Research on strength prediction technology for fiber-reinforced plastic injection-molded productsTechnology
Explanation

Research on strength prediction technology
for fiber-reinforced plastic injection-molded products

OGURA Shogo

Abstract
In anticipation of the introduction of global CO2 emission regulations, there is a growing need to reduce theweight of transportation equipment. Fiber-reinforced
plastic (FRP) is attracting attention as a lightweight material. FRP injection-molded products have the potential
for both weight reduction and cost reduction. However, it
is difficult to predict and control strength because the fiber orientation changes depending on how the products
are made, and this has a significant impact on physicalproperties. Therefore, development has been conducted
on a trial-and-error basis, and optimization of part geometry and processing methods has not been studied. In thisstudy, we use simulation to develop a strength prediction
technique that considers the anisotropy of physical properties due to fiber orientation. This enables us to realize

productivity, so they have limited applications in aircraft,
sporting goods, luxury cars, and others. On the other

Introduction

1. 1 Background of the Research
In anticipation of the introduction of global CO 2
emission regulations and market launches of electricvehicles, there is a growing need to reduce the weight oftransportation equipment. To respond to the weight
reduction need, studies are in progress to replace metallic
parts with plastic components that are lighter and easierto process. Since plastic is inferior in mechanicalproperties to metal, fiber-reinforced plastic (FRP) such as
plastic reinforced with glass or carbon fibers is attracting
attention as a low-density, high-strength material. FRP isused as structural members in a wide range of fields
today.
1. 2 F RP Processing methods and its
Characteristics
F i g . 1 sh o w s t h e m e c h a n i c a l p r o p e r t i e s a n d
productivity characteristics of FRP for various processing
methods 1). FRP varies in mechanical properties andproductivity by fiber length. Continuous fibers aresuperior in mechanical properties but inferior in

Thermosetting
Thermoplastic
熱可塑性シートワインディング
Sheet winding
Mechanical properties(strength, modulus, stability)

1

development without rework and to construct a technology that can optimize the design.
We quantified the fiber orientation in plastic parts,
which has been difficult in the past, and improved theprediction accuracy of fiber orientation by resin flow
analysis. Based on the predicted fiber orientation information, the physical property anisotropy of fiber-reinforced plastic parts was predicted. A material model for
structural analysis was created, and structural analysis
considering fiber orientation was performed to improve
the accuracy of strength prediction for plastic parts.
It was also found that this technique can be used to
predict the fracture behavior of actual plastic part geometry, confirming the importance and effectiveness of studying material strength, including the manufacturing process, when designing fiber-reinforced plastic parts.

RTM (fabrics)

Continuous
fibersDiscontinuous
fibers

SMC
Injection
molding(long fibers)

Injection
molding(short fibers)

Formability (cycle time, geometrical complexity, cost)※RTM:Resin Transfer Molding
SMC:Sheet Molding CompoundFig. 1:― 20 ―

FRP characteristics for various processing methods

KYB TECHNICAL REVIEW No. 67 OCT. 2023

Current- Strength changes
with fiber
orientation- Fiber orientation
changes withprocessing method[1] Material
selection[2] Geometry
study

2

Overview of Prediction TechniqueFig. 3

Material
model

Concept of strength prediction technique

The first step is to conduct a resin flow analysis andthen predict the fiber orientation of injection-molded
parts. The next is to create an anisotropic material model
based on the predicted fiber orientation. The final step isto carry out a structural analysis using the anisotropic
material model, enabling prediction of mechanicalproperties with the fiber orientation taken into account.
Implementation of this technique involves challenges:[1] Quantitative evaluation of fiber orientation[2] I mprovement of fiber orientation prediction
accuracy through flow analysis[3] Improvement of structural analysis accuracy withfiber orientation taken into account[4] Improvement of prediction accuracy for strength
reduction rate of welds
The following chapter describes what we haveaddressed to resolve these challenges.
3

Accuracy Testing with Element
Specimens

3. 1 Quantitative Evaluation of Fiber Orientation
Photo 1 shows an X-ray CT image of an injectionmolded product.

TargetPredict fiber
orientation andmechanicalproperties[3] Mold design[4] Prototyping- Trial-and-error- Longer development period andhigher cost

Fig. 2[5] Quality evaluation

Structural analysis

Fiberorientation

Prediction of physicalpropertiesof materials

In this development study, we predict the anisotropy ofphysical properties from the fiber orientation generated
in the injection molding process and then carry out astructural analysis that considers the anisotropy,
improving the accuracy of strength prediction for FRP parts.
Fig. 3 illustrates the concept of the prediction technique.

Resin flow analysis

hand, discontinuous fibers that can be injection-molded
have a good balance between mechanical properties andproductivity, thereby having the potential for both weight
reduction and cost reduction. This research focuses on
FRP injection-molded products.
1.3 Anisotropy of Physical Properties of FRP
Injection-Molded Products
FRP injection-molded products have a distribution offiber orientation and/or fiber length due to the shear stressand elongation flow that occur when resin flows in themold during injection molding. Because of its higher
reinforcement in the direction of fiber orientation, FRP
shows anisotropy of modulus, strength, coefficient oflinear expansion, and other properties according to thefiber orientation distribution during injection molding.
This poses the problem that it is difficult to predict thestrength, rigidity, and warpage of molded parts. For
example, molded parts may fracture before reaching arequired load if their anisotropy of modulus or strength
have not been considered. In another case whereanisotropy of the coefficient of linear expansion is notconsidered, molded parts may go out of dimensional
tolerance due to warping.
That is why it is difficult to predict the quality
characteristics of FRP injection-molded products. Mold
changes have been repeated on a trial-and-error basis,
resulting in longer development periods and higher
development costs. Furthermore, the part geometry has
not been optimized since the anisotropy of physicalproperties due to fiber orientation cannot be exactly
predicted. Some parts have been produced using moreresin material than necessary in order to ensure quality.
Fig. 2 shows the current and target development flows
for FRP parts. The target development flow will allow us
to predict the anisotropy of physical properties due tofiber orientation and the mechanical properties of molded
parts, thereby enabling the optimization of the partgeometry and mold design on the desk. This willcontribute to higher development efficiency.

- Shorter development period- Optimized
geometry

Current and target development flows
Photo 1
― 21 ―

X-ray CT image of FRPResearch on strength prediction technology for fiber-reinforced plastic injection-molded products

1: Flow direction

1

Degree of fiber orientation

Glass fibers appear in white and plastic in gray. This
injection-molded plastic product contains about 30% to
50% fibers of a thickness of about 10μm. Since the fibers
are three-dimensionally distributed, it is usually difficult
to quantify the fiber orientations. Then, we haveconducted joint research with Kanazawa Institute ofTechnology (KIT) to quantify the fiber orientations from
X-ray CT images using the cylinder-model fitting approach 2).
The following describes how to identify glass fibers
using the cylinder-model fitting approach. First of all, acylinder model is placed over each of the fibers obtainedin the X-ray CT images. The angle and length of thecylinder models are adjusted so that the models matchthe actual fibers well, which will determine the parametervalues. Calculating the angle of individual cylindermodels will quantitatively evaluate the fiber orientation.
Next, the part thickness is divided into 21 layers at allobservation points and the degree of fiber orientation ineach layer is determined. The definition of the degree offiber orientation is illustrated in Fig. 4. The angle offibers is indicated by the in-plane orientation angle Φ andthe out-of-plane orientation angle θ. The orientation
tensor in each direction has been calculated using
equations 1) to 3). “N” indicates the number of fibers.
The orientation tensor is “a11” in the flow direction(MD), “a22” in the direction orthogonal to the flow
direction (TD), and “a33” in the thickness direction (ND)at all observation positions.

MD

0.9

TD

ND

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Thickness (mm)Fig. 5

Quantitative evaluation of fiber orientation

Improvement of Fiber Orientation
Prediction Accuracy through Flow Analysis
To achieve a structural analysis that considers theanisotropy of physical properties due to fiber orientation,
it is necessary to predict the fiber orientation taking place
during injection molding. Then, we predict the fiber
orientation by analyzing the material flow in injection
molding and compare the prediction with the results of
the quantification of actual fiber orientation stated above,in order to verify the prediction accuracy.
Fig. 6 shows a flat plate specimen used in testing. The
specimen is made of PA66 containing 30 wt% glass fibers.
3. 2

2: Orthogonal direction
3: Thickness direction

Φ: In-plane orientation angle (Flow direction: 90˚)
θ: Out-of-plane orientation angle (Thickness direction: 0˚)

Fig. 4

Fig. 6

Definition of the degree of fiber orientation

a11＝

1 N
Σ （sin θi cos φi）2
N i＝1

(1)

a22＝

1 N
Σ （sin θi sin φi）2
N i＝1

(2)

a33＝

1 N
Σ （cos θi）2
N i＝1

(3)

It is now possible to three-dimensionally quantify thefiber orientation, which has conventionally been difficult(Fig. 5).

Overview of specimen geometry

The flow analysis was made with an injection molding
software (CoreTech System Moldex3D®). As a prediction
model for fiber orientation, the Folger-Tucker model 3), which
is a model for predicting orientation behavior of ellipsoids inhigh-concentration solutions, was used in combination with
the iARD (Improved Anisotropic Rotary Diffusion) model4)
to also allow consideration of interference among fibers.
Fig. 7 shows a schematic diagram of the fiber
orientation mechanism. In injection molding, the moltenmaterial is instantaneously cooled to solidify in the areas
where the material has come into contact with the mold.
Inside these areas, the molten resin still continues flowing
in general cases. There arises a velocity gradient between
the solidified layer and the molten layer. It is generally
considered that the difference in velocity causes a shear― 22 ―

stress to make the fibers position in the direction of theresin flow. In this research, specimens were prepared with
two injection speed levels (high and low) since theinjection speed greatly affects the thickness of thesolidified layer. Then, fiber orientation was compared
between the actual test results and the analysis results.
Mold

Fiber

Molten layer(high speed)

Degree offiber orientation
繊維配向度

KYB TECHNICAL REVIEW No. 67 OCT. 2023

Shear stress

Schematic of fiber orientation mechanism

Degree of fiber orientation

Figs. 8 and 9 show the comparison of fiber orientation
distribution between the actual test and the analysis. These
Figures indicate that the analysis results generally reflect theactual fiber orientation distribution, which has been achievedby adjusting the flow analysis parameters to improve theprediction accuracy for fiber orientation. The Figures also
reveal that the trend of fiber orientation distribution varies
with injection speed. Specifically, slower injection producesa thicker layer in the direction of the molten resin flow (MD)close to the wall of the mold. This is probably because thesolidified layer close to the wall is more likely to grow withslower injection and the shear stress occurring between thesolidified and molten layers applies even at its center. Thus,
it is possible to reproduce through analysis the fiber
orientation distribution for varying injection speeds.
MD
ND
SIM TDTD
SIM MDSIM ND

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Thickness (mm)Fig. 8ND

SIM MDSIM TD

SIIM ND

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Thickness(mm)
肉厚(mm)
Fig. 9

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

TD

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Solidified layer(low speed)

Fig. 7

MD

Comparison of fiber orientation distribution between
actual test and analysis (high speed injection)

Comparison of fiber orientation distribution between
actual test and analysis (low speed injection)

3.3 Improvement of Structural Analysis
Accuracy with Fiber Orientation Taken into
Account
This section carries out a structural analysis
considering the fiber orientation distribution predicted
through flow analysis and verifies the analysis accuracy.
A non-linear, multi-scale material modeling software
Digimat® (e-Xtreame) was used to predict anisotropic
physical properties of the material, and homogenizedwith the Mori-Tanaka model5). Digimat uses the mean
field approximation approach. This approach handles thegeometry and orientation of glass fibers approximately as
ellipses and calculates the strain and stress applied to theresin matrix and glass fibers, determining the total
physical properties of the composite containing glass
fibers. The mean field approximation approach focuseson the micro stress-strain characteristics of a material tocalculate its macro physical properties with its
microstructure taken into account. Featuring high-speed
calculation, the approach can be combined with thefinite-element method to calculate and solve equations.
The structural analysis accuracy has been verified withdumbbell-shaped specimens cut out from the flat plate
specimen which was produced in section 3.2, at different
angles (0˚, 45˚, 90˚) to the direction of the resin flow
(Fig. 10). These specimens were subjected to a tensile
test. The resultant stress-strain (S-S) curves werecompared with the analysis results. In general, fibers
contained in an injection-molded part are likely to be
predominantly oriented in the direction of the resin flow.
It is therefore considered that the strength of thespecimens depends on the anisotropy of their physicalproperties due to fiber orientation. Specifically,
specimens cut out at 0˚ have a high strength while thosecut out at 90˚ have a low strength. The following verifies
that these behaviors can be simulated by analysis.

― 23 ―

Research on strength prediction technology for fiber-reinforced plastic injection-molded products

In section 3.2, we already confirmed that changes ininjection speed affect the fiber orientation distribution and thatthe phenomenon can be reproduced by analysis. To determine
the impact of changes in fiber orientation due to variations ininjection speed on the physical properties, both a strength
evaluation and a comparison with analysis results have been
carried out at two injection speed levels: high and low.

200

0˚
0度
45度
45˚
90度
90˚

応力(MPa)Stress(MPa)

160

Resin flow

0˚ SIM
0度SIM
45度SIM
45˚
SIM
90度SIM
90˚
SIM

120

80

40

0
0

Fig. 12

Locations from which strength test specimens were cut out

Fig. 10

Figs. 11 and 12 show the test results. These Figures reveal thatthe analysis model can reproduce the behavior of the actual
specimens. The end point of the S-S curves represents the timing
when the specimen fractured. Fracture was determinedaccording to the Tsai-Hill 3D transverse criterion. By considering
the breaking strain for each fiber orientation, the analysis model
also reproduces fracture timing with good accuracy.
The results also show that the slower the injection speed,
the larger the anisotropy with high strength at 0˚ and low
strength at 90˚. This is probably attributable to the finding insection 3.2 that a higher degree of fiber orientation is found in
the direction of MD for low injection speed. In other words,
the injection molding method impacts the fiber orientation,
which further affects the physical properties. We have verified
that these changes can be reproduced with good accuracy byan analysis model that considers fiber orientation.

0.02
Strainひずみ

0.04Structural analysis accuracy for various cut-out
angles (low speed injection)

Improvement of Prediction Accuracy forStrength Reduction Rate of Welds
When a flow of molten resin meets another flow ofmolten resin during injection molding, a weld line isformed. The weld line substantially degrades the strengthof the composite because of the local change in fiber
orientation and the existence of a fusion interface (Fig.
13). In fact, it is difficult to completely eliminate theformation of weld lines in injection molding of actual
products. Therefore, it is essential to carry out analysis
with weld lines taken into account, in order to improve
the strength analysis accuracy.
3. 4

Gate

Weld line

Fibers

200
0度
0˚
45度
45˚
90度
90˚

Stress(MPa)
応力(MPa)150

0度SIM
0˚ SIM
45度SIM
45˚
SIM
90度SIM
90˚
SIM

Flows of resin

Fig. 13

100

50

0
0

0.02
0.04
ひずみ
StrainFig. 11 Structural analysis accuracy for various cut-out
angles (high speed injection)

Schematic of weld line

As stated above, welds may have lower strength due toa local change in fiber orientation and the existence of afusion interface. Photo 2 shows an X-ray CT image ofthe fiber orientation distribution of a weld. In the portion
where the flows of resin merge, fibers are densely
positioned in the direction perpendicular to the directionof the flows of resin. In this way, the weld is the place
where there is a local change in fiber orientation and islikely to be a source of fracture partly because of theexistence of the fusion interface. By predicting the fiber
orientation at the resin merging point by flow analysis andthen including the lower strength due to the fusion interface
as an analysis variable, we have successfully improved theprediction accuracy for strength of the welds (Fig. 14).
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KYB TECHNICAL REVIEW No. 67 OCT. 2023

Resin flow

Photo 2that the resin flow behavior varies according to the partgeometry, resulting in different areas where the weld line
is formed. We then conducted a structural analysis thatconsiders the fiber orientation and a lower strength of theweld line. As a result, the analysis successfully
reproduced the behavior that the part with geometry [1]fractured while that with geometry [2] did not (Fig. 16).
Thus, we confirmed that, when designing FRP parts, it isimportant and effective to study how to ensure thematerial strength, including the influence of the
manufacturing method.

Resin flow

Geometry
形状① [1]

Geometry
形状② [2]

Geometry
形状①[1]

Geometry
形状②[2]

Fig. 15

Weld lines formed in different locations

Fiber orientation in the weld

250

Stress(MPa)
応力(MPa)200
150
1-gat actual
1gate実物test

100

2-gate actual
test

Weld line

1-gate analysis

50

2-gate analysis

0
0

0.01
Strainひずみ

Fracture occurs when the index exceeds 1)
1 ((Fracture
破壊指標 index:
1を超えたら破壊)

0.02

Geometry
形状① [1]

Fig. 14 Prediction accuracy for strength of welds

Through these efforts, we have established an analysis
technique with consideration given to the fiber orientation
and weld line that substantially affect the physicalproperties of FRP injection-molded products.

形状② [2]
Geometry

0.5

破 壊 部
Fractured
part0Fig. 16

P rediction Accuracy Verification with
4 

Analysis of fracture index during press-fitting into
the outer

Actual Part Geometry

4. 1 C onfirmation of the Effect with Actual Part
Geometry
Since it is now possible to carry out the strength
analysis considering the fiber orientation and weld line,
this chapter verifies the effect of the analysis by using
actual parts. An example for plastic bump stoppers forshock absorbers is introduced as follows. The plastic
bump stopper is press-fitted into the outer. When the
stopper with geometry [1] was press-fitted into the outer,a fracture occurred. Then, the part design was modified
on a trial-and-error basis to have another geometry [2],which eventually eliminated the fracture problem (Fig.
15). We then tried to verify that this phenomenon can be
reproduced by analysis.
First of all, we examined the flow behavior of resin
through resin flow analysis. The examination revealed

5Concluding Remarks

FRP injection-molded products have anisotropy or
distribution of their mechanical properties due to fiber
orientations and/or weld lines generated during themolding process. We have developed a structural analysis
technique that considers fiber orientation and welds inthe molding process, improving the prediction accuracy
for physical properties of plastic parts. It has also beenfound that the technique can be used to predict thefracture behavior of actual parts of different geometries.
We have confirmed that, when designing FRP parts, it isimportant and effective to study material strength,
including the influence of the manufacturing process.

― 25 ―

Research on strength prediction technology for fiber-reinforced plastic injection-molded products

6

References

Future Prospects

This technique has improved the strength prediction
accuracy for plastic parts. We will apply the technique tovarious actual parts to improve the development
efficiency and optimize the part geometry for cost andweight reduction, contributing to higher competitiveness.

1) Nanotec Japan website
https://www.nanonet.go.jp/magazine/feature/10-9innovation/58.html
2) SUZUKI Tohru, SUGITA Toshio, SETO Masahiro,
KAKISHIMA Hironori, TANAKA Hiroaki, YAMABE
Masashi: Seikei-Kakou, 28(6), 239 (2016)
3) Folgar, F. and Tucker, C.L.: Journal of Reinforced
Plastic and Composites, 3.98 (1984)4) Peter H. Foss, Huan-Chang Tseng, John Snawerdt,
Yuan-Jung Chang, Wen-Hsien Yang, Chia-Hsiang
Hsu: Polymer Composites: 35(4), 671 (2014)5) Mori. T., Marzari. N.: Journal of Energy Resources
Technology, 114, 101 (1992)

Author 

OGURA Shogo
Joined the company in 2012.
R&D Sect. No.1, Production
Technology R&D Center,
Engineering Div.
Engaged in development of plastic
molding technology― 26 ―