Mitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018)
1Strength Prediction Technology for Composite Materials
Simulating Damage Phenomena

YUKIHIRO SATO*1

MASAHIRO KASHIWAGI*1

KAZUHIRO MIURA*1

YOSHINORI NONAKA*2

MASAYOSHI SUHARA*1 TAKAYUKI SHIMIZU*2This paper presents a strength prediction technology for composite materials using
numerical analysis. Composite materials typified by fiber reinforced plastics (FRP) are superior tometals in specific strength, and are mainly applied to transportation equipment such as aircraft.
However, the damage phenomena of FRP are complicated, and a large number of tests arerequired to ensure structural reliability, so the development period tends to be lengthy. Therefore,
Mitsubishi Heavy Industries, Ltd. (MHI) is working on the development of an analytical technique
to simulate complex damage phenomena of FRP and predict strength with high accuracy. This
analytical technique expresses damage to the fiber, resin, and interlayer with numerical analysis
and predicts strength by sequentially solving the progress of damage. This report introduces
examples of the analysis of compressive strength reduction due to impact damage, which isparticularly problematic for FRP.

|1. Introduction
Composite materials, which are typified by fiber reinforced plastics (FRP), are superior in
specific strength and have good fatigue properties and corrosion resistance, so application to
structural materials has been progressing especially for transportation equipment such as aircraft,
for which weight saving is effective. When a load is applied to an FRP, damage to the fiber, resin,interlayer, etc., occur in the laminated structure (0.1 mm order), which causes structural failure
while interacting in a complicated manner. It is difficult to consider these complex damage
phenomena theoretically and analytically, and strength prediction was difficult. Meanwhile,transportation equipment that heavily relies on composite materials requires high reliability, and alarge number of tests are required to ensure reliability in product development. This is one reason
for the longer development period. Therefore, it is desirable to build analytical techniques that canrationally predict a wide variety of structural strengths using a small number of basic test data
items.
Therefore, we are working on the development of numerical analysis technology that cansimulate damage to composite materials and predict the strength. This paper outlines thistechnology and explains the analysis examples.

|2. Strength prediction technology
2.1

Lamination structure and damage phenomena of FRPAn FRP is mainly produced by stacking fiber sheets at various angles and solidifying themwith a resin. When a load is applied to an FRP, breakage/kinking of the fiber and tensile/shear
cracking of the resin occur in each laminated layer. In addition, interlaminar delamination occurs
due to tensile and shear loads. These damage phenomena occur and progress while interacting witheach other, leading to the final failure of the entire FRP. The initiation of damage can be predictedby the conventional strength evaluation based on simple stress and strain criteria, but it was notpossible to take into account the behavior in which damage progresses while interacting with otherdamage phenomena, so it is difficult to predict the strength at the time of final failure.
*1*2

Strength Research Department, Research & Innovation Center
Chief Staff Manager, Strength Research Department, Research & Innovation CenterMitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018)22.2

Damage phenomena analysis method

We developed an analytical method to represent damage in numerical analysis in order topredict the strength in consideration of damage phenomena interacting in a diverse and complicatedmanner with each other. This method uses a finite element model simulating the laminatedstructure of an FRP and adopts a material constitutive law considering damage for each layer andthe interlayer.
Each layer was modeled as a normal shell element or solid element, and the influence ofdamage to the fiber and resin were considered for each layer. The initiation of damage wasdetermined on the basis of a stress-based fracture criterion. As the fracture criterion, the LaRC
criterion2,3 proposed by NASA Langley Research Center was applied. The LaRC criterion ischaracterized by refining the evaluation formula of the fiber kinking phenomenon in thecompressive stress field, which could not be evaluated accurately with the conventional fracturecriterion. Progress in the damage is expressed by the deterioration of stiffness. An energy-based
method, in which the stiffness is deteriorated in accordance with the progress of damage and theamount of energy dissipation of the element in a completely damaged state is equal to the fracture
toughness of the material, was used. These damage initiation and progress criteria were formulated
for each damage phenomenon of fiber and resin, and fiber failure and resin cracking weresimulated. A special element called a cohesive element was inserted between the layers. The
cohesive element defines the interfacial behavior using interfacial traction and relative
displacement. Interlaminar delamination was simulated with respect to this interfacial behavior inconsideration of damage initiation based on the stress criterion and damage progression based on
the energy criterion. Figure 1 shows a schematic diagram of this damage modeling. Damage
initiates at the stage when the stress reaches the prescribed value for all damage in terms of fiber
failure, resin cracking and interlaminar delamination, and the stiffness decreases with damageprogression. The area of the triangle surrounded by the stress-strain relationship in the figure
corresponds to the fracture toughness.
In this method, when damage occurs in an element, the redistribution of the stress isexpressed by locally deteriorating the stiffness in the damaged element. Due to this stressredistribution, damage progresses to adjacent elements, and the load by which the load bearing
capacity is ultimately lost is predicted.

Figure 1 Material constitutive law considering damage
After the stress-based damage initiation criteria is satisfied, the behavior
of energy-based damage progression (rigidity deterioration) is shown.

|3. Analysis example
This section introduces an example case where strength prediction was performed byanalyzing the occurrence of internal damage at the time of low-speed impact application and astrength test after the occurrence of impact damage. Such a test is unique to composite materials
and its importance is recognized particularly in the aircraft field. If a weak impact such as thatcaused by the dropping of a tool is applied, no damage is found in appearance, but interlaminardelamination occurs internally in many cases. It is well known that when a compressive load isapplied in this state, the strength greatly decreases compared with a case of no damage. This
strength is called compression after impact (CAI) strength. Aircraft, etc., must be designed to haveMitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018)
3appropriate strength even in the state of impact damage or other defects. CAI strength is one of thefactors leading to an increase in the number of test items.

3.1

Comparative test

The test specimen was a 24-ply quasi-isotropic laminate produced by the VaRTM method
using a high-strength type carbon fiber and epoxy resin used for aircraft and wind turbines. First,drop weight impacts with the impact energy of 20 J and 55 J were applied. Figure 2 depicts theimpact test apparatus. After applying the impact, a compression test of the same specimen wasperformed with the jig shown in Figure 3.

Figure 2Impact test apparatus

The falling weight type test apparatus for application of impact.

Figure 3 CAI test tool
The test tool for applying a compressive load to obtain thestrength after impact damage.

3.2

Analysis procedure

As can be seen in Figure 4, analysis was carried out using a finite element mesh simulating
the laminated structure according to the procedure and the boundary conditions presented inFigure 5. The analysis was performed constantly from damage occurrence caused as a result of theimpact to compression failure to reproduce the test procedure.

Figure 4

Finite element mesh

The mesh simulating the laminar structure of a composite material

Mitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018)
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Figure 5 Analysis procedure and boundary conditions
Analyzing constantly from impact application to compression for reproduction of the test procedure

3.3

Comparison of test results and analysis results

Figure 6 compares the state of interlaminar delamination after impact application obtainedby the impact analysis with the UT (ultrasonic testing) inspection image after the impact test. Thisis a projected figure obtained by superimposing damage for all layers. Figure 7 compares the stateof interlaminar delamination with the observation image in the reference.4 Figure 6 and Figure 7
indicate that generally known delamination of a double helical structure occurred and thedelamination shape seen in the test was obtained.

Figure 6

Interlaminar delamination caused by impact (projection)

Figure 7

Interlaminar delamination caused by impact (each interlayer)

The analyzed completely-damaged interlaminar element and UT inspection image
from the test are shown as a projection.

The analyzed completely-damaged interlaminar element and UT inspection image from the test are shown for each interlayer.

Mitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018)
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Figure 8 presents the relationship between the impact damage projected area and the impact
energy. The area is of the delamination projection diagram (Figure 6) and normalized by the valueof the test results of 55J. As can be seen in Figure 8, the damage area obtained by analysis
displayed good agreement with the test results.

Figure 8 Relation between impact damage projection
area and impact energy

The impact damage projection area was normalized with the area at
55 J impact in the test.

Figure 9 illustrates the progress of interlaminar delamination and fiber damage obtained bycompression analysis. In the vicinity of the maximum load, the damage related to kinking of thefiber progressed in the width direction, indicating that the fracture mode was dominated by fiber
kinking. This was a result caused by bending deformation of local buckling that occurred in the partthat was damaged by the impact.

Figure 9 Progress of interlaminar delamination and fiber
kinking obtained by compression analysis

In the vicinity of the maximum load, the damage related to the kinking of thefiber progressed in the width direction.

Figure 10 gives the relationship between the CAI strength and the impact energy. The CAI
strength is normalized by the value of the test results of the undamaged material. In the test, thestrength was lowered to about 50% as a result of the impact, compared with the non-damaged
material. The strength prediction results using compression analysis showed good agreement withthe test results.

Mitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018)
6Figure 10 Relationship between CAI strength andimpact energy
The CAI strength was normalized by the strength of theundamaged material in the test.

|4. Conclusion
Numerical analysis technology that simulates the damage phenomena of FRP enabledstrength prediction, which was difficult in the past. As a result of the analysis of damage
occurrence at the time of impact, which is a problem peculiar to FRP, as well as CAI strength, it
was confirmed that it is possible to predict the impact damage area and the CAI strength. Thismethod is a versatile analysis method that can be applied to stress concentrating parts,
manufacturing defect parts, etc., in addition to the examples introduced here. We plan to further
improve the analysis to allow for consideration of environmental dependence and morecomprehensive evaluation such as fatigue damage evaluation, etc., in the future.

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Aoki, Y. et al., Effect of delamination propagation on mechanical behavior in compression after impact,
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