Page 145 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C003.fm Page 125 Monday, May 23, 2005 5:42 PM

Elastic-Plastic Fracture Mechanics 125

For load control, C = ∞, and the second term in Equation (3.52) vanishes:
m
 dJ  =   J ∂ 
 da   a ∂  
∆ T P
For displacement control, C = 0, and ∆ = ∆. Equation (3.52) is derived in Appendix 2.2 for the
T
m
linear elastic case.
The conditions during stable crack growth can be expressed as follows:
J J = R (3.53a)

and
T app ≤ T R (3.53b)

Unstable crack propagation occurs when
T app > T R (3.54)

Chapter 9 gives practical guidance on assessing structural stability with Equation (3.50) to
Equation (3.54). A simple example is presented below.

EXAMPLE 3.2

Derive an expression for the applied tearing modulus in the double cantilever beam (DCB) specimen
with a spring in series (Figure 3.21), assuming linear elastic conditions.

Solution: From Example 2.1, we have the following relationships:

Pa 2Pa 3
22
J = = G and ∆= G =
BEI 3EI

FIGURE 3.21 Double cantilever beam specimen with a spring in series.