COMPUTATIONAL MICROMECHANICS OF WIND BLADE

MATERIALS RECENT ACTIVITIES AT THE MATERIALS

RESEARCH DIVISION RISOslash DTU

Leon Mishnaevsky Jr (1) Povl Broslashndsted (1) Hai Qing (1) Huaiwen

Wang (1 2) Rasmus C Oslashstergaard (3) and Bent F Soslashrensen (1)

(1) Materials Research Division Risoslash National Laboratory for

Sustainable Energy Technical University of Denmark Roskilde

Denmark (2) On-leave from Tianjin University of Commerce

China (3) LM Wind Power Blades Composite Mechanics

Roskilde Denmark

ABSTRACT

Recent research works in the area of 3D computational microstructural modelling virtual testing

and numerical optimization of wind blade materials carried out at the Materials Research

Division Risoslash DTU (Programme Composites and Materials Mechanics) are summarized The

works presented here have been carried out in the framework of several research projects EU

FP6 UpWind Danida project ldquoldquoDevelopment of wind energy technologies in Nepalrdquo and Sino-

Danish project ldquo3D Virtual Testing of composites for wind energy applicationsrdquo as well as the

Framework Program ldquoInterface design of composite materialsrdquo and recently established Danish

Centre for Composite Structures and Materials for Wind Turbines Different groups of

materials which are used or have a potential for use for the wind turbine blades are modelled

with the use of the methods of the computational micromechanics in particular (1) glass and

carbon fiber reinforced polymer composites used in the large wind turbine blades (2) different

sorts of timber used in small wind turbines (first of all in developing countries) and (3)

nanoparticle reinforced polymer matrix composites (which have a potential to be used as

components for future high strength wind blades) On the basis of the developed 3D

microstructural finite element models of these materials we analyzed the effect of their

microstructures on damage resistance strength and stiffness The methods of the 3D model

design and results of the simulations are discussed in this paper

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

1 WHY COMPUTATIONAL MICROMECHANICS

The efficiency and practical usability of wind energy technology depend on the reliability and

lifetime of wind turbines (Broslashndsted et al 2005) The repair and maintenance of wind turbines

are typically quite expensive and labor consuming However failure of wind turbine parts

notably wind blades does occur sometimes and it leads to huge expenses and has negative

effect on the public image of wind energy technology But how can one predict and improve the

lifetime of wind blades Wind blades are subject to complex multiaxial cyclic loading and the

failure processes are controlled by microscale degradation of the materials (Mishnaevsky Jr et

al 2010 Zhou et al 2010) Experimental testing of different materials under various service

conditions would require huge efforts and costs The solution for this problem is the application

of numerical experiments in which various materials which are used or have a potential to be

used for wind energy applications are tested in computational models The computational

models used should include both realistic microscale structures of the materials and the realistic

deformation and damage mechanisms The approach in which the mechanical behavior and

strength of a materials is studied as a function of its microstructures on the basis of numerical

models is realized in the framework of computational micro- and mesomechanics of materials

(Mishnaevsky Jr 2007 Schmauder and Mishnaevsky Jr 2008)

In this paper we present some computational micromechanical studies of the strength and

degradation of various wind blade materials carried out at the Materials Research Division

Programme Composites and Materials Mechanics Risoslash DTU during the last few years The

research studies were carried out in the framework of several research projects EU FP6

UpWind Danida project ldquoldquoDevelopment of wind energy technologies in Nepalrdquo and Sino-

Danish project ldquo3D Virtual Testing of composites for wind energy applicationsrdquo as well as

Framework Program ldquoInterface design of composite materialsrdquo (FTP) and recently established

Danish Centre for Composite Structures and Materials for Wind Turbines (DCCSM)

2 POLYMER COMPOSITE MATERIALS FOR LARGE WIND TURBINES

The most widely used group of materials for large and potentially extra large wind turbines are

polymer based composites usually with glass or (more seldom) carbon fiber reinforcement In

this section we consider the development of computational microstructure-based models for the

long fiber reinforced polymer matrix composites and the studies of the material degradation with

the use of the models

21 Glass fiber reinforced polymers Automatic generation of the 3D finite element models of

multifiber unit cells and 3D micromechanical finite elements analysis of microstructure-strength

relationships of the materials In order to study the effect of microscale parameters of wind

turbine blade composites on their strength a special software for the automatic generation of 3D

computational micromechanical models of the composites was developed and used in the

numerical experiments (Mishnaevsky Jr and Broslashndsted 2009a)

Figure 1 shows the micrograph of a fracture surface of a composite and the 3D finite element

model as well as the crack growth scheme Using the developed software we studied the effect

of variability of fiber strengths and viscoelasticity of matrix on the damage evolution and

competition of damage modes The effects of the statistical variability of fiber strengths

viscosity of the polymer matrix as well as the interaction between the damage processes in

matrix fibers and interface are investigated numerically by testing different multifiber unit cell

models of the composites (Mishnaevsky Jr and Broslashndsted 2009a Wang et al 2009)

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

It was demonstrated in the simulations that fibers with constant strengths ensure the higher

strength of a composite at the pre-critical load while the fibers with randomly distributed

strengths lead to the higher strength of the composite at post-critical loads In the case of

randomly distributed fiber strengths the damage growth in fibers seems to be almost

independent from the crack length in matrix while the influence of matrix cracks on the

beginning of fiber cracking is clearly seen for the case of the constant fiber strength

Competition between the matrix cracking and interface debonding was observed in the

simulations in the areas with intensive interface cracking both fiber fracture and the matrix

cracking are delayed Reversely in the area where a long matrix crack is formed the fiber

cracking does not lead to the interface damage

Another important effect of the composite microstructure on its destruction is the crack bridging

by fibers oriented parallel to the cracking plane (called fiber cross-over bridging see Soslashrensen et

al 2008 Oslashstergaard 2008) A micromechanical model of mixed mode fibre cross-over

bridging has been developed (see Figure 2) The model predicts coupled mixed mode bridging

laws (traction-separation relations) both normal and shear tractions depend on the normal and

tangential crack opening displacements It was observed in the simulations that the normal

traction decreases rapidly towards zero with increasing normal and tangential crack opening

displacements In contrast the shear traction increases with increasing normal and tangential

crack opening displacements approaching a constant value corresponding to the shear stress

under a pure Mode II crack opening displacement For a fixed number of bridging ligaments the

toughening due to the cross-over bridging mechanisms is predicted to be much higher under

Mode II and mixed mode than under pure Mode I

Fig 1 Micrograph of a fracture surface of a composite material 3D FE micromechanical

model crack growth between the fibers and fiber bridging over the matrix crack

(Mishnaevsky Jr and Broslashndsted 2009)

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

Fig 2 Micromechanical model Fig 3 Left Schema of statistical

of mixed mode cross-over fiber

bridging (Soslashrensen et al 2008)

models of fibers with randomly

distributed misalignments Right

Comparison of damage (density of

kinked fibers D) for random and

clustered fiber distributions (top view)

22 Carbon fiber reinforced polymers Kinking effect and compression strength A very

promising alternative to the glass fiber composites is the group of carbon fiber reinforced

composites which have much higher strength Glass fiber composites typically have

compressive strengths comparable to the tensile strength In contrast the compressive strength

of carbon composites is significantly lower than their tensile strength While the glass fibers fail

often by cracking both under tensile and compressive loading the carbon fibers demonstrate

one more damage mechanisms under compressive loading namely fiber kinking The carbon

fiber kinking is controlled by both local fiber misalignment and the matrix properties

In order to analyze the mechanisms of the fiber kinking and its dependence on the local

microstructure statistical computational model was developed on the basis of the Monte-Carlo

method and the Budiansky-Fleck fiber kinking condition (Mishnaevsky Jr and Broslashndsted

2009b) The schema of the multifiber unit cell with random misalignments is given in Figure 3

upper With this model the effects of fiber misalignment variability fiber clustering load

sharing rules on the compressive and fatigue strength of rotor blade materials are studied

numerically It is demonstrated that the clustering of fibers has a negative effect of the damage

resistance of a composite (Figure 3 lower)

Further the static compressive loading model is generalized for the case of cyclic compressive

loading with and without microdegradation of the matrix and with and without random

variations of loading It was observed that the random variations of loading shorten the lifetime

of the composite the larger the variability of applied load the shorter the lifetime The model

was further generalized to include the irregular fiber waviness and the interface defects

Considering the cases of small and large interface defects with different density we observed

that the small interface microcracks do not lead to the sufficient reduction of compressive

strength even at unrealistically high microcrack density In contrast large interface defects have

a strong effect on the compressive strength of the composite

D1=024

D2=037

D1=024

D2=043

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

2 TIMBER AS A MATERIAL FOR BLADES OF SMALL WIND

TURBINES FOR DEVELOPING COUNTRIES

In order to reduce the costs of the wind turbines and to make wind energy more attractive for

developing countries natural locally available materials notably wood can be used to produce

parts of the wind turbines instead of conventional composite materials (Mishnaevsky Jr et al

2009) Wood is a natural composite which has relatively light weight and excellent fatigue

properties is relatively cheap and easy to work (Mishnaevsky Jr and Qing 2008) Using of

timber wind blades would allow also to produce the turbine parts locally what would further

reduce the costs and strengthen local manufacturers in developing countries In order to develop

the methods of optimal choice of appropriate timber for low cost locally producible wind

turbines a Danish-Nepalese collaborative research project on ldquoDevelopment of wind energy

technologies in Nepal on the basis of natural materialsrdquo was initiated One of the important

aspects of this project has been the development of hierarchical computational models for 3D

microstructural analysis of wood strength and stiffness

The computational model which takes into account multilevel complex microstructure of wood

includes all the four levels of the heterogeneous microstructure of earlywood (annual rings as

multilayers honeycomb like cells multilayered cell walls unidirectional fibril reinforced

composite type microstructure of each layer) (Qing and Mishnaevsky Jr 2008 2009abc 2010)

o Macrolevel annual rings are modeled as multilayers using the improved 3D rule-of-mixture

(Qing and Mishnaevsky Jr 2010)

o Mesolevel the layered honeycomb like microstructure of cells was modelled as a 3D unit cell

with layered walls The finite element model was generated using the parametric modelling

technique The properties of the layers were taken from the microlevel model

o Submicro- and microlevel Each of the layers forming the cell walls was considered as an

unidirectional fibril reinforced composite Taking into account the experimentally

determined microfibril angles and content of cellulose hemicellulose and lignin in each

layer the elastic properties of the layers were determined with the use of Halpin-Tsai

equations

Figure 4 gives an example of the FE unit model of earlywood Using the developed model the

effects of microstructural parameters of wood on the deformation behaviour of wood were

studied In particular the influence of microfibril angle (MFA) and wood density on the

deformation behaviour was considered Figure 4 (right) shows the influence of microfibril

angles (MFA) in the sublayer S2 (Fig4 left) on the elastic properties while the MFAs in other

sublayers S1 and S3 are fixed on the levels 60o and 75

o respectively From the computation

studies it was concluded that the variation of microfibril angles represents a rather efficient

mechanism of the natural control of stiffness of the main shear load bearing layer of the cell

wall By increasing the MFAs the drastic increase of shear stiffness in 1-2 direction is achieved

without any sizable losses of the transverse Young modulus and shear modulus in the 23 plane

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

Fig 4 Left Computational (finite element) unit cell models of softwood (Qing and

Mishnaevsky Jr 2009a) Right Effect of microfibril angles in the sublayer S2

on the elastic properties

3 HIERARCHICAL COMPOSITES WITH NANOPARTICLE

REINFORCED MATRIX MATERIALS FOR FUTURE WIND BLADES

It is known that adding small amount of nanoparticles reinforcement can lead to the drastic

qualitative improvement of the strength and stiffness of polymers While the nanoparticle

reinforced materials have been rather expensive a few years ago now their prices tend to reduce

and their broad use can be expected in near future So the question arises can the composites

with nanoparticle reinforced components become the future wind energy materials In order to

explore the effect of the nanoreinforcement on the mechanical properties and strength of

polymer matrix a series of computational models of nanocomposites has been developed Using

the effective interface model (Odegard et al 2005) we developed the method of automatic

generation of multiparticle unit cells with spherical plate-like and cylindrical particles

surrounded by the effective interface layers The model can include up to hundreds of particles

and the effective interface layers can overlap Figure 5 (left) shows the multiparticle unit cell of

nanoparticle reinforced composite with effective interface model and the Young modulus of the

composite plotted versus the volume fraction at different interface properties In the simulations

the strong influence of the effective interface properties on the mechanical behavior of

composites was observed Further the effect of the nanoparticle clustering on the mechanical

properties of the nanoparticle reinforced composites has been studied

Fig 5 Multiparticle unit cell of nanoparticle reinforced composite with effective

interface model (Wang et al 2010)

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

The further steps include the modeling of damage behavior and load redistribution in

hierarchicalhybrid composites with nanoparticle reinforced polymer matrix

4 CONCLUSIONS

In this paper the methods of 2D and 3D computational microstructure-based modeling of

different groups of materials for wind turbine blades are presented Using the variety of the

modeling methods presented here one can predict the strength stiffness and lifetime of the

materials optimize their microstructures with view on the better usability for wind turbines or

compare the applicability of different groups of the materials to the use in wind turbines

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support of the European Community via

ldquoUpWindrdquo project the project ldquo3D Virtual Testing of composites for wind energy applicationsrdquo

supported by the Sino-Danish Committee of Scientific and Technological Collaboration and the

Danida Project ldquoDevelopment of wind energy technologies in Nepal on the basis of natural

materialsrdquo (Danida Ref No 104 DAN8-913) Furthermore the authors are grateful to the

Danish Council for Strategic Research for its support via the Danish Centre for Composite

Structures and Materials for Wind Turbines (DCCSM) (contract number 09-067212)

REFERENCES

P Broslashndsted H Lilholt Aa Lystrup (2005) Composite materials for wind power turbine blades Ann

Rev Mater Res 35 505-538

H Qing and L Mishnaevsky Jr (2009a) 3D hierarchical computational model of wood as a cellular

material with fibril reinforced heterogeneous multiple layers Mechanics of Materials Vol 41 9 pp

1034-1049

H Qing and L Mishnaevsky Jr (2009b) Unidirectional high fiber content composites Automatic 3D

FE model generation and damage simulation Computat Materials Science Vol 47 2 pp 548-555

H Qing and L Mishnaevsky Jr (2009c) Moisture-related mechanical properties of softwood 3D

micromechanical modeling Computat Materials Science Vol 46 No 2 pp310-320

H Qing and L Mishnaevsky Jr (2010) 3D multiscale micromechanical model of wood From annual

rings to microfibrils Int J Solids and Structures Vol 47 Issue 9 2010 Pages 1253-1267

L Mishnaevsky Jr (2007) Computational Mesomechanics of Composites John Wiley 280 pp

L Mishnaevsky Jr and P Broslashndsted (2009a) Micromechanical modeling of damage and fracture of

unidirectional fiber reinforced composites A review Comput Materials Science Vol 44 No 4 pp

1351-1359

L Mishnaevsky Jr and P Broslashndsted (2009b) Micromechanisms of damage in unidirectional fiber

reinforced composites 3D computational analysis Composites Sci amp Technol Vol 69 No7-8 pp

1036-1044

L Mishnaevsky Jr and P Broslashndsted (2009c) Statistical modelling of compression and fatigue damage of

unidirectional fiber reinforced composites Composites Sci amp Technol Vol 69 3-4 pp 477-484

L Mishnaevsky Jr P Broslashndsted RNijssen D J Lekou and T P Philippidis (2010) Materials of

Large Wind Turbine Blades Recent Results in Testing and Modeling Wind Energy (submitted)

L Mishnaevsky Jr PFreere R Sharma PBroslashndsted H Qing J I Bech R Sinha P Acharya R

Evans (2009) Strength and Reliability of Wood for the Components of Low-Cost Wind Turbines

Computational and Experimental Analysis and Applications J Wind Engineering Vol 33 No 2 pp

183ndash196

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

1 WHY COMPUTATIONAL MICROMECHANICS

The efficiency and practical usability of wind energy technology depend on the reliability and

lifetime of wind turbines (Broslashndsted et al 2005) The repair and maintenance of wind turbines

are typically quite expensive and labor consuming However failure of wind turbine parts

notably wind blades does occur sometimes and it leads to huge expenses and has negative

effect on the public image of wind energy technology But how can one predict and improve the

lifetime of wind blades Wind blades are subject to complex multiaxial cyclic loading and the

failure processes are controlled by microscale degradation of the materials (Mishnaevsky Jr et

al 2010 Zhou et al 2010) Experimental testing of different materials under various service

conditions would require huge efforts and costs The solution for this problem is the application

of numerical experiments in which various materials which are used or have a potential to be

used for wind energy applications are tested in computational models The computational

models used should include both realistic microscale structures of the materials and the realistic

deformation and damage mechanisms The approach in which the mechanical behavior and

strength of a materials is studied as a function of its microstructures on the basis of numerical

models is realized in the framework of computational micro- and mesomechanics of materials

(Mishnaevsky Jr 2007 Schmauder and Mishnaevsky Jr 2008)

In this paper we present some computational micromechanical studies of the strength and

degradation of various wind blade materials carried out at the Materials Research Division

Programme Composites and Materials Mechanics Risoslash DTU during the last few years The

research studies were carried out in the framework of several research projects EU FP6

UpWind Danida project ldquoldquoDevelopment of wind energy technologies in Nepalrdquo and Sino-

Danish project ldquo3D Virtual Testing of composites for wind energy applicationsrdquo as well as

Framework Program ldquoInterface design of composite materialsrdquo (FTP) and recently established

Danish Centre for Composite Structures and Materials for Wind Turbines (DCCSM)

2 POLYMER COMPOSITE MATERIALS FOR LARGE WIND TURBINES

The most widely used group of materials for large and potentially extra large wind turbines are

polymer based composites usually with glass or (more seldom) carbon fiber reinforcement In

this section we consider the development of computational microstructure-based models for the

long fiber reinforced polymer matrix composites and the studies of the material degradation with

the use of the models

21 Glass fiber reinforced polymers Automatic generation of the 3D finite element models of

multifiber unit cells and 3D micromechanical finite elements analysis of microstructure-strength

relationships of the materials In order to study the effect of microscale parameters of wind

turbine blade composites on their strength a special software for the automatic generation of 3D

computational micromechanical models of the composites was developed and used in the

numerical experiments (Mishnaevsky Jr and Broslashndsted 2009a)

Figure 1 shows the micrograph of a fracture surface of a composite and the 3D finite element

model as well as the crack growth scheme Using the developed software we studied the effect

of variability of fiber strengths and viscoelasticity of matrix on the damage evolution and

competition of damage modes The effects of the statistical variability of fiber strengths

viscosity of the polymer matrix as well as the interaction between the damage processes in

matrix fibers and interface are investigated numerically by testing different multifiber unit cell

models of the composites (Mishnaevsky Jr and Broslashndsted 2009a Wang et al 2009)

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

It was demonstrated in the simulations that fibers with constant strengths ensure the higher

strength of a composite at the pre-critical load while the fibers with randomly distributed

strengths lead to the higher strength of the composite at post-critical loads In the case of

randomly distributed fiber strengths the damage growth in fibers seems to be almost

independent from the crack length in matrix while the influence of matrix cracks on the

beginning of fiber cracking is clearly seen for the case of the constant fiber strength

Competition between the matrix cracking and interface debonding was observed in the

simulations in the areas with intensive interface cracking both fiber fracture and the matrix

cracking are delayed Reversely in the area where a long matrix crack is formed the fiber

cracking does not lead to the interface damage

Another important effect of the composite microstructure on its destruction is the crack bridging

by fibers oriented parallel to the cracking plane (called fiber cross-over bridging see Soslashrensen et

al 2008 Oslashstergaard 2008) A micromechanical model of mixed mode fibre cross-over

bridging has been developed (see Figure 2) The model predicts coupled mixed mode bridging

laws (traction-separation relations) both normal and shear tractions depend on the normal and

tangential crack opening displacements It was observed in the simulations that the normal

traction decreases rapidly towards zero with increasing normal and tangential crack opening

displacements In contrast the shear traction increases with increasing normal and tangential

crack opening displacements approaching a constant value corresponding to the shear stress

under a pure Mode II crack opening displacement For a fixed number of bridging ligaments the

toughening due to the cross-over bridging mechanisms is predicted to be much higher under

Mode II and mixed mode than under pure Mode I

Fig 1 Micrograph of a fracture surface of a composite material 3D FE micromechanical

model crack growth between the fibers and fiber bridging over the matrix crack

(Mishnaevsky Jr and Broslashndsted 2009)

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

Fig 2 Micromechanical model Fig 3 Left Schema of statistical

of mixed mode cross-over fiber

bridging (Soslashrensen et al 2008)

models of fibers with randomly

distributed misalignments Right

Comparison of damage (density of

kinked fibers D) for random and

clustered fiber distributions (top view)

22 Carbon fiber reinforced polymers Kinking effect and compression strength A very

promising alternative to the glass fiber composites is the group of carbon fiber reinforced

composites which have much higher strength Glass fiber composites typically have

compressive strengths comparable to the tensile strength In contrast the compressive strength

of carbon composites is significantly lower than their tensile strength While the glass fibers fail

often by cracking both under tensile and compressive loading the carbon fibers demonstrate

one more damage mechanisms under compressive loading namely fiber kinking The carbon

fiber kinking is controlled by both local fiber misalignment and the matrix properties

In order to analyze the mechanisms of the fiber kinking and its dependence on the local

microstructure statistical computational model was developed on the basis of the Monte-Carlo

method and the Budiansky-Fleck fiber kinking condition (Mishnaevsky Jr and Broslashndsted

2009b) The schema of the multifiber unit cell with random misalignments is given in Figure 3

upper With this model the effects of fiber misalignment variability fiber clustering load

sharing rules on the compressive and fatigue strength of rotor blade materials are studied

numerically It is demonstrated that the clustering of fibers has a negative effect of the damage

resistance of a composite (Figure 3 lower)

Further the static compressive loading model is generalized for the case of cyclic compressive

loading with and without microdegradation of the matrix and with and without random

variations of loading It was observed that the random variations of loading shorten the lifetime

of the composite the larger the variability of applied load the shorter the lifetime The model

was further generalized to include the irregular fiber waviness and the interface defects

Considering the cases of small and large interface defects with different density we observed

that the small interface microcracks do not lead to the sufficient reduction of compressive

strength even at unrealistically high microcrack density In contrast large interface defects have

a strong effect on the compressive strength of the composite

D1=024

D2=037

D1=024

D2=043

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

2 TIMBER AS A MATERIAL FOR BLADES OF SMALL WIND

TURBINES FOR DEVELOPING COUNTRIES

In order to reduce the costs of the wind turbines and to make wind energy more attractive for

developing countries natural locally available materials notably wood can be used to produce

parts of the wind turbines instead of conventional composite materials (Mishnaevsky Jr et al

2009) Wood is a natural composite which has relatively light weight and excellent fatigue

properties is relatively cheap and easy to work (Mishnaevsky Jr and Qing 2008) Using of

timber wind blades would allow also to produce the turbine parts locally what would further

reduce the costs and strengthen local manufacturers in developing countries In order to develop

the methods of optimal choice of appropriate timber for low cost locally producible wind

turbines a Danish-Nepalese collaborative research project on ldquoDevelopment of wind energy

technologies in Nepal on the basis of natural materialsrdquo was initiated One of the important

aspects of this project has been the development of hierarchical computational models for 3D

microstructural analysis of wood strength and stiffness

The computational model which takes into account multilevel complex microstructure of wood

includes all the four levels of the heterogeneous microstructure of earlywood (annual rings as

multilayers honeycomb like cells multilayered cell walls unidirectional fibril reinforced

composite type microstructure of each layer) (Qing and Mishnaevsky Jr 2008 2009abc 2010)

o Macrolevel annual rings are modeled as multilayers using the improved 3D rule-of-mixture

(Qing and Mishnaevsky Jr 2010)

o Mesolevel the layered honeycomb like microstructure of cells was modelled as a 3D unit cell

with layered walls The finite element model was generated using the parametric modelling

technique The properties of the layers were taken from the microlevel model

o Submicro- and microlevel Each of the layers forming the cell walls was considered as an

unidirectional fibril reinforced composite Taking into account the experimentally

determined microfibril angles and content of cellulose hemicellulose and lignin in each

layer the elastic properties of the layers were determined with the use of Halpin-Tsai

equations

Figure 4 gives an example of the FE unit model of earlywood Using the developed model the

effects of microstructural parameters of wood on the deformation behaviour of wood were

studied In particular the influence of microfibril angle (MFA) and wood density on the

deformation behaviour was considered Figure 4 (right) shows the influence of microfibril

angles (MFA) in the sublayer S2 (Fig4 left) on the elastic properties while the MFAs in other

sublayers S1 and S3 are fixed on the levels 60o and 75

o respectively From the computation

studies it was concluded that the variation of microfibril angles represents a rather efficient

mechanism of the natural control of stiffness of the main shear load bearing layer of the cell

wall By increasing the MFAs the drastic increase of shear stiffness in 1-2 direction is achieved

without any sizable losses of the transverse Young modulus and shear modulus in the 23 plane

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

Fig 4 Left Computational (finite element) unit cell models of softwood (Qing and

Mishnaevsky Jr 2009a) Right Effect of microfibril angles in the sublayer S2

on the elastic properties

3 HIERARCHICAL COMPOSITES WITH NANOPARTICLE

REINFORCED MATRIX MATERIALS FOR FUTURE WIND BLADES

It is known that adding small amount of nanoparticles reinforcement can lead to the drastic

qualitative improvement of the strength and stiffness of polymers While the nanoparticle

reinforced materials have been rather expensive a few years ago now their prices tend to reduce

and their broad use can be expected in near future So the question arises can the composites

with nanoparticle reinforced components become the future wind energy materials In order to

explore the effect of the nanoreinforcement on the mechanical properties and strength of

polymer matrix a series of computational models of nanocomposites has been developed Using

the effective interface model (Odegard et al 2005) we developed the method of automatic

generation of multiparticle unit cells with spherical plate-like and cylindrical particles

surrounded by the effective interface layers The model can include up to hundreds of particles

and the effective interface layers can overlap Figure 5 (left) shows the multiparticle unit cell of

nanoparticle reinforced composite with effective interface model and the Young modulus of the

composite plotted versus the volume fraction at different interface properties In the simulations

the strong influence of the effective interface properties on the mechanical behavior of

composites was observed Further the effect of the nanoparticle clustering on the mechanical

properties of the nanoparticle reinforced composites has been studied

Fig 5 Multiparticle unit cell of nanoparticle reinforced composite with effective

interface model (Wang et al 2010)

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

The further steps include the modeling of damage behavior and load redistribution in

hierarchicalhybrid composites with nanoparticle reinforced polymer matrix

4 CONCLUSIONS

In this paper the methods of 2D and 3D computational microstructure-based modeling of

different groups of materials for wind turbine blades are presented Using the variety of the

modeling methods presented here one can predict the strength stiffness and lifetime of the

materials optimize their microstructures with view on the better usability for wind turbines or

compare the applicability of different groups of the materials to the use in wind turbines

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support of the European Community via

ldquoUpWindrdquo project the project ldquo3D Virtual Testing of composites for wind energy applicationsrdquo

supported by the Sino-Danish Committee of Scientific and Technological Collaboration and the

Danida Project ldquoDevelopment of wind energy technologies in Nepal on the basis of natural

materialsrdquo (Danida Ref No 104 DAN8-913) Furthermore the authors are grateful to the

Danish Council for Strategic Research for its support via the Danish Centre for Composite

Structures and Materials for Wind Turbines (DCCSM) (contract number 09-067212)

REFERENCES

P Broslashndsted H Lilholt Aa Lystrup (2005) Composite materials for wind power turbine blades Ann

Rev Mater Res 35 505-538

H Qing and L Mishnaevsky Jr (2009a) 3D hierarchical computational model of wood as a cellular

material with fibril reinforced heterogeneous multiple layers Mechanics of Materials Vol 41 9 pp

1034-1049

H Qing and L Mishnaevsky Jr (2009b) Unidirectional high fiber content composites Automatic 3D

FE model generation and damage simulation Computat Materials Science Vol 47 2 pp 548-555

H Qing and L Mishnaevsky Jr (2009c) Moisture-related mechanical properties of softwood 3D

micromechanical modeling Computat Materials Science Vol 46 No 2 pp310-320

H Qing and L Mishnaevsky Jr (2010) 3D multiscale micromechanical model of wood From annual

rings to microfibrils Int J Solids and Structures Vol 47 Issue 9 2010 Pages 1253-1267

L Mishnaevsky Jr (2007) Computational Mesomechanics of Composites John Wiley 280 pp

L Mishnaevsky Jr and P Broslashndsted (2009a) Micromechanical modeling of damage and fracture of

unidirectional fiber reinforced composites A review Comput Materials Science Vol 44 No 4 pp

1351-1359

L Mishnaevsky Jr and P Broslashndsted (2009b) Micromechanisms of damage in unidirectional fiber

reinforced composites 3D computational analysis Composites Sci amp Technol Vol 69 No7-8 pp

1036-1044

L Mishnaevsky Jr and P Broslashndsted (2009c) Statistical modelling of compression and fatigue damage of

unidirectional fiber reinforced composites Composites Sci amp Technol Vol 69 3-4 pp 477-484

L Mishnaevsky Jr P Broslashndsted RNijssen D J Lekou and T P Philippidis (2010) Materials of

Large Wind Turbine Blades Recent Results in Testing and Modeling Wind Energy (submitted)

L Mishnaevsky Jr PFreere R Sharma PBroslashndsted H Qing J I Bech R Sinha P Acharya R

Evans (2009) Strength and Reliability of Wood for the Components of Low-Cost Wind Turbines

Computational and Experimental Analysis and Applications J Wind Engineering Vol 33 No 2 pp

183ndash196

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

It was demonstrated in the simulations that fibers with constant strengths ensure the higher

strength of a composite at the pre-critical load while the fibers with randomly distributed

strengths lead to the higher strength of the composite at post-critical loads In the case of

randomly distributed fiber strengths the damage growth in fibers seems to be almost

independent from the crack length in matrix while the influence of matrix cracks on the

beginning of fiber cracking is clearly seen for the case of the constant fiber strength

Competition between the matrix cracking and interface debonding was observed in the

simulations in the areas with intensive interface cracking both fiber fracture and the matrix

cracking are delayed Reversely in the area where a long matrix crack is formed the fiber

cracking does not lead to the interface damage

Another important effect of the composite microstructure on its destruction is the crack bridging

by fibers oriented parallel to the cracking plane (called fiber cross-over bridging see Soslashrensen et

al 2008 Oslashstergaard 2008) A micromechanical model of mixed mode fibre cross-over

bridging has been developed (see Figure 2) The model predicts coupled mixed mode bridging

laws (traction-separation relations) both normal and shear tractions depend on the normal and

tangential crack opening displacements It was observed in the simulations that the normal

traction decreases rapidly towards zero with increasing normal and tangential crack opening

displacements In contrast the shear traction increases with increasing normal and tangential

crack opening displacements approaching a constant value corresponding to the shear stress

under a pure Mode II crack opening displacement For a fixed number of bridging ligaments the

toughening due to the cross-over bridging mechanisms is predicted to be much higher under

Mode II and mixed mode than under pure Mode I

Fig 1 Micrograph of a fracture surface of a composite material 3D FE micromechanical

model crack growth between the fibers and fiber bridging over the matrix crack

(Mishnaevsky Jr and Broslashndsted 2009)

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

Fig 2 Micromechanical model Fig 3 Left Schema of statistical

of mixed mode cross-over fiber

bridging (Soslashrensen et al 2008)

models of fibers with randomly

distributed misalignments Right

Comparison of damage (density of

kinked fibers D) for random and

clustered fiber distributions (top view)

22 Carbon fiber reinforced polymers Kinking effect and compression strength A very

promising alternative to the glass fiber composites is the group of carbon fiber reinforced

composites which have much higher strength Glass fiber composites typically have

compressive strengths comparable to the tensile strength In contrast the compressive strength

of carbon composites is significantly lower than their tensile strength While the glass fibers fail

often by cracking both under tensile and compressive loading the carbon fibers demonstrate

one more damage mechanisms under compressive loading namely fiber kinking The carbon

fiber kinking is controlled by both local fiber misalignment and the matrix properties

In order to analyze the mechanisms of the fiber kinking and its dependence on the local

microstructure statistical computational model was developed on the basis of the Monte-Carlo

method and the Budiansky-Fleck fiber kinking condition (Mishnaevsky Jr and Broslashndsted

2009b) The schema of the multifiber unit cell with random misalignments is given in Figure 3

upper With this model the effects of fiber misalignment variability fiber clustering load

sharing rules on the compressive and fatigue strength of rotor blade materials are studied

numerically It is demonstrated that the clustering of fibers has a negative effect of the damage

resistance of a composite (Figure 3 lower)

Further the static compressive loading model is generalized for the case of cyclic compressive

loading with and without microdegradation of the matrix and with and without random

variations of loading It was observed that the random variations of loading shorten the lifetime

of the composite the larger the variability of applied load the shorter the lifetime The model

was further generalized to include the irregular fiber waviness and the interface defects

Considering the cases of small and large interface defects with different density we observed

that the small interface microcracks do not lead to the sufficient reduction of compressive

strength even at unrealistically high microcrack density In contrast large interface defects have

a strong effect on the compressive strength of the composite

D1=024

D2=037

D1=024

D2=043

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

2 TIMBER AS A MATERIAL FOR BLADES OF SMALL WIND

TURBINES FOR DEVELOPING COUNTRIES

In order to reduce the costs of the wind turbines and to make wind energy more attractive for

developing countries natural locally available materials notably wood can be used to produce

parts of the wind turbines instead of conventional composite materials (Mishnaevsky Jr et al

2009) Wood is a natural composite which has relatively light weight and excellent fatigue

properties is relatively cheap and easy to work (Mishnaevsky Jr and Qing 2008) Using of

timber wind blades would allow also to produce the turbine parts locally what would further

reduce the costs and strengthen local manufacturers in developing countries In order to develop

the methods of optimal choice of appropriate timber for low cost locally producible wind

turbines a Danish-Nepalese collaborative research project on ldquoDevelopment of wind energy

technologies in Nepal on the basis of natural materialsrdquo was initiated One of the important

aspects of this project has been the development of hierarchical computational models for 3D

microstructural analysis of wood strength and stiffness

The computational model which takes into account multilevel complex microstructure of wood

includes all the four levels of the heterogeneous microstructure of earlywood (annual rings as

multilayers honeycomb like cells multilayered cell walls unidirectional fibril reinforced

composite type microstructure of each layer) (Qing and Mishnaevsky Jr 2008 2009abc 2010)

o Macrolevel annual rings are modeled as multilayers using the improved 3D rule-of-mixture

(Qing and Mishnaevsky Jr 2010)

o Mesolevel the layered honeycomb like microstructure of cells was modelled as a 3D unit cell

with layered walls The finite element model was generated using the parametric modelling

technique The properties of the layers were taken from the microlevel model

o Submicro- and microlevel Each of the layers forming the cell walls was considered as an

unidirectional fibril reinforced composite Taking into account the experimentally

determined microfibril angles and content of cellulose hemicellulose and lignin in each

layer the elastic properties of the layers were determined with the use of Halpin-Tsai

equations

Figure 4 gives an example of the FE unit model of earlywood Using the developed model the

effects of microstructural parameters of wood on the deformation behaviour of wood were

studied In particular the influence of microfibril angle (MFA) and wood density on the

deformation behaviour was considered Figure 4 (right) shows the influence of microfibril

angles (MFA) in the sublayer S2 (Fig4 left) on the elastic properties while the MFAs in other

sublayers S1 and S3 are fixed on the levels 60o and 75

o respectively From the computation

studies it was concluded that the variation of microfibril angles represents a rather efficient

mechanism of the natural control of stiffness of the main shear load bearing layer of the cell

wall By increasing the MFAs the drastic increase of shear stiffness in 1-2 direction is achieved

without any sizable losses of the transverse Young modulus and shear modulus in the 23 plane

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

Fig 4 Left Computational (finite element) unit cell models of softwood (Qing and

Mishnaevsky Jr 2009a) Right Effect of microfibril angles in the sublayer S2

on the elastic properties

3 HIERARCHICAL COMPOSITES WITH NANOPARTICLE

REINFORCED MATRIX MATERIALS FOR FUTURE WIND BLADES

It is known that adding small amount of nanoparticles reinforcement can lead to the drastic

qualitative improvement of the strength and stiffness of polymers While the nanoparticle

reinforced materials have been rather expensive a few years ago now their prices tend to reduce

and their broad use can be expected in near future So the question arises can the composites

with nanoparticle reinforced components become the future wind energy materials In order to

explore the effect of the nanoreinforcement on the mechanical properties and strength of

polymer matrix a series of computational models of nanocomposites has been developed Using

the effective interface model (Odegard et al 2005) we developed the method of automatic

generation of multiparticle unit cells with spherical plate-like and cylindrical particles

surrounded by the effective interface layers The model can include up to hundreds of particles

and the effective interface layers can overlap Figure 5 (left) shows the multiparticle unit cell of

nanoparticle reinforced composite with effective interface model and the Young modulus of the

composite plotted versus the volume fraction at different interface properties In the simulations

the strong influence of the effective interface properties on the mechanical behavior of

composites was observed Further the effect of the nanoparticle clustering on the mechanical

properties of the nanoparticle reinforced composites has been studied

Fig 5 Multiparticle unit cell of nanoparticle reinforced composite with effective

interface model (Wang et al 2010)

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

The further steps include the modeling of damage behavior and load redistribution in

hierarchicalhybrid composites with nanoparticle reinforced polymer matrix

4 CONCLUSIONS

In this paper the methods of 2D and 3D computational microstructure-based modeling of

different groups of materials for wind turbine blades are presented Using the variety of the

modeling methods presented here one can predict the strength stiffness and lifetime of the

materials optimize their microstructures with view on the better usability for wind turbines or

compare the applicability of different groups of the materials to the use in wind turbines

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support of the European Community via

ldquoUpWindrdquo project the project ldquo3D Virtual Testing of composites for wind energy applicationsrdquo

supported by the Sino-Danish Committee of Scientific and Technological Collaboration and the

Danida Project ldquoDevelopment of wind energy technologies in Nepal on the basis of natural

materialsrdquo (Danida Ref No 104 DAN8-913) Furthermore the authors are grateful to the

Danish Council for Strategic Research for its support via the Danish Centre for Composite

Structures and Materials for Wind Turbines (DCCSM) (contract number 09-067212)

REFERENCES

P Broslashndsted H Lilholt Aa Lystrup (2005) Composite materials for wind power turbine blades Ann

Rev Mater Res 35 505-538

H Qing and L Mishnaevsky Jr (2009a) 3D hierarchical computational model of wood as a cellular

material with fibril reinforced heterogeneous multiple layers Mechanics of Materials Vol 41 9 pp

1034-1049

H Qing and L Mishnaevsky Jr (2009b) Unidirectional high fiber content composites Automatic 3D

FE model generation and damage simulation Computat Materials Science Vol 47 2 pp 548-555

H Qing and L Mishnaevsky Jr (2009c) Moisture-related mechanical properties of softwood 3D

micromechanical modeling Computat Materials Science Vol 46 No 2 pp310-320

H Qing and L Mishnaevsky Jr (2010) 3D multiscale micromechanical model of wood From annual

rings to microfibrils Int J Solids and Structures Vol 47 Issue 9 2010 Pages 1253-1267

L Mishnaevsky Jr (2007) Computational Mesomechanics of Composites John Wiley 280 pp

L Mishnaevsky Jr and P Broslashndsted (2009a) Micromechanical modeling of damage and fracture of

unidirectional fiber reinforced composites A review Comput Materials Science Vol 44 No 4 pp

1351-1359

L Mishnaevsky Jr and P Broslashndsted (2009b) Micromechanisms of damage in unidirectional fiber

reinforced composites 3D computational analysis Composites Sci amp Technol Vol 69 No7-8 pp

1036-1044

L Mishnaevsky Jr and P Broslashndsted (2009c) Statistical modelling of compression and fatigue damage of

unidirectional fiber reinforced composites Composites Sci amp Technol Vol 69 3-4 pp 477-484

L Mishnaevsky Jr P Broslashndsted RNijssen D J Lekou and T P Philippidis (2010) Materials of

Large Wind Turbine Blades Recent Results in Testing and Modeling Wind Energy (submitted)

L Mishnaevsky Jr PFreere R Sharma PBroslashndsted H Qing J I Bech R Sinha P Acharya R

Evans (2009) Strength and Reliability of Wood for the Components of Low-Cost Wind Turbines

Computational and Experimental Analysis and Applications J Wind Engineering Vol 33 No 2 pp

183ndash196

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

Fig 2 Micromechanical model Fig 3 Left Schema of statistical

of mixed mode cross-over fiber

bridging (Soslashrensen et al 2008)

models of fibers with randomly

distributed misalignments Right

Comparison of damage (density of

kinked fibers D) for random and

clustered fiber distributions (top view)

22 Carbon fiber reinforced polymers Kinking effect and compression strength A very

promising alternative to the glass fiber composites is the group of carbon fiber reinforced

composites which have much higher strength Glass fiber composites typically have

compressive strengths comparable to the tensile strength In contrast the compressive strength

of carbon composites is significantly lower than their tensile strength While the glass fibers fail

often by cracking both under tensile and compressive loading the carbon fibers demonstrate

one more damage mechanisms under compressive loading namely fiber kinking The carbon

fiber kinking is controlled by both local fiber misalignment and the matrix properties

In order to analyze the mechanisms of the fiber kinking and its dependence on the local

microstructure statistical computational model was developed on the basis of the Monte-Carlo

method and the Budiansky-Fleck fiber kinking condition (Mishnaevsky Jr and Broslashndsted

2009b) The schema of the multifiber unit cell with random misalignments is given in Figure 3

upper With this model the effects of fiber misalignment variability fiber clustering load

sharing rules on the compressive and fatigue strength of rotor blade materials are studied

numerically It is demonstrated that the clustering of fibers has a negative effect of the damage

resistance of a composite (Figure 3 lower)

Further the static compressive loading model is generalized for the case of cyclic compressive

loading with and without microdegradation of the matrix and with and without random

variations of loading It was observed that the random variations of loading shorten the lifetime

of the composite the larger the variability of applied load the shorter the lifetime The model

was further generalized to include the irregular fiber waviness and the interface defects

Considering the cases of small and large interface defects with different density we observed

that the small interface microcracks do not lead to the sufficient reduction of compressive

strength even at unrealistically high microcrack density In contrast large interface defects have

a strong effect on the compressive strength of the composite

D1=024

D2=037

D1=024

D2=043

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

2 TIMBER AS A MATERIAL FOR BLADES OF SMALL WIND

TURBINES FOR DEVELOPING COUNTRIES

In order to reduce the costs of the wind turbines and to make wind energy more attractive for

developing countries natural locally available materials notably wood can be used to produce

parts of the wind turbines instead of conventional composite materials (Mishnaevsky Jr et al

2009) Wood is a natural composite which has relatively light weight and excellent fatigue

properties is relatively cheap and easy to work (Mishnaevsky Jr and Qing 2008) Using of

timber wind blades would allow also to produce the turbine parts locally what would further

reduce the costs and strengthen local manufacturers in developing countries In order to develop

the methods of optimal choice of appropriate timber for low cost locally producible wind

turbines a Danish-Nepalese collaborative research project on ldquoDevelopment of wind energy

technologies in Nepal on the basis of natural materialsrdquo was initiated One of the important

aspects of this project has been the development of hierarchical computational models for 3D

microstructural analysis of wood strength and stiffness

The computational model which takes into account multilevel complex microstructure of wood

includes all the four levels of the heterogeneous microstructure of earlywood (annual rings as

multilayers honeycomb like cells multilayered cell walls unidirectional fibril reinforced

composite type microstructure of each layer) (Qing and Mishnaevsky Jr 2008 2009abc 2010)

o Macrolevel annual rings are modeled as multilayers using the improved 3D rule-of-mixture

(Qing and Mishnaevsky Jr 2010)

o Mesolevel the layered honeycomb like microstructure of cells was modelled as a 3D unit cell

with layered walls The finite element model was generated using the parametric modelling

technique The properties of the layers were taken from the microlevel model

o Submicro- and microlevel Each of the layers forming the cell walls was considered as an

unidirectional fibril reinforced composite Taking into account the experimentally

determined microfibril angles and content of cellulose hemicellulose and lignin in each

layer the elastic properties of the layers were determined with the use of Halpin-Tsai

equations

Figure 4 gives an example of the FE unit model of earlywood Using the developed model the

effects of microstructural parameters of wood on the deformation behaviour of wood were

studied In particular the influence of microfibril angle (MFA) and wood density on the

deformation behaviour was considered Figure 4 (right) shows the influence of microfibril

angles (MFA) in the sublayer S2 (Fig4 left) on the elastic properties while the MFAs in other

sublayers S1 and S3 are fixed on the levels 60o and 75

o respectively From the computation

studies it was concluded that the variation of microfibril angles represents a rather efficient

mechanism of the natural control of stiffness of the main shear load bearing layer of the cell

wall By increasing the MFAs the drastic increase of shear stiffness in 1-2 direction is achieved

without any sizable losses of the transverse Young modulus and shear modulus in the 23 plane

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

Fig 4 Left Computational (finite element) unit cell models of softwood (Qing and

Mishnaevsky Jr 2009a) Right Effect of microfibril angles in the sublayer S2

on the elastic properties

3 HIERARCHICAL COMPOSITES WITH NANOPARTICLE

REINFORCED MATRIX MATERIALS FOR FUTURE WIND BLADES

It is known that adding small amount of nanoparticles reinforcement can lead to the drastic

qualitative improvement of the strength and stiffness of polymers While the nanoparticle

reinforced materials have been rather expensive a few years ago now their prices tend to reduce

and their broad use can be expected in near future So the question arises can the composites

with nanoparticle reinforced components become the future wind energy materials In order to

explore the effect of the nanoreinforcement on the mechanical properties and strength of

polymer matrix a series of computational models of nanocomposites has been developed Using

the effective interface model (Odegard et al 2005) we developed the method of automatic

generation of multiparticle unit cells with spherical plate-like and cylindrical particles

surrounded by the effective interface layers The model can include up to hundreds of particles

and the effective interface layers can overlap Figure 5 (left) shows the multiparticle unit cell of

nanoparticle reinforced composite with effective interface model and the Young modulus of the

composite plotted versus the volume fraction at different interface properties In the simulations

the strong influence of the effective interface properties on the mechanical behavior of

composites was observed Further the effect of the nanoparticle clustering on the mechanical

properties of the nanoparticle reinforced composites has been studied

Fig 5 Multiparticle unit cell of nanoparticle reinforced composite with effective

interface model (Wang et al 2010)

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

The further steps include the modeling of damage behavior and load redistribution in

hierarchicalhybrid composites with nanoparticle reinforced polymer matrix

4 CONCLUSIONS

In this paper the methods of 2D and 3D computational microstructure-based modeling of

different groups of materials for wind turbine blades are presented Using the variety of the

modeling methods presented here one can predict the strength stiffness and lifetime of the

materials optimize their microstructures with view on the better usability for wind turbines or

compare the applicability of different groups of the materials to the use in wind turbines

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support of the European Community via

ldquoUpWindrdquo project the project ldquo3D Virtual Testing of composites for wind energy applicationsrdquo

supported by the Sino-Danish Committee of Scientific and Technological Collaboration and the

Danida Project ldquoDevelopment of wind energy technologies in Nepal on the basis of natural

materialsrdquo (Danida Ref No 104 DAN8-913) Furthermore the authors are grateful to the

Danish Council for Strategic Research for its support via the Danish Centre for Composite

Structures and Materials for Wind Turbines (DCCSM) (contract number 09-067212)

REFERENCES

P Broslashndsted H Lilholt Aa Lystrup (2005) Composite materials for wind power turbine blades Ann

Rev Mater Res 35 505-538

H Qing and L Mishnaevsky Jr (2009a) 3D hierarchical computational model of wood as a cellular

material with fibril reinforced heterogeneous multiple layers Mechanics of Materials Vol 41 9 pp

1034-1049

H Qing and L Mishnaevsky Jr (2009b) Unidirectional high fiber content composites Automatic 3D

FE model generation and damage simulation Computat Materials Science Vol 47 2 pp 548-555

H Qing and L Mishnaevsky Jr (2009c) Moisture-related mechanical properties of softwood 3D

micromechanical modeling Computat Materials Science Vol 46 No 2 pp310-320

H Qing and L Mishnaevsky Jr (2010) 3D multiscale micromechanical model of wood From annual

rings to microfibrils Int J Solids and Structures Vol 47 Issue 9 2010 Pages 1253-1267

L Mishnaevsky Jr (2007) Computational Mesomechanics of Composites John Wiley 280 pp

L Mishnaevsky Jr and P Broslashndsted (2009a) Micromechanical modeling of damage and fracture of

unidirectional fiber reinforced composites A review Comput Materials Science Vol 44 No 4 pp

1351-1359

L Mishnaevsky Jr and P Broslashndsted (2009b) Micromechanisms of damage in unidirectional fiber

reinforced composites 3D computational analysis Composites Sci amp Technol Vol 69 No7-8 pp

1036-1044

L Mishnaevsky Jr and P Broslashndsted (2009c) Statistical modelling of compression and fatigue damage of

unidirectional fiber reinforced composites Composites Sci amp Technol Vol 69 3-4 pp 477-484

L Mishnaevsky Jr P Broslashndsted RNijssen D J Lekou and T P Philippidis (2010) Materials of

Large Wind Turbine Blades Recent Results in Testing and Modeling Wind Energy (submitted)

L Mishnaevsky Jr PFreere R Sharma PBroslashndsted H Qing J I Bech R Sinha P Acharya R

Evans (2009) Strength and Reliability of Wood for the Components of Low-Cost Wind Turbines

Computational and Experimental Analysis and Applications J Wind Engineering Vol 33 No 2 pp

183ndash196

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

2 TIMBER AS A MATERIAL FOR BLADES OF SMALL WIND

TURBINES FOR DEVELOPING COUNTRIES

In order to reduce the costs of the wind turbines and to make wind energy more attractive for

developing countries natural locally available materials notably wood can be used to produce

parts of the wind turbines instead of conventional composite materials (Mishnaevsky Jr et al

2009) Wood is a natural composite which has relatively light weight and excellent fatigue

properties is relatively cheap and easy to work (Mishnaevsky Jr and Qing 2008) Using of

timber wind blades would allow also to produce the turbine parts locally what would further

reduce the costs and strengthen local manufacturers in developing countries In order to develop

the methods of optimal choice of appropriate timber for low cost locally producible wind

turbines a Danish-Nepalese collaborative research project on ldquoDevelopment of wind energy

technologies in Nepal on the basis of natural materialsrdquo was initiated One of the important

aspects of this project has been the development of hierarchical computational models for 3D

microstructural analysis of wood strength and stiffness

The computational model which takes into account multilevel complex microstructure of wood

includes all the four levels of the heterogeneous microstructure of earlywood (annual rings as

multilayers honeycomb like cells multilayered cell walls unidirectional fibril reinforced

composite type microstructure of each layer) (Qing and Mishnaevsky Jr 2008 2009abc 2010)

o Macrolevel annual rings are modeled as multilayers using the improved 3D rule-of-mixture

(Qing and Mishnaevsky Jr 2010)

o Mesolevel the layered honeycomb like microstructure of cells was modelled as a 3D unit cell

with layered walls The finite element model was generated using the parametric modelling

technique The properties of the layers were taken from the microlevel model

o Submicro- and microlevel Each of the layers forming the cell walls was considered as an

unidirectional fibril reinforced composite Taking into account the experimentally

determined microfibril angles and content of cellulose hemicellulose and lignin in each

layer the elastic properties of the layers were determined with the use of Halpin-Tsai

equations

Figure 4 gives an example of the FE unit model of earlywood Using the developed model the

effects of microstructural parameters of wood on the deformation behaviour of wood were

studied In particular the influence of microfibril angle (MFA) and wood density on the

deformation behaviour was considered Figure 4 (right) shows the influence of microfibril

angles (MFA) in the sublayer S2 (Fig4 left) on the elastic properties while the MFAs in other

sublayers S1 and S3 are fixed on the levels 60o and 75

o respectively From the computation

studies it was concluded that the variation of microfibril angles represents a rather efficient

mechanism of the natural control of stiffness of the main shear load bearing layer of the cell

wall By increasing the MFAs the drastic increase of shear stiffness in 1-2 direction is achieved

without any sizable losses of the transverse Young modulus and shear modulus in the 23 plane

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

Fig 4 Left Computational (finite element) unit cell models of softwood (Qing and

Mishnaevsky Jr 2009a) Right Effect of microfibril angles in the sublayer S2

on the elastic properties

3 HIERARCHICAL COMPOSITES WITH NANOPARTICLE

REINFORCED MATRIX MATERIALS FOR FUTURE WIND BLADES

It is known that adding small amount of nanoparticles reinforcement can lead to the drastic

qualitative improvement of the strength and stiffness of polymers While the nanoparticle

reinforced materials have been rather expensive a few years ago now their prices tend to reduce

and their broad use can be expected in near future So the question arises can the composites

with nanoparticle reinforced components become the future wind energy materials In order to

explore the effect of the nanoreinforcement on the mechanical properties and strength of

polymer matrix a series of computational models of nanocomposites has been developed Using

the effective interface model (Odegard et al 2005) we developed the method of automatic

generation of multiparticle unit cells with spherical plate-like and cylindrical particles

surrounded by the effective interface layers The model can include up to hundreds of particles

and the effective interface layers can overlap Figure 5 (left) shows the multiparticle unit cell of

nanoparticle reinforced composite with effective interface model and the Young modulus of the

composite plotted versus the volume fraction at different interface properties In the simulations

the strong influence of the effective interface properties on the mechanical behavior of

composites was observed Further the effect of the nanoparticle clustering on the mechanical

properties of the nanoparticle reinforced composites has been studied

Fig 5 Multiparticle unit cell of nanoparticle reinforced composite with effective

interface model (Wang et al 2010)

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

The further steps include the modeling of damage behavior and load redistribution in

hierarchicalhybrid composites with nanoparticle reinforced polymer matrix

4 CONCLUSIONS

In this paper the methods of 2D and 3D computational microstructure-based modeling of

different groups of materials for wind turbine blades are presented Using the variety of the

modeling methods presented here one can predict the strength stiffness and lifetime of the

materials optimize their microstructures with view on the better usability for wind turbines or

compare the applicability of different groups of the materials to the use in wind turbines

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support of the European Community via

ldquoUpWindrdquo project the project ldquo3D Virtual Testing of composites for wind energy applicationsrdquo

supported by the Sino-Danish Committee of Scientific and Technological Collaboration and the

Danida Project ldquoDevelopment of wind energy technologies in Nepal on the basis of natural

materialsrdquo (Danida Ref No 104 DAN8-913) Furthermore the authors are grateful to the

Danish Council for Strategic Research for its support via the Danish Centre for Composite

Structures and Materials for Wind Turbines (DCCSM) (contract number 09-067212)

REFERENCES

P Broslashndsted H Lilholt Aa Lystrup (2005) Composite materials for wind power turbine blades Ann

Rev Mater Res 35 505-538

H Qing and L Mishnaevsky Jr (2009a) 3D hierarchical computational model of wood as a cellular

material with fibril reinforced heterogeneous multiple layers Mechanics of Materials Vol 41 9 pp

1034-1049

H Qing and L Mishnaevsky Jr (2009b) Unidirectional high fiber content composites Automatic 3D

FE model generation and damage simulation Computat Materials Science Vol 47 2 pp 548-555

H Qing and L Mishnaevsky Jr (2009c) Moisture-related mechanical properties of softwood 3D

micromechanical modeling Computat Materials Science Vol 46 No 2 pp310-320

H Qing and L Mishnaevsky Jr (2010) 3D multiscale micromechanical model of wood From annual

rings to microfibrils Int J Solids and Structures Vol 47 Issue 9 2010 Pages 1253-1267

L Mishnaevsky Jr (2007) Computational Mesomechanics of Composites John Wiley 280 pp

L Mishnaevsky Jr and P Broslashndsted (2009a) Micromechanical modeling of damage and fracture of

unidirectional fiber reinforced composites A review Comput Materials Science Vol 44 No 4 pp

1351-1359

L Mishnaevsky Jr and P Broslashndsted (2009b) Micromechanisms of damage in unidirectional fiber

reinforced composites 3D computational analysis Composites Sci amp Technol Vol 69 No7-8 pp

1036-1044

L Mishnaevsky Jr and P Broslashndsted (2009c) Statistical modelling of compression and fatigue damage of

unidirectional fiber reinforced composites Composites Sci amp Technol Vol 69 3-4 pp 477-484

L Mishnaevsky Jr P Broslashndsted RNijssen D J Lekou and T P Philippidis (2010) Materials of

Large Wind Turbine Blades Recent Results in Testing and Modeling Wind Energy (submitted)

L Mishnaevsky Jr PFreere R Sharma PBroslashndsted H Qing J I Bech R Sinha P Acharya R

Evans (2009) Strength and Reliability of Wood for the Components of Low-Cost Wind Turbines

Computational and Experimental Analysis and Applications J Wind Engineering Vol 33 No 2 pp

183ndash196

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

Fig 4 Left Computational (finite element) unit cell models of softwood (Qing and

Mishnaevsky Jr 2009a) Right Effect of microfibril angles in the sublayer S2

on the elastic properties

3 HIERARCHICAL COMPOSITES WITH NANOPARTICLE

REINFORCED MATRIX MATERIALS FOR FUTURE WIND BLADES

It is known that adding small amount of nanoparticles reinforcement can lead to the drastic

qualitative improvement of the strength and stiffness of polymers While the nanoparticle

reinforced materials have been rather expensive a few years ago now their prices tend to reduce

and their broad use can be expected in near future So the question arises can the composites

with nanoparticle reinforced components become the future wind energy materials In order to

explore the effect of the nanoreinforcement on the mechanical properties and strength of

polymer matrix a series of computational models of nanocomposites has been developed Using

the effective interface model (Odegard et al 2005) we developed the method of automatic

generation of multiparticle unit cells with spherical plate-like and cylindrical particles

surrounded by the effective interface layers The model can include up to hundreds of particles

and the effective interface layers can overlap Figure 5 (left) shows the multiparticle unit cell of

nanoparticle reinforced composite with effective interface model and the Young modulus of the

composite plotted versus the volume fraction at different interface properties In the simulations

the strong influence of the effective interface properties on the mechanical behavior of

composites was observed Further the effect of the nanoparticle clustering on the mechanical

properties of the nanoparticle reinforced composites has been studied

Fig 5 Multiparticle unit cell of nanoparticle reinforced composite with effective

interface model (Wang et al 2010)

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

The further steps include the modeling of damage behavior and load redistribution in

hierarchicalhybrid composites with nanoparticle reinforced polymer matrix

4 CONCLUSIONS

In this paper the methods of 2D and 3D computational microstructure-based modeling of

different groups of materials for wind turbine blades are presented Using the variety of the

modeling methods presented here one can predict the strength stiffness and lifetime of the

materials optimize their microstructures with view on the better usability for wind turbines or

compare the applicability of different groups of the materials to the use in wind turbines

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support of the European Community via

ldquoUpWindrdquo project the project ldquo3D Virtual Testing of composites for wind energy applicationsrdquo

supported by the Sino-Danish Committee of Scientific and Technological Collaboration and the

Danida Project ldquoDevelopment of wind energy technologies in Nepal on the basis of natural

materialsrdquo (Danida Ref No 104 DAN8-913) Furthermore the authors are grateful to the

Danish Council for Strategic Research for its support via the Danish Centre for Composite

Structures and Materials for Wind Turbines (DCCSM) (contract number 09-067212)

REFERENCES

P Broslashndsted H Lilholt Aa Lystrup (2005) Composite materials for wind power turbine blades Ann

Rev Mater Res 35 505-538

H Qing and L Mishnaevsky Jr (2009a) 3D hierarchical computational model of wood as a cellular

material with fibril reinforced heterogeneous multiple layers Mechanics of Materials Vol 41 9 pp

1034-1049

H Qing and L Mishnaevsky Jr (2009b) Unidirectional high fiber content composites Automatic 3D

FE model generation and damage simulation Computat Materials Science Vol 47 2 pp 548-555

H Qing and L Mishnaevsky Jr (2009c) Moisture-related mechanical properties of softwood 3D

micromechanical modeling Computat Materials Science Vol 46 No 2 pp310-320

H Qing and L Mishnaevsky Jr (2010) 3D multiscale micromechanical model of wood From annual

rings to microfibrils Int J Solids and Structures Vol 47 Issue 9 2010 Pages 1253-1267

L Mishnaevsky Jr (2007) Computational Mesomechanics of Composites John Wiley 280 pp

L Mishnaevsky Jr and P Broslashndsted (2009a) Micromechanical modeling of damage and fracture of

unidirectional fiber reinforced composites A review Comput Materials Science Vol 44 No 4 pp

1351-1359

L Mishnaevsky Jr and P Broslashndsted (2009b) Micromechanisms of damage in unidirectional fiber

reinforced composites 3D computational analysis Composites Sci amp Technol Vol 69 No7-8 pp

1036-1044

L Mishnaevsky Jr and P Broslashndsted (2009c) Statistical modelling of compression and fatigue damage of

unidirectional fiber reinforced composites Composites Sci amp Technol Vol 69 3-4 pp 477-484

L Mishnaevsky Jr P Broslashndsted RNijssen D J Lekou and T P Philippidis (2010) Materials of

Large Wind Turbine Blades Recent Results in Testing and Modeling Wind Energy (submitted)

L Mishnaevsky Jr PFreere R Sharma PBroslashndsted H Qing J I Bech R Sinha P Acharya R

Evans (2009) Strength and Reliability of Wood for the Components of Low-Cost Wind Turbines

Computational and Experimental Analysis and Applications J Wind Engineering Vol 33 No 2 pp

183ndash196

Computational Micromechanics of Wind Blade Materials Recent activities at Risoslash DTU

The further steps include the modeling of damage behavior and load redistribution in

hierarchicalhybrid composites with nanoparticle reinforced polymer matrix

4 CONCLUSIONS

In this paper the methods of 2D and 3D computational microstructure-based modeling of

different groups of materials for wind turbine blades are presented Using the variety of the

modeling methods presented here one can predict the strength stiffness and lifetime of the

materials optimize their microstructures with view on the better usability for wind turbines or

compare the applicability of different groups of the materials to the use in wind turbines

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support of the European Community via

ldquoUpWindrdquo project the project ldquo3D Virtual Testing of composites for wind energy applicationsrdquo

supported by the Sino-Danish Committee of Scientific and Technological Collaboration and the

Danida Project ldquoDevelopment of wind energy technologies in Nepal on the basis of natural

materialsrdquo (Danida Ref No 104 DAN8-913) Furthermore the authors are grateful to the

Danish Council for Strategic Research for its support via the Danish Centre for Composite

Structures and Materials for Wind Turbines (DCCSM) (contract number 09-067212)

REFERENCES

P Broslashndsted H Lilholt Aa Lystrup (2005) Composite materials for wind power turbine blades Ann

Rev Mater Res 35 505-538

H Qing and L Mishnaevsky Jr (2009a) 3D hierarchical computational model of wood as a cellular

material with fibril reinforced heterogeneous multiple layers Mechanics of Materials Vol 41 9 pp

1034-1049

H Qing and L Mishnaevsky Jr (2009b) Unidirectional high fiber content composites Automatic 3D

FE model generation and damage simulation Computat Materials Science Vol 47 2 pp 548-555

H Qing and L Mishnaevsky Jr (2009c) Moisture-related mechanical properties of softwood 3D

micromechanical modeling Computat Materials Science Vol 46 No 2 pp310-320

H Qing and L Mishnaevsky Jr (2010) 3D multiscale micromechanical model of wood From annual

rings to microfibrils Int J Solids and Structures Vol 47 Issue 9 2010 Pages 1253-1267

L Mishnaevsky Jr (2007) Computational Mesomechanics of Composites John Wiley 280 pp

L Mishnaevsky Jr and P Broslashndsted (2009a) Micromechanical modeling of damage and fracture of

unidirectional fiber reinforced composites A review Comput Materials Science Vol 44 No 4 pp

1351-1359

L Mishnaevsky Jr and P Broslashndsted (2009b) Micromechanisms of damage in unidirectional fiber

reinforced composites 3D computational analysis Composites Sci amp Technol Vol 69 No7-8 pp

1036-1044

L Mishnaevsky Jr and P Broslashndsted (2009c) Statistical modelling of compression and fatigue damage of

unidirectional fiber reinforced composites Composites Sci amp Technol Vol 69 3-4 pp 477-484

L Mishnaevsky Jr P Broslashndsted RNijssen D J Lekou and T P Philippidis (2010) Materials of

Large Wind Turbine Blades Recent Results in Testing and Modeling Wind Energy (submitted)

L Mishnaevsky Jr PFreere R Sharma PBroslashndsted H Qing J I Bech R Sinha P Acharya R

Evans (2009) Strength and Reliability of Wood for the Components of Low-Cost Wind Turbines

Computational and Experimental Analysis and Applications J Wind Engineering Vol 33 No 2 pp

183ndash196

Mishnaevsky Jr Broslashndsted Qing Wang Oslashstergaard and Soslashrensen

L Mishnaevsky Jr H Qing (2008) Micromechanical modelling of mechanical behaviour and strength of

wood State-of-the-art review Computational Materials Science Vol 44 No 2 pp 363-370

G M Odegard TC Clancy TS Gates (2005) Modeling of the mechanical properties of

nanoparticlepolymer composites Polymer Vol 46 No 2 12 pp 553-562

S Schmauder L Mishnaevsky Jr (2008) Micromechanics and Nanosimulation of Metals and

Composites Springer 420 pp

B F Soslashrensen E K Gamstedt RC Oslashstergaard S Goutianos Micromechanical model of cross-over

fibre bridging ndash Prediction of mixed mode bridging laws Mechanics of Materials Vol 40 No 4-5

2008 pp 220-234

H W Wang HW Zhou L Mishnaevsky Jr P Broslashndsted LN Wang (2009) Single fibre and

multifibre unit cell analysis of strength and cracking of unidirectional composites Computational

Materials Science Vol 46 No 4 2009 Pages 810-820

HW Wang HWZhou PD Peng L Mishnaevsky Jr (in preparation) Nanoreinforced polymer

composites 3D micromechanical modelling with effective interface concept

HW Zhou L Mishnaevsky Jr P Broslashndsted J Tan L Gui (2010) SEM in situ laboratory

investigations on damage growth in GFRP composite under three-point bending tests Chinese

Science Bulletin Vol55 No12 1199minus1208

R C Oslashstergaard (2008) Buckling driven debonding in sandwich columns Int J Solids and Structures

Vol 45 No 5 pp 1264-1282