Page 389 - Mechanical Behavior of Materials

390 Chapter 8 Fracture of Cracked Members

Comment Due to the state of plane stress in (b), the use of K Ic is conservative. The actual
K c may be somewhat higher than K Ic , and the a c value therefore larger than estimated.

8.8 DISCUSSION OF FRACTURE TOUGHNESS TESTING

The preceding discussion on plastic zone size and the condition of plane strain permits us to now
engage in a more detailed discussion of certain aspects of fracture toughness testing.

8.8.1 Standard Test Methods

Test methods for evaluating fracture toughness on the basis of LEFM include requirements similar
to Eq. 8.40 to qualify a test result as a valid measurement of K Ic . For example, ASTM Standard
No. E399, which applies to metallic materials, explicitly requires that Eq. 8.40 be met for (b − a),
and then the remaining items in Eq. 8.40 are included by recommending that a/b and t/b be near
0.5, and by using specimen geometries where h/b is around 0.5 or greater.
The force versus displacement (P-v) behavior in a fracture toughness test may be similar to
Fig. 8.28, Types I, II, or III. Since the plastic zone is required by Eq. 8.40 to be quite small, any
nonlinearity in the P-v curve must be due to growth of the crack. A smooth curve as in Type I
is caused by a steady tearing type of fracture called slow-stable crack growth. In other cases, the
crack may suddenly grow a short distance, which is called a pop-in (II), or it may suddenly grow to
complete failure (III).
The K Ic test standard for metals handles the problem of defining the beginning of cracking by
drawing a line with a slope that is 95% as large as the initial elastic slope (O-A) in the test. A force
P Q is identified as the point where this line crosses the P-v curve, or as any larger peak value prior
to the crossing point. The stress intensity factor is then evaluated with the use of P Q and the initial
crack length:

K Q = f (a i , P Q ) (8.41)

If this K Q satisfies Eq. 8.40, it is then considered to be a valid K Ic value. However, there is one
additional requirement designed to assure that the test involves sudden fracture with little slow-
stable crack growth, specifically that the maximum load reached cannot exceed P Q by 10%.
If the plane strain condition is not satisfied in the test, then it is necessary to use a larger test
specimen so that the comparisons of Eq. 8.40 are more favorable. As a result, quite large specimens
may be required for materials with relatively low yield strength but high fracture toughness. For
example, the large compact specimen of Fig. 8.29 (with b = 61 cm) was required to obtain the
◦
K Ic value plotted for 10 C for A533B steel in Fig. 8.33.
A successful fracture toughness test requires an initially sharp flaw, called a precrack, that is
equivalent to a natural crack; otherwise the measured K Ic will be artificially elevated. For metals,
this is achieved by using cyclic loading at a low level to start a natural fatigue crack at the end of a
machined slot. For plastics (polymers), the usual procedure is to press a razor blade into the material
at the end of the machined slot.