Page 389 - Forensic Structural Engineering Handbook

11.20 MATERIAL-SPECIFIC FORENSIC ANALYSES

and
⎛ P +( P +9 P ) ⎞
2
2 0.5
L = ⎜ b b m ⎟
⎝ ( 31 − ) α ⎠
c (11.6)
α =
W
where P = primary membrane stress
m
P = primary bending stress
b
Successful application of these solutions also requires the fracture toughness and ten-
sile properties for the structure. Accordingly, coupons should be removed from critical
22
21
locations for material testing. While tensile testing (ASTM A370 or E8 ) is relatively
inexpensive and tensile properties are only secondarily dependent upon temperature, frac-
ture toughness testing is considerably more complex and expensive, and is strongly depen-
dent on temperature. As previously mentioned, an alternative and significantly simpler
and less expensive methodology for determining fracture toughness is the use of small
23
specimen CVN impact test results conducted per ASTM E23. In this regard, many inves-
tigators use empirical correlations between CVN impact data and more formal fracture
mechanics tests to establish approximate values of fracture toughness, K , to use in cal-
C
culations of critical flaw sizes in structures. This methodology also has its complications
since it is necessary to compensate for strain rate effects and constraint effects related to
thickness, but it is an invaluable tool for assessing fracture conditions when only CVN
toughness data are available. This methodology is also well described in Refs. 3 and 8 and
is as follows:
K and K can be estimated from CVN test results according to the following procedure: 8
1c
1d
1. Perform standard CVN impact testing from the lower shelf to the transition temperature
regime
2. For each test temperature, calculate K using the following empirical correlation:
1d
K = 5(CVN E ) (11.7)
2
1
d
where K is the dynamic fracture toughness (psi√in), E is the modulus of elasticity
1d
(psi), and CVN is the absorbed energy (ft-lb) from the CVN tests.
3. Determine the temperature shift (T shift , °F) between K and K using the following cor-
1d
1c
relations:
T shift = 215 – 1.5·σ Y for 36 ksi ≤σ ≤ 140 ksi (11.8)
y
T = 0 for σ > 140 ksi
shift y
where σ is the material yield strength in ksi.
y
4. Determine K as a function of temperature by shifting K values at each temperature
1c 1d
obtained in step 3.
This procedure is reasonably conservative and limited to the lower end of CVN transi-
tion curve where CVN values in ft-lb are less than about half of the yield strength in ksi.
Since notch acuity and loading rate do not significantly affect fracture toughness in the
8
upper shelf and upper transition regimes, the following CVN-K relationship can be used
1c