fracture mechanics techniques for the design of structural

Fracture Mechanics techniques for the design of structural components with adhesive joints for wind turbines.

Iñaki Nuin*, Carlos Amézqueta, Daniel Trias, Javier Estarriaga, Marcos del Río, Ana Belén Fariñas

National Renewable Energy Centre (CENER)

Wind Energy Department Ciudad de la Innovación

31621 Sarriguren, Navarra, Spain *e-mail: [email protected] Phone: +34 948 25 28 00

Abstract One of the issues to be solved when up scaling wind turbines is the design of improved structural components. This work is focused on those composite components which include adhesive joints carrying loads. Since traditional finite element computations are extremely element size dependent when working in local effects, fracture mechanic techniques appear as an initial solution to solve these problems. This work shows some of the efforts carried out at the Spanish National Centre for Renewable Energies (CENER) in order to improve the design of structural components with adhesive joints by means of Fracture Mechanics methods. Particularly, an in-house application code based on VCCT (virtual crack closure technique) has been developed. Also, a cohesive elements based approach included in a commercial finite element code has been studied. In this paper, two examples are described deeply; the first one, focused on the validation of the in-house code with a steel-composite subcomponent test and, the second one, focused on the comparison between Virtual Crack Closure Technique (VCCT) and cohesive elements approach considering a representative blade spar cap and web substructure joined together by adhesive bonding lines. Simulation results are compared with experimental data stemming from tests performed at CENER facilities in Sangüesa and also, within the FP6-Upwind project, where CENER is an active member. The results obtained with this work are very promising and show that fracture mechanics techniques constitute a valid approach for the design of components with adhesive joints from an industrial application point of view.

1 Introduction

Although both bonded components and composite materials can exhibit troubling fracture, this paper is solely focused on adhesive joints characterization with fracture mechanics approach. Fractures occur when the bonding of micro structural elements (basic particles) within a material is broken in some way. Once initiated, they can grow into voids, notches or cracks. They have the effect of producing extra boundaries to the body, which under load can cause severe stress concentrations, which could have a direct consequence on future operation. Some structures, designed under stress criterion (maximum predicted stress value lower than yield stress limit of the material) could fail if such a crack appears. Afterwards, the crack may grow either

very rapidly, slowly and in a controlled way, or it may even stabilize. The purpose of fracture mechanics is to analyse the stability of existing cracks. At a given load level, depending on the size of the plastic zone surrounding the crack tip and if plasticity effects can be neglected, its growing mechanism is governed by linear elastic fracture mechanics (LEFM). On the other hand, if the plastic zone is considerable, then elastic-plastic fracture mechanics (EPFM), sometimes known as post yield fracture mechanics (PYFM), is assumed [1]. Figure. 1-1 shows an example of LEFM and EPFM theories application depending on the plastic zone at the crack tip. Also, for EPFM, small scale yielding (SSY) and large scale yielding (LSY) approaches are identified. Guidelines for deciding which theory to apply are available when the load level and yield stress are known.

Figure. 1-1. Conditions around the crack tip.

2 Linear Elastic Fracture Mechanics (LEFM)

The foundations of Fracture Mechanics were introduced by Griffith and Irwin during the first quarter of the last century [2]. Their theories were developed and introduced in computational mechanics for the first time during the 1970s [3]. However, these methods were applied only in universities and research centres were mainly standard tests and simple joints were simulated. In the recent years the possibility of advanced pre and post processing tools has opened its application also to large structures and consequently to industry. Fracture Mechanics analyzes the propagation of cracks for a given stress measured far away from the crack tip. This makes the theory very interesting for cracked structures such as composite materials, adhesives and generally for brittle materials whose failure depends strongly on the size of the cracks. Fracture Mechanics allows the analysis of crack propagation in terms of the energy release rate (G), which is the energy absorbed by the structural component when making a new unit area of crack. Thus, based on Griffith criterion [1], the crack propagation will occur if the work done by the applied loads is greater than or equal to the change of elastic energy plus the energy absorbed at the crack tip;

atGUWC

el ∂+∂≥ ..δ (1)

With:

W∂ : Work done by the external loads when the defect grows a∂ el

U∂ : Change of the elastic energy

CG : Critical energy release rate

t : Thickness of the plate

In the other hand, if the external work is lower than this previous value, the crack will not propagate and remains stable. As shown in Figure. 2-1, a crack may propagate in three different modes: opening mode (called mode I), sliding mode (mode II) or tearing mode (mode III). The propagation conditions of any crack can always be decomposed as a combination of the three modes.

Figure. 2-1 Crack propagation modes, from left to right: mode I (opening), mode II (sliding), mode III (tearing).

Those propagation modes which are the combination of the three basic modes are called mixed modes. However, the interaction of modes is a complicated phenomenon. Consequently, superposition cannot be applied for the critical values of energy release rate. For this reason, some authors have proposed propagation criteria which account for the interaction and combination of modes. For instance, one of these criteria provides a weighting factor for each mode:

1<

+

+

ββα

IIIC

III

IIC

II

IC

I

G

G

G

G

G

G (2)

Where α, β and γ are to be fitted experimentally and are material properties. Other criteria do not take into account the interaction of the different propagation modes.

ICIGG < ;

IICIIGG < ;

IIICIIIGG < (3)

An interesting review of these criteria is presented at [4]. Generally for usual materials the following relation stands:

IIICIICICGGG << (4)

The development of standard tests to obtain these properties for inter-laminar cracks has been under discussion in the recent years [5, 6]. There exist several standards to measure GIC using the Double Cantilever Beam (DCB) set up (see ASTM [7], ISO [8], DIN [9] and JIS [10]). This last standard also defines how to measure GIIC with a Stabilized End Notched Flexure Test (ENF) specimen. The ASTM standard may appear soon, using an end-notched flexure test (ENF) [11] which is already used by DIN [12]. The measuring of GIIIC seems to be still far from standardization but a few approaches have already been proposed [13, 14]. For mixed mode I/II, the ASTM [15] standard seems to be the mainly adopted one. Focused only on LEFM, and considering the results of a finite element analysis, there are various methodologies in order to calculate the potential energy release rate of one defect to grow under a certain load level. The following list includes the most important theories, based on energy concepts, which have the advantage of remaining stable as the mesh size of the model is getting lower;

• Energy difference technique

• Virtual crack extension method

• J-Integral

• Crack closure / opening work

• Weight functions

• Cohesive elements

3 Virtual Crack Closure Technique

Virtual Crack Closure Technique is probably the computational tool derived from Fracture Mechanics which can be applied in a more straight-forward manner to the analysis of large structures.

3.1 Why dealing with VCCT

Let imagine, we have a single lap joint loaded in tension. If the problem is solved with Finite Element Analysis (FEA) techniques and post processed with stress criterion, the local stress values obtained at bonding line corners are singular. Also, as the mesh size decreases, local stress values increase with no convergence.

Figure. 3.1-1. Influence of mesh size on peeling local stress values.

If this effect is translated into a real engineering problem; e.g. a fifty meters long blade, the instability of the method does not allow to define bonded areas dimensions with enough confidence to achieve a reliable design. For these tasks, VCCT appears as a stable method. With this approach, as the mesh size decreases, the energy release rate value also decreases yielding a converged value.

Figure. 3.1-2. Influence of mesh size on GII values.

3.2 In-house developed code

The code developed at CENER is based on a VCCT approach [16]. Its architecture is explained in detail in [17], which was presented at the European Wind Energy Conference (EWEC) celebrated in 2006. The calculation procedure is sub-structured into three main steps;

• Step 1: Based on a FE model with rigid links at bonded areas and taking into account the adhesive elastic properties and thicknesses, a new FE model is automatically defined and analysed considering bonded lines stiffness.

• Step 2: Initial crack locations are identified based on local stresses criterion and bonding critical areas. Consequently, cracked FE model is defined and analysed automatically.

• Step 3: Potential elastic energy rate values are calculated for each mode (GI, GII, GIII) and compared with critical values. Different approaches are checked to define the possibility of the crack to start growing or to remain stable.

3.3 First application example

In this application, the ultimate static load for a metallic component which is bonded to a composite panel needs to be estimated. The load direction of the subcomponent is 45º referred to the composite panel plane.

Figure. 3.3-1. Subcomponent test set up.

First, the elastic properties of the materials are characterized. For steel, standard values are considered. Mechanical tests are performed at CENER facilities in order to define the elastic properties of the composite panel and the adhesive paste.

Young Modulus (MPa) 7972

Poisson 0.088

Young Modulus (MPa) 3.1

Poisson 0.45

Figure. 3.3-2. Elastic properties characterization for composite panel and adhesive.

Later on, critical energy release rate values for the interface between adherents and adhesive are characterized. Two different sets of specimens are manufactured to define this parameter. All the tests are performed under ASTMD3433 standard [18]. The following pictures and tables show the results obtained from these tests.

• Metal-adhesive DCB specimens.

Figure. 3.3-3. Metal-adhesive DCB coupons preparation. Mode I test.

Failure Type

Pmax (N)

Max. Extension

(mm)

Panel Modulus (MPa)

Coupon width (mm)

a (mm) Panel

Thickness (mm)

GIc (N/mm2)

Adhesive Thickness

(mm)

Coupon 1 Adhesive 5411.7 2.1 210000 25.3 30 15.2 0.726 1.0

Coupon 2 Adhesive 5131.1 2.4 210000 24.9 30.5 15.3 0.691 0.8

Coupon 3 Adhesive 4787.3 2.2 210000 25.2 30 15 0.590 1.0

Coupon 4 Adhesive 4940.4 2.4 210000 24.9 30 15.2 0.632 1.3

Coupon 5 Adhesive 5168.5 2.6 210000 24.9 31 15.3 0.715 0.9

Mean 5087.8 2.34 210000 25.0 30.3 15.2 0.671 1.0

St. Deviation 237.34 0.19 0.00 0.19 0.45 0.12 0.06 0.19

Table. 3.3-1. Numerical results obtained from tests.

• Composite-adhesive DCB specimens.

Figure. 3.3-4. Composite-adhesive DCB coupons preparation. Mode I test.

Failure Type

Pmax (N)

Max. Extension

(mm)

Panel Modulus (MPa)

Coupon width (mm)

a (mm) Panel

Thickness (mm)

GIc (N/mm2)

Adhesive Thickness

(mm)

Coupon 1 No valid - - 7972 25 25.6 8.00 - 2.5

Coupon 2 No valid - - 7972 25.2 32.5 7.80 - 2.6

Coupon 3 Interlaminar 276.9 5.2 7972 25.2 26.3 8.10 0.244 2.1


Coupon 5 Interlaminar 372 3.8 7972 24 25.8 8.30 0.436 1.8

Coupon 6 No valid - - 7972 25.43 24.82 8.68 - 1.4



Coupon 9 No valid - - 7972 25.18 25.97 8.36 - 1.8


Mean 388.1 3.89 7972 24.6 25.8 8.30 0.445 1.7

St. Deviation 17.30 0.15 0.00 0.60 0.96 0.25 0.01 0.89

Table. 3.3-2. Numerical results obtained from tests.

The values for GIC shown in previous tables are calculated according to ASTM3433 standard. The mathematical approach for this theory does not consider the stiffness of the glued film. This formulation is accurate enough for epoxy based adhesives with low thicknesses bonded lines. However, as this thickness gets higher and the elastic modulus gets weaker (polyurethane based adhesives) this effect can not be neglected and the ASTM3422 standard goes into non accurate results [19]. New GIC values have been calculated considering other analytical approaches [20, 21, 22] and the in-house VCCT developed method.

Steel - Adhesive DCB Coupons. GIc (N/mm)

ASTM D3433 0.671

Classical Beam Theory 0.619

Modified Classical Beam Theory 1.099

Orthotropic model 1.102

Adhesive model 7.606

Finite Crack extension method (FCEM) 1.555

Crack Closure Technique (CCT) 1.555

Virtual Crack Closure Technique (VCCT) 1.584

Figure. 3.3-5. Steel – Adhesive DCB coupons. GIC values for other analytical theories.

Composite - Adhesive DCP Coupons. GIc (N/mm)

ASTM D3433 0.445

Classical Beam Theory 0.430

Modified Classical Beam Theory 0.621

Orthotropic model 0.636

Adhesive model 1.645

Finite Crack extension method (FCEM) 0.401

Crack Closure Technique (CCT) 0.401

Virtual Crack Closure Technique (VCCT) 0.407

Figure. 3.3-6. Composite – Adhesive DCB coupons. GIC values for other analytical theories.

The following conclusions are observed from tests results;

• The weakest point of the bonded area is located at the interface between the composite panel and the adhesive. At this interface, GIC is 0.407N/mm (from VCCT approach), while the critical value at the interface between the steel and the adhesive paste is 3.9 times higher.

• Ultimate load values from DCB tests are quite spread, especially for the composite-steel coupons. This effect is directly a consequence of all the factors and uncertainties related with the manufacturing and bonding process, with dry zones, uncontrolled cure cycles, variable bonding line thicknesses, etc.

• Each analytical theory results in different GIC values, due to the use of different assumptions. The results obtained from FE models are comparable to each other, due to the fact that same mesh sizes, material properties, boundary conditions and analysis parameters are used.

• In order to predict an accurate ultimate load for the subcomponent test it is recommended to compare potential and critical energy release rate values based on the same analysis approach. In case of FE models, the element size must be of such size, that the values of G have converged.

Finally, a FE model is defined considering the geometry, boundary conditions and load direction for the real subcomponent test. Linear analyses are performed for different load levels, and the values of the potential energy release rate are post processed. Numerical results are compared against real values.

Figure. 3.3-7. Subcomponent FE model. Ultimate load; 9428N. These results are compared against tests values. The location of the initial debonding point obtained in the test matches exactly the one predicted by the model, but the maximum ultimate load is 11400N. However, discontinuities in the applied force appear at values between 8000N and 9000N which could be associated to small cracks propagation.

Figure. 3.3-8. Subcomponent test. Ultimate load; 11400N.

3.4 Second application example

This application exercise is focused on the comparison between VCCT and cohesive elements approach considering a representative blade spar cap and web substructure joined by adhesive bonding lines. A three point bending test is performed. The experimental results are compared with the numerical ones. The quality of this correlation is not demonstrated since GC values of the interface between the composites and the adhesive paste has not been characterized. The mechanical data of the materials are obtained by tests, performed within the FP6-Upwind project [23], where CENER is an active member. These data are attached below;

UNIDIRECTIONAL

Tension (MPa)

Compression (MPa)

E1 38100 38100

E2 11000 11000

E3 11000 11000

G12 3950 3950

G13 3950 3950

G23 2903 2903

υ12 0.26 0.26

υ13 0.26 0.26

υ23 0.89 0.89

BIDIRECTIONAL

Tension (MPa)

Compression (MPa)

E1 11620 11620

E2 11620 11620

E3 3170 11620

G12 1230 1230

G13 1796 1796

G23 1796 1796

υ12 0.29 0.29

υ13 0.29 0.29

υ23 0.29 0.29

ADHESIVE

E (MPa) 4200

Poisson 0.45

Ultimate Stress (MPa) 15.00

Reduction Factor 1.20

GIc (N/mm) 0.475

GIIc (N/mm) 1.975

Thickness (mm) 1.2

Cohesive law

Vm (mm) 0.0768

Vc (mm) 0.0036

Shear Normal Coefficients

Cohesive Energy (Nm) 4.16

Max Stress Factor 1

Figure. 3.4-1. Mechanical properties of the materials used in I-Beam test.

The layup of the I-Beam consists of four unidirectional glass fiber plies located at upper and lower flanges, and four biaxial glass fiber plies located at C-webs. These laminates are infused separately with epoxy resin and glued together with the adhesive paste (Epikote - Resin MGS BPR 135 G3) Considering the geometry of the I-Beam, the material data shown in Figure. 3.4-1, and the boundary conditions and loads of the bending test, two different models have been defined with different analysis assumptions.

• Linear model: Solved with MSC.NASTRAN. VCCT technique is applied via in-house code. Small displacements and linear behaviour assumptions are considered.

• Non linear model: Solved with MSC.MARC. Cohesive elements based on bilinear theory [24] are implemented. Large displacements and material linear behaviour assumptions are considered.

The stiffness of these two models fits exactly with the test results corresponding to the initial part of the curve. From the fracture mechanics point of view, the initial critical debonding point identified by both VCCT and Cohesive Elements approach is exactly the same, but no comparison can be performed against test results because buckling effects appeared prior to adhesive failure. Cohesive model predicts that this initial failure is not catastrophic and that the structure can take higher loads.

Figure. 3.4-2. Initial critical point debonding, from left to right: Linear model, 48.1KN; Non linear model, 40.6KN

4 Conclusions and future work

Considering all the technical aspects described before and taking into account the correlation accuracy between numerical analysis and experimental results, following ideas are remarked:

• Fracture mechanic approach seems to be a reliable method when designing bonded components.

• VCCT describes the possibility of one crack to grow, nothing about how it grows.

• Nevertheless, due to uncontrolled factors (adhesive layer thicknesses, inside voids, dry areas, adhesive cure cycle, etc) reasonable security factors should be considered in the design process.

For future work, it is planned to develop the mathematical basics of the in-house code in order to consider non linear and coupled behaviour of the springs located at the bonded areas of the component. Also, a detailed validation plan will be performed considering polyurethane and epoxy adhesives for mode I, mode II and mixed mode coupons. Finally, some representative wind subcomponents will be tested to validate the potential of the code.

5 References

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fracture mechanics techniques for the design of structural

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