A methodology that accounts for both delaminaton onset and growth in composite structural components is proposed for improved fatigue life prediction to reduce life cycle costs and improve accept/reject criteria for manufacturing flaws. The benefits of using a Delamination Onset Threshold (DOT) approach in combination with a Modified Damage Tolerance (MDT) approach is highlighted. The use of this combined approach to establish accept/reject criteria, requiring less conservative initial manufacturing flaw sizes, is illustrated

OBrien, Thomas K.

NASA Technical Reports Server

 16TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS 
  
1 
 
 
 
 
Abstract  
A methodology that accounts for both delaminaton 
onset and growth in composite structural 
components is proposed for improved fatigue life 
prediction to reduce life cycle costs and improve 
accept/reject criteria for manufacturing flaws. The 
benefits of using a Delamination Onset Threshold 
(DOT) approach in combination with a Modified 
Damage Tolerance (MDT) approach is highlighted. 
The use of this combined approach to establish 
accept/reject criteria, requiring less conservative 
initial manufacturing flaw sizes, is illustrated.  
 
1   Current State of the Art 
The current safe life approach used for establishing 
retirement times for aircraft components, such as 
rotor blades for rotary wing vehicles, does not 
account for any pre-existing flaws, cracks, or 
delaminations. Over the past 25 years, significant 
progress has been made in research efforts to utilize 
fracture mechanics principles to characterize and 
predict delamination fatigue failures in composites 
laminates [1] and more recently in composite rotor 
hub flexbeams and stiffened panels [2,3].  These 
studies have utilized a Delamination Onset 
Threshold (DOT) methodology where fatigue life of 
the part is determined by the onset of delamination 
under cyclic loading from an initial flaw or material 
discontinuity. This approach utilizes a 
characterization in the form of the maximum cyclic 
strain energy relase rate, Gmax, plotted as a function 
of the number of cycles to delamination onset, Nth 
(fig.1). 
 
 
 
Fig. 1.  Delamination onset threshold 
 
The virtual crack closure technique (VCCT) [4] is 
widely used for computing energy release rates 
based on results from continuum (2D) and solid 
(3D) finite element analyses to supply the mode 
separation required when using a mixed-mode 
fracture criterion. A comprehensive summary of the 
development and application of VCCT was recently 
published [5].  
 
Although these studies have demonstrated the 
promise of this approach, they have also highlighted 
some of the difficulties and differences between the 
DOT approach and the classical damage tolerance 
(CDT) methodology used for metallic structures. For 
example, using the DOT methodology to define the 
life of the component as the onset of delamination 
from a very small initial delamination, established 
by the detection threshold for Non-Destructive 
Inspection (NDI) methods, may prove overly 
conservative. Alternatively, the CDT approach has 
been used to determine the rate of delamination 
growth with fatigue cycles as a function of the 
maximum applied cyclic strain energy release rate, 
Gmax. The delamination growth is usually described 
TOWARDS A DELAMINATION FATIGUE 
METHODOLOGY FOR COMPOSITE MATERIALS 
 
T. Kevin O’Brien  
U.S. Army Research Laboratory 
 
Keywords: fatigue, delamination  
 
https://ntrs.nasa.gov/search.jsp?R=20070030303 2019-08-30T01:30:33+00:00Z
T. K. O’BRIEN  
2 
as a log-log plot of da/dN vs. Gmax as shown in fig. 
2. 
 
 
 
Fig. 2.  Delamination growth law 
 
In analogy with metals, the delamination growth rate 
can therefore be expressed as a power law function 
! 
da
dN
= A Gmax( )
n     (1) 
where A and n are determined by a curve fit to the 
experimental data. However, the exponent “n” is 
typically high for composite materials compared to 
metals. The exponent for composites may vary 
between 6 and 10 for mode I delamination growth. 
This exponent may be lower (between 3 to 5) for 
mode II delamination growth and for toughened 
resin composites. However, typical exponents for 
metallic materials are around 1 to 2. As a 
consequence, very small changes in Gmax can result 
in large changes in the delamination growth rate, 
which makes it difficult to establish reasonable 
inspection intervals for implementing the CDT slow 
crack growth methodology used for metals.  
 
2 Proposed Methodology 
Several modifications to the classical Paris law have 
been suggested, including normalization by the static 
R-curve and adding additional terms to account for 
R-ratio effects and near threshold non-linearity [6-
7]. These studies indicate that a Modified Damage 
Tolerance (MDT) methodology where the Gmax is 
normalized by the static R-curve will result in lower 
power law exponents that would enable inspection 
intervals to be established that are more reasonable. 
Currently, ASTM committee D30 is conducting a  
round robin exercise to evaluate these modifications 
for Mode I delamination growth using the Double 
Cantilever Beam specimen. More benefits may be 
obtained by combining the delamination fatigue 
threshold characterization with a modified Paris law 
for slow delamination growth.  
 
3   Combined threshold and slow growth 
approach for establishing acceptable flaw size. 
 
In order to assess the acceptability of manufacturing 
flaws, herein assumed to be initial delaminations, an 
approach may be adopted that utilizes both the slow 
growth characterization in the MDT approach and a 
delamination threshold characterization in the DOT 
approach. To illustrate this combined approach, the 
following heuristic explanation is developed which 
assumes constant amplitude cyclic loading and 
ignores, for the moment, complexities such as the 
mixed-mode dependence on delamination onset and 
growth.  
 
Typically, in a slow crack growth approach, the 
smallest initial delamination, ai, is assumed to be the 
smallest flaw that is detectable by Non-Destructive 
Investigation (NDI). For the MDT approach, the 
slow crack growth law has the form  
! 
da
dN
= A
Gmax
GR
" 
# 
$ 
% 
& 
' 
n
 
  
(2) 
where Gmax = f(a), and GR = f(a) is the crack growth 
resistance curve determined experimentally. Using a 
slow growth approach alone assumes that the initial 
delamination, ai, starts to grow on the first cycle. 
The extent of the delamination at any point is 
determined by integration of eq. 2. Solving for the 
number of cycles required for a given extent of 
delamination yields 
! 
1
A
Gmax(a)
GR(a)
" 
# 
$ 
% 
& 
' 
(n
da
ai
a
) =
1
N
) dN  
  
(3) 
The functional relationship must be determined by 
analysis of the particular configuration and loading 
to obtain Gmax(a) and by performing interlaminar 
fracture tests to determine GR(a).  As shown in fig. 
3, a maximum slow growth life (or initial inspection 
interval), Lsgai = Nsgai/f , where f is the cyclic 
frequency, may be defined that corresponds to the 
point where a = ac and unstable delamination growth 
would occur. 
 3  
TOWARDS A DELAMINATION METHODOLOGY FOR COMPOSITE 
MATERIALS  
 
 
Fig. 3. Maximum possible lives for slow growth 
evaluation 
 
As also shown in fig. 3, if a larger manufacturing 
flaw in the form of an initial delamination, am > ai, 
exists, then the slow growth life, Lsgam would be less 
than Lsgai. In both cases, however, the assumption 
that the initial delamination will begin to grow on 
the first cycle of loading is overly conservative 
because the onset of growth from an existing 
delamination requires a finite number of cycles to 
initiate depending on the maximum cyclic load 
level, Pmax [1-3].  
 
Delamination onset threshold behavior of composite 
materials is typically characterized through 
development of a delamination onset threshold 
curve, Gmax vs. Nth (fig.1), where Nth is the number 
of cycles for delamination onset. These curves may 
be obtained by fitting the data to an equation of the 
form 
 
! 
Gmax =GcNth
"m   (4) 
 
where “m” is a positive constant determined from 
curve fit of the data generated in a delamination 
fatigue characterization test (fig.1) [8] . 
Solving for Nth yields 
! 
Nth =
Gc
Gmax
" 
# 
$ 
% 
& 
' 
1
m  
 (5) 
Hence, a delamination threshold life, were Nth=Lth f, 
would be  
! 
Lth =
1
f
Gc
Gmax
" 
# 
$ 
% 
& 
' 
1
m  
 (6) 
 
As noted earlier, in general Gmax is a function of 
delamination length, a. For simplicity of further 
illustration, assume a structural configuration where 
the maximum cyclic strain energy release rate, Gmax,  
is proportional to the delamination length, a, and the 
square of the maximum applied cyclic load, Pmax,  
 
! 
G
max
=CPmax
2
a
  (7) 
 
where C is a coefficient determined by analysis of 
the particular structural configuration and loading. 
Substituting eq.7 into eq.6 for the threshold life, Lth, 
yields 
 
! 
Lth =
1
f
Gc
CPmax
2 a
" 
# 
$ 
$ 
% 
& 
' 
' 
1
m  
           
(8) 
 
Hence, the threshold life, Lth, is inversely 
proportional to the delamination length, a. 
Therefore, for am > ai, Ltham < Lthai, as shown in fig. 
4. 
 
 
Fig. 4.  Delamination onset threshold curves 
 
In the limit, as a = ac, and CP2maxac = Gc, failure 
occurs in the first cycle, Nth = Lthf = 1. 
 
T. K. O’BRIEN  
4 
If we were to take advantage of both the threshold 
life and the slow growth life, a total life could be 
determined for a given flaw size, as illustrated by 
combining fig. 3 and fig. 4 in fig. 5.  
 
Fig. 5.  Maximum possible lives utilizing a combined      
threshold plus slow growth approach 
 
Hence, for example, the total life for an initial 
delamination, ai, would be 
! 
Lai = Lthai + Lsgai
    (9) 
whereas the total life for a larger initial 
delamination, am, corresponding to a manufacturing 
flaw would be 
! 
Lam = Ltham + Lsgam
    (10) 
 
For the purpose of defining accept/reject criteria, an 
alternative way of demonstrating the benefit of this 
combined approach would be to ask the following 
question: using this combined approach, what size 
manufacturing flaw, am, would yield a life that is 
equivalent to the life defined by assuming the 
smaller NDI threshold flaw size, ai, and the slow 
growth approach alone? This is illustrated in fig. 6, 
where 
! 
Lsgai = Ltham + Lsgam
    (11) 
 
 
 
 
 
Fig. 6.  Equivalence of slow growth life for NDI flaw and 
total growth life for manufacturing flaw 
 
Integration of eq.3 from ai to ac, yields the slow 
growth life, Lsgai=Nsgai/f, as  
! 
Lsgai =
1
f
1+
1
A
Gmax(a)
GR(a)
" 
# 
$ 
% 
& 
' 
(n
ai
ac
) da
* 
+ 
, 
, 
, 
- 
. 
/ 
/ 
/ 
 
           
(12) 
Similary, integration of eq.3 from am to ac, yields the 
slow growth life, Lsgam=Nsgam/f, as  
! 
Lsgam =
1
f
1+
1
A
Gmax(a)
GR(a)
" 
# 
$ 
% 
& 
' 
(n
am
ac
) da
* 
+ 
, 
, 
, 
- 
. 
/ 
/ 
/ 
 
           
(13) 
For simplicity, if we were to assume a flat R curve 
such that GR=Gc=constant, and we further assume, 
as in our earlier example, that Gmax is a linear 
function of a, as in eq.7, then eq.12 becomes 
! 
Lsgai =
1
f
1+
1
A
CPmax
2
Gc
" 
# 
$ 
$ 
% 
& 
' 
' 
(n
a
(n
ai
ac
) da
* 
+ 
, 
, 
, 
- 
. 
/ 
/ 
/ 
 
           
(14) 
which, upon integration, yields 
! 
Lsgai =
1
f
1+
1
A 1" n( )
CPmax
2
Gc
# 
$ 
% 
% 
& 
' 
( 
( 
"n
ai( )
1"n
" ac( )
1"n# 
$ % 
& 
' ( 
) 
* 
+ 
+ 
+ 
, 
- 
. 
. 
. 
 
           
(15) 
Similarly, integration of eq.13 from am to ac, yields 
the slow growth life, Lsgam=Nsgam/f, as  
! 
Lsgam =
1
f
1+
1
A 1" n( )
CPmax
2
Gc
# 
$ 
% 
% 
& 
' 
( 
( 
"n
am( )
1"n
" ac( )
1"n# 
$ % 
& 
' ( 
) 
* 
+ 
+ 
+ 
, 
- 
. 
. 
. 
 
           
(16) 
 5  
TOWARDS A DELAMINATION METHODOLOGY FOR COMPOSITE 
MATERIALS  
The threshold life for the larger manufacturing flaw, 
Ltham, is obtained from eq.8 as 
! 
Ltham =
1
f
Gc
CPmax
2 am
" 
# 
$ 
$ 
% 
& 
' 
' 
1
m  
         
(17) 
Substituting eqs.15-17 into eq.11 yields the 
following algebraic equation that may be solved for 
am 
! 
0 =Q am( )
1"n
" ai( )
1"n# 
$ % 
& 
' ( 
+ R
1
am
) 
* 
+ 
, 
- 
. 
1
m  
         
(18) 
where   
! 
Q =
1
A 1" n( )
CPmax
2
Gc
# 
$ 
% 
% 
& 
' 
( 
( 
"n
 
         
(19) 
and  
! 
R=
Gc
CPmax
2
" 
# 
$ 
$ 
% 
& 
' 
' 
1
m  
         
(20) 
 
Hence, using this combined delamination onset 
threshold and slow growth methodology, a 
manufacturing flaw size, am, that is greater than the 
maximum size based on an NDI technique threshold, 
ai, may be determined that could reduce the number 
of rejected parts. In general, for complex part 
geometries with geometrically non-linear structural 
response, Gmax(a) will need to be determined 
numerically. Therefore, for these more complex 
structural cases, we would substitute Ltham from eq.6, 
Lsgai from eq.12, and Lsgam from eq.13 into eq.11 to 
implement this methodology.  
 
Summary 
The benefits of using a Delamination Onset 
Threshold (DOT) approach in combination with the 
Modified Damage Tolerance (MDT) approach to 
establish more accurate expected life was illustrated. 
This combined threshold and slow growth approach 
may be used to establish accept/reject criteria that 
require less conservative initial manufacturing flaw 
sizes, and hence, reduces the number of rejected 
parts.  
 
References 
[1] O’Brien,T.K., “Towards a Damage Tolerance 
Philosophy for Composite Materials and 
Structures,” Composite Materials:  Testing and 
Design, vol. 9, ASTM STP 1059, S. P. Garbo, 
Ed., ASTM, Philadelphia, pp.7-33, 1990. 
[2] Murri, G.B., O'Brien, T.K., and Rousseau, C.Q. 
“Fatigue Life Methodology for Tapered 
Composite Flexbeam Laminates,” Journal of the 
American Helicopter Society, vol. 43, No.2, 
April, pp. 146-155, 1998. 
[3] Krueger, R., Paris, I.L., O'Brien, T.K. and 
Minguet, P.J., “Fatigue Life Methodology for 
Bonded Composite Skin/Stringer 
Configurations,” Journal of Composites 
Technology and Research, vol. 24, pp. 56-79, 
2002. 
[4] Rybicki, E.F. and Kanninen, M.F., “A Finite 
Element Calculation of Stress Intensity Factors 
by a Modified Crack Closure Integral,” Eng. 
Fracture Mech., vol. 9,  pp. 931-938, 1977. 
[5] Krueger, R., “The Virtual Crack Closure 
Technique: History, Approach and 
Applications,” Applied Mechanics Reviews, vol. 
57, pp. 109-143, 2004. 
[6]  Shivakumar, K.N., Abali, F., and Chen, H., 
“Assessment of Damage Tolerance Standard 
Test Methods and Development of Delamination 
Growth Rate Equations for Composite 
Structures,” Int. J. of Fatigue, vol.28, pp. 33-42, 
2006. 
[7] Martin, R., “Load History Effects on 
Delamination in Composite Materials,” 
Materials Engineering Research Laboratory 
(MERL) NASA Contractor Final Report, Oct. 
2003. 
[8] ASTM Standard Test Method D6115-97, 
Standard Test Method for Mode I Fatigue 
Delamination Growth Onset of Unidirectional 
Fiber Reinforced Composite materials, in 
Annual Book of ASTM Standards, vol. 15.03, 
ASTM International, West Conshohocken, PA, 
1998. 
 
 


Towards a Delamination Fatigue Methodology for Composite Materials

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server