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J.McPherson_draft_thesis_081814.pdf
Methodology for Analytical Assessment of
Fiber Reinforced Laminates with Known
Void Content
Jim McPherson ([email protected])
A Thesis Proposal Submitted to the Graduate Faculty
of Rensselaer Polytechnic Institute,
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF SCIENCE in MECHANICAL ENGINEERING
Major Subject: Solid Mechanics
Approved:
___________________________________
Ernesto Gutierrez-Miravete, Thesis Advisor
Rensselaer Polytechnic Institute
Hartford, Connecticut
August 2014
(For Graduation December 2014)
CONTENTS
LIST OF FIGURES ...................................................................................................... III
ABSTRACT ............................................................................................................. IV
1.
INTRODUCTION ............................................................................................. 1
2.
METHODOLOGY ............................................................................................ 4
CLASSICAL LAMINATE THEORY ................................................................................................... 4
ANALYTICAL APPROACH ........................................................................................................... 4
VOID GEOMETRY .................................................................................................................... 5
CARBON/EPOXY LAMINATES ..................................................................................................... 9
TEST DATA .......................................................................................................................... 10
% POROSITY ........................................................................................................................ 10
MODULUS REDUCTION .......................................................................................................... 10
STRENGTH REDUCTION........................................................................................................... 14
3.
IMPLEMENTATION........................................................................................ 19
FINITE ELEMENT MODEL ........................................................................................................ 19
ANSYS PROGRAMMING ........................................................................................................ 19
SOURCE CODE ...................................................................................................................... 19
4.
SUMMARY OF RESULTS ................................................................................. 24
5.
REFERENCES ............................................................................................... 25
ii
LIST OF FIGURES
Figure 1 - Micrograph of carbon/epoxy laminate with porosity before testing showing
triangular voids. [7] ........................................................................................................ 6
Figure 2 - Micrograph of tested carbon/epoxy laminate with porosity, showing crack
emanating from a void. [7] ............................................................................................. 7
Figure 3 - Micrograph of carbon/BMI laminate with porosity before testing showing
elongated voids. [7] ......................................................................................................... 8
Figure 4 - Micrograph of tested carbon/BMI laminate with porosity showing cracks
emanating from voids. [7] ................................................................................................ 9
Figure 5 - ASTM D7264 3 Point Bending Test Configuration ........................................... 11
Figure 6 - Longitudinal and transverse tensile modulus variations as a function of void
content [6] ....................................................................................................................... 11
Figure 7 – Bending Modulus Variation as a Function of Void Content [6] ...................... 12
Figure 8 - Flexural Modulus - Compressive Modulus Relationship ................................. 12
Figure 9 - Calculated Compressive Modulus from Flexural Testing ................................ 13
Figure 10 - Carbon/Epoxy Modulus Fraction vs Void Content ........................................ 13
Figure 11 - Longitudinal and transverse tensile modulus variations as a function of void
content [6] ....................................................................................................................... 14
Figure 12 - P/A Compressive Stress vs Void Content [10] ............................................... 15
Figure 13 - Tabular Compressive Stress vs Void Content [10] ......................................... 16
Figure 14 - Laminate Stiffness Matrix (ABD) for 4% Voids .............................................. 16
Figure 15 - Plywise Failure Stresses for 4% Voids ............................................................ 17
Figure 16 - Calculated Compressive Strength Fraction vs Void Content ......................... 17
Figure 17 - Exponential Curve fit for Compressive Strength Fraction vs Void Content .. 18
iii
ABSTRACT
The purpose of this paper is the develop a methodology for simulating the structural
behavior of porous carbon/epoxy composite materials. Research and testing has been
performed to quantify the impact on some of the mechanical properties however no
solution for collecting and utilizing all of the data has been published. The first aspect
of this thesis will cover mechanical property degradation that is available and then
utilize what test data is published to derive the remaining aspects. The single most
missing property data was found to be compressive modulus and strength. Since
inplane compression is a matrix dominated failure mode, this is a critical aspect to
accurate analytical assessment. Flexure testing of porous laminates was used to
characterize compressive modulus fraction versus void content. Then compressive
strength was calculated using reduced modulus, failure loads, and classical laminate
theory. Once the material properties were all identified, a structural methodology was
developed. Generally composite materials are modeled using a single modulus for
tension and compression loading. While this may be fairly accurate for laminates with
less that 2% porosity, it is not an accurate solution when more voids are present.
Recognizing that tensile and compressive moduli degrade differently with respect to
void content, a material model that could accurately capture this must be employed.
The generalized anisotropic Hill potential model was utilized. This model provides the
ability to specify six moduli in the three orthogonal planes as well as six different failure
stress values, which is far superior to typical orthotropic modeling.
iv
1. INTRODUCTION
Fiber reinforced composite materials are used in wide variety of applications including
aerospace, automotive, and defense industries. Composites materials are generally
chosen for the high strength characteristics and reduced weight to produce efficient
designs. As a result, oftentimes the loads imposed on composite designs are significant
and mechanical properties are critical to the success of the product. A layup consisting
of several plies, each oriented at a specific angle and with a desired matrix to fiber ratio
is necessary to achieve required directional strength characteristics. Achieving these
mechanical properties requires manufacturing processes that combine the constituent
materials (fiber and matrix in this case), compaction, and curing cycles. The
compaction/curing process can be performed by several molding techniques including
vacuum bag and autoclave. Within each of these processes, defects are introduced
based on manufacturing parameters such as autoclave/vacuum pressure and cure
temperature. While it is possible to control these parameters, doing so directly impacts
the cost of the part. Cost is one of the major downfalls of fiber reinforced composite
materials; therefore any opportunity to control and/or reduce is usually desirable.
1
Common defects found in fiber reinforced composites are delaminations and porosity
(i.e. void content). Experimental data exists for laminates containing both defects
mentioned however analytical methodology showing good correlation to the test data
does not. Delaminations have been studied and virtual crack closure and cohesive zone
modeled theories have been proposed and utilized. Porosity also bears significance to
the mechanical properties of the laminate, however does not currently have a
convenient technique for analytical assessment.
Several attempts have been made to quantify the effect of void content on mechanical
properties, many of which are empirical in nature and do not demonstrate accurate
correlation between void content and mechanical properties such as stiffness and
strength. These techniques are formulated with little consideration for the physical
microstructure of the laminate and as a result; do not accurately predict the effect of
defect variation. Huang and Talreja [3] utilize a micromechanic study to quantify the
effect of voids on elastic modulus for graphite/epoxy laminates manufactured with the
autoclave process. Finite element modeling was used to investigate relationship
between laminate stiffness and void characteristics. A similar approach will be applied
through the development of this thesis and will build upon the work already
established to develop a methodology for structural assessment using a simplified shell
model approach which does not currently exist.
It has been cited by many sources that manufacturing defects have detrimental effects
to mechanical properties of fiber reinforced composite materials. Experimental studies
have been performed to quantify the effects of defects relative to material strength
and stiffness properties for composites however; simplified analytical methods for
correlating this test data do not exist for void content defects. Generally speaking,
composite materials are expensive and require considerable time to manufacture. As a
result of void content beyond generally acceptable levels (>1-5% in some cases), the
parts are scraped and the time and cost of the raw materials is wasted.
2
The purpose of this thesis is to derive a methodology for analytical assessment of fiber
reinforced composite laminates with void content that can be applied quickly and easily
to basic FE models.
3
2. METHODOLOGY
Classical Laminate Theory
Classical laminate theory is based upon Kirchhoff’s hypothesis in which a orthogonal
line passing through the geometric midplane of a laminated plate does not deform, but
instead transforms and rotates as the plate deflects under applied loading. Therefore,
if the deformations of the midplane surface are known, deformation and stress/strain
of points along this line can be derived by virtue of their linear relationship. This
implies that all points within the laminate exhibit plane stress, such that in-plane
stresses are dominant and out-of-plane stresses are equal to zero. In addition, all
layers are assumed to be perfectly bonded and act as a single layer. Classical laminate
theory will be utilized throughout this thesis to calculate lamina level effects of void
content. Laminate stiffness matrices will be adjusted based on the test data available
and the lamina level effects will be derived accordingly.
Analytical Approach
A simplistic approach to assessing part capability would involve creating a finite
element model of the hardware and reducing the stiffness of the elements containing
excessive void content to zero. This is a conservative approach that does not truly
represent the structural capability of the hardware and oftentimes, still results in
scraping parts that have adequate structural capability because load within the part is
forced to redistribute globally to areas adjacent to the defect. In reality, the voids are
relatively small and localized load redistribution around the void itself should be
considered. Also, during void formation, the entrapped air displaces matrix material,
moves fibers from their original location, and effects spacing relative to adjacent fibers.
This locally changes the fiber volume fraction which corroborates a change in strength
in the void region.
A more generalized approach would be to investigate the effect of the defects on a
lamina level by modeling the test specimens with void(s) present. Derivation of lamina
4
level properties are then facilitated through classical laminate theory. This results in
more accurate load distribution in the laminate and provides insight into localized
failure mechanisms that can then be applied to laminates of various construction.
Once the micromechanics study is complete and showing good correlation to available
test data, simulation of this mechanical behavior will be captured using more simplified
modeling technique to avoid the necessity of test various laminates/void content. An
approach utilizing shell elements and modified layup properties defined with ANSYS
Finite Element Software will be employed. ANSYS Parametric Design Language (APDL)
macros have been included as part of this thesis to automate the modification of
laminate definition within finite element models. The macros are based upon a conical
or cylindrical shaped pressure vessel and modify mechanical properties based upon
user input for % porosity, spatial and through-thickness location.
Void Geometry
Carbon/epoxy laminates typically exhibit triangular shaped voids located at the crossing
of the woven fibers which also tend to be resin rich areas. Carbon/BMI laminate voids
however, are more uniformly distributed and are bubble or torpedo shaped. Void
geometry comparisons confirm that the triangular shaped voids found in carbon/epoxy
laminates are more likely to be crack initiation points to the relative high kt found at
these locations. For the purpose of this thesis, to form generalized relationship
between void content and elastic properties and implement them into a finite element
model, the carbon/epoxy laminates will be utilized.
5
Figure 1 - Micrograph of carbon/epoxy laminate with porosity before testing showing triangular voids. [7]
6
Figure 2 - Micrograph of tested carbon/epoxy laminate with porosity, showing crack emanating from a void. [7]
7
Figure 3 - Micrograph of carbon/BMI laminate with porosity before testing showing elongated voids. [7]
8
Figure 4 - Micrograph of tested carbon/BMI laminate with porosity showing cracks emanating from voids. [7]
Carbon/Epoxy Laminates
Carbon/epoxy laminates are commonly used in aerospace, automotive, and defense
industries where they are specifically chosen for their high strength to weight ratios.
Given their popularity, they are one of the more tested fiber reinforced composite
material systems. While it is a common material system, there are still variations in the
constituent materials that are not explicitly addressed here. For instance, carbon
(graphite) fiber cross sectional shape is different for PAN and pitch derived fibers.
Fibers undergo graphitization in which they are heat treated to reorganize the
crystalline structure; however the skin region of the fibers is susceptible to
reorganization of the microstructure which contributes to fiber failure under loading.
9
This thesis will focus on generalized trends due to void content and analytical
implementation.
Test Data
Since constituent materials and layups vary widely amongst fiber reinforced composite
materials, generalizations regarding the effects of void content are limited. Similarly,
test data for porous laminates is not abundant. As a result, this thesis is based on the
limited data that is available for carbon/epoxy laminates.[6][8]
Data from multiple sources provides insight into the reduction in mechanical properties
of carbon epoxy laminates when void contents exceed the industry accepted levels (12%). The most readily available information found pertains to tensile and interlaminar
shear properties. While these are necessary to consider, the effect on compressive
capability often times is not present. This thesis will derive the compressive mechanical
properties from information available and propose a methodology for inclusion in
structural finite element model simulations.
% Porosity
While the impact of porosity to the mechanical strength of composites is difficult to
quantify, correlating non-destructive measurement techniques to percent voids also
presents issues. Several ultrasonic methods have been employed to measure throughthickness porosity content such as absolute attention and longitudinal wavespeed.
Because of this added difficulty, samples were cutup and subjected to micrograph
inspection.
Modulus Reduction
Tensile and flexure testing was conducted [6] in an attempt to quantify the effect of
void content on tensile properties. Coupon laminate specimens were constructed of
(16) 0° unidirectional ply lamina. Void content of the coupons varied from 0.3 – 10.3%
10
and were subjected the three point bending and longitudinal and transverse tension
tests. The three point bending test setup utilized is similar to that pictured in Figure 5.
Figure 5 - ASTM D7264 3 Point Bending Test Configuration
Data collected from the tensile testing shows that there is very little effect of voids on
longitudinal tensile modulus and much more significant impact to transverse modulus
as shown in Figure 6. This is explainable because voids create discontinuities in the
matrix material and disrupt the structural integrity. Fibers are displaced by the voids
and may locally kink causing insignificant degradation of mechanical properties.
Figure 6 - Longitudinal and transverse tensile modulus variations as a function of void content [6]
11
Flexure modulus testing shows a fairly significant degradation of bending stiffness for
both longitudinal and transverse directions as shown in Figure 7. This may seem
counter intuitive at first since the flexure test is a measure of tensile stress vs strain of
the tensile surface, however upon further consideration of matrix dominated
sensitivity, the compressive modulus has decreased, thus reducing the flexure modulus.
While compressive modulus derivation was not the objective of the testing performed
in reference [6], it will be calculated herein for incorporation into the forthcoming
analytical methodology.
Figure 7 – Bending Modulus Variation as a Function of Void Content [6]
As mentioned above, the longitudinal compressive modulus appears to impact the
flexural modulus. A relationship between flexural, tensile, and compressive moduli was
documented in reference [8] as follows:
Figure 8 - Flexural Modulus - Compressive Modulus Relationship
Where: Ec – Compressive Modulus, Et – Tensile Modulus, Ef – Flexural Modulus
12
This relationship was applied to the void content testing performed in reference [6] as
follows:
Figure 9 - Calculated Compressive Modulus from Flexural Testing
Once the compressive modulus was calculated for various void content; flexural,
tensile, and compressive modulus fraction was plotted as shown in Figure 10.
Figure 10 - Carbon/Epoxy Modulus Fraction vs Void Content
The data plotted above was then curve fit using exponential functions to facilitate
analytical modeling methodology. The plot also confirms that the compressive
modulus is more significantly impacted by the presence of voids. Again, this is
13
consistent with the fact that voids are more detrimental to matrix dominated failure
modes.
The exponential formulas that describe the dataset are as follows:
Tensile Modulus: y = 0.9823e0.0035x
Compressive Modulus: y = 1.011e-1.282x
Flexural Modulus: y = 0.9969e-0.657x
Where y – modulus fraction, x – void content
Strength Reduction
Similar to tensile modulus trends, longitudinal tensile strength varies little with change
in void content while transverse effects are more severe as shown in Figure 11.
Figure 11 - Longitudinal and transverse tensile modulus variations as a function of void content [6]
Compressive strength reduction is not calculated by this test but can be derived
knowing the effect on modulus. Reference Error! Reference source not found.
14
provides test data collected from compression testing of laminates containing various
void content. The test setup did not properly constrain the ends of the coupon samples
so the maximum compressive stresses are reported based on total failure load divided
by cross sectional area in Figure 12. With the calculated compressive modulus and
known failure loads, classical laminate theory will be utilized to derive the first ply
failure stress for the various coupon samples. The laminate coupons were constructed
on carbon/epoxy unidirectional tape arranged in a 16 ply quasi-isotropic orientation
[45,-45,0,90]2s.
Figure 12 - P/A Compressive Stress vs Void Content Error! Reference source not found.
15
Figure 13 - Tabular Compressive Stress vs Void Content Error! Reference source not found.
Using Classical Laminate theory, the test layup was defined and laminate stiffness
matrix was calculated for each sample as shown in Figure 14.
Figure 14 - Laminate Stiffness Matrix (ABD) for 4% Voids
Once the laminate equivalent properties were calculated, peak compressive stresses
were calculated as shown in Figure 15.
16
Figure 15 - Plywise Failure Stresses for 4% Voids
This process was repeated for all coupon samples available and calculated peak
compressive stresses are presented in Figure 16 assuming first ply failure. Compressive
strength fraction are then calculated, plotted, and curve fit as shown in Figure 17.
Figure 16 - Calculated Compressive Strength Fraction vs Void Content
17
Figure 17 - Exponential Curve fit for Compressive Strength Fraction vs Void Content
The data plotted above was then curve fit using exponential functions to facilitate
analytical modeling methodology.
The exponential formulas that describe the compressive strength reduction is as
follows:
Compressive Strength: y = 83.992e-0.033x
Where y – compressive strength fraction, x – void content
18
3. IMPLEMENTATION
Finite Element Model
ANSYS Programming
ANSYS Parametric Design Language is a scripted language embedded in the ANSYS
Finite Element Software package used to automate FEM workflow. APDL is used to
eliminate the tedious process of locating the finite elements that coincide with the
defect location and group them into components for further processing. Components
are created for the region containing porosity and adjacent. Mechanical properties are
copied from the parent laminate, modified, and applied to the region containing voids.
Source Code
ESEL,S,MAT,,3
NCN='1G'
CYL_HALF='UPPER'
LENGTH=6.66
WIDTH=0.72
TAN_DIM1=14.24
TAN_EOP=0
AX_DIM1=1.28
AX_EOP='AFT'
!!!!!!!!!!!!!!!!!!!!
CSYS,12
PID=3.14159265359
AX_LOC1=AX_DIM1
AX_LOC2=AX_DIM1+WIDTH
TAN_LOC1=TAN_DIM1
TAN_LOC2=TAN_DIM1+LENGTH
19
*IF,AX_EOP,EQ,'AFT',THEN
AX_LOC1=165.71-AX_LOC1+0.1205
AX_LOC2=AX_LOC1-WIDTH
*ELSEIF,AX_EOP,EQ,'FWD',THEN
AX_LOC1=103.81+AX_LOC1-0.1205
AX_LOC2=AX_LOC1-WIDTH
*ENDIF
ESEL,S,MAT,,3
ALLSEL,BELOW,ELEM
NSEL,R,LOC,Z,AX_LOC1 - 0.12,AX_LOC1 + 0.12
CM,AX_NODES,NODE
NSEL,R,LOC,Y,-0.05,0.05
*GET,TAN_NODE1,NODE,,NUM,MIN
CMSEL,S,AX_NODES
NSEL,R,LOC,Y,179.99,180.01
*GET,TAN_NODE2,NODE,,NUM,MIN
RAD_LOC=(DISTND(TAN_NODE1,TAN_NODE2))/2
*IF,CYL_HALF,EQ,'LOWER',THEN
CMSEL,S,LOWER
ALLSEL,BELOW,ELEM
*IF,TAN_EOP,EQ,0,THEN
TAN_ANG1=90+(TAN_LOC1/RAD_LOC)*180/PID
TAN_ANG2=90+(TAN_LOC2/RAD_LOC)*180/PID
NSEL,R,LOC,Z,AX_LOC1 + 0.1,AX_LOC2 - 0.1
NSEL,R,LOC,Y,TAN_ANG1-1,TAN_ANG2+1
*ELSEIF,TAN_EOP,EQ,180,THEN
TAN_ANG1=-90-(TAN_LOC1/RAD_LOC)*180/PID
TAN_ANG2=-90-(TAN_LOC2/RAD_LOC)*180/PID
NSEL,R,LOC,Z,AX_LOC1 + 0.1,AX_LOC2 - 0.1
20
NSEL,R,LOC,Y,TAN_ANG1+1,TAN_ANG2-1
*ENDIF
ESLN,R,ALL
CM,NC_%NCN%,ELEM
/COLOR,ELEM,ORAN
NSLE,S
ESLN,S
CMSEL,U,NC_%NCN%
CM,NC_%NCN%_ADJ,ELEM
/COLOR,ELEM,DGRA
ALLSEL,ALL
*ELSEIF,CYL_HALF,EQ,'UPPER',THEN
CMSEL,S,UPPER
ALLSEL,BELOW,ELEM
*IF,TAN_EOP,EQ,0,THEN
!TAN_ANG2 WILL BE
LARGER THAN TAN_ANG1
TAN_ANG1=-90+(TAN_LOC1/RAD_LOC)*180/PID
TAN_ANG2=-90+(TAN_LOC2/RAD_LOC)*180/PID
NSEL,R,LOC,Z,AX_LOC1 + 0.1,AX_LOC2 - 0.1
NSEL,R,LOC,Y,TAN_ANG1-1,TAN_ANG2+1
*ELSEIF,TAN_EOP,EQ,180,THEN
!TAN_ANG1 WILL BE
LARGER THAN TAN_ANG2
TAN_ANG1=90-(TAN_LOC1/RAD_LOC)*180/PID
TAN_ANG2=90-(TAN_LOC2/RAD_LOC)*180/PID
NSEL,R,LOC,Z,AX_LOC1 + 0.1,AX_LOC2 - 0.1
NSEL,R,LOC,Y,TAN_ANG1+1,TAN_ANG2-1
*ENDIF
ESLN,R,ALL
CM,NC_%NCN%,ELEM
21
/COLOR,ELEM,ORAN
NSLE,S
ESLN,S
CMSEL,U,NC_%NCN%
CM,NC_%NCN%_ADJ,ELEM
/COLOR,ELEM,DGRA
ALLSEL,ALL
*ENDIF
!
! CREATE COMPONENTS FOR NON_CONFORMANCE ELEMENTS BASED ON LAYUP
!
CMSEL,S,NC_%NCN%
*GET,ELEM_COUNT_%NCN%,ELEM,,COUNT
*GET,ELEM_MIN_%NCN%,ELEM,,NUM,MIN
ELEM_QUERY_%NCN% = ELEM_MIN_%NCN%
*DO,I,1,ELEM_COUNT_%NCN%
ESEL,R,,,ELEM_QUERY_%NCN%
ELMSEC = ELMIQR(ELEM_QUERY_%NCN%,-4)
*GET,COMP_TEST,COMP,NC_%NCN%_%ELMSEC%,TYPE
*IF,COMP_TEST,EQ,0,THEN
CM,NC_%NCN%_%ELMSEC%,ELEM
*ELSE
CMSEL,A,NC_%NCN%_%ELMSEC%
CM,NC_%NCN%_%ELMSEC%,ELEM
*ENDIF
CMSEL,S,NC_%NCN%
ELEM_QUERY_%NCN% = ELNEXT(ELEM_QUERY_%NCN%)
*ENDDO
!
22
! CREATE COMPONENTS FOR ADJACENT ELEMENTS BASED ON LAYUP
!
CMSEL,S,NC_%NCN%_ADJ
*GET,ELEM_COUNT_%NCN%_ADJ,ELEM,,COUNT
*GET,ELEM_MIN_%NCN%_ADJ,ELEM,,NUM,MIN
ELEM_QUERY_%NCN%_ADJ = ELEM_MIN_%NCN%_ADJ
*DO,I,1,ELEM_COUNT_%NCN%_ADJ
ESEL,R,,,ELEM_QUERY_%NCN%_ADJ
ELMSEC = ELMIQR(ELEM_QUERY_%NCN%_ADJ,-4)
*GET,COMP_TEST,COMP,NC_%NCN%_ADJ_%ELMSEC%,TYPE
*IF,COMP_TEST,EQ,0,THEN
CM,NC_%NCN%_ADJ_%ELMSEC%,ELEM
*ELSE
CMSEL,A,NC_%NCN%_ADJ_%ELMSEC%
CM,NC_%NCN%_ADJ_%ELMSEC%,ELEM
*ENDIF
CMSEL,S,NC_%NCN%_ADJ
ELEM_QUERY_%NCN%_ADJ = ELNEXT(ELEM_QUERY_%NCN%_ADJ)
*ENDDO
ALLSEL,ALL
23
4. SUMMARY OF RESULTS
The expected outcome from this thesis is to develop a methodology for modeling the
effects of void content in a given composite material with shell elements and layup
properties specific to the region of defect. This will enable an analyst to include global
defects within a structural assessment and minimize/eliminate the need for 3d
modeling, while still capturing accurate structural results within the defect region.
24
5. REFERENCES
[1] Muller de Almeida, S. and Nogueira Neto, Z., “Effect of Void Content on the
Strength of Composite Laminates”, Composite Structures, 28, (1994),139-148
[2] Park, C.H., Lebel, A., Saouab, A., Bread, J., Lee, W., “Modeling and Simulation of
Voids and Saturation in Liquid Composite Materials”, Composites: Part A, 42,
(2011),658-668
[3] Huang, H., Talreja, R., “Effects of Voids on Elastic Properties of Unidirectional Fiber
Reinforced Composites”, Composites Science and Technology, 65, (2005)1964-1981
[4] Zhu, H., Li, D., Zhang, D., Wu, B., Chen, Y., “Influence of Voids on Interlaminar Shear
Strength of Carbon/Epoxy Fabric Laminates”, Trans. Nonferrous Met. Soc. China, 19,
(2009), 470-475
[5] Zhu, H., Li, D., Zhang, D., Wu, B., Chen, Y.,, “Influence of Voids on the Tensile
Performance of Carbon/Epoxy Fabric Laminates”, J. Mater Sci. Technol., 27, (2011),
69-73
[6] Olivier P, Cottu JP, Ferret B. “Effects of cure cycle pressure and voids on some
mechanical properties of carbon/epoxy laminates.” Composites 1995;26:509–15.
[7] Costa, M., Almeida, S., Rezende, M., “The influence of porosity on the interlaminar
shear strength of carbon/epoxy and carbon/bismaleimide fabric laminates” ,
Composites Science and Technology, 61, (2001)2101-2108
[8] Stevanovic, M., Sekulic, DP., Macromechanical Characteristics Deduced from ThreePoint Flexure Tests on Unidirectional Carbon/Epoxy Composites
[9] ASTM D7264 “Standard Test Method for Flexural Properties of Polymer Matrix
Composite Materials”
[10]
Uhl, KM., Lucht, B., Jeong H., Hsu, DK., “Mechanical Strength Degradation of
Graphite Fiber Reinforced Thermoset Composites Due to Porosity”, Center for NDE:
Iowa State University
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