Copyright ⓒ The Korean Society for Aeronautical & Space SciencesReceived: March 2, 2017 Revised: June 21, 2017 Accepted: June 22, 2017
436 http://ijass.org pISSN: 2093-274x eISSN: 2093-2480
PaperInt’l J. of Aeronautical & Space Sci. 18(3), 436–449 (2017)DOI: http://dx.doi.org/10.5139/IJASS.2017.18.3.436
Multi-scale Progressive Failure Analysis of Triaxially Braided Textile Composites
Tsinuel N. Geleta*Department of Civil Systems Engineering, Chungbuk National University, Chungbuk 28644, Republic of Korea
Kyeongsik Woo**School of Civil Engineering, Chungbuk National University, Chungbuk 28644, Republic of Korea
Abstract
In this paper, the damage and failure behavior of triaxially braided textile composites was studied using progressive failure
analysis. The analysis was performed at both micro and meso-scales through iterative cycles. Stress based failure criteria
were used to define the failure states at both micro- and meso-scale models. The stress-strain curve under uniaxial tensile
loading was drawn based on the load-displacement curve from the progressive failure analysis and compared to those by test
and computational results from reference for verification. Then, the detailed failure initiation and propagation was studied
using the verified model for both tensile and compression loading cases. The failure modes of each part of the model were
assessed at different stages of failure. Effect of ply stacking and number of unit cells considered were then investigated using
the resulting stress-strain curves and damage patterns. Finally, the effect of matrix plasticity was examined for the compressive
failure behavior of the same model using elastic, elastic – perfectly plastic and multi-linear elastic-plastic matrix properties.
Key words: Triaxially braided composites, Progressive failure analysis (PFA), Failure criteria, Unit cell, Stress – Strain curve,
Failure progression behavior
1. Introduction
In order to use composite materials for structural
applications in engineering fields, their mechanical properties
have to be determined beforehand. These properties include
the elastic and failure behaviors often represented by the
full stress-strain curve. This curve can be determined from
experimental tests on the material, analytical methods or
computational tools. While providing the true nature of the
material behavior, the experimental test, however, is much
more expensive and sometimes takes more time to conduct
making it difficult and uneconomical to use. The analytical
method, on the other hand, is the easiest, cheapest and
fastest; but has limited reliability since it is based on many
assumptions. This leaves computational tools midway in all
aspects, which calculate the values based on the mechanical
properties of the constituent fiber and matrix materials.
Triaxially braided textile composites are not different in
choosing the methodology for the determination of their
mechanical properties. All the three methods can be applied
to draw their stress-strain curves.
Over the years, researchers have been conducting
experiments on specimens targeting the required type of
response. Littell et al. [1] conducted a series of experiments
to examine the damage characteristics of triaxial braided
composites under tensile loading. They discussed the failure
loads and mode of failure in different parts of the braided
composite. Similarly, Ivanov et al. [2] studied the multiple
stages of damage in triaxial braids and compared the results
to FE model. Miravete et al. [3] also described analytical
meso-mechanical approach for the prediction of elastic and
failure properties valid for triaxial and 3D braided composite
This is an Open Access article distributed under the terms of the Creative Com-mons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduc-tion in any medium, provided the original work is properly cited.
* Master Student ** Professor, Corresponding author:[email protected]
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Tsinuel N. Geleta Multi-scale Progressive Failure Analysis of Triaxially Braided Textile Composites
http://ijass.org
materials. They used a unit cell scheme in which the
geometry of both fiber and matrix has been considered. They
also conducted experimental tests for result validation.
Another less expensive alternative to predict the failure
properties of triaxially braided composites is through the
use of computational methods. Brief review of some of
these methods and a broader explanation of the element
failure method (EFM) are given by Tay et al. [4]. One of these
methods is through the use of material property degradation
method (MPDM) within continuum damage mechanics
(CDM) scheme. Blackketter et al. [5] applied this method to
model damage in a plain weave fabric reinforced composite
material. Naik [6] also used it for woven and braided
composites considering the discrete slices of the tows and
solved the effective stiffness and failure predictions using FE
technique. He used material property degradation method
based on maximum stress and strain in the constituent
materials. PFA and plastic behavior of biaxial braids was
studied by Tang et al. [7] and Goyal et al [8], respectively.
Nobeen et al. [9] also used MPDM by applying 3D-Hashin
[10, 11] and Stassi [12] failure criteria for the progressive
damage of constituent materials. Xu et al. [13] conducted
multiscale analysis between mesoscale and microscale
regimes. The constituent stresses are related to mesoscale
stresses using stress amplification factor.
Other computational technique that can be applied for
triaxial braids is cohesive zone modeling (CZM). Xie et al.
[14] applied discrete CZM to simulate static fracture in 2D
triaxially braided carbon fiber composites by inserting spring
elements between the nodes of bulk plane stress elements.
They compared their results with that of experimental tests
as well. In the paper of Li et al. [15] failure initiation and
progressive material degradation has been simulated using
MPDM while CZM is used to model the fiber tow-matrix
interface.
These methods can be used to predict either the tensile
or compressive behavior of the textile composites. Some
examples of researches on the tensile behavior of triaxial
braids are Littell et al. [1], Miravete et al. [3], Xu et al. [13],
and Li et al. [15]. All of them considered the tensile damage
behavior of triaxial braided composites when loaded in the
axial direction although they have different configurations.
Compressive failure behavior, on the other hand, has been
studied by Littell et al. [1] and Li et al. [15] in different
methods.
In comparison to unidirectional laminates and other non-
textile composites, textile composites, especially braided
textile composites are not studied very well for their damage
and failure behavior. The common way of determining
these behaviors is using experimental techniques which
are relatively expensive. Therefore, computational methods
such as the PFA provide insight into the detailed damage and
failure distribution when applied at meso- and micro levels.
This type of analysis enables the determination of damage
and failure scheme based on the individual constituent
material properties.
This study is organized in two major sections. Firstly,
the configuration, material properties and modeling of the
selected triaxial braid is discussed followed by over-view
of progressive failure analysis methodology. The types and
description of the failure criteria applied is also discussed
in this section. Then, the results of the PFA are presented by
discussing the damage progression behavior and modes of
failure. The method is then validated using tensile failure
results from references before discussions on the damage
and failure behavior. The effects of finite thickness and
stacking assumption on the damage behavior are examined.
Finally, the damage behavior is discussed in compression
loading case before closing with conclusion.
2. Analysis
2.1 Configuration
Triaxially braided textile composites have complex
interlaced structures of axial and bias tows. The tows in turn
consist of both fibers and matrix at the final form. Due to the
complicated fiber tow geometry as well as the composition of
fiber and matrix materials, the modeling of these composites
is a very formidable task.
The modeling of triaxially braided textile composites can
be done in multi-scales. Since the material is made from
interlacing of fiber bundles called tows, the modeling of these
tows and the matrix between them is regarded as mesoscale
modeling. On the other hand, since individual tows are made
from thousands of fiber strands, their mechanical behavior
can be modeled at individual filament level which is called
microscale modeling.
Triaxially braided textile composite model is characterized
by a number of geometric parameters. Since it is not possible
to perfectly model the real braid geometry, simplified
geometric models are made for the tows. The modeling scale
at these tows and matrix between them is called mesoscale
modeling. One important parameter is the braiding angle (θ)
defined as the acute angle between the axial tow and bias.
The axial tows are the straight tows running in the major
material direction while bias tows are the undulating tows
running below and above the axial tows and other bias
tows. The other important parameters are the widths (wa,
DOI: http://dx.doi.org/10.5139/IJASS.2017.18.3.436 438
Int’l J. of Aeronautical & Space Sci. 18(3), 436–449 (2017)
wb), thicknesses (ta, tb) and in-between gaps (εa, εb) of the
axial and bias tows, respectively. All of these parameters are
shown in Fig. 1.
Other parameters defining a triaxially braided composite
are the three different volume fractions. The first is the tow
volume fraction (v tow) which is the ratio of volume of tows
to the total volume of the model. The second is the tow fiber
volume fraction (vftow) defined as the ratio of the volume of
fiber in the tows and the volume of the tow. The last volume
fraction is the total fiber volume fraction (vf0) defined as the
total volume of fiber in the whole braid divided by the total
volume of the braid. It can also be defined in terms of the tow
volume fraction and tow fiber volume fraction as shown in
equation 1 below:
6
�������� � ��������� (1)
The geometric modeling of the tows is based on some assumptions to simplify the geometric
parameters such as cross-sectional shape and tow paths. Both the axial tow and bias tows are assumed
to have lenticular cross-sections of circular arcs. The bias tows are modelled by sweeping the
lenticular cross-section along an undulating tow path while the cross-section is kept parallel to the
bias tows running in the other direction. Then, these tows are duplicated and arranged to create the
full braid model from which the repeating unit cell can be cut out. Some geometric components of the
bias tow which was partitioned in to a number of groups for material orientation assignment. (See Fig.
3.) Detailed description of the modeling has been discussed in detail in a paper preceding this one [16].
The triaxially braided composite used in this study is a regular braid with a braiding angle of 30⁰. The width (��), thickness (��) and in-between gaps (��) of the axial tows are 2.40 mm, 0.50 mm and
2.38 mm, respectively. Similarly, the width (��), thickness (��) and in-between gaps (��) of the bias
tows were 2.20 mm, 0.50 mm and 1.94 mm, respectively. The braided unit cell is shown in Fig. 2 with
the dimensions. The tow volume fraction (����), fiber volume fraction (�����) and total fiber volume
fraction (���) were 34.1%, 78.0% and 26.6%, respectively.
Fig. 2. Unit cell of the 30⁰ triaxial braid used in this study
W = 9.56 mm
t = 1.54 mm
L = 8.28 mm
. (1)
The geometric modeling of the tows is based on some
assumptions to simplify the geometric parameters such as
cross-sectional shape and tow paths. Both the axial tow and
bias tows are assumed to have lenticular cross-sections of
circular arcs. The bias tows are modelled by sweeping the
lenticular cross-section along an undulating tow path while
the cross-section is kept parallel to the bias tows running
in the other direction. Then, these tows are duplicated
and arranged to create the full braid model from which
the repeating unit cell can be cut out. Bias tow segments
were partitioned in to a number of groups for material
orientation assignment. (See Fig. 3.) Detailed description of
the modeling has been discussed in a paper preceding this
one [16].
The triaxially braided composite used in this study is a
regular braid with a braiding angle of 30⁰. The width (wa),
thickness (ta) and in-between gaps (εa) of the axial tows are
2.40 mm, 0.50 mm and 2.38 mm, respectively. Similarly, the
width (wb), thickness (tb) and in-between gaps (εb) of the bias
tows were 2.20 mm, 0.50 mm and 1.94 mm, respectively. The
braided unit cell is shown in Fig. 2 with the dimensions. The
tow volume fraction (v tow), fiber volume fraction (vftow) and
total fiber volume fraction (vf0) were 34.1%, 78.0% and 26.6%,
respectively.
2.2 Material Properties
The triaxial braid considered in this study is made from
carbon fiber and epoxy matrix constituent materials. The
elastic and failure properties of these materials are given
in Tables 1 and 2. These material properties are used at the
micro-scale computation to get the homogenized properties
for the tows. The homogenization is based on modified
classical laminate theory and micromechanics that has
been incorporated in a commercial software called MCQ-
Composites [17]. These calculations were made throughout
the progressive failure analysis process since the degradation
of material properties was made at the micro level. This
process is discussed in detail later.
The homogenized properties were assigned to the tows
in the mesoscale unit cells which needed the material
orientation assignments. The material orientation was
assigned by aligning the fiber direction to the tangent of the
tow paths while the transverse directions were perpendicular
to it. This material orientation definition is shown in Fig. 3.
5
Triaxially braided textile composite model is characterized by a number of geometric parameters.
Since it is not possible to perfectly model the real braid geometry, simplified geometric models are
made for the tows. The modeling scale at these tows and matrix between them is called mesoscale
modeling. One important parameter is the braiding angle ( ) defined as the acute angle between the
axial tow and bias. The axial tows are the straight tows running in the major material direction while
bias tows are the undulating tows running below and above the axial tows and other bias tows. The
other important parameters are the widths ( , ), thicknesses ( , ) and in-between gaps ( , )
of the axial and bias tows, respectively. All of these parameters are shown in Fig. 1.
Fig. 1. Major geometric parameters defining triaxially braided textile composite
Other parameters defining a triaxially braided composite are the three different volume fractions.
The first is the tow volume fraction ( ) which is the ratio of volume tows to the total volume of the
model. The second is the tow fiber volume fraction ( ) defined as the ratio between the volume of
fiber in the tows and the volume of the tow. The last volume fraction is the total fiber volume fraction
( ) defined as the total volume of fiber in the whole braid divided by the total volume of the braid. It
can also be defined in terms of the tow volume fraction and tow fiber volume fraction as shown in
equation 1 below.
wa εa ta
θ
εbwb
tb
θ – Braiding angle wa – Width of axial tow wb – Width of bias tow ta – Thickness of axial tow tb – Thickness of bias tow a – Gap between axial towsb – Gap between bias tows
Fig. 1. Major geometric parameters defining triaxially braided textile composite
6
�������� � ��������� (1)
The geometric modeling of the tows is based on some assumptions to simplify the geometric
parameters such as cross-sectional shape and tow paths. Both the axial tow and bias tows are assumed
to have lenticular cross-sections of circular arcs. The bias tows are modelled by sweeping the
lenticular cross-section along an undulating tow path while the cross-section is kept parallel to the
bias tows running in the other direction. Then, these tows are duplicated and arranged to create the
full braid model from which the repeating unit cell can be cut out. Some geometric components of the
bias tow which was partitioned in to a number of groups for material orientation assignment. (See Fig.
3.) Detailed description of the modeling has been discussed in detail in a paper preceding this one [16].
The triaxially braided composite used in this study is a regular braid with a braiding angle of 30⁰. The width (��), thickness (��) and in-between gaps (��) of the axial tows are 2.40 mm, 0.50 mm and
2.38 mm, respectively. Similarly, the width (��), thickness (��) and in-between gaps (��) of the bias
tows were 2.20 mm, 0.50 mm and 1.94 mm, respectively. The braided unit cell is shown in Fig. 2 with
the dimensions. The tow volume fraction (����), fiber volume fraction (�����) and total fiber volume
fraction (���) were 34.1%, 78.0% and 26.6%, respectively.
Fig. 2. Unit cell of the 30⁰ triaxial braid used in this study
W = 9.56 mm
t = 1.54 mm
L = 8.28 mm
Fig. 2. Unit cell of the 30⁰ triaxial braid used in this study
Table 1. Mechanical properties of carbon fiber IM7 [18]
7
2.2. Material Properties
The triaxial braid considered in this study is made from carbon fiber and epoxy matrix constituent
materials. The elastic and failure properties of these materials has been given in Tables 1 and 2. These
material properties are used at the micro-scale computation to get the homogenized properties for the
tows. The homogenization based on modified classical laminate theory and micromechanics that has
been incorporated in a commercial software called MCQ-Composites [17]. These calculations were
made throughout the progressive failure analysis process since the degradation of material properties
was made at the micro level. This process is discussed in detail later.
Table 1. Mechanical properties of carbon fiber IM7 [18]
Elastic properties Longitudinal modulus (GPa) 276.0 Transverse modulus (GPa) 27.6 In-plane shear modulus (GPa) 138 Transverse modulus (GPa) 7.8 Poisson’s ratio 0.3 Poisson’s ratio 0.8 Strength properties Longitudinal tensile strength (MPa) 3800 Longitudinal compressive strength (MPa) 2980
Table 2. Mechanical properties of the matrix [13]
Elastic properties Elastic modulus (GPa) 3.0 Poisson’s ratio 0.35 Strength properties Tensile strength (MPa) 65 Compressive strength (MPa) 130
These homogenized properties were assigned to the tows in the mesoscale unit cells which needed
the material orientation assignments. The material orientation was assigned by aligning the fiber
direction to the tangent of the tow paths while the transverse directions were perpendicular to it. This
Table 2. Mechanical properties of the matrix [13]
7
2.2. Material Properties
The triaxial braid considered in this study is made from carbon fiber and epoxy matrix constituent
materials. The elastic and failure properties of these materials has been given in Tables 1 and 2. These
material properties are used at the micro-scale computation to get the homogenized properties for the
tows. The homogenization based on modified classical laminate theory and micromechanics that has
been incorporated in a commercial software called MCQ-Composites [17]. These calculations were
made throughout the progressive failure analysis process since the degradation of material properties
was made at the micro level. This process is discussed in detail later.
Table 1. Mechanical properties of carbon fiber IM7 [18]
Elastic properties Longitudinal modulus (GPa) 276.0 Transverse modulus (GPa) 27.6 In-plane shear modulus (GPa) 138 Transverse modulus (GPa) 7.8 Poisson’s ratio 0.3 Poisson’s ratio 0.8 Strength properties Longitudinal tensile strength (MPa) 3800 Longitudinal compressive strength (MPa) 2980
Table 2. Mechanical properties of the matrix [13]
Elastic properties Elastic modulus (GPa) 3.0 Poisson’s ratio 0.35 Strength properties Tensile strength (MPa) 65 Compressive strength (MPa) 130
These homogenized properties were assigned to the tows in the mesoscale unit cells which needed
the material orientation assignments. The material orientation was assigned by aligning the fiber
direction to the tangent of the tow paths while the transverse directions were perpendicular to it. This
439
Tsinuel N. Geleta Multi-scale Progressive Failure Analysis of Triaxially Braided Textile Composites
http://ijass.org
2.3. FE Model and Periodic Boundary Condition
The finite element model for the meso-scale unit cell was
generated using 3D four node tetrahedral linear elements
(C3D4). In order to simulate the repeating nature of the unit
cells, periodic boundary conditions (PBC) were applied to
the opposite faces of the unit cell. The faces of the unit cell are
named as shown in Fig. 4. The number of linear tetrahedral
elements and nodes used for the unit cell are 42,052 and
8,476, respectively. Three different types of ply stackings have
been modeled by varying the boundary condition applied on
the top-bottom pair of faces. The first is the antisymmetric
stacking infinite number of plies where PBCs are applied in
all faces. The second one is the symmetric stacking infinite
plies where PBCs are applied at the in-plane boundary faces
while multi-point constraints (MPCs) were applied to the
z-direction degree of freedom of the out-of-plane boundary
faces. This makes the z-displacements of all nodes in the top
and bottom faces to be constants, which means the faces
stay flat after loading. The third is single ply or free-free case
where the top and the bottom faces are simply set free of any
kind of boundary condition, while applying PBCs at the in-
plane boundary faces. All of these boundary conditions are
summarized in Table 3.
2.4 Multi-scale Progressive Failure Analysis
Progressive failure analysis is a computational method
8
material orientation definition is shown in Fig. 3.
Fig. 3. Material orientation
2.3. FE Model and Periodic Boundary Condition
The finite element model for the meso-scale unit cell was generated using 3D four node tetrahedral
linear elements (C3D4). In order to simulate the repeating nature of the unit cells, periodic boundary
conditions (PBC) were applied to the opposite faces of the unit cell. The faces of the unit cell are
named as shown in Fig. 4. The number of linear tetrahedral elements and nodes used for the unit cell
are 42,052 and 8,476, respectively. Three different types of ply stacking have been modeled by
varying the boundary condition applied on the top-bottom pair of faces. The first is the antisymmetric
stacking infinite number of plies where PBCs are applied in all faces. The second one is the
symmetric stacking infinite plies where PBCs are applied at the in-plane boundary faces while multi-
point constraints (MPCs) were applied to the z-direction degree of freedom of the out-of-plane
boundary faces. This makes the z-displacements of all nodes in the top and bottom faces to be
Coordinate systems x, y, z - Global x1, y1, z1 - Tow path 1, 2, 3 - Local material axis
Fig. 3. Material orientation
9
constants, which means the faces stay flat after loading. The third is single ply or free-free case where
the top and the bottom faces are simply set free of any kind of boundary condition, while applying
PBCs at the in-plane boundary faces. All of these boundary conditions are summarized in Table 3.
Fig. 4. Matching opposite faces of meso-scale unit cell mesh
Table 3. Boundary conditions applied to unit cell for different ply stacking types
Ply stacking Top-Bottom Front-Back Left-Right
Single ply – PBC PBC
Symmetric multiple MPC PBC PBC
Antisymmetric multiple PBC PBC PBC
2.4. Multi-scale Progressive Failure Analysis
Progressive failure analysis is a computational method using finite element analysis with which the
step-by-step damage and failure of materials is simulated. This method is applied by iteratively
conducting finite element analyses on a model by progressively changing either the load or the
material properties. The overall load on the structure is systematically increased gradually with each
iteration by monitoring the amount of damage and structural stability. The damage and fracture of the
structure is represented by local degradation of material property and removal of elements,
respectively. The decision whether or not to degrade the material properties is decided based on
conditions called failure criteria. The process of PFA starts with the ordinary FEA of the model using
Left
Right
Front
Back
Top
Bottom
Fig. 4. Matching opposite faces of meso-scale unit cell mesh
Table 3. Boundary conditions applied to unit cell for different ply stacking types
9
constants, which means the faces stay flat after loading. The third is single ply or free-free case where
the top and the bottom faces are simply set free of any kind of boundary condition, while applying
PBCs at the in-plane boundary faces. All of these boundary conditions are summarized in Table 3.
Fig. 4. Matching opposite faces of meso-scale unit cell mesh
Table 3. Boundary conditions applied to unit cell for different ply stacking types
Ply stacking Top-Bottom Front-Back Left-Right
Single ply – PBC PBC
Symmetric multiple MPC PBC PBC
Antisymmetric multiple PBC PBC PBC
2.4. Multi-scale Progressive Failure Analysis
Progressive failure analysis is a computational method using finite element analysis with which the
step-by-step damage and failure of materials is simulated. This method is applied by iteratively
conducting finite element analyses on a model by progressively changing either the load or the
material properties. The overall load on the structure is systematically increased gradually with each
iteration by monitoring the amount of damage and structural stability. The damage and fracture of the
structure is represented by local degradation of material property and removal of elements,
respectively. The decision whether or not to degrade the material properties is decided based on
conditions called failure criteria. The process of PFA starts with the ordinary FEA of the model using
Left
Right
Front
Back
Top
Bottom
DOI: http://dx.doi.org/10.5139/IJASS.2017.18.3.436 440
Int’l J. of Aeronautical & Space Sci. 18(3), 436–449 (2017)
using finite element analysis with which the step-by-step
damage and failure of materials is simulated. This method
is applied by iteratively conducting finite element analyses
on a model by progressively changing either the load or
the material properties. The overall load on the structure
is systematically increased gradually with each iteration by
monitoring the amount of damage and structural stability.
The damage and fracture of the structure is represented
by local degradation of material property and removal
of elements, respectively. The decision whether or not
to degrade the material properties is decided based on
conditions called failure criteria. The process of PFA starts
with the ordinary FEA of the model using a small load. Then,
the stress and strain of every element is checked against the
failure criteria defined by every stress or strain component or
their combinations.
The complete process of the progressive failure analysis
is done in two levels of computations conjugated in to one
cycle. The lower level is the micro-scale analysis where
the local material property homogenization, micro-stress
computation and degradation takes place. The other level is
the meso-scale analysis in which generalized finite element
analysis and stability of the structure is computed. The multi-
scale analysis is discussed in detail in Section 2.4.2.
The process of PFA described here has been applied
using the commercial software GENOA [19]. The software is
capable of importing the input file from ABAQUS, another
commercial software, and apply all the required failure
criteria before running. The advantage of this software is
that it can run both micro and meso-scale analysis within
the broader PFA. It checks for the micro failures and
degrades the corresponding matrix or fiber properties before
homogenizing them for the next iteration. The microscale
analysis is done by MCQ-Composites [17]. The whole PFA
process used by these programs and the failure criteria
applied are described in the following section.
2.4.1 Failure Criteria
Failure criteria are functions in stress or strain which
identify material elements that are in “failed” state from the
“un-failed” ones. From the long list failure criteria [20, 21],
maximum stress criteria have been applied in this study.
At each individual load step, the orthotropic composite
domain such as matrix pocket, tow matrix and tow stresses
and strains are obtained from micro-stress analysis. The
first twelve failure modes are associated with the positive
and negative limits of the six local stress components in the
material direction as follows [19]:
10
a small load. Then, the stress and strain of every element is checked against the failure criteria defined
by every stress or strain component or their combinations.
The complete process of the progressive failure analysis is done in two levels of computations
conjugated in to one cycle. The lower level is the micro-scale analysis where the local material
property homogenization, micro-stress computation and degradation takes place. The other level is the
meso-scale analysis in which generalized finite element analysis and stability of the structure is
computed. The multi-scale analysis is discussed in detail in Section 2.4.2.
The process of PFA described here has been applied using the commercial software GENOA [19].
The software is capable of importing the input file from ABAQUS, another commercial software, and
apply all the required failure criteria before running. The advantage of this software is that it can run
both micro and meso-scale analysis within the broader PFA. It checks for the micro failures and
degrades the corresponding matrix or fiber properties before homogenizing them for the next iteration.
The microscale analysis is done by MCQ-Composites [17]. The whole PFA process used by these
programs and the failure criteria applied are described in the following section.
2.4.1. Failure Criteria
Failure criteria are functions in stress or strain which identify material elements that are in “failed”
state from the “un-failed” ones. From the long list failure criteria [20, 21], maximum stress criteria
have been applied in this study.
At each individual load step, the orthotropic composite domain such as matrix pocket, tow matrix
and tow stresses and strains are obtained micro-stress analysis. The first twelve failure modes are
associated with the positive and negative limits of the six local stress components in the material
direction as follows [19]:
(2a) , (2a)
11
(2b)
(2c)
(2d)
(2e)
(2f)
where S, C and T indicate the strength in the specified direction, compression mode and tension mode,
respectively. Each of the terms on the left and right of the inequality in equation 2 are defined in Table
4. These failure criteria represent the micro-scale matrix and fiber failure which in-turn defines the
individual tow failures. These criteria can also be assigned to isotropic pure matrix pockets between
tows even though the three material directions behave in the same way.
The failure criteria application in the current study is grouped in to two. The first is, the criteria for
the pure matrix elements where the criteria simplify to compression, tension and shear modes. Since
there is no fiber in the pure matrix pocket, the strength parameters of the matrix are directly used to
check the status of the matrix. All the three criteria were turned on for both damage and fracture. This
means, fracture of an element in any mode will cause its damage and eventual removal.
For the fiber tows, on the other hand, all of the failure criteria depicted in Table 4 were applied for
the damage and fracture modeling. However, the only criteria turned on to fracture the tows was the
longitudinal tensile criteria. This is because the elements of the fiber tows should not be removed but
damaged unless fiber breakage occurs. The fiber breakage means loss of longitudinal tensile strength
of the tows. The rest of the failure criteria will only cause degradation of the material properties in
that particular direction or damage.
2.4.2. PFA Process
The damage tracking process can be illustrated in terms of load – displacement curve as shown in Fig.
5. At point A of the load increment, assessment of initial composite material damage based on the
, (2b)
11
(2b)
(2c)
(2d)
(2e)
(2f)
where S, C and T indicate the strength in the specified direction, compression mode and tension mode,
respectively. Each of the terms on the left and right of the inequality in equation 2 are defined in Table
4. These failure criteria represent the micro-scale matrix and fiber failure which in-turn defines the
individual tow failures. These criteria can also be assigned to isotropic pure matrix pockets between
tows even though the three material directions behave in the same way.
The failure criteria application in the current study is grouped in to two. The first is, the criteria for
the pure matrix elements where the criteria simplify to compression, tension and shear modes. Since
there is no fiber in the pure matrix pocket, the strength parameters of the matrix are directly used to
check the status of the matrix. All the three criteria were turned on for both damage and fracture. This
means, fracture of an element in any mode will cause its damage and eventual removal.
For the fiber tows, on the other hand, all of the failure criteria depicted in Table 4 were applied for
the damage and fracture modeling. However, the only criteria turned on to fracture the tows was the
longitudinal tensile criteria. This is because the elements of the fiber tows should not be removed but
damaged unless fiber breakage occurs. The fiber breakage means loss of longitudinal tensile strength
of the tows. The rest of the failure criteria will only cause degradation of the material properties in
that particular direction or damage.
2.4.2. PFA Process
The damage tracking process can be illustrated in terms of load – displacement curve as shown in Fig.
5. At point A of the load increment, assessment of initial composite material damage based on the
, (2c)
11
(2b)
(2c)
(2d)
(2e)
(2f)
where S, C and T indicate the strength in the specified direction, compression mode and tension mode,
respectively. Each of the terms on the left and right of the inequality in equation 2 are defined in Table
4. These failure criteria represent the micro-scale matrix and fiber failure which in-turn defines the
individual tow failures. These criteria can also be assigned to isotropic pure matrix pockets between
tows even though the three material directions behave in the same way.
The failure criteria application in the current study is grouped in to two. The first is, the criteria for
the pure matrix elements where the criteria simplify to compression, tension and shear modes. Since
there is no fiber in the pure matrix pocket, the strength parameters of the matrix are directly used to
check the status of the matrix. All the three criteria were turned on for both damage and fracture. This
means, fracture of an element in any mode will cause its damage and eventual removal.
For the fiber tows, on the other hand, all of the failure criteria depicted in Table 4 were applied for
the damage and fracture modeling. However, the only criteria turned on to fracture the tows was the
longitudinal tensile criteria. This is because the elements of the fiber tows should not be removed but
damaged unless fiber breakage occurs. The fiber breakage means loss of longitudinal tensile strength
of the tows. The rest of the failure criteria will only cause degradation of the material properties in
that particular direction or damage.
2.4.2. PFA Process
The damage tracking process can be illustrated in terms of load – displacement curve as shown in Fig.
5. At point A of the load increment, assessment of initial composite material damage based on the
(+), (2d)
11
(2b)
(2c)
(2d)
(2e)
(2f)
where S, C and T indicate the strength in the specified direction, compression mode and tension mode,
respectively. Each of the terms on the left and right of the inequality in equation 2 are defined in Table
4. These failure criteria represent the micro-scale matrix and fiber failure which in-turn defines the
individual tow failures. These criteria can also be assigned to isotropic pure matrix pockets between
tows even though the three material directions behave in the same way.
The failure criteria application in the current study is grouped in to two. The first is, the criteria for
the pure matrix elements where the criteria simplify to compression, tension and shear modes. Since
there is no fiber in the pure matrix pocket, the strength parameters of the matrix are directly used to
check the status of the matrix. All the three criteria were turned on for both damage and fracture. This
means, fracture of an element in any mode will cause its damage and eventual removal.
For the fiber tows, on the other hand, all of the failure criteria depicted in Table 4 were applied for
the damage and fracture modeling. However, the only criteria turned on to fracture the tows was the
longitudinal tensile criteria. This is because the elements of the fiber tows should not be removed but
damaged unless fiber breakage occurs. The fiber breakage means loss of longitudinal tensile strength
of the tows. The rest of the failure criteria will only cause degradation of the material properties in
that particular direction or damage.
2.4.2. PFA Process
The damage tracking process can be illustrated in terms of load – displacement curve as shown in Fig.
5. At point A of the load increment, assessment of initial composite material damage based on the
(+), (2e)
11
(2b)
(2c)
(2d)
(2e)
(2f)
where S, C and T indicate the strength in the specified direction, compression mode and tension mode,
respectively. Each of the terms on the left and right of the inequality in equation 2 are defined in Table
4. These failure criteria represent the micro-scale matrix and fiber failure which in-turn defines the
individual tow failures. These criteria can also be assigned to isotropic pure matrix pockets between
tows even though the three material directions behave in the same way.
The failure criteria application in the current study is grouped in to two. The first is, the criteria for
the pure matrix elements where the criteria simplify to compression, tension and shear modes. Since
there is no fiber in the pure matrix pocket, the strength parameters of the matrix are directly used to
check the status of the matrix. All the three criteria were turned on for both damage and fracture. This
means, fracture of an element in any mode will cause its damage and eventual removal.
For the fiber tows, on the other hand, all of the failure criteria depicted in Table 4 were applied for
the damage and fracture modeling. However, the only criteria turned on to fracture the tows was the
longitudinal tensile criteria. This is because the elements of the fiber tows should not be removed but
damaged unless fiber breakage occurs. The fiber breakage means loss of longitudinal tensile strength
of the tows. The rest of the failure criteria will only cause degradation of the material properties in
that particular direction or damage.
2.4.2. PFA Process
The damage tracking process can be illustrated in terms of load – displacement curve as shown in Fig.
5. At point A of the load increment, assessment of initial composite material damage based on the
(+), (2f)
where S, C and T indicate the strength in the specified
direction, compression mode and tension mode,
respectively. Each of the terms on the left and right of the
inequality in equation 2 are defined in Table 4. These failure
criteria represent the micro-scale matrix and fiber failure
which in-turn defines the individual tow failures. These
criteria can also be assigned to isotropic pure matrix pockets
between tows even though the three material directions
behave in the same way.
The failure criteria application in the current study is
grouped in to two. The first is the criteria for the pure matrix
elements where the criteria simplify to compression, tension
and shear modes. Since there is no fiber in the pure matrix
pocket, the strength parameters of the matrix are directly
used to check the status of the matrix. All the three criteria
were turned on for both damage and fracture. This means,
fracture of an element in any mode will cause its damage and
eventual removal.
For the fiber tows, on the other hand, all of the failure
criteria depicted in Table 4 were applied for the damage
and fracture modeling. However, the only criteria turned
on to fracture the tows was the longitudinal tensile criteria.
This is because the elements of the fiber tows should not be
removed but damaged unless fiber breakage occurs. The
fiber breakage means loss of longitudinal tensile strength
of the tows. The rest of the failure criteria will only cause
degradation of the material properties in that particular
direction or damage.
2.4.2 PFA Process
The damage tracking process can be illustrated in terms
of load – displacement curve as shown in Fig. 5. At point A of
the load increment, assessment of initial composite material
damage based on the proposed failure criteria is made.
Based on the selected failure criteria, the material properties
are degraded and the FEM repeated. The applied load is
maintained at a certain value (Pa) at which equilibrium
was achieved while running a number of trials with a load
increment until the next equilibrium is attained at point B.
Whenever an equilibrium point like B is achieved, the whole
structure is checked for stability. If it is not stable, then PFA
441
Tsinuel N. Geleta Multi-scale Progressive Failure Analysis of Triaxially Braided Textile Composites
http://ijass.org
process is deemed complete and the program terminates
which is represented by point N in Fig. 5. Otherwise, the
current point B will turn in to point A for the next iteration
until the structure becomes unstable.
In its simplest form, material property degradation is
done by factoring the Young’s moduli and shear modulus
with degradation factors. A simplified form used by Tan et al.
[22] is shown by equation 3 as:
12
proposed failure criteria is made. Based on the selected failure criteria, the material properties are
degraded and the FEM repeated. The applied load is maintained at a certain value ( ) at which
equilibrium was achieved while running a number of trials with a load increment until the next
equilibrium is attained at point B. Whenever an equilibrium point like B is achieved, the whole
structure is checked for stability. If it is not stable, then PFA process is deemed complete and the
program terminates which is represented by point N in Fig. 5. Otherwise, the current point B will turn
in to point A for the next iteration until the structure becomes unstable.
In its simplest form, material property degradation is done by factoring the Young’s moduli and
shear modulus with degradation factors. A simplified form used by Tan et al. [22] is shown by
equation 3 as:
(3a)
(3b)
(3c)
, (3a)
12
proposed failure criteria is made. Based on the selected failure criteria, the material properties are
degraded and the FEM repeated. The applied load is maintained at a certain value ( ) at which
equilibrium was achieved while running a number of trials with a load increment until the next
equilibrium is attained at point B. Whenever an equilibrium point like B is achieved, the whole
structure is checked for stability. If it is not stable, then PFA process is deemed complete and the
program terminates which is represented by point N in Fig. 5. Otherwise, the current point B will turn
in to point A for the next iteration until the structure becomes unstable.
In its simplest form, material property degradation is done by factoring the Young’s moduli and
shear modulus with degradation factors. A simplified form used by Tan et al. [22] is shown by
equation 3 as:
(3a)
(3b)
(3c)
, (3b)
12
proposed failure criteria is made. Based on the selected failure criteria, the material properties are
degraded and the FEM repeated. The applied load is maintained at a certain value ( ) at which
equilibrium was achieved while running a number of trials with a load increment until the next
equilibrium is attained at point B. Whenever an equilibrium point like B is achieved, the whole
structure is checked for stability. If it is not stable, then PFA process is deemed complete and the
program terminates which is represented by point N in Fig. 5. Otherwise, the current point B will turn
in to point A for the next iteration until the structure becomes unstable.
In its simplest form, material property degradation is done by factoring the Young’s moduli and
shear modulus with degradation factors. A simplified form used by Tan et al. [22] is shown by
equation 3 as:
(3a)
(3b)
(3c)
, (3c)
where Ed11, Ed
22 and Gd12 are the effective material properties of
the damaged elements while E 011, E 022 and G 012 are those of the
elements before damage. D1, D2, and D6 are the directional
damage parameters for extension and shear. Similarly,
Camanho and Matthews [23] considered four damage modes 12
proposed failure criteria is made. Based on the selected failure criteria, the material properties are
degraded and the FEM repeated. The applied load is maintained at a certain value ( ) at which
equilibrium was achieved while running a number of trials with a load increment until the next
equilibrium is attained at point B. Whenever an equilibrium point like B is achieved, the whole
structure is checked for stability. If it is not stable, then PFA process is deemed complete and the
program terminates which is represented by point N in Fig. 5. Otherwise, the current point B will turn
in to point A for the next iteration until the structure becomes unstable.
In its simplest form, material property degradation is done by factoring the Young’s moduli and
shear modulus with degradation factors. A simplified form used by Tan et al. [22] is shown by
equation 3 as:
(3a)
(3b)
(3c)
Fig. 5. PFA in the form of load – displacement curve [19]
Table 4. Maximum stress failure criteria [19]
13
Fig. 5. PFA in the form of load – displacement curve [19]
Table 4. Maximum stress failure criteria [19]
Mode of failure Expression Longitudinal tensile
Longitudinal compressive
Fiber crushing mode:
Delamination mode:
Micro-buckling mode:
The minimum value of , and is considered as ply longitudinal compressive strength
, ,
Transverse tensile strength
Transverse compressive strength
In-plane shear strength
Longitudinal normal shear (through-the-thickness) strength
Transverse normal shear (through-the-thickness) strength
where , and are the effective material properties of the damaged elements while ,
DOI: http://dx.doi.org/10.5139/IJASS.2017.18.3.436 442
Int’l J. of Aeronautical & Space Sci. 18(3), 436–449 (2017)
by using Hashin’s failure theory. For the degradation, they
considered the damage of constituent materials individually
including compression as shown by equation 4.
Matrix tensile or shear cracking:
14
���� and ���� are those of the elements before damage. ��, ��, and �� are the directional damage
parameters for extension and shear. Similarly, Camanho and Matthews [23] considered four damage
modes by using Hashin’s failure theory. For the degradation, they considered the damage of
constituent materials individually including compression as shown by equation 4.
Matrix tensile or shear cracking:
��� � ����� � ���� � ������ � ���� � ������ ����
Fiber tensile fracture:
��� � ����� ����
Matrix compressive or shear cracking:
��� � ����� � ���� � ������ � ���� � ������ ����
Fiber compressive fracture:
��� � ����� ����
where superscripts d, C and T represent degraded property, compression and tension, respectively. The
degradation factors used in this study are all taken from the default values used by GENOA software
[19]. The degradation factors used are ��� � ��� � �� ; ��� � ��� ; ��� � ��� � ��� and
��� � ���.
The overall process of the progressive failure analysis has been summarized in Fig. 6 divided into
(4a)
Fiber tensile fracture:
14
���� and ���� are those of the elements before damage. ��, ��, and �� are the directional damage
parameters for extension and shear. Similarly, Camanho and Matthews [23] considered four damage
modes by using Hashin’s failure theory. For the degradation, they considered the damage of
constituent materials individually including compression as shown by equation 4.
Matrix tensile or shear cracking:
��� � ����� � ���� � ������ � ���� � ������ ����
Fiber tensile fracture:
��� � ����� ����
Matrix compressive or shear cracking:
��� � ����� � ���� � ������ � ���� � ������ ����
Fiber compressive fracture:
��� � ����� ����
where superscripts d, C and T represent degraded property, compression and tension, respectively. The
degradation factors used in this study are all taken from the default values used by GENOA software
[19]. The degradation factors used are ��� � ��� � �� ; ��� � ��� ; ��� � ��� � ��� and
��� � ���.
The overall process of the progressive failure analysis has been summarized in Fig. 6 divided into
, (4b)
Matrix compressive or shear cracking:
14
���� and ���� are those of the elements before damage. ��, ��, and �� are the directional damage
parameters for extension and shear. Similarly, Camanho and Matthews [23] considered four damage
modes by using Hashin’s failure theory. For the degradation, they considered the damage of
constituent materials individually including compression as shown by equation 4.
Matrix tensile or shear cracking:
��� � ����� � ���� � ������ � ���� � ������ ����
Fiber tensile fracture:
��� � ����� ����
Matrix compressive or shear cracking:
��� � ����� � ���� � ������ � ���� � ������ ����
Fiber compressive fracture:
��� � ����� ����
where superscripts d, C and T represent degraded property, compression and tension, respectively. The
degradation factors used in this study are all taken from the default values used by GENOA software
[19]. The degradation factors used are ��� � ��� � �� ; ��� � ��� ; ��� � ��� � ��� and
��� � ���.
The overall process of the progressive failure analysis has been summarized in Fig. 6 divided into
(4c)
Fiber compressive fracture:
14
���� and ���� are those of the elements before damage. ��, ��, and �� are the directional damage
parameters for extension and shear. Similarly, Camanho and Matthews [23] considered four damage
modes by using Hashin’s failure theory. For the degradation, they considered the damage of
constituent materials individually including compression as shown by equation 4.
Matrix tensile or shear cracking:
��� � ����� � ���� � ������ � ���� � ������ ����
Fiber tensile fracture:
��� � ����� ����
Matrix compressive or shear cracking:
��� � ����� � ���� � ������ � ���� � ������ ����
Fiber compressive fracture:
��� � ����� ����
where superscripts d, C and T represent degraded property, compression and tension, respectively. The
degradation factors used in this study are all taken from the default values used by GENOA software
[19]. The degradation factors used are ��� � ��� � �� ; ��� � ��� ; ��� � ��� � ��� and
��� � ���.
The overall process of the progressive failure analysis has been summarized in Fig. 6 divided into
, (4d)
where superscripts d, C and T represent degraded property,
compression and tension, respectively. The degradation
factors used in this study are all taken from the default values
used by GENOA software [19]. The degradation factors used
are DT1 = DT
2 = 1%; DT4 = 10%; DC
1 = DC2 =20% and DC
4.
The overall process of the progressive failure analysis
has been summarized in Fig. 6 divided into two scales. At
the micro-scale, elastic property homogenization, material
property degradation and micro-stress computations are
done. This level involves the constituent matrix and fiber
properties. At this level, there is no finite element model
involved, instead modified classical laminate theory and
other micromechanics principles are used [17]. The other
level of analysis is the mesoscale where the 3D finite element
model is used to represent different parts of the unit cell. At
this level, the geometric and finite element models discussed
before are used to represent the fiber bundle tows and pure
matrix parts of the unit cell.
The failure criteria discussed before can be selectively
applied, for damage and fracture assessment. Here, a
damaged element means the one with reduced properties but
can transfer displacements and/or has considerable stiffness
and strength in other directions. Fractured element, on the
other hand, is an element that has no capability to transfer
force or displacement in any direction. Therefore, a fractured
element can be removed from the full model as described in
the PFA process. In the current case, for instance, even if tows
are damaged in their transverse direction in either tension,
compression or tension, the elements are not deemed to be
fractured as long as the tensile fracture of fibers occurs. This
is reasonable because, tows are even capable of resisting
tensile load even without matrix. However, the isotropic
matrix is analyzed with both damage and fracture turned on
for all failure criteria considered.
15
two scales. At the micro-scale, elastic property homogenization, material property degradation and
micro-stress computations are done. This level involves the constituent matrix and fiber properties. At
this level, there is no finite element model involved, instead modified classical laminate theory and
other micromechanics principles are used [17]. The other level of analysis is the mesoscale where the
3D finite element model is used to represent different parts of the unit cell. At this level, the geometric
and finite element models discussed before are used to represent the fiber bundle tows and pure
matrix parts of the unit cell.
Fig. 6. Multiscale progressive failure analysis process [19]
Start
Generate elastic properties from constituent properties
Compute generalized stresses using FEM
Compute micro-stresses for stuffer, filler and
weaver of the composite
Did local damage/ fracture occur?
Equilibrium reached, increase load
Too many nodes failed, reduce the load
and restart from the previous equilibrium
New damaged/ fractured nodes >
the limit?
Entire structure collapsed?
Print out the ultimate loads and all relative
End
Separate all elements connecting to the fractured
nodes, create additional nodes & renumber
Degrade the material properties for the damaged nodes according to the damage model
YN
N
Y
Y
N
Meso-scale Micro-scale
Fig. 6. Multiscale progressive failure analysis process [19]
,
,
,
,
,
,
443
Tsinuel N. Geleta Multi-scale Progressive Failure Analysis of Triaxially Braided Textile Composites
http://ijass.org
3. Results and Discussion
The PFA analysis was performed on a number of models
of the triaxially braided textile composite. Firstly, the
methodology was validated by comparing the results
obtained to experimental and computational results from
two different references. Then, the same configuration was
used to discuss the damage mode and progress with the
use of the stress-strain curve. Next, the effect of ply stacking
and boundary conditions has been discussed. Finally, the
compressive failure behavior is discussed using the three
material behavior assumptions for matrix.
3.1 Axial Tension and Compression Failure
Before conducting validation of the method an attempt
was made to achieve a reasonable convergence of mesh. For
this single ply stacking model was used, in which PBCs were
applied in the in-plane direction and free-free boundary
condition in the out-of-plane direction. Next, the mesh
dependency of damage behavior was investigated. Fig. 7
shows the stress-strain curve for four meshes with different
element sizes. However, the variation of the curves did not
converge to a specific value. For instance, comparing the
maximum stress values, percentage variation increased from
9.7% to 16.3% as the mesh size decreased from 0.4 mm to 0.3
mm and from 0.3 mm to 0.2 mm, respectively.
This is because of the inherent behavior of continuum
damage mechanics employed in GENOA that it does not
consider the energy dissipation through the process of
damage and fracture. Therefore, it varies with the variation
of mesh no matter how fine the mesh size is [24]. Rather
than trying to find a ‘best’ mesh, a mesh size was chosen in
two steps. The first was from the convergence of the elastic
solution. Then a mesh size which resulted in the closest
stress-strain curve to the experimental test was chosen.
This is reasonable because if someone wants to apply this
model to a larger application, use of the same mesh with the
same material set will result in reasonably similar damage
behavior. Therefore, a mesh size of 0.3 mm was chosen by
comparing the stress-strain curves which produced less
than 1% difference in initial elastic modulus compared to
that of the refined reference mesh and used for the rest of
the analyses.
Figure 8 shows the PFA predicted complete stress-strain
curve for the triaxial braid unit cell model under uniaxial
tension in the axial direction. Also plotted in the figure
are the experimental result by Miravete et al. [3] and the
analysis result by Xu et al. [13] using Micro-Mechanics of
Failure (MMF) model. The model used for this comparison
had infinitely stacked antisymmetric boundary condition
applied. The comparison was made using the stress-strain
curve which showed very good match with the experimental
results. As can be seen in the figure, a better match in
shape of the curve was obtained as compared to the MMF
prediction by Xu et al. [13]. However, the predicted strength
is slightly lower than that of the experimental model. This is
because of the possible difference in fiber volume fraction
and geometric dimensions assumed from the test specimen,
in addition to the uncertainty of mesh dependency of
CDM approach employed in GENOA. Since the geometric
dimensions and fiber volume fraction were directly taken
from the work of Xu et al. [13], the difference between the
current analysis and the experimental result is within a
reasonable range.
The progress of damage was demonstrated using the same
configuration with infinite plies in antisymmetric stacking.
This progress is shown in Fig. 9 and Table 5. The percentage
values shown in the table indicate the proportion of
damaged elements facing the specified failure mode relative
17
For instance, comparing the maximum stress values, percentage variation increased from 9.7% to 16.3%
as the mesh size decreased from 0.4 mm to 0.3 mm and from 0.3 mm to 0.2 mm, respectively.
This is because of the inherent behavior of continuum damage mechanics employed in GENOA
that it does not consider the energy dissipation through the process of damage and fracture. Therefore,
it varies with the variation of mesh no matter how fine the mesh size is [24]. Rather than trying to find
a ‘best’ mesh, a mesh size was chosen in two steps. The first was from the convergence of the elastic
solution. Then a mesh size which resulted in the closest stress-strain curve to the experimental test
was chosen. This is reasonable because if someone wants to apply this model to a larger application,
use of the same mesh with the same material set will result in reasonably similar damage behavior.
Therefore, a mesh size of 0.3 mm was chosen by comparing the stress-strain curves which produced
less than 1% difference in initial elastic modulus compared to that of the refined reference mesh and
used for the rest of the analyses.
Fig. 7. Mesh dependency of damage and failure progression
Figure 8 shows the PFA predicted complete stress-strain curve for the triaxial braided unit cell
model under uniaxial tension in the axial direction. Also plotted in the figure are the experimental
0
100
200
300
400
500
0.0% 0.5% 1.0% 1.5% 2.0%
Stre
ss (M
Pa)
Strain
0.2 mm
0.25 mm
0.4 mm
0.3 mm
Fig. 7. Mesh dependency of damage and failure progression
18
result by Miravete et al. [3] and the analysis result by Xu et al. [13] using Micro-Mechanics of Failure
(MMF) model. The model used for this comparison had infinitely stacked antisymmetric boundary
condition applied. The comparison was made using the stress-strain curve which showed very good
match with the experimental results. As can be seen in the figure, a better match in shape of the curve
was obtained as compared to the MMF prediction by Xu et al. [13]. However, the predicted strength is
slightly lower than that of the experimental model. This is because of the possible difference in fiber
volume fraction and geometric dimensions assumed from the test specimen, in addition to the
uncertainty of mesh dependency of CDM approach employed in GENOA. Since the geometric
dimensions and fiber volume fraction were directly taken from the work of Xu et al. [13], the
difference between the current analysis and the experimental result is within a reasonable range.
Fig. 8. Validation of PFA result against test and computational results from references for axial tension
loading
The progress of damage was demonstrated using the same configuration with infinite plies in
antisymmetric stacking. This progress is shown in Fig. 9 and Table 5. The percentage values shown in
the table indicate the proportion of damaged elements facing the specified failure mode relative to the
total number of elements in the considered unit cell part at that particular stage of fracture. (See Table
0
100
200
300
400
500
600
0.0% 0.5% 1.0% 1.5% 2.0%
Stre
ss (M
Pa)
Strain (%)
Test [3]
Current
MMF [10]
Fig. 8. Validation of PFA result against test and computational results from references for axial tension loading
DOI: http://dx.doi.org/10.5139/IJASS.2017.18.3.436 444
Int’l J. of Aeronautical & Space Sci. 18(3), 436–449 (2017)
to the total number of elements in the considered unit cell
part at that particular stage of fracture. (See Table 4 for the
explanation of the damage mode symbols.) The first elastic
portion of the stress-strain curve continues up to point P1
of Fig. 9 which has a strain and stress value of about 0.69%
and 290.9 MPa, respectively. The first sign of damage was
seen in most of the bias tows and edges of the axial tows as
shown by the segment from point P1 to P2 in Table 5. Most of
the damage seen in the bias tows is the in-plane shear that
resulted from their diagonal orientation from the loading
direction. The axial tows also showed slight damage at their
edges in transverse compression mode resulting from the
Poisson’s effect. However, this has very small effect on the
stress-strain curve since the axial tows are supporting the
load in their fiber direction while the damage is occurring in
perpendicular direction. At this stage, no significant damage
was seen in the pure matrix pocket.
The next stage of damage is shown by the segment of the
stress-strain curve from P2 to P3 of Fig. 9 and Table 5. At this
20
tows running in the two different directions. However, there is almost no additional damage or failure
observed in the bias tows at this stage. Therefore, the predominant modes of failure leading to the
major failure are the starting of axial tow fiber breakage and the damage to some parts of the matrix
pocket in crushing and mode II interface separation.
From point to of Fig. 9, the material shows slight resistance until the remaining matrix
pockets fail in similar fashion as before. The axial tows also keep failing in the form of tow fiber
breakage leading to point of Fig. 9. Beyond this point, most of the fiber in the axial tow has
already been damaged and is no longer supporting the axial load. Therefore, the bias tows start to
deform excessively with some failure in the axial direction.
Fig. 9. Stress-strain curve for damage progress in infinite antisymmetric stacking triaxial braid loaded
in axial tension
0
100
200
300
400
500
0.0% 0.5% 1.0% 1.5% 2.0%
Stre
ss (M
Pa)
Strain (%)
P1(0.69%, 290.9)
P2(1.04%, 388.8)
P3(1.21%, 439.6)
P4(1.25%, 331.3)P5(1.31%, 326.2)
P6(1.34%, 184.6)
P7(1.68%, 71.8)
Fig. 9. Stress-strain curve for damage progress in infinite antisymmet-ric stacking triaxial braid loaded in axial tension
Table 5. Damage modes with progressing damage in infinite antisymmetric stacking loaded in axial tension
Table 1. Damage modes with progressing damage in infinite antisymmetric stacking loaded in axial
tension
Damage and failure modes at levels shown by points on stress-strain curve in Fig. 9
Mat
rix
Dam
aged
All
Axi
al to
ws
-2.15% -18.9% -56.4% -78.7% -3.33% -2.86%
-89.0% -3.45% -5.44%
-89.8% -7.97% -5.59% -6.60%
-90.3% -10.9% -5.72% -9.57%
Bia
s tow
s
All
Dam
aged
-10.8% -86.1%-4.72%-2.88%
-95.7% -6.97% -2.88%
-95.8% -5.60%-4.44%
-95.8% -6.00%-5.32%
-94.6% -7.31% -5.01%
-96.3% -13.2% -12.0%
No damage Damaged Fractured
(Percentage values indicate the portion of elements facing the specified mode of failure from the current number elements in the corresponding unit cell part)
445
Tsinuel N. Geleta Multi-scale Progressive Failure Analysis of Triaxially Braided Textile Composites
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stage the only significant damages were more transverse
compression in axial tows and complete damage of the bias
tows through in-plane shear. However, the curve does not
seem to show significant change in slope, which is because
the axial tow damage in the transverse mode has very little
effect and the bias tow damage was very little as compared to
the number of elements already damaged in this mode. Once
again, the damage to the matrix pocket is still not occurring.
In both of these stages the pure matrix pocket is not damaged
because modes of failure in the tows are internal to the tows
instead of interfacial interaction with the matrix pocket.
The peak stress or the failure strength occurs at point
P3 of Fig. 9, beyond which the major failure of the braided
structure happens. The stress and strain values at this
point are 439.6 MPa and 1.21%, respectively. From point
22
Damage progress in the case of compressive loading has been shown in Fig. 10 and Table 6. The
first sign of damage occurred in small region of the axial tow edges indicated by point with a
strain and stress values of 0.44% and 185.3 MPa. Then, further increase in the axial compression
resulted in fiber micro-crushing in the axial tows as shown by point of the stress-strain curve
(0.49% and 202.3 MPa) and pictures. At this stage, the bias tows also start to show compressive
failure in the form of fiber micro-buckling. The next stage is the major drop in strength of the whole
braided structure shown as the part from to . The sudden drop in strength is mainly because of
the compressive fiber micro buckling damage in the bias tows and compressive failure in the pure
matrix pocket. Beyond this point, the stress did not change significantly while the strain increased.
However, the amount matrix pocket damage increases with increase in the global strain level as
shown by the damage patterns at point .
Fig. 10. Stress-strain curve for damage progress in infinite antisymmetric stacking of triaxial braid
loaded in axial compression
0
50
100
150
200
250
0.0% 0.2% 0.4% 0.6% 0.8% 1.0% 1.2% 1.4%
Stre
ss (M
Pa)
Strain (%)
P1(0.44%, 185.3)P2(0.49%, 202.3)
P3(0.52%, 60.5) P4(1.32%, 58.3)
Fig. 10. Stress-strain curve for damage progress in infinite antisym-metric stacking of triaxial braid loaded in axial compression
Table 6. Damage modes with progressing damage in infinite antisymmetric stacking with axial compression loading
Table 2. Damage modes with progressing damage in infinite antisymmetric stacking with axial
compression loading
Damage and failure modes at levels shown by points on stress-strain curve in Fig. 10
Mat
rix
Dam
aged
All
Axi
al to
ws
-8.03%-1.89%-8.03%-6.15%
-40.5%-32.1%-40.5%-8.54%
-67.9%-34.5%-67.9%-30.2%
-71.6%-34.6%-71.6%-32.5%
Bia
s tow
s
Dam
aged
All
-0.1%-0.1%-0.1%
-0.13%-0.13%-0.13%
-13.2%-13.2%-10.1%-3.61%
-26.3%-26.3%-17.1%
No damage Damaged Fractured(Percentage values indicate the portion of elements facing the specified mode of failure from the current number elements in the corresponding unit cell part)
DOI: http://dx.doi.org/10.5139/IJASS.2017.18.3.436 446
Int’l J. of Aeronautical & Space Sci. 18(3), 436–449 (2017)
P3 to P4, the stress-strain curve drops suddenly due to the
fiber breakage in some parts of the axial tow as well as the
beginning of damage in the matrix pocket. The matrix pocket
started damage and failure at some parts of the confined
spaces between axial tow and bias tows as well as the thin
matrix layer covering the bias tow in the top and bottom
faces of the unit cell. The failure mode in the pure matrix is
mainly in compression and shear. This kind of matrix pocket
failure may lead to interface separation in mode II. On the
other hand, the axial tow failure in the form of fiber breakage
has started at the ends of the axial tow where it is closely
confined between the bias tows running in the two different
directions. However, there is almost no additional damage or
failure observed in the bias tows at this stage. Therefore, the
predominant modes of failure leading to the major failure
are the starting of axial tow fiber breakage and the damage
to some parts of the matrix pocket in crushing and mode II
interface separation.
From point P4 to P5 of Fig. 9, the material shows slight
resistance until the remaining matrix pockets fail in similar
fashion as before. The axial tows also keep failing in the form
of tow fiber breakage leading to point P6 of Fig. 9. Beyond
this point, most of the fiber in the axial tow has already
been damaged and is no longer supporting the axial load.
Therefore, the bias tows start to deform excessively with
some failure in the axial direction.
Damage progress in the case of compressive loading has
been shown in Fig. 10 and Table 6. The first sign of damage
occurred in small region of the axial tow edges indicated by
point P1 with a strain and stress values of 0.44% and 185.3
MPa. Then, further increase in the axial compression resulted
in fiber micro-crushing in the axial tows as shown by point P2
of the stress-strain curve (0.49% and 202.3 MPa) and pictures.
At this stage, the bias tows also start to show compressive
failure in the form of fiber micro-buckling. The next stage
is the major drop in strength of the whole braided structure
shown as the part from P2 to P3. The sudden drop in strength
is mainly because of the compressive fiber micro buckling
damage in the bias tows and compressive failure in the pure
matrix pocket. Beyond this point, the stress did not change
significantly while the strain increased. However, the amount
matrix pocket damage increases with increase in the global
strain level as shown by the damage patterns at point P4.
3.2 Effect of Ply Stacking Type on Damage Behavior
The number and type of stacking of plies was checked if it
has effect on the damage and failure behavior of the triaxial
braid. The number of ply and stacking plays an important
role when there is a significant out-of-plane displacement
up on loading. The PFA was run on three conditions of ply
stacking under the same axial tensile loading condition;
single ply, infinite symmetric and anti-symmetrically stacked
cases. All three cases had the PBCs applied at the in-plane
boundaries. For the case of infinite number of plies stacked
in antisymmetric manner, periodic boundary conditions that
the displacement pattern is repeating is applied at the out-
of-plane faces of the unit cell. For the symmetrically stacked
infinite plies, the out-of-plane displacement in the top and
bottom faces are restrained to be flat after deformation. For
the single ply, the free-free condition is applied at the out-of-
plane boundaries.
For the current braid configuration, the variation of elastic
modulus in the axial direction has been shown to have very
small variation in the previous work [16]. It was shown that
under axial tension the predominant part of the load was
transferred by the axial tow exhibiting limited amount of
deformation at the bias tows. Therefore, the elastic behavior
of the whole assembly did not vary by changing the stacking
types since the stacking type varies the amount of out-of-
plane constraint.
The variation of stress-strain curves with the three ply
stacking conditions loaded in axial tension are shown in
Fig. 11. The results show very small variation between these
three conditions. This is because as shown in [16] the axial
x-direction tensile loading results in relatively small out-of-
plane deformation in the ply. Therefore, whether the unit
cell is restrained or not, its effect on the axial strength of the
triaxial braiding is found not significant.
3.3. Single Versus Multiple Unit Cell
The repeating nature of the unit cell is generally expected
to be seen in the elastic stress distribution. In other words,
the pattern of geometric repetition in the unit cell is reflected
25
Fig. 11. Variation of failure and damage behavior with ply stacking conditions
To verify this, larger models were made having dimensions in integer multiple of the single unit cell.
Firstly, the repeating nature of stress distribution was checked at the linear region of the stress-strain
curve as shown in Fig. 12. The comparison was made between single unit cell, nine unit cells and
twenty-five unit cells arranged in square fashion. In all three cases the load applied was in x –
direction which resulted in equal values of nominal stress (��� � 277 MPa) and strain (��̅ = 0.67%) at
the ply level. This point lies in the linear range of the stress-strain curves in Fig. 12. The repeating
nature of the stress can be seen very well, which proves the ability of the periodic boundary condition
to model the pattern of stress distribution.
However, repeating nature of the elastic range stress distribution does not guarantee the repeating
nature of the damage progression. Naturally, the repeating nature of unit cells goes up to the
occurrence of the first damage. Sometimes, once the initial damage has occurred, the next stage of
damage is more governed by numerical uncertainties than the geometry of the structure. (This can be
an equivalent representation of many material and structural uncertainties in the real specimen.)
Therefore, the pattern of damage post the initial one may or may not have repeating nature.
0
100
200
300
400
500
0.0% 0.5% 1.0% 1.5% 2.0%
Stre
ss (M
Pa)
Strain (%)
Antisymmetric_infiniteSymmetric_infiniteFree-free_single ply
Fig. 11. Variation of failure and damage behavior with ply stacking conditions
447
Tsinuel N. Geleta Multi-scale Progressive Failure Analysis of Triaxially Braided Textile Composites
http://ijass.org
in the stress distribution.
To verify this, larger models were made having dimensions
in integer multiple of the single unit cell. Firstly, the repeating
nature of stress distribution was checked at the linear region
of the stress-strain curve as shown in Fig. 12. The comparison
was made between single unit cell, nine unit cells and
twenty-five unit cells arranged in square fashion. In all three
cases the load applied was in x –direction which resulted in
equal values of nominal stress
25
Fig. 11. Variation of failure and damage behavior with ply stacking conditions
To verify this, larger models were made having dimensions in integer multiple of the single unit cell.
Firstly, the repeating nature of stress distribution was checked at the linear region of the stress-strain
curve as shown in Fig. 12. The comparison was made between single unit cell, nine unit cells and
twenty-five unit cells arranged in square fashion. In all three cases the load applied was in x –
direction which resulted in equal values of nominal stress (��� � 277 MPa) and strain (��̅ = 0.67%) at
the ply level. This point lies in the linear range of the stress-strain curves in Fig. 12. The repeating
nature of the stress can be seen very well, which proves the ability of the periodic boundary condition
to model the pattern of stress distribution.
However, repeating nature of the elastic range stress distribution does not guarantee the repeating
nature of the damage progression. Naturally, the repeating nature of unit cells goes up to the
occurrence of the first damage. Sometimes, once the initial damage has occurred, the next stage of
damage is more governed by numerical uncertainties than the geometry of the structure. (This can be
an equivalent representation of many material and structural uncertainties in the real specimen.)
Therefore, the pattern of damage post the initial one may or may not have repeating nature.
0
100
200
300
400
500
0.0% 0.5% 1.0% 1.5% 2.0%St
ress
(MPa
)Strain (%)
Antisymmetric_infiniteSymmetric_infiniteFree-free_single ply
and strain
25
Fig. 11. Variation of failure and damage behavior with ply stacking conditions
To verify this, larger models were made having dimensions in integer multiple of the single unit cell.
Firstly, the repeating nature of stress distribution was checked at the linear region of the stress-strain
curve as shown in Fig. 12. The comparison was made between single unit cell, nine unit cells and
twenty-five unit cells arranged in square fashion. In all three cases the load applied was in x –
direction which resulted in equal values of nominal stress (��� � 277 MPa) and strain (��̅ = 0.67%) at
the ply level. This point lies in the linear range of the stress-strain curves in Fig. 12. The repeating
nature of the stress can be seen very well, which proves the ability of the periodic boundary condition
to model the pattern of stress distribution.
However, repeating nature of the elastic range stress distribution does not guarantee the repeating
nature of the damage progression. Naturally, the repeating nature of unit cells goes up to the
occurrence of the first damage. Sometimes, once the initial damage has occurred, the next stage of
damage is more governed by numerical uncertainties than the geometry of the structure. (This can be
an equivalent representation of many material and structural uncertainties in the real specimen.)
Therefore, the pattern of damage post the initial one may or may not have repeating nature.
0
100
200
300
400
500
0.0% 0.5% 1.0% 1.5% 2.0%
Stre
ss (M
Pa)
Strain (%)
Antisymmetric_infiniteSymmetric_infiniteFree-free_single ply
at the ply level. This point lies in the linear range
of the stress-strain curves in Fig. 12. The repeating nature of
the stress can be seen very well, which proves the ability of
the periodic boundary condition to model the pattern of
stress distribution.
However, repeating nature of the elastic range stress
distribution does not guarantee the repeating nature of
the damage progression. Naturally, the repeating nature
of unit cells goes up to the occurrence of the first damage.
Sometimes, once the initial damage has occurred, the next
stage of damage is more governed by numerical uncertainties
than the geometry of the structure. (This can be an equivalent
representation of many material and structural uncertainties
in the real specimen.) Therefore, the pattern of damage post
the initial one may or may not have repeating nature.
Previously, it has been established that the current
configuration starts its damage in the form of in-plane shear
in the bias tows. In order to check the damage pattern, a single
unit cell model was compared to a nine-unit cell model. Fig.
13 shows this comparison made between these two models
at two different nominal stress levels. The first is at a nominal
stress and strain level of 270 MPa and 0.64%, respectively. At
this stage, there is very small amount of damage in the bias
tows which has very good match. This can be considered the
end of the linear stress range for the model. Then, at nominal
stress and strain level of 328 MPa and 0.80%, respectively,
the damage in the bias tows can be seen in both single unit
cell and nine-unit cell models. The damage shape begins to
lose the repeating pattern beyond this point, and the damage
cannot be guaranteed to be the same between models since
it becomes too sensitive to be stable.
3.4 Effect of Matrix Plasticity on Compression Failure
The effect of plasticity in the matrix was investigated for the
compressive failure case. Ernst et al. [25] showed that epoxy
resin behaves in brittle manner when it fails under tension
while it shows some plasticity in shear mode. Therefore,
it was thought to be needed to investigate the effect of the
plasticity of the epoxy matrix for the compressive failure.
The plasticity of the matrix was considered by taking two
different types of the assumptions based on experimental
test result taken from reference. The first is the elastic-
perfectly plastic assumption where the failure stress and
failure strain correspond to those of the experimental data.
26
Fig. 12. Repeating nature of stress patterns in single and multi-cell models under the same macro
stress and strain levels (��� �277 MPa, ��̅ �0.67%)
Previously, it has been established that the current configuration starts its damage in the form of in-
plane shear in the bias tows. In order to check the damage pattern, a single unit cell model was
compared to a nine-unit cell model. Fig. 13 shows this comparison made between these two models at
two different nominal stress levels. The first is at a nominal stress and strain level of 270 MPa and
0.64%, respectively. At this stage, there is very small amount of damage in the bias tows which has
very good match. This can be considered the end of the linear stress range for the model. Then, at
nominal stress and strain level of 328 MPa and 0.80%, respectively, the damage in the bias tows can
be seen in both single unit cell and nine-unit cell models. The damage shape begins to lose the
repeating pattern beyond this point, and the damage cannot be guaranteed to be the same between
models since it becomes too sensitive to be stable.
3.4. Effect of Matrix Plasticity on Compression Failure
The effect of plasticity in the matrix was investigated for the compressive failure case. Ernst et al.
[25] showed that epoxy resin behaves in brittle manner when it fails under tension while it shows
some plasticity in shear mode. Therefore, it was thought to be needed to investigate the effect of the
plasticity of the epoxy matrix for the compressive failure.
σ11(MPa)
25
15
5
x
y
1 RUC
9 RUCs
25 RUCs
Fig. 12. Repeating nature of stress patterns in single and multi-cell models under the same macro stress and strain levels (
26
Fig. 12. Repeating nature of stress patterns in single and multi-cell models under the same macro
stress and strain levels (��� �277 MPa, ��̅ �0.67%)
Previously, it has been established that the current configuration starts its damage in the form of in-
plane shear in the bias tows. In order to check the damage pattern, a single unit cell model was
compared to a nine-unit cell model. Fig. 13 shows this comparison made between these two models at
two different nominal stress levels. The first is at a nominal stress and strain level of 270 MPa and
0.64%, respectively. At this stage, there is very small amount of damage in the bias tows which has
very good match. This can be considered the end of the linear stress range for the model. Then, at
nominal stress and strain level of 328 MPa and 0.80%, respectively, the damage in the bias tows can
be seen in both single unit cell and nine-unit cell models. The damage shape begins to lose the
repeating pattern beyond this point, and the damage cannot be guaranteed to be the same between
models since it becomes too sensitive to be stable.
3.4. Effect of Matrix Plasticity on Compression Failure
The effect of plasticity in the matrix was investigated for the compressive failure case. Ernst et al.
[25] showed that epoxy resin behaves in brittle manner when it fails under tension while it shows
some plasticity in shear mode. Therefore, it was thought to be needed to investigate the effect of the
plasticity of the epoxy matrix for the compressive failure.
σ11(MPa)
25
15
5
x
y
1 RUC
9 RUCs
25 RUCs
=277 MPa,
26
Fig. 12. Repeating nature of stress patterns in single and multi-cell models under the same macro
stress and strain levels (��� �277 MPa, ��̅ �0.67%)
Previously, it has been established that the current configuration starts its damage in the form of in-
plane shear in the bias tows. In order to check the damage pattern, a single unit cell model was
compared to a nine-unit cell model. Fig. 13 shows this comparison made between these two models at
two different nominal stress levels. The first is at a nominal stress and strain level of 270 MPa and
0.64%, respectively. At this stage, there is very small amount of damage in the bias tows which has
very good match. This can be considered the end of the linear stress range for the model. Then, at
nominal stress and strain level of 328 MPa and 0.80%, respectively, the damage in the bias tows can
be seen in both single unit cell and nine-unit cell models. The damage shape begins to lose the
repeating pattern beyond this point, and the damage cannot be guaranteed to be the same between
models since it becomes too sensitive to be stable.
3.4. Effect of Matrix Plasticity on Compression Failure
The effect of plasticity in the matrix was investigated for the compressive failure case. Ernst et al.
[25] showed that epoxy resin behaves in brittle manner when it fails under tension while it shows
some plasticity in shear mode. Therefore, it was thought to be needed to investigate the effect of the
plasticity of the epoxy matrix for the compressive failure.
σ11(MPa)
25
15
5
x
y
1 RUC
9 RUCs
25 RUCs
=0.67%)
27
Fig. 13. Repeating nature of initial failure with multiple unit cells (Single ply model)
The plasticity of the matrix was considered by taking two different types of the assumptions based
on experimental test result taken from reference. The first is the elastic-perfectly plastic assumption
where the failure stress and failure strain correspond to those of the experimental data. The second
assumption is taking multilinear elastic-plastic curve by taking different points on the experimental
curve. Both kinds of assumptions are shown in Fig. 14 relative to the test data.
The same configuration mentioned in the foregoing discussions was used for the compressive
failure analysis of triaxial braiding. The infinite antisymmetric stacking case was considered for the
compressive analysis with the three assumptions of the matrix material behavior shown in Fig. 14.
The resulting stress-strain curves are shown in Fig. 15 with multi-linear elastic-plastic, perfectly
σ = 270 MPa ε = 0.64%
σ = 328 MPa, ε = 0.80%
Nine cell model Single cell model
x
y
Damaged No Damage
Fig. 13. Repeating nature of initial failure with multiple unit cells (Single ply model)
DOI: http://dx.doi.org/10.5139/IJASS.2017.18.3.436 448
Int’l J. of Aeronautical & Space Sci. 18(3), 436–449 (2017)
The second assumption is taking multilinear elastic-plastic
curve by taking different points on the experimental curve.
Both kinds of assumptions are shown in Fig. 14 relative to
the test data.
The same configuration mentioned in the foregoing
discussions was used for the compressive failure analysis of
triaxial braiding. The infinite antisymmetric stacking case
was considered for the compressive analysis with the three
assumptions of the matrix material behavior shown in Fig.
14. The resulting stress-strain curves are shown in Fig. 15
with multi-linear elastic-plastic, perfectly elastic and elastic-
perfectly plastic matrix material properties. In a similar loading
scenario, Li et al. [15] obtained results for perfectly plastic
matrix model with 60⁰ triaxial braid. Comparing their result
with the current stress-strain curve of the elastic-perfectly
plastic model qualitatively, it shows resemblance that the slope
reduces significantly once major damage starts to occur.
All three cases had the same initial linear portion matching
until the first sign of damage shows. After very slight change
in shape, the braid with perfectly elastic matrix model drops
suddenly. This is because the failure in the matrix does not
allow any plastic deformation. For the other two, however,
the slope of the stress-strain curve changes smoothly before
the sudden drop occurs. The change in the slope is higher
for the elastic-perfectly plastic model than the multi- linear
elastic-plastic model. However, the multilinear elastic-
plastic case reaches the maximum strength earlier than the
elastic-perfectly plastic model.
4. Conclusion
Progressive failure analysis of a triaxially braided textile
composite was successfully conducted using repeating unit
cell models. Maximum stress based failure criteria were used
based on individual components to enable directional damage
and failure of elements. Since the analyses were conducted
in multi-scale between micro and meso-scale, damage
and failure was modeled at constituent material level. The
progressive failure analysis was conducted on the FE model by
progressively degrading the material properties and eventually
removing completely failed elements based on the defined
failure criteria until the whole model becomes unstable.
The analysis result was verified against test and
computational results from references which showed very
good match. Under uniaxial tensile load, the initial damage
in the model occurred due to in-plane shear of bias tows.
However, this did not have the biggest contribution to the
major failure. The major damage that causes the sudden
drop in the stress-strain curve occurred due to local damage
of pure matrix pocket and beginning of axial tow fiber
breakage. The matrix pocket failed in shear and compression
at the region where the bias tows and axial tows overlap.
Beyond the major failure, propagation of matrix pocket
failure, axial tow breakage continues. At high level of strain,
bias tow breakage starts once the whole assembly becomes
very soft with low stress and large deformation. The same
approach was used to investigate compressive failure case of
the same configuration.
The effect of unit cell geometry and material property
variation on the damage and fracture patterns was
parametrically investigated. The variation in the ply stacking
arrangement in which free-free single ply, antisymmetric
infinite ply and symmetric infinite ply arrangements were
considered resulted in no significant difference in the stress-
strain curves between these three cases. This was because
of the limited out-of-plane deformation of the model when
it is subjected to axial tension. The repeating nature of stress
distribution and initial failure was demonstrated by comparing
single unit cell models with nine-unit cell and twenty-five
28
Fig. 14. Bi-linear and multi-linear models for plastic stress-strain curve of the epoxy matrix
Fig. 15. Stress-strain curves for triaxial braid unit cells loaded in axial compression with different
matrix materials
elastic and elastic-perfectly plastic matrix material properties. In a similar loading scenario, Li et al.
[15] obtained results for perfectly plastic matrix model with 60⁰ triaxial braid. Comparing their result
with the current stress-strain curve of the elastic-perfectly plastic model qualitatively, it shows
0
10
20
30
40
50
60
70
0% 1% 2% 3% 4%
Stre
ss (M
Pa)
Strain (%)
Multi-linear elastic-plastic [13]
Elastic - perfectly plastic
Test [13]
0
50
100
150
200
250
0.0% 0.4% 0.8% 1.2% 1.6% 2.0%
Stre
ss (M
Pa)
Strain (%)
Multi-linear elastic-plasticPerfectly elasticElastic - perfectly plastic
Fig. 14. Bi-linear and multi-linear models for plastic stress-strain curve of the epoxy matrix
28
Fig. 14. Bi-linear and multi-linear models for plastic stress-strain curve of the epoxy matrix
Fig. 15. Stress-strain curves for triaxial braid unit cells loaded in axial compression with different
matrix materials
elastic and elastic-perfectly plastic matrix material properties. In a similar loading scenario, Li et al.
[15] obtained results for perfectly plastic matrix model with 60⁰ triaxial braid. Comparing their result
with the current stress-strain curve of the elastic-perfectly plastic model qualitatively, it shows
0
10
20
30
40
50
60
70
0% 1% 2% 3% 4%
Stre
ss (M
Pa)
Strain (%)
Multi-linear elastic-plastic [13]
Elastic - perfectly plastic
Test [13]
0
50
100
150
200
250
0.0% 0.4% 0.8% 1.2% 1.6% 2.0%
Stre
ss (M
Pa)
Strain (%)
Multi-linear elastic-plasticPerfectly elasticElastic - perfectly plastic
Fig. 15. Stress-strain curves for triaxial braid unit cells loaded in axial compression with different matrix materials
449
Tsinuel N. Geleta Multi-scale Progressive Failure Analysis of Triaxially Braided Textile Composites
http://ijass.org
unit cells model. Finally, the effect plasticity of matrix on the
compressive failure behavior of the triaxially braided composite
was investigated. The results showed that the perfectly elastic
matrix modeling resulted in early failure while the multi-linear
elastic-plastic case had highest strength value.
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[6] Naik, R. A., “Failure Analysis of Woven and Braided
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