the published literature for a further background.

4.1 DYNAMIC FRACTURE AND CRACK ARREST

As any undergraduate engineering student knows, dynamics is more difficult than statics. Problems
become more complicated when the equations of equilibrium are replaced by the equations of motion.
In the most general case, dynamic fracture mechanics contains three complicating features that are
not present in LEFM and elastic-plastic fracture mechanics: inertia forces, rate-dependent material
behavior, and reflected stress waves. Inertia effects are important when the load changes abruptly or
the crack grows rapidly; a portion of the work that is applied to the specimen is converted to kinetic
energy. Most metals are not sensitive to moderate variations in strain rate near ambient temperature,
but the flow stress can increase appreciably when the strain rate increases by several orders of magni-
tude. The effect of rapid loading is even more pronounced in rate-sensitive materials such as polymers.
When the load changes abruptly or the crack grows rapidly, stress waves propagate through the material
and reflect off free surfaces, such as the specimen boundaries and the crack plane. Reflecting stress
waves influence the local crack-tip stress and strain fields which, in turn, affect the fracture behavior.
In certain problems, one or more of the above effects can be ignored. If all three effects are
neglected, the problem reduces to the quasistatic case.
The dynamic version of LEFM is termed elastodynamic fracture mechanics, where nonlinear
material behavior is neglected, but inertia forces and reflected stress waves are incorporated when
necessary. The theoretical framework of elastodynamic fracture mechanics is fairly well established,
and practical applications of this approach are becoming more common. Extensive reviews of this
subject have been published by Freund [1–5], Kanninen and Poplar [6], Rose [7], and others. Elas-
todynamic fracture mechanics has limitations, but is approximately valid in many cases. When the
plastic zone is restricted to a small region near the crack tip in a dynamic problem, the stress-
intensity approach, with some modifications, is still applicable.
Dynamic fracture analyses that incorporate nonlinear, time-dependent material behavior are a
relatively recent innovation. A number of researchers have generalized the J integral to account for
inertia and viscoplasticity [8–13].

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