206_Composite_Delamination

8/7/2019 206_Composite_Delamination

1/16

Delamination Modeling of Composites

for Improved Crash Analysis

David C. Fleming

Aerospace Engineering Program

Florida Institute of Technology

150 W. University Blvd.

Melbourne, FL 32901

ABSTRACT

Modeling of crashworthy composite structures is limited by the inability of currentgenerations of finite element crash codes to effectively model certain critical failure modes, such

as delamination. Previous efforts to model delamination and debonding failure modes using crash

codes have typically relied on ad hoc failure criteria and quasistatic fracture data. Improvements

to these modeling procedures can be made by using an approach based on fracture mechanics. A

study of modeling delamination using the finite element crash code MSC/DYTRAN was

conducted. This investigation demonstrates the potential for improving the crash modeling of

composites through improved delamination modeling. Further developments to this approach may

result in improved analytical tools that can be used to model delamination using current

generation crash codes.

INTRODUCTION

Substantial progress has been made in improving the crash safety and crashworthiness of

aerospace vehicles. The development of the Aircraft Crash Survival Design Guide and MIL-STD

1290A resulted in aircraft designs that have been demonstrated to effectively protect occupants

under crash conditions [1]. The increased use of composite materials in aerospace structures,

however, requires improved understanding of these materials under crash conditions. Various

efforts [2,3] have demonstrated the potential for composites to be effectively used in efficient

crashworthy designs. These efforts have been experimentally oriented, utilizing a range of

methods from characterizing the crushing response of laminates to full-scale crash testing of

composite airframes. As analytical techniques for modeling crash behavior mature, the possibilityof supplementing these experimental techniques with analytical tools becomes attractive. For

example, if an analytical model of an aircraft can be developed, parametric studies of the response

of the aircraft under a broad range of crash conditions may be conducted that would be cost

prohibitive to perform experimentally. To take full advantage of the possibilities offered by

analytical crash modeling techniques, however, improved models of composite structures must be

developed and incorporated into these tools.


2/16

The need for improved modeling of composite materials in crash analysis has long been

recognized. At the Workshop on Computational Methods for Crashworthiness held at the NASA

Langley Research Center in 1992 [4], modeling composite crushing behavior was identified as a

critical need. Still, commercial finite element crash codes do not include procedures for detailed

crash modeling of composite structures. Critical features such as out-of-plane failure models for

composites are not included in the commercial codes, although several researchers haveimplemented models of delamination behavior using crash codes [5,6]. These models, however,

are based upon either ad hoc failure criteria, or have relied upon quasistatic data. There is a need

to improve these techniques to take better advantage of existing research in fracture mechanics.

This will allow crash models to more fully capture the behavior of composites under crushing

loads.

CRASH MODELING OF COMPOSITE STRUCTURES

Previous efforts toward applying crash modeling to composite structures can be divided

into two categories. The first is component-level modeling, in which attempts are made to modelcomposite crushing phenomenology in detail. Such models are fundamental in nature and are

compared with small-scale experimental test specimens, such as tubes under uniaxial crushing

loads. For direct application to engineering problems, a second approach, structural-level

modeling, is used. In this approach, the response of the composite elements is modeled more

simply to allow easier evaluation of the global behavior of large-scale structures. Previous

research in each of these areas is reviewed in the following sections.

Component-Level Modeling

Detailed modeling of composite crushing is limited due to the complexity of the crushingphenomenology. Composite materials under crushing may experience a wide variety of interacting

failure modes, including fiber and matrix fracture, delamination, local instability, and others [2,7].

A comprehensive crushing model, therefore, requires demanding computational algorithms for

failure prediction, frictional contact, and other significant behaviors. Furthermore, these effects

must be captured on a small scale, perhaps on the order of the ply thickness. To reduce the

complexity of the modeling problem, a limited subset of the experimentally-observed crushing

mechanisms are included in the models. This reduces the modeling difficulty and computational

expense of the models, but also reduces their generality.

Perhaps the earliest attempt to model the crushing behavior of composites was reported by

Farley and Jones [8]. They used a static finite element model to predict the crushing performance

of composite tubes. The laminate was modeled by an assembly of plate elements representing each

ply, joined by springs representing the ply interfaces. Delamination was predicted by calculating a

strain energy release rate, G. The model did not allow for the direct calculation of strain energy

release rates. Instead, computation was based on the difference between the strain energy in the

model under a given load, and the strain energy in a model with a slightly larger delamination

under the same load. The strain energy release rate computation relies on the symmetry of the

model so that the calculated G value is equivalent to the strain energy release rate at any point


3/16

along the delamination front. Furthermore, this approach does not permit the partitioning ofG

into components for the various fracture modes. Correlation with experimental results was

reasonable given the limited phenomenology modeled.

Linear models were used by some researchers to gain insight into specific aspects of

crushing behavior. Sigalas et al [9] used an axisymmetric, static finite element model to

qualitatively assess the performance of chamfered crushing triggers on the crush performance ofcomposite tubes. The model is limited in scope and applicability, and cannot be extended to model

the overall crush behavior of the specimens. Hamada and Ramakrishna [10] developed a finite

element model for the crushing of composite tubes that exhibit a splaying failure mode, in which a

single primary delamination divides the laminate into two fronds that are forced away from each

other by a wedge of compacted debris. The initial finite element mesh included a representation of

a pre-existing debris wedge and delamination crack. Extension of the central crack separating the

fronds was predicted by calculating a stress intensity factor, K, at the crack tip from a linear

elastic solution. The load required for further crack extension is predicted by scaling the load such

that Kreaches a critical value. From this linear load-displacement response, the energy absorption

under quasistatic loading is estimated. This approach is limited by its reliance on a predefined

crush zone morphology and linear computation as well as by limitations in the fracture mechanicsused in the model.

Progressive damage models were developed by several researchers for more detailed

application to crushing analysis. Kindervater [11] describes a quasistatic finite element model used

to study the initiation of crushing damage in a composite laminate under quasistatic crushing

loads. In the structure modeled, delamination damage initiated in a curved connection between a

flat beam and the skin structure. The initiation and propagation of delamination damage was

modeled by predicting failure in resin layers modeled between plies in the finite element mesh. The

author, with Vizzini [12] developed a 2-D, quasistatic finite element model applicable to the

crushing of composite plates. Delamination between plies was modeled based on strain energy

release rates computed using the virtual crack closure technique. The model qualitatively captured

some of the physical behavior of plate crushing, but due to the limited failure phenomenologyincluded in the model did not yield accurate predictions of crushing stress.

One of the most recent models of the crush behavior of a composite laminate was reported

by Kamoulakos and Kohlgrber [13]. They modeled the crushing of a composite semi-circular

laminate using the finite element crash code PAM-CRASH. The laminate was modeled by

discretizing each ply separately. Plies were held together by multipoint constraints or so-called

spot weld elements. Delamination growth was predicted based on the forces resulting from the

constraints. The model showed qualitative agreement with experiments in terms of the

deformation shape, though the crushing force was underpredicted.

The models described above demonstrate the potential for modeling composite crushing

behavior by using finite element models based on simplified crushing phenomenology. Good

correlations are obtained in many cases using models that do not fully capture all aspects of

crushing damage observed experimentally, provided sufficient attention is given to the aspects of

crushing that most directly control the response. In most of the previous studies, delamination is

identified as a critical component of crushing behavior. Experiments on the crushing of composite

laminates under axial crushing loads has shown that the appearance and growth of delaminations

can significantly influence the energy absorbency of the laminate [14,15]. Large delaminations

may result in reduced amounts of fiber and matrix damage in a laminate if crushing displacement


4/16

can be accommodated by bending of the sublaminates. Therefore, delamination modeling is

critical for accurate modeling of the crushing behavior of composite laminates. Various

techniques, most based on relatively simple models, are used to model delamination in the studies

described above. Improvement to crush modeling may be possible if improved delamination

models are developed.

Structural-Level Modeling

For crash analysis of large scale composite structures in engineering applications, detailed

analysis of the crushing behavior of composite components, as described above, is not currently

attempted. Instead, simplified material models of composites are applied. The nature of the

simplified modeling approach used can significantly influence the fidelity of the resulting model.

One approach to modeling large scale structures containing composite structural elements

is to model the crushing behavior of the composite elements based directly on empirically

obtained crushing data. For example, a beam in a crushable subfloor may be modeled as a simple

nonlinear spring, whose load-displacement characteristics are obtained from experimental crushtesting of a laminate or a small subcomponent of the floor structure. This procedure results in a

hybrid experimental/analytical approach, permitting crash analyses to be conducted using

significantly fewer computing resources than would be required if detailed modeling of all

elements were required [16]. However, the computed solution is only accurate if the failure

modes experienced by the composite component in the actual crash condition being modeled are

identical to those that appeared in the experimental test from which the spring properties are

derived. Because the in-service loading condition and geometric constraints are likely to be

considerably different from those of the experimental test, the utility of this modeling method may

be limited. Crash codes such as KRASH [1] and DYCAST [17] have been developed using this

hybrid modeling approach, and good correlations between results from such models and full-scale

crash testing have been demonstrated for a variety of aircraft. These codes rely upon a substantialinput of experimental data from either component or substructure testing and require significant

artistry in their application to yield good results.

As computing power increases, there is an increasing trend to move away from hybrid

empirical/analytical modeling approaches in favor of detailed finite element modeling of crash

behavior. Finite element crash codes, in which all structural members are modeled based on

fundamental material property data may require less extensive experimental input than hybrid

codes, and offer greater potential for detailed crash analysis. Several commercial transient

dynamic finite element codes have been developed for use in crash modeling. These codes have

gained acceptance in the automotive industry and have been applied to models of automotive

substructures as well as models of complete automobiles [4]. A wide variety of material models

for metals is included in the commercial transient dynamic codes. By contrast, the material models

included in these codes for composites are limited.

Typically, finite element crash codes allow for modeling of laminates using classical

lamination theory. Ply degradation models based on quasistatic in-plane fracture properties are

often used to model failure. Reference 18 describes a typical composite material model, as

implemented in the code PAM-CRASH. The model includes a scalar damage parameter

simulating matrix micro-cracking. The stiffness matrix is reduced according to the value of the


5/16

damage parameter, which is determined based on values of the strain invariants. This material

model can be supplemented with other in-plane fracture criteria to improve its accuracy. A similar

damaging material model was adapted to account for high strain rate effects and applied to the

study of hypothetical glass/epoxy highway guard rails using the code ABAQUS/explicit [19].

These models, however, do not allow for out-of-plane failures such as delamination or debonding.

This limitation reduces the ability to apply finite element crash codes to the design of aircraftstructures, both because the crushing behavior of composite laminates may not be accurately

modeled, and because adhesive bonding, which may be present in a composite airframe may not

be rigorously treated. Despite these limitations, finite element models have been developed to

describe the crash behavior of composite aircraft structures. The following paragraphs describe

some such efforts reported in the literature.

Johnson and his collaborators [20,21] describe recent efforts to model crushing response

of composite elements. Among the structures modeled are cruciform elements, which represent

the intersection of beams in a subfloor structure. They employed the homogenous orthotropic

damaging model, described above, in the finite element crash code PAM-CRASH. Their model

compared well with experiments on fabric glass/aramid/epoxy hybrid test specimens in terms of

peak load, energy absorbency and failure mode. For carbon/aramid hybrid laminates, the failuremode was accurately predicted, although the computed loads and energy absorbency values were

substantially low. The structures modeled in this case failed predominantly in a folding mode.

Delamination and debonding did not significantly contribute to the energy absorbency of the

tested configurations. Other models based on the damaging model have been demonstrated for

simple beam and column structures [18], as well as for box core beams (sandwich beams whose

core is comprised of adjacent, filled square tubes) [22]. Models of full-scale fuselage sections

containing composite components following a similar approach have also been performed and

correlated with experimental data [13,20,23].

These models appear to be effective for structures whose failure modes are governed by

large-scale laminate failure and local instability. However, the material models upon which they

are based do not capture the full range of behavior that may be present in the crushing of acomposite specimen. In particular, crushing behavior in which wholesale destruction of the

laminate contributes significantly to the overall energy absorbency cannot be accurately modeled

by these approaches. Further, if delamination or debonding forms a significant part of the

behavior, specialized procedures must be introduced into the model.

As computing capabilities increase, and improvements to the capability of crash modeling

software are developed, there is an increasing desire to implement improved crash models of

composites into detailed finite element codes. Such efforts should include the ability to model a

greater range of failure modes of composites, including delamination, and further consideration of

dynamic effects must be made. Therefore, improved techniques for modeling the dynamic

crushing behavior of composite structures are necessary before widespread application of

advanced finite element crash codes to the analysis of composite airframe structures can be

achieved. The two aspects of composite modeling described above, component modeling focusing

on detailed crush modeling and structural modeling of large scale aircraft components are

beginning to merge as improved understanding of the modeling of crush phenomenology is

integrated into larger scale models. Reference 13, for example, describes the use of a detailed


6/16

finite element code to model the small-scale crushing behavior of a composite test article. This

paper describes another step in this direction. Procedures for integrating fracture mechanics-based

delamination modeling into a finite element crash code, MSC/DYTRAN, are developed and

studied.

PROCEDURE

There have been previous efforts at modeling the delamination of composites using finite

element crash codes [5,6,13]. There is also a body of research on characterizing the dynamic

delamination and debonding of composites and adhesively-bonded structures [24-26]. As yet,

these two areas of investigation have not been successfully integrated into a useful tool for

modeling the crash behavior of composite structures. This research is directed toward meeting

this need by studying the feasibility of applying the results of dynamic fracture mechanics testing

to finite element crash modeling. The research was conducted at the NASA Langley Research

Center under the NASA/ASEE Summer Faculty Fellowship Program, under the supervision of

Dr. Karen E. Jackson.Previous efforts to model delamination using finite element crash codes have used

specialized or simplified failure criteria. Reference 5 describes a DYNA3D model of the crushing

of rectangular composite columns made by joining hat sections with either mechanical fasteners or

adhesive. The adhesive was modeled by massless springs connecting nodes on opposite sides of

the joint. Failure was predicted based on the forces developed in the beams. This modeling

approach is similar to that in Reference 13, described previously, which also used a force-based

criterion to predict delamination. Reedy and Mello [6] developed a delamination modeling

technique and applied it to the transient dynamic finite element code PRONTO3D. Their

implementation uses a specially-defined hex element that joins shell elements representing two

sublaminates. The delamination element penalizes relative displacement between the two joined

sublaminates, effectively acting as three-dimensional springs. Delamination is predicted based onaverage stresses in the delamination element and the relative displacements across the joint. The

stress-displacement response is assumed to take a triangular form, based on a cohesive failure

model. Two parameters are therefore required to describe failure. The first, the area under the

stress-displacement curve, is defined in terms of the critical strain energy release rate. The second

parameter may be either a critical force, or the length of the cohesive zone, properties which are

not conventionally reported in fracture testing.

The present research differs from these approaches in several ways. Delamination is

predicted based only on the well-known critical strain energy release rate, rather than a less

rigorous force-based failure criteria or one requiring unconventional property data. Further, the

approach does not require defining a new element type, and is therefore applicable without special

access to the program source code.


7/16

MODELING TECHNIQUES

The analytical procedures used here for modeling delamination are based on the

straightforward stacked sublaminate approach whereby a laminate is modeled as two or more

sublaminates held together with spring elements. The spring elements effectively model aninterlaminar region and failure of spring elements in the model represents crack growth. This

approach has been used successfully by numerous researchers for modeling delamination growth

in both static and specialized dynamic models, including References 6, 8 and 12. Failure models

based on fracture mechanics were used to produce models that accurately capture the dynamic

delamination response of composites. These procedures were implemented using

MSC/DYTRAN. The implementation was carried out using user-defined spring properties and as

such required no special access to the program source code. To evaluate the resulting modeling

technique, results are compared with fracture mechanics testing data available in the literature.

These data provide a means for validating the performance of the resulting procedures and failure

models.

The modeling approach requires prior identification of interply or bondline regions wheredelamination is expected to be critical to the response. In these regions, the structure is modeled

as sublaminates separated by the bond. The bondline itself is modeled by springs connecting nodes

on opposite sides of the bond. For simplicity of computation, it was assumed that nodes located

on opposite sides of the bond fall upon the same normal vector. No offset in the plane of the bond

is permitted between the endpoints of the springs. Three springs are co-located at each nodal

location on the bond surface, acting in mutually perpendicular directions corresponding to the

three fracture modes. MSC/DYTRAN accommodates user-defined inputs for certain element

properties, including those of 1-D springs. Prediction of fracture of the bond is controlled by a

user-defined subroutine, ELASEX, defining the behavior of the springs. The subroutine performs

the following steps for each spring:

1)Determine whether the given spring is located at a crack front in the structure. If not,no further action is taken

2)If the location is located at a crack front, the mesh direction of the advancing crack is

determined.

3)The strain energy release rate is computed based on simple nodal variables, as described

below.

4)When all strain energy release rate components at a given location are computed, a

mixed-mode fracture criterion is checked.

5)If debonding is predicted at that site, the stiffness of all springs at the site is reduced by

several orders of magnitude.

The strain energy release rate components are computed using the virtual crack closure

technique. For mode I, the strain energy release rate is computed as follows:

Ga

F u uI I +

1

2( ) ,

where FIis the force in the spring aligned with the mode I direction, and u+ and u- are the nodal

displacements in the mode I direction at the nodes immediately ahead of the crack front.


8/16

Displacements are computed relative to a rotating coordinate frame defined relative to the bond

surface.

This method for computing strain energy release rates imposes limitations on the model.

The accuracy of the strain energy release rate computation is dependent upon the size of the

elements, a , in the vicinity of the crack front. Therefore, the regions near where delamination or

debonding is expected require mesh refinement. This increases the number of elements required ina model. Further, in a code with explicit integration, the maximum time step is usually limited by

the minimum element dimension. Therefore, mesh refinement in a delamination-critical region may

reduce the maximum acceptable time step, thereby increasing the run time of the model. The

spring elements themselves may also impose limitations on the time step, due to their small size.

This problem may be addressed by substituting rigid elements for the springs used here.

In the following examples, crack growth is predicted by a linear fracture law:

G

G

G

G

G

G

I

I

II

II

III

IIIc c c

+ + = 1.

The procedures are written generally, however, so that alternate mixed-mode fracture criteria may

be easily substituted. Critical values for strain energy release rates are obtained from the literaturefor use in the following examples. The procedures as used in this study do not permit different

values of the critical strain energy release rates to be used for initiation and propagation, though in

principle such effects may be easily added.

All models used in the present study used solid elements. Although shell elements may

result in improved computational efficiency, the solid elements allow easier application of the

stacked sublaminate approach used in the present study. Using solid elements, nodal forces due to

the springs are applied directly to the interface and any number of delaminations through the

thickness may be easily accommodated. Models were generated and analyzed using

MSC/PATRAN for pre- and post- processing. Interfacial springs were added directly to the

PATRAN-generated DYTRAN input deck by a user-written FORTRAN program. Material

properties for the following examples were obtained from the literature corresponding to each testcase considered.

RESULTS

Because the present research was strictly numerical in nature, results of the approach were

compared with experimental results from the literature. Comparison with some fundamental

fracture tests are shown in this section.

Figures 1 and 2 show results from the present DYTRAN model for double cantilever

beam (DCB) specimens fabricated from graphite/epoxy laminates bonded with epoxy film

adhesive. Specimens are loaded dynamically under displacement-controlled conditions. Theseresults are compared with experimental results reported by Blackman et al [24]. No strong

loading rate dependence on the critical strain energy release rates was observed in the experiments

modeled, although the strain energy release rate upon crack arrest was somewhat different from

the initiation value. Constant values of the critical strain energy release rate, obtained from the

initiation values given in Reference 24, were used in the finite element model. The results in

Figures 1 and 2 correspond to Figures 15 (c) and (e) from Reference 24.


9/16

Figure 1 Calculated response of an adhesively bonded double cantilever beamspecimen loaded with an opening displacement rate of 2.1 m/s

For the opening displacement rate of 2.1 m/s, both the computation shown in Figure 1 and

the experimental results from Reference 24 show a decrease in average crack velocity near a time

of 5 ms and a crack length of 60 mm, though the delamination initiation is more abrupt in the

finite element model than in the experiment. Such changes in crack velocity are characterized in

Reference 24 as a stick-slip behavior resulting from alternate periods of crack growth and crack

arrest and occurs several times in the experiment at this opening rate. This behavior is also evident

in the finite element results shown in Figure 1. At higher loading rates, the prominence of this

stick-slip behavior diminished in the experimental behavior, resulting in a single plateau in the

crack length versus time curve, beginning at about 1.5 ms. A similar, though shorter, plateau

occurs in the finite element results shown in Figure 2. For each of these cases, the time to final

failure of the DCB specimens computed by the finite element model is within about 10% of the

experimentally measured values. These results demonstrate the ability of the current approach to

accurately capture significant aspects of dynamic fracture behavior.

20

40

60

80

100

120

0 5 10 15 20 25 30

DCB bonded with Epoxy film adhesiveOpening displacement rate 2.1 m/s

Crack

Length,

[mm]

time, [ms]


10/16


11/16

20

40

60

80

100

120

0 0.5 1 1.5 2 2.5

DCB bonded with Epoxy film adhesiveOpening displacement rate 23.0 m/s

Crack

Length,

[mm]

time, [ms]

Figure 2 Calculated response of an adhesively bonded double cantilever beamspecimen loaded with an opening displacement rate of 23 m/s

In addition to the DCB tests, Mode II end notched flexure (ENF) and a mixed-mode

fixed-ratio mixed-mode (FRMM) tests were modeled. Figure 3 shows a sequence of deformed

shapes representing a dynamically-loaded ENF test. The specimen is supported on the left-hand

side by frictionless, fixed supports simulating the roller supports commonly used in ENF tests.

The starting delamination is approximately one half of the length of the specimen. Progress of the

delamination is visible in the PATRAN output shown in Figure 3. Prior to delamination growth,

the interface appears as a light (yellow) color. Following delamination growth, in the final figure,

the region on the interface where delamination has spread appears as a dark (red) color.


12/16

Figure 3 Deformation sequence of a end-notched flexure specimen under dynamic

tip loading

For the FRMM model, an interesting result was observed. The ratio of Mode I to Mode II

behavior was significantly larger under dynamic loading than expected from static analysis. For

equal sublaminate thickness, static analysis predictsG

GI

II= 133. . The FEM computation showed

this ratio to be typically greater than 2. It is not clear whether this is a real effect or a modeling

artifact.

Another demonstration was made by creating a model of a through-the-width

delamination buckling problem using the procedures developed for this problem. Deformation

shapes for this problem are presented in Figure 4. Failed springs are visible as lines connecting thethin sublaminate to the rest of the laminate. No dynamically loaded data were available for

comparison, so a quantitative comparison is not possible, though the displacement shape seems

reasonable.


13/16

Figure 4 Deformation sequence for a plate with a through-the-width delaminationunder axial compressive loads

DISCUSSION

Results of this study demonstrate the potential for modeling delamination and debonding

of composites using a commercial finite element crash code. Further development is necessary,

however, to improve the procedures. There were instances in the experimental program described

in Reference 24 and 26 where the loading rate produced significant effects on critical fracture

parameters that were not included in this study. Furthermore, issues relating to the computational

efficiency of the procedures have not been fully addressed. For example, the models used in thepreliminary study employed solid elements. More efficient models may be obtained if shell

elements are used in place of the solid elements. Also, the procedures need to be demonstrated for

practical problems related to crash modeling. Models of the crushing of composite laminates

(which will be directly useful for laminate characterization studies) and models of the crash

performance of structural components are needed to verify the utility of the method.


14/16

SUMMARY

Delamination modeling was applied to a transient dynamic finite element crash code,

MSC/DYTRAN. The approach followed the methods of fracture mechanics, and used the virtual

crack closure technique to calculate strain energy release rates in the model and predictdelamination growth. Comparison with results from the literature for the dynamic fracture of

composites showed good correlation. However, significant issues relating to the implementation

and computational efficiency of the method must be resolved before the method may be applied to

the crash modeling of aircraft structures.

ACKNOWLEDGEMENTS

The research was conducted at the NASA Langley Research Center under the

NASA/ASEE Summer Faculty Fellowship Program, under the supervision of Dr. Karen E.

Jackson. Thanks to Professor J. G. Williams for permission to use data from Reference 24 in thispaper.

REFERENCES

1. J. D. Cronkhite and L. T. Mazza, Bell ACAP Full-Scale Aircraft Crash Test and KRASH

Correlation, Proceedings of the 44th American Helicopter Society Annual Forum, Washington,

DC, June 16-18, 1988, pp. 849-863.

2. G. L. Farley and R. M. Jones, Energy-Absorption Capability of Composite Tubes and

Beams, NASA TM 101634, 1989.

3. J. D. Cronkhite, Design of Helicopter Composite Structures for Crashworthiness, inComposites in Manufacturing Case Studies, A. B. Strong, ed., SME, 1991, pp. 79-92.

4. A. K. Noor and H. D. Carden, compilers, Computational Methods for Crashworthiness,

NASA CP 3223.

5. S. Kerth, A. Dehn, M. Ostgathe and M. Maier, Experimental Investigation and Numerical

Simulation of the Crush Behavior of Composite Structural Parts, Proceedings of the 1996 41st

International SAMPE Symposium and Exhibition, Vol. 2, pp. 1397-1408.

6. E. D. Reedy, F. J. Mello and T. R. Guess, Modeling the Initiation and Growth of

Delaminations in Composite Structures, Journal of Composite Materials, Vol. 31 (8), 1997, pp.

812-831.


15/16

7. A. G. Mamalis, D. E. Manolakos, G. A. Demosthenous, and M. B. Ioannidis, Analytical

Modelling of the Static and Dynamic Axial Collapse of Thin-Walled Fibreglass and Composite

Conical Shells, International Journal of Impact Engineering, Vol. 19 (5-6), pp. 477-492, 1997.

8. G. L. Farley, R. M. Jones, Prediction of the Energy-Absorption Capability of Composite

Tubes, Journal of Composite Materials, Vol. 26 (3), 1992, pp. 388-404.

9. I. Sigalas, M. Kumosa, and D. Hull, Trigger Mechanisms in Energy-Absorbing Glass

Cloth/Epoxy Tubes, Composites Science and Technology, Vol. 40, 1991, pp. 265-287.

10. H. Hamada and S. Ramakrishna, A FEM Method for Prediction of Energy Absorption

Capability of Crashworthy Polymer Composite Materials, Journal of Reinforced Plastics and

Composites, Vol. 16 (3), 1997, pp. 226-242.

11. C. M. Kindervater, Crashresistant Composite Helicopter Structural Concepts - Thermoset

and Thermoplastic Corrugated Web Designs, Proceedings of the National Technical Specialists

Meeting on Advanced Rotorcraft Structures, Williamsburg, VA, 1995.

12. D. C. Fleming, A. J. Vizzini, Off-Axis Energy Absorption Characteristics of Composites forCrashworthy Rotorcraft Design, Journal of the American Helicopter Society, Vol. 41, (3), 1996,pp. 239-246.

13. A. Kamoulakos and D. Kohlgrber, Validation of Numerical Simulation of CompositeHelicopter Sub-floor Structures Under Crash Loading, Proceedings of the 54th AHS AnnualForum, Washington, DC, May 20-22, 1998.

14. G. L. Farley and R. M. Jones, Crushing Characteristics of Continuous Fiber-Reinforced

Composite Tubes, Journal of Composite Materials, Vol. 26, (1), 1992, pp. 37-50.

15. D. Hull, A Unified Approach to Progressive Crushing of Fibre-Reinforced Composite

Tubes, Composites Science and Technology, Vol. 40, 1991, p. 377-421.

16. K. E. Jackson, An Assessment of the State-of-the Art in Crash Modeling and Simulation,

Vehicle Structures Directorate Internal Report, VSD NR 95-05, 1995.

17. R. Winter, A. B. Pifko and J. D. Cronkhite, Crash Simulation of Composite and Aluminum

Helicopter Fuselages Using a Finite Element Program, Journal of Aircraft, Vol. 17 (8), 1980,

pp. 591-597.

18. E. Haug, O. Fort, A. Trameon, M. Watanabe and I. Nakada, Numerical CrashworthinessSimulation of Automotive Structures and Components Made of Continuous Fiber ReinforcedComposite and Sandwich Assemblies, SAE Technical Paper Series 910152, 1991.


16/16

19. J. A. Nemes and G. Bodelle, Simulation of Vehicle Impact on Steel and Composite Highway

Guardrail Structures, Proceedings of the 1995 ASME International Mechanical Engineering

Congress and Exposition, ADM-Vol. 210/BED-Vol. 30, Nov. 12-17, 1995, pp. 179-190.

20. A. F. Johnson, C. M. Kindervater, D. Kohlgrber and M. Ltzenburger, Predictive

Methodologies for the Crashworthiness of Aircraft Structures, Proceedings of the 52nd

AmericanHelicopter Society Annual Forum, Washington, DC, June 4-6, 1996, pp. 1340-1352.

21. A. F. Johnson and D. Kohlgrber, Modelling the Crash Response of Composite Structures,

J. Phys IV France, Vol. 7, 1997, pp. C3-981-C3-986.

22. A. F. Johnson and D. Kohlgrber, Modelling the Crash Response of Composite Structures,Journal de Physique IV France, Vol. 7, Colloque C3, Supplment au Journal de Physique III, (inEnglish), August 1997, pp. C3-981-C3-986.

23. E. L. Fasanella, K. H. Lyle, and K. E. Jackson, Crash Simulation of an Unmodified Lear Fan

Fuselage Section Vertical Drop Test, Proceedings of the 54th

AHS Annual Forum, Washington,DC, May 20-22, 1998.

24. B. R. K. Blackman, J. P. Dear, A. J. Kinloch, H. Macgillivray, Y. Wang, J. G. Williams and P.

Yayla, The Failure of Fibre Composites and Adhesively Bonded Fibre Composites under High

Rates of Test, Part I Mode I Loading -Experimental Studies, Journal of Materials Science, Vol.

30, 1995, pp. 5885-5900.

25. B. R. K. Blackman, A. J. Kinloch, Y. Wang, and J. G. Williams, The Failure of Fibre

Composites and Adhesively Bonded Fibre Composites under High Rates of Test, Part II Mode I

Loading -dynamic effects, Journal of Materials Science, Vol. 31, 1996, pp. 4451-4466.

26. B. R. K. Blackman, J. P. Dear, A. J. Kinloch, H. Macgillivray, Y. Wang, J. G. Williams and P.

Yayla, The Failure of Fibre Composites and Adhesively Bonded Fibre Composites under High

Rates of Test, Part III Mixed-mode I/II and Mode III Loadings, Journal of Materials Science,

Vol. 31, 1996, pp. 4467-4477.

206_Composite_Delamination

Documents

Transcript of 206_Composite_Delamination