The use of fracture mechanics for predicting fracture and fatigue crack growth in metals is presented

Hudson, C. M.

English

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ASPECTS OF FRACTURE MECHANICS IN CRYOGENIC MODEL DESIGN 
PAKT I -FUNDAMENTALS OF FRACTUREMECHANICS 
C. Michael Hudson 
NASA Langley Research Center 
Hampton, Virginia 
31 
https://ntrs.nasa.gov/search.jsp?R=19830010480 2020-03-22T00:00:10+00:00Z
This presentation provides a fundamental introduction to the use of fracture 
mechanics for predicting fracture and fatigue crack growth in metals. First, 
consider figure 1. The stresses Co,, ox, 
crack tip can be defined in terms of 
TV) at any point in the vicinity of a 
three parameters. These parameters are (1) r, 
the distance from the crack tip to the point under consideration; (2) a function of 
6, the angle between the x axis and r; and (3) KI, the stress intensity factor. 
The term KI is given by 
KI= S/G (1) 
where S is the applied stress and a is one-half the length of the crack, for 
the following stress and configuration conditions: 
1. A through-the-thickness crack 
2. An infinite-width plate 
3. A uniformly distributed stress 
(Considerably more complex relationships apply for other configurations and stress 
conditions.) 
When the failure process occurs under plane strain conditions, the value of 
KIC tends to remain constant for a given material and temperature. This constant 
value is defined as the plane strain fracture toughness of the material. For the 
specimen configuration shown in figure 2, KIC can be defined as 
K Ic = SJna critical (2) 
Once K has been determined, it can be used to predict the failure of cracked 
struct&s under plane strain conditions. (Considerably more complex procedures 
are required for predicting failure under plane stress conditions.) For example, 
if both KIc and the crack size have been determined for a certain component, the 
stress required to fail that component can be calculated. Similarly, the critical 
flaw size can be calculated if both KIc and the applied stress are known. 
Many factors can affect the value of KIc for a given material. One of the 
most dominating factors is temperature. For many materials, the value of KIc 
drops precipitously with decreasing temperature. Figure 3 shows a generally linear 
drop in K 
6" 
with decreasing temperature for 18 Ni-(250) maraging steel (ref. 1). 
Figure 4 s ows a rapid drop from approximately -75'F to -2OOOF (the transition 
temperature region), followed by a more gradual drop for temperatures below -2OOOF 
(ref. 1). (The data in figure 4 are from tests on A517 Grade F steel.) In both 
cases, the reduced values of KIc indicate that for a given stress condition, the 
critical flaw size decreases with decreasing temperature. This in turn indicates 
that greater care must be taken in inspecting structures for cryogenic applications. 
Next, consider the fatigue crack growth aspects of fracture mechanics. Basic 
fatigue crack growth data can be generated using the center-cracked specimen shown 
in figure 5. This specimen is a flat sheet specimen containing a notch in the 
center. (Other specimen configurations are also used.) When this specimen is 
subjected to a cyclic loading, such as that shown in figure 6, a fatigue crack will 
initiate at the two ends of the notch. With continued cyclic loading, these cracks 
will grow towards the edges of the specimen. Figure 7 shows the variation of crack 
length against cycles for the loading condition shown in figure 6. The slope of 
32 
this fatigue crack growth curve at any point is defined as the fatigue crack growth 
rate, da/dN. 
The stress intensity range AK can also be defined for any point on the 
fatigue crack growth curve. This stress intensity range is given by 
AK = & (Smax - s min > (3) 
for the specimen in figure 5 when that specimen has an effectively infinite width. 
The terms Smax and Smin are defined in figure 6. 
Once da/dN and AK have been calculated for a series of points along the 
fatigue crack growth curves, they can be plotted against each other, as shown in 
figure 8 (ref. 2). The correlation of these factors is quite good. 
A relationship developed by Forman et al. (ref. 3) has been found to fit the 
plots of da/dN against AK quite well. This relationship is given by 
da/dN = CAKn (1 - R)KI~ - AK 
for plane strain conditions. In equation (4), the terms C and n are empirical 
constants and R is defined by 
R = 'min"max 
This R term can have a significant effect on fatigue crack growth. 
Figure 9 (ref. 2) shows plots of da/dN against AK for various R values. The 
data for a given R value fall into discrete scatterbands. However, the scatterbands 
for different R values are not coincident. Generally, the higher the R value 
for a given value of AK, the higher the rate of fatigue crack growth. Forman's 
equation (ref. 3) fit each of these scatterbands quite well with one coefficient and 
one exponent (See fig. 9.) Thus Forman's equation accounts for the R value 
effect quite well, 
Once the coefficient and exponent have been determined, equation (4) can be 
numerically integrated to predict the life of cracked components. Figure 10 
presents the results of one set of such predictions. For this set, the coefficient 
and exponent were calculated using data from tests on center-cracked specimens. 
Equation (4) was then used to predict the number of cycles required to grow surface 
cracks from their initial flaw sizes to failure (ref. 4). Tests were then conducted 
on specimens having these flaw sizes, and the actual fatigue lives were determined. 
Figure 10 shows the ratios of the tests lives to predicted lives. These ratios 
ranged from 0.51 to l.S4. Considering that the normal scatter in fatigue crack 
growth rates may range from a factor of 2 to 4 under identical loading conditions, 
these ratios are quite good. 
33 
REFERENCES 
1. Barson, J. M.; and Rolfe, S. T.: Correlations Between KIc and Charpy V-Notch 
Test Results in the Transition Temperature Range. Impact Testing of Metals, 
ASTM STP 466, 1970, pp. 281-302. 
2. Hudson, C. Michael: Effect of Stress Ratio on Fatigue Crack Growth in 7075-T6 
and 2024-T3 Aluminum-Alloy Specimens. NASA TN D-5390, 1969. 
3. Forman, R. G.; Kearney, V. E.; and Engle, R. M.: Transactions, American 
Society of Mechanical Engineers. Series D, J. of Basic Engineering, vol. 89, 
no. 3, Sept. 1967, pp. 459-464. 
4. Hudson, C. M.; and Lewis, P. E.: NASA Langley Research Center's Participation 
in a Round-Robin Comparison Between Some Current Crack-Propagation Methods. 
Part-Through Crack Fatigue Life Prediction, J. B. Chang, ed., ASTM STP 687, 
1979, pp. 113-128. 
34 
Figure l.- Stress characterization in the vicinity of a crack tip. 
-i-k- 2a 
Figure 2.- Stress intensity solution for a through-the-thickness 
crack in an infinite-width plate. 
35 
60- 
40- 
20- 
0- 
-1 
I I I I I I I I 
I50 - 300 -250 -200 -150 -100 -50 0 50 
TEST TEMPERATURE, F 
Figure 3.- Variation of Klc with temperature for 18 Ni-(250) 
maraging steel. (From ref. 1.) 
TEST TEMPERATURE, F 
Figure 4.- Variation of Klc with temperature for ASTM A517 
Grade F steel. (From ref. 1.) 
36 
2 Holes 
W 13 Dia. 7 
Stress 
S max 
S min 
, 
-&LA Ei o 4(l& . 
. 
WI2 
t ‘- 
w/2 ~ 
min c-w, min. 
C-W, min. min 
I 0. g,lug I 
T 
W 
-I- 
Figure 5.- Center-cracked tension specimen. 
Time 
Figure 6.- Variation of stress with time. 
37 
Crack 
Length 
Number of Cycles 
Figure 7.- Variation of crack length with number of cycles. 
lo- 
lo-; 
10-z 
Rate. 
in/cycle 
lo-’ 
lo-5 
1o-6 
10 
1- 
I-
1 
A k, MNh3i2 
IO 20 30 40 
1 
0 
C 
:o 0 
Q 00 O 0 
g&O0 
I 
I 
- I’ 
J II 
0 5 10 15 20 
Ak, ksi-in”’ 
25 30 35 
O5 
o4 
Rate, 
M!/CyCle 
Figure 8.- Variation of da/dN with AK. (From ref. 2.) 
38 
Ak,MN/m3’2 Ak ,MN/mY2 A k ,MN/m3’2 
IO 20 30 40 0 I IO 70 30 40 0 IO 20 50 40 
10-3 
Rate, 
idcycle 
IO-.+ 
Ak, ksi-in”’ Ak. ksi-in”’ 
7075-T6 alloy 
lo” 
A=0.33 
/ i 
AA 
IO” 
AA 
A Rate ^- ,r.,r 1, 
-10" 
R=O.E 
- IO” 
Rate, 
nm/cycle 
l/IL 
0 5 IO I5 
Ak. ksi-in”’ 
Figure 9.- Variation of da/dN with AK for various R values. 
(From ref. 2.) 
39 
II I II II II n IIIIlllllllllIIllI 
23-10 1.00 
23-12 I. IS 
23-13 Ii3 
23-14 1.05 
23-16 0.65 
23-17 0.60 
23-18 1.26 
23-76 0.51 
37-2 1.84 
37-3 0.70 
TEST UVEWPREDICTED UVES 
Figure lO.- Ratios of test lives to predicted lives. 
40 


Aspects of fracture mechanics in cryogenic model design. Part 1: Fundamentals of fracture mechanics

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