Mitsubishi Heavy Industries Technical Review Vol. 58 No. 4 (December 2021)
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Numerical Simulation Technology
by Damage Modeling in Mechanically-fastened
Composite Joints under Combined Loads
RYOSUKE HASHIZUME*1 YUYA NAGATOMO*2
YUKIHIRO SATO*1

MASAYOSHI SUHARA*1

KOJI ESAKI*3

TAKAYUKI SHIMIZU*3When applying composites such as fiber reinforced plastics (FRP) in product structures,challenges lie in the necessity of conducting many tests to ensure the structural reliability and theconsequent prolonged period of time required for development. Mitsubishi Heavy Industries, Ltd.
(MHI) has therefore worked on the development of simulation technology to predict the strengthwith high accuracy, by enabling the complexities of damage in composites to be represented innumerical analysis and simulating the damage progression in sequence. This report focuses onmechanically-fastened joints, the strength of which has been difficult to predict in advance becauseof their complex loading conditions and various modes of failure. By analyzing how damage wasinitiated and developed, we assessed/compared the results with those of the structural element test
and internal inspection.

|1. Introduction
Because of their high specific strength, high specific stiffness and high fatigue and corrosion
resistance, composites such as carbon fiber reinforced plastics (CFRP) are often adopted as materials
for the primary structure components of aerospace vehicle to reduce the weight of the structure. In
recent years, composites have also been used in automobiles, although limited to certain types ofvehicles such as luxury cars and sports cars.
One bottleneck for application of composite structures is the necessity of conducting a verylarge number of qualification tests to ensure conformity with the high reliability requirements for
products such as aerospace vehicle. This is because composites show a strong anisotropy inmechanical properties such as strength and elastic modulus and exhibit complexly varying dominantmodes of failure, depending on the combination of dissimilar materials of reinforcing fiber andmatrix resin.
Under such circumstances, projects are under way around the world to enable “virtual testing”,
by which numerical simulation is used to replace as many development tests as possible. MHI has
also worked on research and development for its application to product development(1)(2).
This report focuses on mechanically-fastened joints such as bolts and rivets. Their joint
strength and dominant mode of failure change in a complex manner with design factors such asloading conditions, environmental conditions, laminate configuration and thickness and are therefore
difficult to predict in advance. As a result, the number of tests required naturally tends to increase.
In the following chapters, we present our simulations for these mechanically-fastened joints(3)(4).

|2. Damage modeling technology in mechanically-fastened composite
joints2.1

Failure modes of mechanically-fastened composite joints

Macroscopic failure modes of mechanically-fastened composite joints are classified as shownin Figure 1(5). When the bearing load which is contact pressure load at the interface between themechanical joint and the composite and the bypass load transferred through the composite itself areapplied in a combined manner, the static failure load varies depending on the degree of each of these*1

Strength Research Department, Research & Innovation Center, Mitsubishi Heavy Industries, Ltd.

*2

Manufacturing Technology Research Department, Research & Innovation Center, Mitsubishi Heavy Industries, Ltd.

*3

Chief Staff Researcher, Strength Research Department, Research & Innovation Center, Mitsubishi Heavy Industries, Ltd.

Mitsubishi Heavy Industries Technical Review Vol. 58 No. 4 (December 2021)
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acting stresses. Therefore, it is necessary to obtain data on the strength by testing under suchcombined loading conditions.

Figure 1 Failure modes of mechanically-fastened composite joints(5)2.2

Damage modeling technology overview

In damage modeling technology for composites, the nonlinear finite element method is usedto predict the macroscopic failure behavior and strength, by modeling the behavior of microscopic
damage at its onset and progression in the composite failure process according to the constitutive lawof the element of each ply in a laminated composite and the element interfaces.
Firstly, regarding the inside of the element, microscopic damage such as fiber fracture, fiber
kinking and matrix cracking is predicted by the failure criteria called LaRC (developed mainly byNASA Langley Research Center). The softening behavior is modeled considering energy dissipation
during damage progression based on continuum damage mechanics (CDM) (6).
In-plane cracking such as inter-ply delamination and splitting, which occurs and develops
along the direction of reinforcing fiber, is modeled with Cohesive Zone Elements (CZE) as cracks
occurring and developing at the element interfaces(7).

2.3Analysis model

Figure 2 gives the analysis model. Using Abaqus, a commercial finite element solver, theassessment area of each ply in a specimen is divided into solid elements, while the jig, bolt andspecimen are to be in contact with one another. The occurring and developing behavior of
microscopic damage in the element was analyzed by incorporating our original code as a user
subroutine.

Figure 2

Analysis model|3. Comparison of results between damage simulation and structuralelement test
3.1

Damage initiation comparison

The structural element test and internal inspection were carried out to compare the occurrenceof damage. Specifically, five types of specimens with varying stacking sequence, thickness, etc.,
were subjected to different levels of maximum tensile load before being unloaded. The specimens
were then removed to observe their cross-sections by X-ray CT and optical microscope andcharacterize the load at which microscopic damage was initiated. The results were compared withthe predictions of the analysis.

Mitsubishi Heavy Industries Technical Review Vol. 58 No. 4 (December 2021)
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Given as an example in Figure 3 are the results of cross-sectional observation for a 24-ply
quasi-isotropic laminate, which is considered as the reference case in this test. The cross-sectional
images shown herein correspond to the three levels of maximum tensile load. Those at the bottom
row are of a specimen with the lowest applied load, showing no occurrence of damage. On the otherhand, the images at the middle and upper rows, which are of specimens subjected to higher levels ofload, indicate the presence of damage in the form of fiber kinking. Therefore, it can be consideredthat damage was occurred at a certain level of load between the bottom and the middle rows.

Figure 3 Example of cross-sectional observation images

In this way, the level of load at which damage is initiated was characterize for each type of thespecimens. The results were shown in Figure 4, together with the predictions of the analysis. The
lower bound of the error bar represents the maximum value of the load at which no damage wasobserved in the cross-sections, while the upper bound represents the minimum value of the load at
which damage was observed. Although there are some variations depending on the type of specimen,
it has been confirmed that the predictions are generally in good agreement with the test results.

Figure 4

Damage onset analysis and the test results

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Comparison of damage developing behavior

This section presents the results of a comparison of damage developing behavior. Specifically,
the results of failure mode simulation are compared with those of the structural element test. It has
been reported that mechanically-fastened composite joints exhibit macroscopically different modesof failure when the dimensions of the specimen change(8). Using specimens with the geometricalconfiguration listed in Table 1, we compared both results and confirmed that the analysis can predictthe change in the dominant failure mode.
Table 1

List of specimen configurations for both analysis and testing toconfirm change in failure mode
Bearing

Shear-out

Net-tension

Failure Mode(8)GeometryFE Modelw/d5

53e/d

2.5

1.5

2.5

The dimensions of the specimen were set with the expectation that each would exhibit the corresponding
failure fracture mode as noted in the upper row.

Table 2 compares the results between the testing and the analysis. The analysis results
successfully predicted the change in the dominant failure mode shown in the test and the predicted
failure loads were also within ±15% of those obtained by the test. Fiber kinking was the main damage
mechanism under the conditions in which bearing is the dominant failure mode. On the other hand,as the distance between the hole in the specimen and the free edge (indicated as e in the table) or thewidth of the specimen (w in the table) became smaller, matrix cracking became the prevailingdamage mechanism. The dominant failure mode was changed accordingly to shear-out (in the caseof smaller e values) or net-tension (smaller w values), which was indicated by both the test and theanalysis. Furthermore, both results also showed the lowering of the load in these cases, which wascaused by the matrix crack having originated from the edge of the hole and developed until theyreached the free edge.
Table 2Comparison of test and analysis results to confirm change in failure mode
Net-tension■: Kink■: Matrix cracking

Shear-out―: Test―:Simulation

Load-Displacement

Simulation

Bearing

The damage progression results of the test and the analysis to confirm the relationship between the onset/progression of
microscopic damage and the macroscopic failure mode. Regarding the analysis results, the elements damaged by fiber kinking
are colored in yellow (■), while those damaged by matrix cracking are in red (■).

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53.3

Comparison of failure load predictions

Lastly, Figure 5 presents the accuracy validation results for strength prediction under
combined loading conditions. The figure also includes the failure modes obtained by analysis under
the loading conditions other than in Table 2 (which is bearing load only). As comparison results, thesimulated failure loads are within approximately ±15% of the test results. It has therefore been
confirmed that the test results and the analysis predictions are correlated with each other in terms offailure mode. Especially when subjected to combined loads of bearing and compressive bypass, thelocation of local buckling caused by the developing of microscopic damage and inter-ply
delamination is different from that occurring under the load of compressive bypass only. Thisphenomenon was also successfully reproduced by simulation.

Figure 5 Strength prediction results under combined loading conditions|4. Conclusion
This report pertains to the development of simulation technology to accurately predict thestrength by modeling in detail the occurrence and developing behavior of microscopic damage incomposites, presenting an example case of mechanical joints that can exhibit a variety of failuremodes depending on the loading conditions. We will promote the use of such simulation technologies
to ease the burden of conducting many development tests, reduce product costs and shorten the periodof time required for development. It can also be considered that proceeding effectively with thedetailed damage risk assessment and the measures from the early stages of product design willcontribute to improving product value, for example, in terms of enhanced reliability and a reductionin the structure weight.
Looking forward, we will further improve this simulation technology and expand its
applicability by employing it not only in mechanical joints, but also in various other cases ranging
from structural element testing to component testing, while validate the prediction accuracy andreliability.

Mitsubishi Heavy Industries Technical Review Vol. 58 No. 4 (December 2021)
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