NASA/TM—2010-216079 SAMPE Paper No. L0 10

Multiscale/Multifunctional Probabilistic

Composite Fatigue

Christos C. Chamis

Glenn Research Center, Cleveland, Ohio

March 2010
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NASA/TM—2010-216079 SAMPE Paper No. L0 10

Multiscale/Multifunctional Probabilistic

Composite Fatigue

Christos C. Chamis

Glenn Research Center, Cleveland, Ohio

Prepared for the

SAMPE 08

sponsored by the Society for the Advancement of Material and Process Engineering

Long Beach, California, May 18–22, 2008

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

March 2010
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Available electronically at http://gltrs.grc.nasa.gov
Multiscale/Multifunctional Probabilistic Composite Fatigue

Christos C. Chamis

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

A multilevel (multiscale/multifunctional) evaluation is demonstrated by applying it to three different

sample problems. These problems include the probabilistic evaluation of a space shuttle main engine

blade, an engine rotor and an aircraft wing. The results demonstrate that the blade will fail at the highest

probability path, the engine two-stage rotor will fail by fracture at the rim and the aircraft wing will fail at

109 fatigue cycles with a probability of 0.9967.

Introduction

Fatigue life of structural components is a combination of local material characteristics and structural

component configuration. The local material characteristics include grain structures, grain boundaries,

grain size and attendant strengths, fracture toughness, etc. These in turn are very much controlled by the

specific fabrication process that was used to make the material as well as the manufacturing procedure

that was used to manufacture the structural component—multifunctional. The structural configuration of

the component includes the geometric shape, the supports and the loading conditions (mechanical,

thermal, dynamic, etc.). The variables used to describe both the material characteristics and the structured

configuration do not have single values, but some scatter about mean values and certainly need multiscale

mechanics formulations. Most of the multiscale mechanics formulations used to predict fatigue life

(damage initiation, propagation, slow growth, and unstable state and/or fast growth) assumes single

values for all participating variables. However, fatigue life data shows considerable scatter. The scatter is

usually bounded predicatively by author-favorite method and is usually curve-fitted with the data scatter.

It is very desirable, therefore, to have a multiscale predictive method that can bind the data based on the

scatter ranges in the fundamental different scales variables and the structural components variables that

were mentioned previously. The objective of the proposed paper is to describe one multilevel method

(multiscale/multifunctional) that has been used with some success to a priori predict fatigue life of

structural components. The method is a judicious combination of multiscale composite mechanics, finite

element structural analysis, fracture mechanics concepts, probabilistic concepts and efficient

computational algorithms. The multiscale composite mechanics in particular include a multifactor

interaction model that describes the material degradation from attendant service environment factors. In

essence, the multilevel method is a computational simulation procedure (multiscale/multifunctional) that

is illustrated by applying it to an engine blade, to an engine two-stage rotor, and to an aircraft wing.

Results show that the blade will fracture along a most probable fracture path, the rotor will fracture due to

multiple fracture modes, and a build-up aircraft wing will fail at 10 9 fatigue cycles with a probability of

0.9967.

Fundamental Consideration

Every structure does not fail instantaneously. It fails initially gradually and then it speeds up to its

final collapse state. In a computational simulation scheme each one of this type of behavior is

characterized by time scales. There is a time scale where the structure may remain intact for several

hours. The second stage is when the structure exhibits observable initial damage. A different time scale

characterized the initial linear growth. Another one characterizes the constant growth and finally the last

NASA/TM—2010-216079
one which characterizes the rapid growth to fracture (Fig. 1). The truly predictive computational

simulation scheme should be able to transcend all the above time scales continuously from the smallest

(material local behavior, non-observable) to the largest scale (structural) which is definitely observable.

What that approach will then require is to combine the material behavior through all the structure

(multifunctional) and through all the different scales (multiscale). Composite structures subjected to

fatigue inherently contain both of these (multilevel). A composite structure is naturally multiscale because

of its angle ply configuration and at the same time is a multifunctional since each ply may be from

different constituents (fibers/matrices) different fiber volume ration as well as different void volume ratio.

Similar comments can be made of metallic structures subjected to different failure criteria. The

subsequent discussion describes the probabilistic simulation of two metallic structures and one composite

built-up aircraft structure.

Multifactor Simulation Model

The multifactors that influence a metered behavior are represented by a multifactor interaction model

of multiplicative form where each factor is expressed in expanded form, as shown in Figures 2 and 3. The

exponents are selected so that they satisfy the initial and final conditions, Reference 1. The exponent can

have any value which describes the factor behavior from its initial value to its final value as shown in

Figure 4. There are two restrictions in selecting exponents: One is that they only can take positive values

and the second is that the factor within the parenthesis must have absolute value. The material

degradation behavior of both the metallic structures and the composite aircraft component structure are

characterized by the multifactor interaction model.

NASA/TM—2010-216079 2
NASA/TM—2010-216079
Probabilistic Computational Simulation

The probabilistic simulation (Ref. 2) cycle of a multilayer composite structure (multiscale) is

graphically illustrated in Figure 5. The deterministic equations to perform the simulation depicted in

Figure 5 are summarized in Figure 6. Results obtained for a deterministic simulation are show in Figure 7.

Figure 7 is very important because it illustrated all the multifunctional, multiscale (multilevel) simulations

described above and it is also similar in shape to Figure 1.

Multifunctional/Multiscale Simulation of Turbine Blade

A space shuttle main engine blade which demonstrates a multilever simulation is shown

schematically in Figure 8. The blade is subjected to variable pressures and temperatures and rotational

load as illustrated in Figure 9. The probabilistic damage propagation path which has the largest

probability (0.0002) of occurring is illustrated in Figure 10. The frequency degradation along this path is

shown graphically in Figure 11. Each portion in this figure illustrates the degradation in each of the four

first frequencies for a total of four frequencies. This figure is very important because it graphically

illustrates the damage degradation which occurs in each frequency with its respective probability. For

example, the first frequency will degrade at the mean from about 5500 to 1500 cycles per second (cps) as

it approached fracture. The degradation qualifies for on board health monitoring with such dramatic drop.

The fourth frequency with substantial lower amplitude will degrade at the mean from about 15,000 to

3,000 cps. This is a much greater decrease. However, the instrumentation required to measure these low

amplitude frequencies may be limited.

NASA/TM—2010-216079 4
NASA/TM—2010-216079
NASA/TM—2010-216079
Another important measure in the highest probability path is the strain energy release rate as the

damage progresses from no damage to its final value. This plot is illustrated in Figure 12. This plot is

another important result because illustrates probabilistic fracture toughness of the material from which the

blade is made. For example, the last point before the damage starts increasing very rapidly is point 3

which corresponds to finite element node number 14. The fracture toughness is measured at the instant

the material damage starts to grow very rapidly, the measurement of which is very intricate. In this

simulation the fracture toughness is about 20 lb.-in. and a critical corresponding length of about one-half

of the blade width. The very important observation in this discussion is that the fracture toughness is

obtained as a by-product of the analysis without usage of intricate instrumentations, specimen preparation

and careful measurement. In addition, the fracture path is evaluated probabilistically.

The second metallic example is two adjacent discs as is illustrated in Figure 13. The probabilistic

simulation of the example requires both multifunctional and multiscale. Multifunctional because of the

different analyses included in the bottom of the figure and the multiscale because of the different

NASA/TM—2010-216079 7
components. As is seen in this figure, the fracture at the rim has the largest probability and coincides,

almost, with the system failure probability. This fracture mode is that of the rim which holds the blades.

Note that the fractures evaluated are identified at the bottom of the figure. They include: (1) disc burst, (2)

fracture at the bore, (3) fracture at the rim, and (4) progressive damage of the ring in yield. The ring ties

the two discs. Note that the insert to the right of the figure represents the survival probability as a function

of the exhausted resistance. The multiscale is illustrated in Figure 14 which shows the probabilistic

sensitivities at failure listed from the highest to the lowest. This figure is instructive in that it illustrates

that the fracture toughness parameters RKIC right toughness, Kt stress concentration, A0 initial damage

size, A-LCF low cycle fatigue and N1 number of cycles are relatively low valued varying from 0.0731 to

about 810-6, respectively. What can we learn from these sensitivities is that fracture toughness has

relatively low significance as compared to other failure modes in the design of engine disc components.

NASA/TM—2010-216079
Composite Aircraft Wing

The last example of multilevel probabilistic evaluation is a simulated composite wing. The multiscale

of this example is illustrated in Figure 15 which shows the span-wise construction and in Figure 16 which

shows the loading conditions (multifunctional). It is observed in Figure 15 that the wing is 5.49 m (18 ft)

long by a tapering width from 1.83 m (6 ft) at the root to 1.22 m (4 ft) at the tip. The sections in this

figure indicate that the internal wing structure consists of three longitudinal spans and five bulkheads. The

multiscale simulation is represented by a finite element model whereas the multifunctional model is

represented by the composite mechanics which describe the thermal and hygral properties in the

composite at each one of its scales.

The probabilistic results of the multilevel evaluation are shown in Figure 17 which depicts both the

cumulative and the density probabilistic functions. The probability density function indicates that the

mean value of this combined set of multifunctional evaluation is about 8.5 × 106 cycles while the

cumulative distribution shows that the wing will fail at about 9 × 106 fatigue cycle with a probability of

0.9967. This evaluation demonstrates that both the multifunctional and multiscale composite problems

can be evaluated by a judicious combination of composite mechanics, finite element analysis and

expedient probabilistic algorithms. The probabilistic sensitivity factors of this multilevel problem are

depicted in Figure 18. The figure summarizes these factors that have a relative significance of greater than

0.1. As is indicated in this figure, the greatest significance is the cyclic loading and the fiber volume ratio

and the fiber modulus, and matrix shear strength of the skin followed by the fiber modulus and the fiber

volume ration of the frame, the matrix tensile strength of the skin and the void volume ratio. The

significance of this evaluation is that the multitude of information that comes out of a probabilistic

evaluation. Note that in the sensitivity information the multifunctional evaluation dominates the results.

NASA/TM—2010-216079 9
NASA/TM—2010-216079 10
Summary Comments

Probabilistic composite/metal structures are simulated by a multilevel simulation scheme. The

multilevel evaluation includes all factors that influence component/system reliability. Multilevel is

evaluated by the cumulative distribution function of the system response. Another important aspect of

probabilistic multilevel evaluations is the probability sensitivities of all the variables that constitute the

system design. The sensitivities are important because they are used to fine-tune the design and/or

optimization variables in optimization evaluations. Probability multilevel evaluation coupled with

progressive structural fracture is general for any multilevel materials and structure. Probabilistic

multilevel fracture determines safe-life and fail-safe, the damage tolerance of the structure with

quantifiable probability of occurrence.

References

1. Chamis, C.C., “Probabilistic Usage of the Multi-Factor Interaction Model,” ASC 22 nd Annual

Technical Conference, September 17-19, 2007, Seattle, WA.

2. Chamis, C.C., “IPACS-Integrated Probabilistic Assessment of Composite Structures: Code

Development and Applications,” Third NASA Advanced Composites Technology Conference (1992).

NASA/TM—2010-216079 11
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14. ABSTRACT

A multilevel (multiscale/multifunctional) evaluation is demonstrated by applying it to three different sample problems. These problems

include the probabilistic evaluation of a space shuttle main engine blade, an engine rotor and an aircraft wing. The results demonstrate that

the blade will fail at the highest probability path, the engine two-stage rotor will fail by fracture at the rim and the aircraft wing will fail at

109 fatigue cycles with a probability of 0.9967.

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Modeling methodology; Degradation; Carbon fiber composites

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