Two quantitative models based on experimentally observed fatigue damage processes have been made: (1) a model of low cycle fatigue life based on fatigue crack growth under general-yielding cyclic loading; and (2) a model of accelerated fatigue crack growth at elevated temperatures based on grain boundary oxidation. These two quantitative models agree very well with the experimental observations

Liu, H. W.

English

NASA Technical Reports Server

~~ 
NASA Contractor Report 182 129 
The Analysis of Fatigue Crack Growth 
Mechanism and Oxidation and Fatigue 
Life at Elevated Temperatures 
8 8- 2 29 87 (A1SA-CB-182129) THE AIJALYSIS OF F U ’ L G U E  
CRACK G R O U T f i  f!ECEANISPI AND O X I D A T I O N  AND 
PBTIGUE LIFE AT ELEVATED TEHPERATURES F i n a l  
Contractor Report [ S y r a c u s e  Univ. 1 12 p Unclas  CSCL 1 1 P  63/26 0145919 
H.W. Liu 
Syracuse University 
Syracuse, New York 
May 1988 
c 
Prepared for 
Lewis Research Center 
Under Grant NAG3-348 
National Aeronautics and 
Space Administration 
https://ntrs.nasa.gov/search.jsp?R=19880013603 2020-03-20T06:13:05+00:00Z
THE ANALYSIS OF FATIGUE CRACK GROWTH MECHANISM 
AND 
OXIDATION AND FATIGUE LIFE AT ELEVATED TEWERATUKES 
H . W .  Liu 
Department o f  Hechanica l  and Aerospace Engineer ing  
Syracuse  U n i v e r s i t y  
Syracuse ,  NY 13244 
Sumnary 
Two q u a n t i t a t i v e  models based on e x p e r i m e n t a l l y  observed  f a t i g u e  
damage p r o c e s s e s  have been made: (1) a model of low c y c l e  f a t i g u e  l i f e  
based on f a t i g u e  c r a c k  growth under  g e n e r a l - y i e l d i n g  c y c l i c - l o a d i n g ,  and 
(2) a model of accelerated f a t i g u e  c r a c k  growth at e l e v a t e d  temperatures 
based on g r a i n  boundary o x i d a t i o n .  These two q u a n t i t a t i v e  models agree 
v e r y  well w i t h  t h e  expe r imen ta l  o b s e r v a t i o n s .  
FINAL REPORT 
The Analysis of Fatigue Crack Growth Mechanism and 
Oxidation and Fatigue Life at Elevated Temperatures 
Grant Number: NAG 3-348  
Fundinq Period: October 30, 1982 to November 31, 1987 
Principal Investigators: Hao-wen Liu and Yoshiki Oshida 
Monitoring Scientist: Jack Telesman 
Objective: 
Fatigue life consists of fatigue crack nucleation and propagation 
periods. In order to predict fatigue life accurately, the methodology 
for the quantitative assessments of these two fatigue damage processes 
has to be developed. 
The objectives of this research program are to analyze low cycle 
fatigue life in terms of fatigue crack propagation, to study grain 
boundary oxidation and its effects on fatigue crack nucleation and 
propagation, and to study the crystal orientation effects on crack tip 
slip systems and the shear-decohesion fatigue crack growth mechanism. 
With a thorough understanding of the crack nucleation and propagation 
processes based on the physical damage mechanisms, more accurate 
fatigue life prediction will be possible. 
Significant Accomplishments: 
Fatigue life consists of crack nucleation and propagation periods. 
For high cycle fatigue, stage I shear fatigue crack nucleation and 
growth consists of the major portion of the total fatigue life. On the 
other hand, low cycle fatigue life consists of primarily tensile crack 
growth. At elevated temperatures, oxidation might accelerate both 
2 
processes of crack nucleattion and propagation. We have made 
substantial progress in the analysis of low cycle fatigue life, in the 
study of grain boundary oxidation and its effects on crack nucleation 
and propagation, and in the analysis of shear fatigue crack growth. 
At the room temperature, the crack initiation period is only a 
small portion of the total low cycle fatigue life. Hence, low cycle 
fatigue life can be analyzed entirely in terms of fatigue crack 
propagation. 
Fatigue crack growth under a general-yielding cyclic-loading was 
found to be related AJ and AJ was found to be related to the 
deformation work density. The analysis leads to a simple power law 
relationship between low cyclic fatigue life and the cyclic deforamtion 
work density. The low cycle fatigue life data of a number of materials 
agree very well with the non-linear fracture mechanics analysis. 
The deformation work density, in turn, is related to the applied 
stress range and the imposed cyclic strain range. It is shown that the 
Manson-Coffin low cycle fatigue law can be derived by a rational 
analysis based on fatigue crack growth under a general-yielding cyclic- 
loading. (References: 4 ,  7, 8, 11). 
Dr. Liu was invited to present their recent results on the low 
cycle fatigue life analysis at the Second International Conference on 
Low Cycle Fatigue in Munich, FRG, in September 1987. 
Two primary damage mechanisms of high temperature low cycle 
fatigue are creep and oxidation. Both of these two mechanisms are 
thermally activated as illustrated in the figure. 
The question is not which of these two mechanisms is the dominant 
one. The more pertinent question is rather which of these two 
mechanisms is dominant in the high temperature region and which one is 
dominant in the low temperature region. Quantitative studies on both 
creep and oxidation damage mechanisms are necessary in order to answer 
3 
t h i s  q u i s t i o n .  
In R 
The schematic plot of two rate processes. 
A q u a n t i t a t i v e  s t u d y  on g r a i n  boundary o x i d a t i o n  and  i t s  e f f e c t s  
on f a t i g u e  l i f e  w a s  conducted .  (Refe rences :  3 ,  5, 6 ,  10, 12) 
Gra in  boundary i s  a p a t h  of  r a p i d  d i f f u s i o n .  Gra in  boundary 
o x i d a t i o n  is c o n t r o l l e d  by t h e  d i f f u s i o n  of  oxygen a l o n g  t h e  g r a i n  
boundary.  The r a p i d  oxygen d i f f u s i o n  c a u s e s  a deep g r a i n  boundary 
o x i d a t i o n  p e n e t r a t i o n ,  and  t h e  f a s t  o x i d a t i o n  p e n e t r a t i o n  c a u s e s  t h e  
a c c e l e r a t e d  i n t e r g r a n u l a r  f a t i g u e  f r a c t u r e s  a t  h i g h  t e m p e r a t u r e s .  
Two d i f f e r e n t  g r a i n  boundary o x i d e  morphologies  w e r e  found:  t h e  
pancake t y p e  and  t h e  cone t y p e .  The l a r g e r  and deeper pancake t y p e  i s  
more damaging. 
Gra in  boundary o x i d a t i o n  p e n e t r a t i o n ,  a,, i n  a n i c k e l  base  
s u p e r a l l o y  (TAZ-8A) w a s  measured a s  a f u n c t i o n  o f  t h e  o x i d a t i o n  
t empera tu re ,  T ,  and t h e  exposure  t i m e ,  t .  
4 
am = a t  n exp ( - E )  Q 
Q = a p p a r e n t  a c t i v a t i o n  energy  
The c o e f f i c i e n t  of c o r r e l a t i o n  is  0 . 9 6  f o r  144 d a t a  p o i n t s .  
T h i s  q u a n t i t a t i v e  r e l a t i o n s h i p  f o r  t h e  g r a i n  boundary o x i d a t i o n  
k i n e t i c s  can  be used  t o  s t u d y  t h e  a c c e l e r a t e d  f a t i g u e  crack n u c l e a t i o n  
and f a t i g u e  c r a c k  growth r a t e  a t  e l e v a t e d  t e m p e r a t u r e s .  
G r a i n  boundary ox ide  p e n e t r a t i o n  v a r i e s  w ide ly .  Th i s  w i d e  
v a r i a t i o n  of o x i d e  p e n e t r a t i o n  r a t e  may c a u s e  t h e  v a r i a t i o n s  i n  t h e  
r a t e s  of c r a c k  n u c l e a t i o n  and growth and t h e  sca t te r  of  t h e  f a t i g u e  
l i f e  d a t a .  
The  s t a t i s t i c a l  s c a t t e r  of t h e  g r a i n  boundary o x i d e  p e n e t r a t i o n  
d e p t h  f o l l o w s  t h e  W e i b u l l ' s  d i s t r i b u t i o n  law. The e m p i r i c a l  
d i s t r i b u t i o n  law can  b e  used  t o  e x t r a p o l a t e  t h e  d a t a  o b t a i n e d  i n  a 
l a b o r a t o r y  u s i n g  s m a l l  samples  t o  a much l a r g e r  s t r u c t u r a l  component i n  
s e r v i c e .  
When an  ox ide  r e a c h e s  a c r i t i c a l  s i z e ,  it w i l l  f r a c t u r e .  A g r a i n  
boundary ox ide  c r a c k  becomes a f a t i g u e  c r a c k  n u c l e u s  o r  a p r e - c r a c k .  
The p re -c rack  w i l l  s h o r t e n  t h e  c r a c k  n u c l e a t i o n  p e r i o d  and  t h e  t o t a l  
f a t i g u e  l i f e .  T h i s  r e d u c t i o n  i n  n u c l e a t i o n  l i f e  w i l l  be s u b s t a n t i a l ,  
i f  t h e  c y c l i c  f r equency  is  v e r y  low, t h e  t e m p e r a t u r e  i s  v e r y  h igh ,  and 
t h e  o x i d a t i o n  exposure  t i m e  is  ve ry  long .  
I t  h a s  been found t h a t  t h e  r a t i o  between t h e  f a t i g u e  l i f e  of a 
p r e c r a c k e d  specimen and t h e  f a t i g u e  l i f e  of a smooth specimen i s  a 
f u n c t i o n  of t h e  p re -c rack  s i z e .  
N f i / N f o  = f (p re -c rack  s i z e )  
5 
N f i  = f a t i g u e  l i f e  of  a pre-cracked  specimen 
N f o  = f a t i g u e  l i f e  of  a smooth specimen 
For a g i v e n  p re -c rack  s i z e ,  t h e  r a t i o  w a s  found t o  be c o n s t a n t .  The 
f u n c t i o n a l  r e l a t i o n s h i p  between t h e  r a t i o  and t h e  p re -c rack  s i z e  can be 
found e m p i r i c a l l y .  
The w i d e  v a r i a t i o n s  i n  o x i d a t i o n  p e n e t r a t i o n  and  o x i d e  c r a c k  s i z e  
may c a u s e  a w i d e  v a r i a t i o n  i n  N f i  and i n  t h e  t o t a l  f a t i g u e  l i f e .  A 
large s t r u c t u r a l  component h a s  a h i g h  p r o b a b i l i t y  of hav ing  a l a r g e  
o x i d e  c r a c k  and a s h o r t  f a t i g u e  l i f e .  The empir ica l  r e l a t i o n  of 
Equat ion  ( 2 )  t o g e t h e r  w i th  t h e  g r a i n  boundary o x i d e  p e n e t r a t i o n  
k i n e t i c s  and  t h e  Weibul l  d i s t r i b u t i o n  would be able t o  predict t h e  
e f f e c t  of  t h e  o x i d e  crack on t h e  n u c l e a t i o n  l i f e  o f  a large s t r u c t u r a l  
component. 
The b a s i c  concept  of  g r a i n  boundary o x i d a t i o n  k i n e t i c s  w a s  used  t o  
a n a l y z e  f a t i g u e  crack growth r a t e  a t  t h e  e l e v a t e d  t e m p e r a t u r e s .  A h igh  
t e m p e r t u r e  f a t i g u e  c r a c k  growth model based on i n t e r m i t t e n t  micro- 
r u p t u r e s  of g r a i n  boundary o x i d e s  was proposed .  The model i s  
c o n s i s t e n t  w i th  t h e  obse rved  i n t e r g r a n u l a r  f r a c t u r e  and t h e  observed  
i n v e r s e  r e l a t i o n s h i p  between c r a c k  growth ra te  and  t h e  c y c l i c  f requency  
i n  t h e  l o w  f r equency  r e g i o n .  (References :  1, 5, 6 ,  9, 10). I n  t h e  
h i g h  f r equency  r e g i o n ,  f a t i g u e  f a i l u r e  i s  mixed i n t e r g r a n u l a r  and 
t r a n s g r a n u l a r  o r  t r a n s g r a n u l a r  e n t i r e l y .  
The f a t i g u e  c r a c k  growth i n  large g r a i n  p o l y c r y s t a l s  and s i n g l e  
c r y s t a l s  h a s  been i n v e s t i g a t e d .  The s h e a r  decohes ion  mechanism of  
f a t i g u e  c r a c k  growth h a s  been proposed  and obse rved  by  a number o f  
r e s e a r c h e r s .  Shear  decohes ion  i s  caused  by d i s l o c a t i o n  s l i p  a t  a c r a c k  
t i p .  Shear  decohes ion  i s  caused  by t h e  f o r c e  a c t i n g  on t h e  
d i s l o c a t i o n s  a t  a c r a c k  t i p  and t h e  f o r c e  on a d i s l o c a t i o n  is  r e l a t e d  
t o  t h e  r e s o l v e d  s h e a r  stresses on t h e  s l i p  p l a n e .  The re fo re ,  it i s  
reasonab le  t o  e x p e c t  t h a t  t h e  d u c t i l e  f a t i g u e  crack growth mechanism of 
s h e a r  decohes ion  i s  r e l a t e d  t o  t h e  r e s o l v e d  s h e a r  stresses on t h e  s l i p  
6 
p l a n e s  i n  t h e  c r a c k  t i p  r e g i o n .  I t  w a s  found t h a t  t h e  c r a c k  p l a n e  i n  a 
c r y s t a l  can be de te rmined  by t h e  s l i p  p l a n e s  w i t h  t h e  h i g h e s t  r e s o l v e d  
s h e a r  stress i n t e n s i t y  c o e f f i c i e n t  . T h i s  o b s e r v a t i o n  i n d i c a t e s  
s t r o n g l y  t h a t  f a t i g u e  crack growth i n  large g r a i n s  and  s i n g l e  c r y s t a l s  
can  be ana lyzed  i n  t e r m s  on t h e  crack t i p  r e s o l v e d  s h e a r  stress 
i n t e n s i t y  c o e f f i c i e n t .  (References :  2 ,  7 ,  13) 
I n  conc lus ion ,  c o n s i d e r a b l e  p r o g r e s s  has  been made on t h e  
q u a n t i t a t i v e  s t u d i e s  based on t h e  p h y s i c a l  damage mechanisms. Such 
s t u d i e s  w i l l  lead t o  a q u a n t i t a t i v e  damage assesment  and  an  improved 
l i f e  p r e d i c t i o n  methodology. 
7 
S t u d e n t s  Suppor ted :  
N a m e  Dates 
Gerhard Maurer:  11 /1 /82  - 5 /1 ,83  M.S. 
Qi Chen: 5 / 1 / 8 3  - p r e s e n t  M.S. 
Degree 
I n  a d d i t i o n ,  t h e  g r a n t  h a s  s u p p o r t e d  50% of  D r .  Yoshiki  O s h i d a ' s  
t i m e  f o r  a period of two y e a r s  and  M r .  Zheng Minzhong f o r  h i s  computer 
t i m e  and manusc r ip t  p r e p a r a t i o n  and  p u b l i c a t i o n  c o s t s .  
P u b l i c a t i o n s :  
Thus far twe lve  papers and NASA report s  have been publ i shed  and 
one i s  i n  p r e p a r a t i o n .  The r e p r i n t s  of t h e  p a p e r s  have been s e n t  t o  
t h e  m o n i t o r i n g  s c i e n t i s t  o f  t h e  g r a n t  a s  t h e y  w e r e  p u b l i s h e d .  
1. OSHIDA, Y . ,  and  L I U ,  H . W .  Oxidation and Low Cycle Fatigue Life 
Prediction, Proceed ings  of  Hot S e c t i o n  Technology Conference ,  NASA 
L e w i s  Research C e n t e r ,  C leve land  Ohio, O c t .  1984. 
2 .  MAURER, G . ,  and  L I U ,  H . W .  Morphological Study o f  Near Threshold 
Fatigue Crack Growth in a Coarse Grain Aluminum Alloy, Proceed ings  
of t h e  Second I n t e r n a t i o n a l  Conference on F a t i g u e  and  F a t i g u e  
Thresho ld ,  Birmingham, England, September 1984. 
Lives at Elevated Temperatures, NASA C o n t r a c t  Report 174639, March 1984. 
3 .  L I U ,  H . W . ,  and  OSHIDA, Y .  Literature Survey on Oxidation and Fatigue 
4 .  ZHENG, MINZHONG,  a.nd L I U ,  H . W .  Crack Tip Field and Fatigue Crack Growth 
in General Yielding and Low Cycle Fatigue, NASA Cont rac t  Repor t  
174686, S e p t .  1984. 
5 .  OSHIDA, Y . ,  and  L I U ,  H . W .  Grain Boundary Oxide Crack, Oxidation 
Accelerated Fatigue Crack Growth and Fatigue Life, 
Proceed ings  of t h e  40th  Meeting of t h e  Mechanical F a i l u r e s  P r e v e n t i o n  
Group, Symposium on t h e  U s e  of N e w  Technology t o  Imporve Mechanical 
Readiness ,  R e l i a b i l i t y  and  M a i n t a i n a b i l i t y ,  N a t i o n a l  Bureau of 
S t a n d a r d s ,  G a i t h e r s b u r g ,  MD, Cambridge U n i v e r s i t y  Press, A p r i l  1985. 
pp. 287-295 
6 .  L I U ,  H . W .  , and  OSHIDA, Y .  Grain Boundary Oxidation and Oxidation 
Accelerated Fatigue Crack Nucleation and Propagation, Proceed ings  of 
t h e  Minnowbrook Conference on L i f e  P r e d i c t i o n  f o r  High Temperature 
Gas Turb ine  M a t e r i a l s ,  Blue Mountain Lake, NY, Aug. 1985. 
8 
7. 
8. 
9. 
LIU, H.W., Shear Fatigue Crack Growth: A Literature Survey. the 
International J. of Fatigue and Fracture of Engineering Materials and 
Structures, Vol. 8, No. 4, pp. 295-313, 1985. 
Zheng, Minzhong and LIU, H.W., Fatigue Crack Growth under General- 
Yielding Cyclic-Loading, J. of Engineering Materials and Technology, 
ASME Transactions, Vol. 108, pp. 201-205, July 1986 
LIU, H.W. and OSHIDA, Y., Grain Boundary Oxidation and Fatigue Crack 
Growth at Elevated Temperatures", Theoretical and Applied Fracture 
Mechanics, Vol. 6, No 2. pp. 85-94, Oct. 1986 
10. Liu, H. W. and Oshida, Yoshiki, Grain Boundary Oxidation and Its 
Effects on High Temperature Fatigue Life, Turbine Engine Hot Section 
Technology, NASA Conference, Cleveland, Ohio, Oct., 1986 
11. Liu, H. W.; Zheng, Minzhong; and Chen, Qi, Low Cycle Fatigue Life -- 
An Analysis Based on Fatigue Crack Growth Behavior under General- 
Yielding Cyclic-Loading, Accepted as an invited paper to be 
published in the Proceedings of the Second International Conference 
on Low Cycle Fatigue and Elastic-Plastic Behavior of Materials, 
Munich, West Germany, September, 1987 
1 2 .  Y. Oshida and H. W. Liu "Grain Boundary Oxidation and an Analysis 
of the Effects of Pre-oxidation on Subsequent Fatigue Life", ASTM 
Symposium on 'Low Cycle Fatigue -- Direction for the Future' Lake 
George, NY, 1985. 
13. Qi Chen and H. W. Liu, "Resolved Shear Stress Intensity 
Coefficient and Fatigue Crack Growth in Large Crystals" in 
preparation. 
, 
9 
___ ---__ 
1 Report No 
NASA CR-182129 
The A n a l y s i s  o f  Fa t igue  Crack Growth Mechanism and 
O x i d a t i o n  and Fa t igue  L i f e  a t  E leva ted  Temperatures 
- ____-- 
2 Government Accession No 
7. Author(!$ 
H . W .  L i u  
17 Key Words (Suggested by Author@)) 
Fat igue;  Crack growth mechanisms; 
Ox ida t i on ;  Crack n u c l e a t i o n ;  C r y s t a l  
o r i e n t a t i o n ;  Crack t i p  s l  l p  systems; 
L i f e  p r e d i c t i o n  
9. Performing Organization Name and Address 
Syracuse U n i v e r s i t y  
Department o f  Mechanical and Aerospace Eng ineer ing  
Syracuse, New York 13244 
18 Distribution Statement 
U n c l a s s i f i e d  - U n l i m i t e d  
S u b j e c t  Category 26 
~~~~ 
12 Sponsoring Agency Name and Address 
Na t iona l  Ae ronau t i cs  and Space A d m i n i s t r a t i o n  
Lewis Research Center 
Cleveland,  Ohio 441 35-31 91 
19 Security Classif (of this report) 20 Security Classif (of this page) 
Unclass f f i ed Unc 1 ass i f 1 ed 
3. Recipient's Catalog No. 
21. No of pages 22 Price' 
10 A02 
5. Report Dale 
May 1988 
6. Performing Organization Code 
8. Performing Organization Report No. 
None 
IO. Work Unit No. 
505-63-1 B 
11. Contract or Grant No. 
NAG3-348 
13. Type of Report and Period Covered 
C o n t r a c t o r  Repor t  
F i n a l  
14. Sponsoring Agency Code 
15. zpplemenlary Notes 
P r o j e c t  Manager, Jack Telesman, S t r u c t u r e s  D i v i s i o n ,  NASA Lewis Research Center .  
6 Abstract 
Two q u a n t i t a t i v e  models based on e x p e r i m e n t a l l y  observed f a t i g u e  damage processes 
have been made: ( 1 )  a model o f  low c y c l e  f a t i g u e  l i f e  based on f a t i g u e  c r a c k  
growth under g e n e r a l - y i e l d i n g  c y c l i c - l o a d i n g ,  and ( 2 )  a model o f  a c c e l e r a t e d  
f a t i g u e  c r a c k  growth a t  e l e v a t e d  temperatures based on g r a i n  boundary o x i d a t i o n .  
These two q u a n t i t a t i v e  models agree v e r y  w e l l  w i t h  t h e  exper imenta l  o b s e r v a t i o n s .  
, 
~~~ ~ 
'For sale by the National Technical Information Service, Springfield, Virginia 22161 4SA FORM 1626 O C T  86 


The analysis of fatigue crack growth mechanism and oxidation and fatigue life at elevated temperatures

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