NASA/TM—2010-216103

Probabilistic Simulation for

Nanocomposite Fracture

Christos C. Chamis

Glenn Research Center, Cleveland, Ohio

March 2010
NASA STI Program . . . in Profile

Since its founding, NASA has been dedicated to the

advancement of aeronautics and space science. The

NASA Scientific and Technical Information (STI)

program plays a key part in helping NASA maintain

this important role.

The NASA STI Program operates under the auspices

of the Agency Chief Information Officer. It collects,

organizes, provides for archiving, and disseminates

NASA’s STI. The NASA STI program provides access

to the NASA Aeronautics and Space Database and

its public interface, the NASA Technical Reports

Server, thus providing one of the largest collections

of aeronautical and space science STI in the world.

Results are published in both non-NASA channels

and by NASA in the NASA STI Report Series, which

includes the following report types:

TECHNICAL PUBLICATION. Reports of

completed research or a major significant phase

of research that present the results of NASA

programs and include extensive data or theoretical

analysis. Includes compilations of significant

scientific and technical data and information

deemed to be of continuing reference value.

NASA counterpart of peer-reviewed formal

professional papers but has less stringent

limitations on manuscript length and extent of

graphic presentations.

• TECHNICAL MEMORANDUM. Scientific

and technical findings that are preliminary or

of specialized interest, e.g., quick release

reports, working papers, and bibliographies that

contain minimal annotation. Does not contain

extensive analysis.

• CONTRACTOR REPORT. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scientific and technical

conferences, symposia, seminars, or other

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientific,

technical, or historical information from

NASA programs, projects, and missions, often

concerned with subjects having substantial

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific and

technical material pertinent to NASA’s mission.

Specialized services also include creating custom

thesauri, building customized databases, organizing

and publishing research results.

For more information about the NASA STI

program, see the following:

• Access the NASA STI program home page at

http://www.sti.nasa.gov

• E-mail your question via the Internet to help@

sti.nasa.gov

• Fax your question to the NASA STI Help Desk

at 443–757–5803

• Telephone the NASA STI Help Desk at

443–757–5802

• Write to:

NASA Center for AeroSpace Information (CASI)

7115 Standard Drive

Hanover, MD 21076–1320
NASA/TM—2010-216103

Probabilistic Simulation for

Nanocomposite Fracture

Christos C. Chamis

Glenn Research Center, Cleveland, Ohio

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

March 2010
This report is a formal draft or working

paper, intended to solicit comments and

ideas from a technical peer group.

This report contains preliminary fi ndings,

subject to revision as analysis proceeds.

Trade names and trademarks are used in this report for identifi cation

only. Their usage does not constitute an offi cial endorsement,

either expressed or implied, by the National Aeronautics and

Space Administration.

Level of Review: This material has been technically reviewed by technical management.

Available from

NASA Center for Aerospace Information National Technical Information Service

7115 Standard Drive 5285 Port Royal Road

Hanover, MD 21076–1320 Springfi eld, VA 22161

Available electronically at http://gltrs.grc.nasa.gov
Probabilistic Simulation for Nanocomposite Fracture

Christos C. Chamis

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

A unique probabilistic theory is described to predict the uniaxial strengths and fracture properties of

nanocomposites. The simulation is based on composite micromechanics with progressive substructuring

down to a nanoscale slice of a nanofiber where all the governing equations are formulated. These

equations have been programmed in a computer code. That computer code is used to simulate uniaxial

strengths and fracture of a nanofiber laminate. The results are presented graphically and discussed with

respect to their practical significance. These results show smooth distributions from low probability to

high.

Introduction

The research in the nanoscale technology has exploded over the recent past. An indication of this

explosion is that the Society of Aerospace Material and Processing Engineers (SAMPE) Conference is

devoting four sessions of about six papers each in the last 5 years. These papers cover practically all

current research activities. The majority of the research is devoted to processing because of the difficulties

involved in making a useful material (Ref. 1). A few investigators have been fortunate to make some

testing samples, which they subsequently tested to obtain limited data (Ref. 2). A few other investigators

researched the characterization of fatigue (Ref. 3) and creep (Ref. 4). A couple of papers explored the

construction of nanocomposites for rocket ablative material (Ref. 5) and for carbon nanotubes for

adaptive structures (Ref. 6). One paper ventured to describe a computer simulation of macroscopic

properties of carbon nanotubes polymer composites (Ref. 7). However, there are no results of what

special macroscopic properties are included. Reference 7 shows one stress strain curve and citation of

several references. One recent article (Ref. 8) describes multiscale modeling and simulation of

nanostructural materials from atomistic to micromechanics. This article does not include information on

nanocomposites, but it mentions that mechanistic models will be needed in the end. It is becoming

abundantly clear that no holistic approach has been used to investigate the mechanistic prediction of

uniaxial strength and fracture.

In this paper a unique mechanistic method is described to probabilistically simulate five uniaxial

strengths and fracture of a nanofiber uniaxial composite. The mechanistic deterministic simulation of all

uniaxial properties is described in a previous paper (Ref. 9).

Fundamentals

The fiber alignment with uniform dispersion is not met in nanocomposites. It is assumed herein that

the fibers are aligned only for predicting “point” through-the-thickness properties. The fussiness can be

simulated by estimating the angle of single fibers through the thickness. Therefore, it is assumed that an

aligned unidirectional typical section of a nanocomposite is as illustrated schematically in Figure 1 on the

left 1(a). A nanoply is schematically shown in Figure 1 on the right 1(b). The input includes the

constituent material properties, Tables 1 and 2, the fabrication parameters, environmental, and the loading

conditions.

NASA/TM—2010-216103
TABLE 1.—T300 GRAPHITE NANOFIBER (PYROGRAF II) PROPERTIES

[Conversion factors: 110 nm = 2.756 × 10–6 in.; psi = 6.89 Pa; lb/in.3 = 1146 kg/cm3 ; in./in./°F = (2/5); cm/cm/°F; Btu = 1055 joules.]

Description Symbol Value Units

Number of fibers per end Nf 1.0 number

Filament equivalent diameter df 2.756× 10−6 in.

Weight density Rhof 0.064 lb/in.**3

Normal moduli (11) Ef1 1 1.0× 109

psi

Normal moduli (22) Ef22 7.0× 107

psi

Poisson’s ratio (12) Nuf12 0.2 Nondimensional

Poisson’s ratio (23) Nuf23 0.25 Nondimensional

Shear moduli (12) Gf12 5.0× 107

psi

Shear moduli (23) Gf23 3.5× 107

psi

Thermal expansion coefficient (11) A1faf1 1 −5.5× 10−7 in./in./°F

Thermal expansion coefficient (22) Alfaf22 5.6× 10−6 in./in./°F

Heat conductivity (11) Kf1 1 444.0 Btu/hr/ft2/°F/in.

Heat conductivity (22) Kf22 4.0 Btu/hr/ft2/°F/in.

Heat capacity Cf 0.22 Btu/lb/°F

Dielectric strength (11) KeF1 1 0.0 V/in.

Dielectric strength (22) Kef22 0.0 V/in.

Dielectric constant (11) Gamma1 1 0.0 in./V

Dielectric constant (22) Gamma22 0.0 in./V

Capacitance Cef 0.0 V

Resistivity Ref 0.0 Ω-in.

Tensile strength SfT 8.0× 105psi

Compressive strength SiC 6.0× 105psi

Shear strength SfS 4.0× 105psi

Normal damping capacity (11) psi1 1f 0.38 %Energy

Normal damping capacity (22) psi22f 6.3 %Energy

Shear damping capacity (12) psi12f 3.34 %Energy

Shear damping capacity (23) psi23f 6.3 %Energy

Melting temperature TMf 6000.0 °F

TABLE 2.—INTERMEDIATE MODULUS HIGH-STRENGTH MATRIX (EPOXY)

[Conversion factors: 110 nm = 2.756 × 10–6 in.; psi = 6.89 Pa; lb/in3 = 1146 kg/cm3 ; in./in./°F = (2/5); cm/cm/°C; Btu = 1055 joules]

Description Symbol Value Units

Weight density Rhom 0.044 lb/in.**3

Normal modulus Em 500000.0 psi

Poisson’s ratio Num 0.35 Nondimensional

Thermal expansion coefficient Alfa m 3.6× 10−5 in./in./°F

Heat conductivity Km 0.008681 Btu/hr/ft2/° F/in.

Heat capacity Cm 0.25 Btu/lb/°F

Dielectric strength Kem 0.0 V/in.

Dielectric constant Gammam 0.0 in./V

Capacitance Cem 0.0 V

Resistivity Rem 0.0 Ω-in.

Moisture expansion coefficient Betam 0.0033 in./in./%moisture

Diffusivity Dm 2.16× 10−7 in.**2/hr

Saturation Mm 0.0 %moisture

Tensile strength SmT 15000.0 psi

Compressive strength SmC 35000.0 psi

Shear strength SmS 13000.0 psi

Allowable tensile strain eps mT 0.02 in./in.

Allowable compression strain eps mC 0.05 in./in.

Allowable shear strain eps mS 0.035 in./in.

Allowable torsional strain eps mTOR 0.035 in./in.

Normal damping capacity psiNM 6.6 %energy

Shear damping capacity psiSm 6.9 %energy

Void heat conductivity Kv 0.0012 Btu/hr/in./°F

Glass transition temperature Tgdr 420.0 °F

Melting temperature TMm 0.0 °F

NASA/TM—2010-216103
Figure 1.—Unidirectional nanocomposite typical section. (a) Nanocomposite.

(b) Nanoply.

diiamefer

(2.I756x1i)46}

Figure 2.—Nanoscale isolation of a typical part (units are in in.).

Figure 3.—Nanofiber substructuring. (a) Several slices through the

thickness. (b) Nanofiber sliced.

The strength prediction is expedited by the following geometric diagrams: An exploded view of

nanoscale isolation of a typical part is shown in Figure 2 with nanoscale dimensions. A single nanofiber

schematic with substructuring is shown in Figure 3(a), and a typical subslice is shown in Figure 3(b).

A nanosubply with its corresponding stresses is shown in Figure 4. The nanomechanics predictive

equations are derived by using Figure 4. The equations used are all programmed in ICAN/JAVA

(Ref. 10).

Prior to describing the results obtained, it is instructive to describe the interphase and how it is

modeled. The schematics in Figure 5 show a vertical section, upper figure part, with unit thickness of the

nanocomposite and a single fiber in it. As can be seen in the slice, lower figure, the fiber interphase is

represented by a series of progressively larger volume voids starting with the smallest near the matrix

interface and ending with the largest in the fiber interface. It can be visualized that the stress in the matrix

will be magnified because of the voids. This magnification is shown in Figure 6 for a specific

nanocomposite with 0.05 fiber volume ratio and with void volume ratio varying from 0.05 to 0.4. The

NASA/TM—2010-216103
interesting point to note in the lower part of Figure 5 is that the matrix is continuous even though it is

filled with progressively larger nano voids; otherwise the stresses will not be continuous in the matrix. It

is instructive to elaborate a bit further with the geometry of Figure 5, lower part. In order to fill up a

conventional ply of 0.005 in. thick and a width of 1 in., it will require about 1 × 106

 nanofibers, a very

large number indeed. The magnification factor of the voids effect in the interphase is show in Figure 6. As

can be seen in Figure 6, the magnification factor increases from a value of about 1.1 to a maximum of

about 2. Therefore, the maximum void effect will be nearest to the fiber interface. The author is not

aware of any experimental data that shows these effects. It is important to note that this is the only

mechanics approach to the interphase description.

Figure 4.—Nanostresses on a nanosubply (units are in in.).

Figure 5.—Vertical section of a composite nanocell through nanofiber center.

NASA/TM—2010-216103 4
Figure 6.—Nanocomposite magnification factor.

Results and Discussion

In this section the probabilistic results are presented and discussed starting with the large voids in the

interphase. The probabilistic void magnification factor is shown graphically in Figure 7. It can be seen in

Figure 7 that the larger the void content the greater the deviation. The left most figure is closest to the

matrix interphase fiber interface while the right most curve is closest to the interphase interface. The

respective scatter is about 0.1 for the curve closest to the matrix to about 1 for the curve closest to the

fiber. The corresponding sensitivities are shown in Figure 8. It can be seen in this figure that the void

sensitivities on the magnification factor is large. The probabilistic void effects on the uniaxial strengths

are plotted in Figure 9. Figure 9(a) shows the spread in the longitudinal tensile strength; Figure 9(b), in

the longitudinal compressive strength; Figure 9(c), in the transverse tensile strength and Figure 9(d) in the

transverse compressive strength. It can be seen in Figure 9 that the distribution for the two longitudinal

strengths is relatively large. It is from 150 to 650 ksi, for tensile strength and with a distribution of about

500 ksi, and for the compressive strength is from 140 to 500 ksi or a distribution of about 360 ksi. The

corresponding probabilistic sensitivities are plotted in Figure 10 for tensile and Figure 11 for

compressive. It can be seen in these two figures that there is no difference in the sensitivities for the three

probabilities. The probabilistic intralaminar shear strength is plotted in Figure 12. The distribution in this

strength is from about 6,000 to ~16,000 psi or ~10 ksi spread. It is a relatively wide distribution from

lowest probability to the highest. The corresponding probability sensitivities are plotted in Figure 13 for

uniaxial nano transverse tensile strength. Note that these probabilistics are for 0.0001, 0.50, and 0.9999.

They are about the same and may be easily interchangeable as well as for three fiber volume ratios.

The respective sensitivities for the other nanouniaxial strengths are the same and are not shown. The

fracture for uniaxial nanofiber composites are the same as their respective uniaxial nanofiber uniaxial

strengths.

NASA/TM—2010-216103
&4 - [ .

ƒ ( ' kV <[0-1^1

g m

< - I

`^ !\r 1 R ±a # ±m »t

q«nic o t t

Figure 7.—Probabilistic magnification factor of voids in the interph ase.

±o Oa f + AyS R o

^

a -.

/ 4y .0 OV®'

^ »»^

b: #

<R&

-0.:8

Figure 8.—Voids sensitivities on the interphase magnification factor.

NASAfTM—20 !0-2!6!03 6
@ ¢b 3 ]: ]

Tra, ns + 'con Transverse m

Figure 9.—Probabilistically plotted na no uniax ial strengths.

+a

} -

2

4^

^ ^ & - J

^ f :

Figure 10.—Probabilistic sensitivities for nano longitudinal uniax ial strength.

yR

^ }

.^ J

ƒ §

7 ±

« 4

/

«

Figure 11.—Probabilistic sensitivities for the na no co mpressiv e uniax ial strength.

NASA/TM—20!0-2!6!03 7
'Shear strength

Figure 12.—Probabilistically plotted

intralaminar uniaxial shear strength.

-Q 2 — ,q ^KF

;,:,-a>4 - ;n 'BEM

jy ; q ,EF,22,

f9 aY6 :q SMT

Q^0001 ^Oa5000 ;0=9999

I ran "sverse `iensile'(USC22T) IKF i = 07025

Figure 13.—Probabilistic sensitivities for nanouniaxial transverse tensile strength

for three different probabilities.

4.0 Concluding Remarks

The salient remarks from an investigation to characterize an aligned monofiber nanolaminate are as

follows:

(1) The characterization for the nanolaminate (composite) was based on a series of progressive

substructuring down a sliced single-nano diameter fiber.

(2) The theoretical development and all the equations are included in a computer code called

ICAN/JAVA.

(3) The uniaxial strength and fracture includes two fabrication parameters, 5-nano-uniaxial

strengths/fracture.

(4) The nanolaminate investigated consists of single nanofiber laminate with 0.05 fiber volume ratio.

(5) The effects of the interphase are especially important and are represented by progressively large

amounts of nano voids from the matrix interface to the fiber interphase.

NASA/TM—2010-216103 8
(6) The probabilistic evaluation characterizes the effects of uncertainties in all participating variables.

(7) The voids uncertainties indicate as the void volume ratio increases the distribution increases as

well.

(8) The voids contribute significantly to matrix dominated strengths/fracture. That is, longitudinal

compression, transverse tension and compression, and all intralaminar/interlaminar properties.

References

1. M. Jose, J. Tyner, E. Nyairo, D. Dean, Synthesis and processing of aligned carbon nanotube based

fibers, 49th Int SAMPE Symp and Exhib Conf Proc, 2004.

2. G. Ayalasomayajuala, A. Garg, S. Kapila, K. Chandrashekhara, V. Flanigan, Fabrication and

evaluation of rice hull derived nano silica composites, SAMPE, 49th Int Symp and Exhib Conf Proc,

2004.

3. T. Karaki, J.P. Killgore, J.C. Seferis, Characterization of fatigue behavior of polynanomeric matrix

composites, SAMPE, 49th Int Symp and Exhib Conf Proc, 2004.

4. A. Ranade, N.A. D’Souza, K. Nayak, B. Gnade, D. Fairbrother, Correlation between creep-recovery,

crystallization and dispersion of linear low density polyethylene nanocomposite films, SAMPE, 48th

Int Symp and Exhib Conf Proc, 48, 1, 2164–2176, 2003.

5. J.H. Koo, H. Stretz, J. Weispfenning, Z.P. Luo, W. Wootan, Nanocomposite rocket ablative materials:

Subscale ablation test, 49th Int SAMPE Symp and Exhib Conf Proc, 2004.

6. S. Muhle, H.P. Monner, P. Wiersch, P., Carbon-nanotubes for adaptive structures, SAMPE, 48th Int

Symp and Exhib, 48, 1, 1181–1190, 2003.

7. D. Srivastava, C. Wei, Computer simulations of macroscopic properties of carbon-nanotube polymer

composites, SAMPE, 48th Int Symp and Exhib, 48, 1, 2153–2163, 2003.

8. T.S. Gates et al., Computational materials: Multi-scale modeling and simulation of nanostructural

materials. Comp Sci T, 65 (2005), 2416–2434.

9. C.C. Chamis, Composite nanomechanics properties prediction, NASA/TM—2007-214673.

10. L.M. Handler, C.C. Chamis, ICAN/JAVA computer code.

NASA/TM—2010-216103 9
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the

data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302.

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB

control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To)

01-03-2010 Technical Memorandum

4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER

Probabilistic Simulation for Nanocomposite Fracture

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S) 5d. PROJECT NUMBER

Chamis, Christos, C.

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 432938.11.01.03.02.03.01

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

National Aeronautics and Space Administration REPORT NUMBER

John H. Glenn Research Center at Lewis Field E-16748

Cleveland, Ohio 44135-3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITOR'S

National Aeronautics and Space Administration ACRONYM(S)

Washington, DC 20546-0001 NASA

11. SPONSORING/MONITORING

REPORT NUMBER

NASA/TM-2010-216103

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited

Subject Categories: 24, 61, and 65

Available electronically at http://gltrs.grc.nasa.gov

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

A unique probabilistic theory is described to predict the uniaxial strengths and fracture properties of nanocomposites. The simulation is

based on composite micromechanics with progressive substructuring down to a nanoscale slice of a nanofiber where all the governing

equations are formulated. These equations have been programmed in a computer code. That computer code is used to simulate uniaxial

strengths and fracture of a nanofiber laminate. The results are presented graphically and discussed with respect to their practical

significance. These results show smooth distributions from low probability to high.

15. SUBJECT TERMS

Fiber composites; Multifactor model; Fast probability integrator; Constituent materials

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON

ABSTRACT OF

PAGES

STI Help Desk (email:help@sti.nasa.gov)

a. REPORT b. ABSTRACT c. THIS 19b. TELEPHONE NUMBER (include area code)

U U PAGE UU 15 443-757-5802

U

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18