Principal strain induced fiber orientation evolution in the Csf/Mg composites with a large...

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Principal strain induced fiber orientation evolution in the Csf/Mg composites with a large deformation

Journal: Journal of Composite Materials

Manuscript ID: JCM-14-0472.R2

Manuscript Type: Original Manuscript

Date Submitted by the Author: 27-Oct-2014

Complete List of Authors: Tian, Wenlong; Northwestern Polytechnical University, School of Mechanical Engineering Qi, Lehua; Northwestern Polytechnical University, School of Mechanical Engineering zhou, Jiming; Northwestern Polytechnical University, School of Mechanical Engineering Xu, Yiren

Keywords: Csf/Mg composites, Finite element analysis, Fiber orientation evolution,

Extrusion, Principal strains

Abstract:

In this article, the fiber orientation evolution in the Csf/Mg composites with a large deformation is investigated. The principal strain driveninduced fiber orientation evolution mechanism, which states that the fiber orientation evolution in the extruded Csf/Mg composites with a large deformation is determined by the principal strains, is proposed. The fiber orientation distribution factor , which is a functiontaking the form of the principal strains is proposed to quantitatively characterize the fiber orientation distribution in the extruded Csf/Mg composites. The fiber orientation factors predicted by the FE simulations based on the principal strain driveninduced fiber orientation evolution mechanism are compared against

those measured from the micrographs of the extrusion experiments of Csf/Mg composites. The results show demonstrate that the principal strain driveninduced fiber orientation evolution mechanism is valid and convenient to predict the fiber orientation evolution in the Csf/Mg composites with a large deformation. And t In the extruded Csf/Mg composites, the fibers are reoriented towards the direction of the maximum principal strain and deviated from the direction of the minimum principal strain in the extruded Csf/Mg composites with a large deformation.

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Principal strain driveninduced fiber orientation evolution in the extruded

Csf/Mg composites with a large deformation

Wenlong Tian, Lehua Qi*, Jiming Zhou, Yiren Xu

School of Mechanical Engineering, Northwestern Polytechnical University, 127

Youyi West Road, Xi’an 710072, P. R. China

*Corresponding author. Tel.: +86-29-88460447, Fax: +86-29-88491982, E-mail:

[email protected].

Abstract

In this article, the fiber orientation evolution in the Csf/Mg composites with a large

deformation is investigated. The principal strain driveninduced fiber orientation

evolution mechanism, which states that the fiber orientation evolution in the

extruded Csf/Mg composites with a large deformation is determined by the principal

strains, is proposed. The fiber orientation distribution factors ( 1,2 3)iF i and= F ,

which is a functiontaking the form of the principal strains is proposed to

quantitatively characterize the fiber orientation distribution in the extruded Csf/Mg

composites. The fiber orientation factors s

iF predicted by the FE simulations based

on the principal strain driveninduced fiber orientation evolution mechanism are

compared against those m

iF measured from the micrographs of the extrusion

experiments of Csf/Mg composites. The results show demonstrate that the principal

strain driveninduced fiber orientation evolution mechanism is valid and convenient

to predict the fiber orientation evolution in the Csf/Mg composites with a large

deformation. And t In the extruded Csf/Mg composites, the fibers are reoriented

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towards the direction of the maximum principal strain and deviated from the

direction of the minimum principal strain in the extruded Csf/Mg composites with a

large deformation.

Keywords: Csf/Mg composites; Extrusion; Finite element analysis; Fiber orientation

evolution; Principal strains

1. Introduction

The increasing applications of short-fiber-reinforced composites have sustained a

vigorous scientific and engineering interest in the area of the prediction of their

effective mechanical and thermal properties [1-4]. Short-carbon-fiber reinforced

magnesium alloy matrix (Csf/Mg) composites is One one typical representative of

these short-fiber-reinforced composites, which have important potentials in many

cutting-edge industries including automotive, aviation, aerospace and national

defense industries, etc., due to their lightweight, excellent mechanical properties,

low thermal expansion coefficient, and high damping capacities [51-73]. The

increasing applications of these advanced composites have sustained a vigorous

scientific and engineering interest in the area of the prediction of their effective

mechanical and physical properties [4-7]. It has been pointed out that the fiber

orientation distribution in the composites strongly influences affects the mechanical

responses of composites [8-10] on one hand. FurthermoreOn the other hand, the

processing route has a significant influence on the fiber orientation distribution in

the composites [11, 12]. Given that the effect of the processing route on the fiber

orientation evolution in the forming process of composites was understood clearly,

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the fibers might be reoriented to turn towards the predetermined directions, which

would be a great advantage for the applications of composites [13-15]. Therefore, it

is important to investigate the fiber orientation evolution in the forming process of

composites.

The motivation for the present article is the fiber orientation evolution of Csf/Mg

composites in the extrusion forming process. Until now, many attemptsresearch on

the fiber orientation of composites mainly focused on the effect of fiber orientation

on the mechanical properties of composites and the fiber orientation evolution in

the forming process of composites.

The fiber orientation evolution in the short-fiber-reinforced composites, has

received the considerable attention in the literatures. Attention The study was

initially focused on the fiber suspensions systems and the injection molding process

of composites owing to the pioneering research work of Jeffery [16], which had

become the groundwork for the later fiber suspensions flow studying. And lLots of

research works [17-20] about relating to the fiber suspensions system have has

been carried on. Regarding the fiber orientation evolution of composites in the

injection molding process of composites, many theoreticaltheory models have been

established, such as the scheme developed by Advani and Tucker [21] and Bay and

Tucker [22], the FT model [23] and two modified FT model [24-25].

Comparatively, the work towards However, less attention has been directed towards

the fiber orientation evolution in the solid forming process of composites is seldom

reported. Li [26] investigated the effect of the extrusion ratios on the rotation of the

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whiskers by using the transformation of the streamline grids to represent the flow

of the whiskers in the SiCw/6061 composites, and learned . The results showed that

the degree of the whiskers reorientation were was reoriented more intensively with

the increasing of the extrusion ratio. Su [27] studied the fiber orientation evolution

in the different axial regions of Csf/Mg composites during the extrusion forming

process, and obtained the conclusionshared the idea that with the strain increasing,

the fibers in the Csf/Mg composites were reoriented along the extrusion direction

more obviously with increasing strain.

In this article, the fiber orientation evolution of in the Csf/Mg composites in the

extrusion forming processwith a large deformation is investigated. The principal

strain driveninduced fiber orientation evolution mechanism that the fiber

orientation evolution of fibers in the Csf/Mg composites is determined by the

principal strains, is proposed. The fiber orientation distribution factors F iF areis

proposed defined to characterize the fiber orientation distribution in the Csf/Mg

composites. The fiber orientation distribution factors s

iF predicted by the FE

simulations are compared against those m

iF measured from the micrographs to

verify the validity of the principal strain driveninduced fiber orientation evolution

mechanism. Finally, the fiber orientation distribution in the extruded Csf/Mg

composites is analyzed.

2. The principal strain driveninduced fiber orientation evolution mechanism

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During the extrusion forming process of Csf/Mg composites, some hypotheses are

made in connection withregarding to the translation and rotation of short carbon

fibers:

(1) Perfect interface bonding between the fibers and matrix of Csf/Mg composites;

(2) No bending deformation of fibers;

(3) No translation and rotation interference between fibers;

(4) No fiber damage and fracture;

(5) The absolutely rRandom initial fiber orientation distribution in the Csf/Mg

composites.

Figure 1 illustrates the diagrammatic sketch of the fiber orientation evolution in the

Csf/Mg composites deforming under the transverse tensile and longitudinal

compression loads. Before Csf/Mg composites deform, the fiber orientation

distribution is absolutely random (Figure 1(a)). However, the fiber orientation

distribution changes when Csf/Mg composites deform under the applied loads.

According to the aforementioned hypotheses, the fibers will be translated and

rotated along towards the direction of the matrix deformation (Figure 1(c)).

Therefore, the final fiber orientation distribution mainly depends on the

deformation of Csf/Mg composites.

Fig.1 Diagrammatic sketch of the fiber orientation evolution in the Csf/Mg composites

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The size of short carbon fiber is far smaller than that of Csf/Mg composites,

resulting that the deformation of Csf/Mg composites, at the scale of fiber, can be

simplified to be homogeneous. Therefore, the principal strain driveninduced fiber

orientation evolution mechanism states that the final fiber orientation distribution

of the extruded Csf/Mg composites with a large deformation depends on the

principal strains of Csf/Mg composites.

In the two-dimensional space, point o is a random point in the inside of Csf/Mg

composites, and a local plane Cartesian coordinate system oxy is established. The

deformation of Csf/Mg composites is constrained in the planeoxy . The fiber length

has no effect on the fiber orientation evolution of fibers such that all the fiber length

is set to 1 length unit in the Csf/Mg composites without deformation. We can

translate all fibers in the vicinity of point o to make one end points of these fibers

coincide with point o and the other end points be located on the circle with the a

radius of 1 length unit, which is named the orientation circle and shown in Figure 2

(a). When Csf/Mg composites deform, the shape of the orientation circle becomes to

an ellipse, which accordingly is named the orientation ellipse, as shown in Figure 2

(b).

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Fig.2 The orientation circle with a radius of 1 length unit and orientation ellipse

Figure 2 illustrates that short carbon fibers are translated and rotated to the

direction of the major axis and deviated from the direction of the minor axis of the

orientation ellipse as the Csf/Mg composites deform. Note that the directions of the

maximum and minimum principal strains are consistent with the directions of the

major and minor axis axes of the orientation ellipse, respectively. Therefore, the

fibers are reoriented to the direction of the maximum principal strain and deviated

from the direction of the minimum principal strain when Csf/Mg composites have a

large deformation in the two dimensional space. FurthermoreAnalogically, the same

conclusion can be drawn when Csf/Mg composites deform in the three-dimensional

space.

3. Governing equations of the fiber orientation factor

The fiber orientation distribution probability function [22] and the fiber orientation

tensor [21] are the most used parameters to express the fiber orientation

distribution in the composites. However, in this article the fiber orientation

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distribution factors iF is are proposed to characterize the fiber orientation

distribution based on the principal strain driveninduced fiber orientation evolution

mechanism. The fiber orientation distribution factors iF arefactor F is defined for

the first time as follows: Point A represents an arbitrary point within the Csf/Mg

composites. And the vVector n is the unit direction vector of the principal strain of

the point A. Then the factors ( 1,2 3)iQ i and= is are defined to represent the

average angle between all fibers in the vicinity of the point A and its the unit

direction vectornof its principal strain. The fiber orientation distribution factors

distribution iF F is are given as,

1 sini iF Q= − ⑴

Therefore, iF F can express the orientation distribution degree of fibers fiber

orientation distribution and ranges from 0 to 1. The factor iF of 0 and 1 represents

that the fibers are perpendicular and parallel to the given directions, respectively.

Fig.3 The fiber orientation sphere and orientation ellipsoid

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In the three-dimensional space, the orientation sphere referring to the fiber

orientation becomes the orientation ellipsoid when Csf/Mg composites have a

deformation, whose major axis and two minor axes are set to be parallel to the

directions of the z , y and x axis axes of the Cartesian coordinate systemoxyz , as

shown in Figure 3. The segments OP and 'OP represent an arbitrary fiber in the

composites without and with a deformation, respectively. Here donate by 1e , 2e and

3e the maximum, mediumintermediate and minimum principal strains, respectively.

Note that the strain here refers to the engineering strain instead of the logarithmic

strain. The intercepts a , b and c of the orientation ellipsoid on the x , y and z axis

axes taking the form of 1e ,

2e and 3e can be written as

3 2 11 , 1 , 1a e b e c e= + = + = + ⑵

When Before Csf/Mg composites have no deformation, the coordinates of the point

P are given as

sin cos , sin sin , cosx y zϕ θ ϕ θ ϕ= = = ⑶

And wWhen Csf/Mg composites have a large deformation, the coordinates of the

point 'P are given as

sin cos , sin sin , cosx a y b z cϕ θ ϕ θ ϕ′ ′ ′= = = ⑷

The tangent of the angle between the segment 'OP and the z axis is given as

2 22 2

3 2

1 1

1 1tan ( , ) tan cos sin

1 1

x y e e

z e eϕ ϕ θ ϕ θ θ

′ ′ + + +′ = = + ′ + +

⑸

Letting S indicate the surface area of the fiber orientation sphere, we can get

that 4S π= . When Csf/Mg composites have a deformation, the factor 1Q is given as

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1

( , )dQ S

S

ϕ ϕ θ′= ∫∫ ⑹

where dS can be written as

d sin d dS ϕ ϕ θ= ⑺

According to the symmetry of the fiber orientation sphere and ellipsoid, the first

quadrants of the orientation sphere and ellipsoid are selected to for calculate

calculating the factor 1Q ,

/2 /2

1

0 0

( , )sin d d

/ 8Q

S

π π ϕ ϕ θϕ ϕ θ

′= ∫ ∫ ⑻

Substituting Eq. (5), the equation Eq. (8) can be rewritten

2 2

3 22 21

0 01 1

1 12sin arctan tan cos sin d d

1 1

e eQ

e e

π π

ϕ ϕ θ θ ϕ θπ

+ + = + + + ∫ ∫ ⑼

Therefore, the fiber orientation factors 1F , 2F and 3F take the form of the principal

strains and are given as

2 2

3 22 21

0 01 1

1 121 sin sin arctan tan cos sin d d

1 1

e eF

e e

π π

ϕ ϕ θ θ ϕ θπ

+ + = − + + + ∫ ∫

⑽-a

2 2

312 22

0 02 2

1121 sin sin arctan tan cos sin d d

1 1

eeF

e e

π π

ϕ ϕ θ θ ϕ θπ

++ = − + + + ∫ ∫

⑽-b

and

2 2

2 12 23

0 03 3

1 121 sin sin arctan tan cos sin d d

1 1

e eF

e e

π π

ϕ ϕ θ θ ϕ θπ

+ + = − + + + ∫ ∫

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⑽-c

4. Results and discussions

4.1 Finite element model

In this section, an FE model is simulated to acquire the principleprincipal strain field

of the extruded Csf/Mg composites. The reinforcement and matrix of Csf/Mg

composites are T300 short carbon fibers and AZ91D magnesium alloy, respectively.

The fiber volume fraction in the extruded Csf/Mg composites is about10% , and the

average fiber length and average fiber diameter are 105 mµ and7 mµ , respectively.

The extrusion forming process of Csf/Mg composites is shown in Figure 4. The

diameter of the extrusion forming mold is 45mm and the extrusion aspect ratio and

mold angle are 5 and 55o , respectively.

Fig.4 Diagrammatic sketch of the extrusion forming process of Csf/Mg composites

The axisymmetric FE model is created as shown in Figure 5. Compared with Csf/Mg

composites, the extrusion forming mold has a much larger stiffness so that the

analytical rigid body is used to represent the extrusion forming mold in the FE

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model. Because of symmetry, the displacement xu in the x-direction on the left

boundary of the FE model is constrained. On the right boundary of the FE model, the

surface-surface contact constraint is set, in which the maximum friction condition is

adopted. The extrusion velocity on the top boundary of the FE model is 1 /mm s .

Plastic strain 0 0.01 0.02 0.03 0.04

True stress/MPa 18.86 53.64 71.15 76.96 77.16

Table 1 Plastic strain-stress data of Csf/Mg composites

The extrusion process of Csf/Mg composites is instantaneous with little temperature

variation so that the effect of the temperature variation on the strain field is

ignoredneglected. Csf/Mg composites are homogenized as the effective elasto-plastic

material, at the macro level, in the extrusion forming process and the homogenized

mechanical properties of the Csf/Mg composites come from the tensile experiments.

The Elastic modulus and Poisson ratio of Csf/Mg composites are 5.3GPa and0.33 ,

respectively. The von Mises yield criterion and the isotropic hardening model are

introduced to simulate the plasticity flow of Csf/Mg composites and the plastic

properties are listed in Table 1.

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Fig.5 The FE model and its boundary conditions

The CAX4R element (A 4-node bilinear axisymmetric quadrilateral, reduced

integration, hourglass control element) is used to mesh the FE model, in which there

are 2050 elements with 2167 nodes. To solve the mesh distortion in the case of a

large deformation, the arbitrary Lagrangian-Eulerian adaptive meshing technology is

adopted [27]. Meanwhile, the mass scaling [28] method is used to improve the

calculation speed of the explicit finite element analysis.

4.2 The fiber orientation distribution factor

To verify the validity of the principal strain driveninduced fiber orientation

evolution mechanism, the fiber orientation distribution factors s

iF acquired

predicted from the FE simulations and those m

iF from the extrusion experiments

are compared. 8 sample points in the Csf/Mg composites extrusion product are

selected, which are shown in Figure 56. Note that at each sample point, five

micrographs are selected and analyzed to obtain the average fiber orientation

distribution factors. One group of the micrographs at the selected sample points is

given in Figure 56 and the sizes of these micrographs are about575 450m mµ µ× .

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Fig. 6 The positions of the selected sample points and their microstructures

The directions and magnitudes of the principal strains at the sample points,

predicted by the FE simulation (shown in Figure 8 7 and Figure 98), are given in

Table 2. Note that n is the unit direction vector of the principal strains strain, and 1e ,

2e and 3e are the magnitudes of the maximum, mediumintermediate and minimum

principal strains, respectively. Having used these magnitudes of the principal

strains,Therefore, the fiber orientation distribution factors s

iF are calculated and

listed in Table 3, in which the fiber orientation distribution factors m

iF measured

and averaged from the micrographs of the extrusion experiments of Csf/Mg

composites with an image recognition technique [30, 31] is are included. Here, the

image recognition procedures of the micrographs of are given as follows,

(1) Binarization of the images;

(2) Reconstruction of the fiber crossing sections (which are simplified to be ellipses

and Seeshown in Figure 9);

(3) Feature extraction of the elliptical crossing sections (such as the length of the

major and minor axes and the orientation of the major axis);

(4) Calculation of the unit direction vector ( , , )i i i il m n=νννν of the i th− fiber;

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(5) Calculation of the angles between the x, y and z axes and the fibers, and the

average angles, then and the fiber orientation distribution factor.

Point 1n 2n 3n 1e 2e 3e

a -0.993 0.000 -0.116 0.390 -0.167 -0.169

b -0.997 0.000 -0.072 3.235 -0.517 -0.520

c -1.000 0.000 -0.007 3.881 -0.546 -0.547

d -1.000 -0.003 0.000 2.890 -0.491 -0.496

e -0.691 0.000 -0.722 1.048 -0.047 -0.513

f -0.635 0.000 -0.772 8.186 -0.296 -0.826

g -1.000 0.000 -0.024 17.078 -0.452 -0.846

h -0.999 0.000 -0.037 3.432 -0.506 -0.546

Table 2 The directions and magnitudes of the principal strains at the sample points

Fig. 7 The magnitudes of the principal strains in the extruded Csf/Mg composites

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The fiber orientation distribution factors s

iF predicted by the FE simulations are

compared against those m

iF measured and averaged from the micrographs are

compared in Figure 10, which illustrates that the fiber orientation distribution

factors s

iF predicted by the FE simulations coincide well with those m

iF measured

and averaged from the micrographs. It This proves that the principal strain

driveninduced fiber orientation evolution mechanism is valid and the fiber

orientation distribution factors iF F is are effective and convenient to characterize

the fiber orientation distribution in the Csf/Mg composites with a large deformation.

Sample Point 1

sF 1

mF 2

sF 2

mF 3

sF 3

mF

a 0.2263 0.1369 0.1284 0.1908 0.1277 0.2006

b 0.618 0.6035 0.0279 0.0584 0.0276 0.0345

c 0.6917 0.5924 0.0185 0.026 0.018 0.0255

d 0.6145 0.5138 0.027 0.026 0.0281 0.0343

e 0.3514 0.3011 0.1288 0.151 0.0479 0.0549

f 0.7524 0.6896 0.0256 0.0531 0.0023 0.0146

g 0.9179 0.9211 0.0041 0.0114 5E-4 0.0073

h 0.6806 0.6281 0.0208 0.0335 0.0183 0.0345

Table 3 The predicted and measured fiber orientation distribution factors

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Fig. 8 The directions of the principal strains in the extruded Csf/Mg composites

Fig.9 The reconstruction of the fiber crossing sections

The fiber orientation factors s

iF predicted by the FE simulations show that the

fibers are reoriented towards the direction of the maximum principal strain and

deviated from the direction of the minimum principal strain, while the fiber

orientation degree of fibers along the direction of the mediumintermediate

principal strain ranges between that those along the directions of the maximum and

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minimum principal strain. The same results can be found from the fiber orientation

distribution factors m

iF measured from the micrographs of the extrusion

experiments of Csf/Mg composites.

Fig. 10 The fiber orientation factors iF F1, F2 and F3 predicted by the FE simulations and

measured from the micrographs

4.3 Fiber orientation distribution

The fiber orientation distribution and plastic strain field in the extruded Csf/Mg

composites are given in Figure 11 and Figure 12. According to the plastic strain field

in the extruded Csf/Mg composites, the deformation within the Csf/Mg composites

can be divided into three regions: the non-plastic deformation zone (Region 1), the

severe plastic deformation zone (Region 2) and the steady plastic deformation zone

(Region 3), as shown in Figure 13. Moreover, the Region 1 can be further divided

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into two parts: the general elastic deformation zone (Part 1, marked B and C in

Figure 13) and the dead deformation zone (Part 2, marked A in Figure 13).

Fig. 11 The fiber orientation distribution in the extruded Csf/Mg composites

Fig.12 The plastic strain field in the extruded Csf/Mg composites product

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From the fiber orientation distribution contours, it can be found that in the general

elastic deformation zone the fiber orientation maintains the approximately random

distribution, and the fibers closing to the extrusion mold are slightly reoriented

along the direction of the maximum principal strain. However, in the severe plastic

deformation zone, the fiber orientation has the following characteristics: the fibers

in the composites near the extrusion mold are approximately reoriented along the

tapered surface generatrix of the extrusion mold. And tThe fiber orientation of

fibers near the center of the extrusion mold is approximately parallel to the axial

direction of the extrusion mold. In the steady plastic deformation zone, the fiber

orientation is relatively uniform and close to be parallel to the axial direction of the

extrusion mold except for the bottom region, in which the fiber orientation is

relatively random. In the dead deformation zone the fiber orientation maintains the

approximately random distribution.

According to the fiber orientation distribution and the directions of the principal

strains, the schematic fiber orientation of some special sample points (Figure 14) in

the extruded Csf/Mg composites is given, regarding that the fiber orientation in the

cross section are considered of the extruded Csf/Mg composites product while the

those in the circumference circumferential direction are neglected.

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Fig.13 Three deformation regions in the extruded Csf/Mg composites

Fig.14 Diagrammatic sketch of the fiber orientation distribution at some sample points

5. Conclusion

In this articlework, the principal strain driveninduced fiber orientation evolution

mechanism is proposed, which states that the fiber orientation evolution of fibers in

the Csf/Mg composites with a large deformation is determined by the principal

strains. The fiber orientation factors iF areis proposed to characterize the fiber

orientation distribution in the extruded Csf/Mg composites, which is a function of

the principal strains. Through tThe fiber orientation factors s

iF predicted by the FE

simulations coinciding well with those m

iF measured from the micrographs of the

extrusion experiments demonstrates the validity of the principal strain

driveninduced fiber orientation evolution mechanism is verified.

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The fiber orientation evolution in the Csf/Mg composites during the extrusion

forming process is investigated. and findThe results show that the fibers are

reoriented towards the direction of the maximum principal strain and deviated

from the direction of the minimum principal strain, while the fiber orientation

degree of fibers along the direction of the mediumintermediate principal strain

ranges between that those along the directions of the maximum and minimum

principal strains.

Acknowledgements

The work presented here was financially supported by the National Nature Science

Foundation of China (No. 51275417 and No. 51221001), the Doctorate Foundation

of Northwestern Polytechnical University (CX201312) and the Short-term Oversea

Visiting Scholar Program of Gradual School at Northwestern Polytechnical

University.

References

[51] Wang WG, Xiao BL and Ma ZY. Evolution of interfacial nanostructures and stress

states in Mg matrix composites reinforced with coated continuous carbon fibers.

Compos Sci Technol 2012; 72: 152–158.

[62] Liu J, Qi LH, Guan JT, et al. Compressive behavior of Csf/AZ91D composites by

liquid-solid extrusion directly following vacuum infiltration technique. Mater Sci

Eng: A 2012; 531: 164-170.

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[73] Qi LH, Liu J, Guan JT, et al. Tensile properties and damage behaviors of Csf/Mg

composite at elevated temperature and containing a small fraction of liquid. Compos

Sci Technol 2012; 72: 1774-1780.

[4] Pahr DH and Arnold SM. The applicability of the generalized method of cells for

analyzing discontinuously reinforced composites. Compos Part B: Eng 2002; 33:

153-170.

[5] Monfareda V and Mondalib M. Semi-analytically presenting the creep strain rate

and quasi shear-lag model as well as finite element method prediction of creep

debonding in short fiber composites. Mater Des 2014; 54: 368-374.

[6] Yang WS, Biamino S, Padovano E, et al. Microstructure and mechanical

properties of short carbon fiber/SiC multilayer composites prepared by tape casting.

Compos Sci Technol 2012; 72: 675-680.

[7] Li WW, Liu L and Shen B. The fabrication and properties of short carbon fiber

reinforced copper matrix composites. J Compos Mater 2011; 45:2567-2571.

[8] Jiang B, Liu C, Zhang C, et al. The effect of non-symmetric distribution of fiber

orientation and aspect ratio on elastic properties of composites. Compos Part B: Eng

2007; 38: 24-34.

[9] Hou XN, Acar M and Silberschmidt Vadim V. Finite element simulation of low-

density thermally bonded nonwoven materials: Effects of orientation distribution

function and arrangement of bond points. Comput Mater Sci 2011; 50: 1292–

1298.

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123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

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24

[10] Taha I and Abdin YF. Modeling of strength and stiff ness of short randomly

oriented glass fiber-polypropylene composites. J Compos Mater 2011; 45: 1805-

1821.

[11] Jiang XY, Gao Q and Kang GZ. Numerical simulation of microstructure and

strength prediction for short-fiber-reinforced metal matrix composites.Compos Sci

Technol 1998; 58: 1685-1695.

[12] Sirkis JS, Cheng A, Dasgupta A, et al. Image processing based method of

predicting stiffness characteristics of short fiber reinforced injection molded parts.

J Compos Mater 1994; 28: 784-799.

[13] Yamashita S, Hatta H, Sugano T, et al. Fiber orientation control of short

fiber composites: experiment. J Compos Mater 1989; 23: 32-41.

[14] C. G. Kang and S. S. Kang. Effect of extrusion on fiber orientation and breakage

of aluminar short fiber composites. J Compos Mater 1994; 28: 155-166.

[15] Watanabe Y. Evaluation of fiber orientation in ferromagnetic short-fiber

reinforced composites by magnetic anisotropy. J Compos Mater 2002; 36: 915-923.

[16] Jeffery GB. The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid.

Proc R Soc Lond A 1922; 102: 161-179.

[17] Bretherton FP. The motion of rigid Particles in a shear flow at low Reynolds

number. J Fluid Mech 1962; 14: 284-304.

[18] Chinesta F, Poitou A and Torres R. A semi-lagrangian strategy to predict the

fiber orientation in the steady flows of reinforced thermoplastics. Comput Method

Appl M 2000; 189: 233-247.

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123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

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25

[19] Givler RC, Crochet MJ and Pipes RB. Numerical prediction of fiber orientation in

dilute suspensions. J Compos Mater 1983; 17: 330-343.

[20] Trevelyan BJ and Mason SG. Particle motions in sheared suspensions. I.

Rotations. J Colloid Sci 1951; 6: 354-367.

[21] Advani SG and Tucker Cl. The use of tensors to describe and predict fiber

orientation in short fiber composites. J Rheol 1987; 31: 751–784.

[22] Bay RS and Tucker CL. Fiber orientation in simple injection moldings. Part I:

Theory and numerical methods. Polym Composite 1992; 13: 317-331.

[23] Folgar F and Tucker CL. Orientation behavior of fibers in concentrated

suspensions. J Reinf Plasti Comp 1984; 3: 98-119.

[24] Eberle APR, Velez-Garcia GM, Baird DG, et al. Fiber orientation kinetics of a

concentrated short glass fiber suspension in startup of simple shear flow, J Non-

Newton Fluid 2010; 165: 110-119.

[25] Wang J, O’gara JF and Tucker CL. An objective model for slow orientation

kinetics in concentrated fiber suspensions: theory and rheological evidence. J Rheol

2008; 52: 1179-1200.

[26] Li JH, Li CF and Deng JH. Finite element analysis of whisker rotation of

SiCw/6061 composite under extrusion deformation with velocity field. J Plast Eng

2007; 14: 104-107.

[27] Su LZ. Researches on technology and mechanism of the extrusion directly

following vacuum infiltration for Magnesium Composites. PhD Dissertation,

Northwestern Polytechnical University, China, 2010.

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[28] Chen GQ, Shi QY, Li YJ, et al. Computational fluid dynamics studies on heat

generation during friction stir welding of aluminum alloy. Comput Mater Sci 2011;

79: 540-546.

[29] Abaqus 6.11 HTML Documentation / Abaqus GUI Toolkit User’s Manual, 2011.

[30] Zhu YT, Blumenthal WR and Lowe TC. Determination of non-symmetric 3-d

fiber-orientation distribution and average fiber length in short-fiber composites. J

Compos Mater 1997; 31:1287-1301.

[31] Chen G, Ozden UA, Bezold A, et al. A statistics based numerical investigation on

the prediction of elasto-plastic behavior of WC–Co hard metal. Comput Mater Sci

2013; 80: 96-103.

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423x92mm (300 x 300 DPI)

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221x107mm (96 x 96 DPI)

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120x64mm (96 x 96 DPI)

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396x220mm (96 x 96 DPI)

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1765x574mm (72 x 72 DPI)

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966x723mm (72 x 72 DPI)

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821x729mm (72 x 72 DPI)

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438x254mm (288 x 288 DPI)

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1018x687mm (72 x 72 DPI)

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1052x769mm (72 x 72 DPI)

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558x140mm (96 x 96 DPI)

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1962x1133mm (96 x 96 DPI)

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Principal strain induced fiber orientation evolution in the Csf/Mg composites with a large...

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