LDA’s Applicability for Predicting Fatigue Crack Growth in FML’s under VA Loading S.U. Khan∗ , R.C. Alderliesten† , R. Benedictus‡ Structures and Materials Laboratory, Faculty of Aerospace Engineering, Delft University of Technology, P.O. Box 5058, 2600 GB Delft, The Netherlands.

This paper presents the experimental and analytical research on the applicability of Linear Damage Accumulation Rule for fatigue crack growth in Fibre reinforced Metal Laminates under variable amplitude loading. A recently developed constant amplitude analytical prediction model has been extended to predict fatigue crack growth under variable amplitude loading using a linear damage accumulation rule. The modified model has been compared with crack growth tests on Fibre reinforced Metal Laminates centre-cracked tension specimen. In the end it is discussed to what extent or under what conditions the linear damage accumulation predictions are sufficiently accurate for Fibre reinforced Metal Laminates structures.

I.

Introduction

I

n reality, the mechanical and structural components are often loaded under variable amplitude (VA) loading. The majority of structural failures happen due to the mechanical fatigue. For fatigue crack growth predictions under VA loading a number of prediction models have been developed.1 These models range from simple models like linear damage accumulation (LDA) to the more complex yield zone, crack closure and strip yield models. This variety of prediction models is the result of the required prediction accuracy and integration of physical phenomena like plastic zone and crack closure2 in the formulation of the models. It has been observed that the fatigue crack growth predictions of LDA rule are not accurate in metallic structures.3 Fibre reinforced Metal Laminates (FML) being a hybrid material of metal and composite, have both metallic as well as composite properties.4 It is assumed that linear damage accumulation predictions for VA loading are more accurate than in metals due to the existence of fibre bridging restraining crack opening similar to crack closure. ∗

PhD Student, Faculty of Aerospace Engineering, [email protected] Astt. Professor, Faculty of Aerospace Engineering, [email protected] ‡ Professor, Faculty of Aerospace Engineering, [email protected]

†

1 of 5 American Institute of Aeronautics and Astronautics

II.

Linear Damage Accumulation

The linear damage accumulation model is based on a cycle-by-cycle analysis independent of previous load history. It is an integration of calculated crack growth increments ∆ai using crack growth laws 5 ,after every load cycle to obtain a prediction for the full load spectrum. As a result, it is the simplest model to predict the crack growth rate under VA loading. The advantage of LDA rule is computational efficieny. In general, this rule can be presented mathematically as: a = a0 +

n X

f (∆K, r, ..) = a0 +

i=1

III.

N X

∆ai

(1)

i=1

Fibre Reinforced Metal Laminates

After ARALL,6 GLARE (GLAss-REinforced) is the second member of the FML material family. Like its predecessor, Glare also has very favourable fatigue crack growth properties. FML’s are built up of alternating metal- and fiber layers as shown in figure 1. For standard GLARE, aluminium (alloy) 2024-T3 sheets and S2-glass fibres are bonded together with FM94 epoxy adhesive to form a laminate. This stack is cured in an autoclave at 120 ◦ C and 6 bar for 1 21 hour. The fibre orientation is defined with respect to the rolling direction of the aluminium layers and each orientation represents a prepreg layer of 0.133mm thickness. Detailed description of Glare grades are shown in table 1.

Glare

Sub

Glare 1

Glare 2A

Prepreg OriMetal Sheet entation in Thickeach fiber ness[mm] layer 0.3-0.4 0/0 0.2-0.4 0/0

Glare 2B Glare 4A

0.2-0.5 0.2-0.5 0.2-0.5

90/90 0/90 0/90/90

Glare 4B Glare 6A

0.2-0.5 0.2-0.5 0.2-0.5

90/0/90 0/90/90/0 +45/-45

Glare 6B

0.2-0.5

-45/+45

Glare 2 Glare 3 Glare 4 Glare 5 Glare 6 Figure 1. GLARE

Table 1. Standard Glare grades

Since 1980, the FML concept has been investigated, developed and tested especially at Delft University of Technology. This development was speeded up in 1996 after the decision of Airbus to apply GLARE on Airbus A380.7 In April 2005 this newly-build aircraft with GLARE on major structural fuselage parts, performed its first maiden flight.

2 of 5 American Institute of Aeronautics and Astronautics

IV.

Selective Variable Amplitude

A selective variable amplitude load spectrum (figure 28 ) is defined as a constant amplitude spectrum with few load variations like single overload/underlod, multiple overload/underload and their combinations. These selective load variations are the building blocks of the (aircraft) service spectrum. The selective variable amplitude spectrum has been utilized to get the basic understanding of crack growth behaviour of FMLs’ under aircraft spectra.

V.

(a)

(b)

(g)

(f)

(j)

k(i)

(e)

(d)

(c)

(h)

k(ii)

(i)

k(iii)

Figure 2. (a)single OL;(b)block of OL;(c)period blocks of OL;(d) single UL; (e)block of UL;(f ) period blocks of UL;(g) single OL-UL;(h)single UL-OL;(i)periodic OL-UL blocks;(j)periodic ULOL blocks; and (k)two-level block loading.k(i)HILO;k(ii)LO-HI; and k(iii)both maximum and minimum load.

Research Approach

A model has been developed using the LDA rule (equation (1)), in order to investigate the prediction accuracy of LDA rules for FML under VA loading. The CA model of Alderliesten9 has been used as the basis for development of this VA prediction model using LDA rule for FMLs’. The flow diagram of the LDA prediction model is shown in figure 3(a). Matlab is used for the programming and simulation tasks. In order to make the code functional for all sort of variable spectra, an input file system is programmed. The model is validated with fatigue crack growth experiments on Glare 3-4/3-0.3 with cross-ply fibre orientation. Load variations were applied on a CA baseline spectrum with a maximum stress Smax of 120 MPa and a stress ratio R of 0.1. The single overload spectrum has an overload Sol of 175 MPa at 100 kcycles. The multiple overload spectrum has three overloads i.e. Sol1 = 175M P a, Sol2 = 158M P a and Sol3 = 139M P a at 100, 160 and 220 kcycles respectively. Block loading spectra are constituted of two stress levels Smax1 = 100M P a, Smax2 = 140M P a and vice-versa with 0.1 stress ratio. Apart from these selective VA loading spectra, representative complex flight spectra are also used for the model validation. The fatigue crack growth tests have been performed on centre-cracked tension (CCT) specimens, illustrated in figure 3(b). The starter notches are made by drilling a hole of 3 mm diameter with two saw cuts, directing perpendicular to the loading direction. The total length of the starter notch (2a0 )is approximately 5 mm.

VI.

Simulation Example

One of the simulations performed using block load spectrum LO-HI sequence (LO: Smin = 10M P a, Smax = 100M P a; HI: Smin = 14M P a, Smax = 140M P a) is shown in figure 4. In this figure, plots are shown comparing the test results with LDA predictions. From the plot, it is clear that the predictions are close to the test results. However, it has been observed that the predictions made from LDA depend on the nature of spectrum.

3 of 5 American Institute of Aeronautics and Astronautics

Ø 10

3

580 370 5

210 25 All dimensions in mm

25 25 25 25

70

(a) Flow diagram for the crack growth prediction model

70

(b) Centred-cracked Specimen geometry

Figure 3. Research Approach

Crack Length -a Vs. Number of Cycles - N

Crack Growth Rate - da/dN Vs. Crack Length -a 0.001

25

Experimental Measurements

Experimental Measurements

Transition of Smax

Transition of Smax

LDA Predicition

Crack Growth Rate - da/dN [mm/cycle]

LDA Predicitions

Crack Length - a [mm]

20

15

10

0.0001

5

0 0

50

100

150

200

250

300

0.00001 3

5

Number of Cycles - N [cycle]

7

9

11

13

15

17

Crack Length - a [mm]

(a) Crack length vs. number of cycles

(b) Crack growth rate vs. crack length

Figure 4. Comparison of test results with linear damage accumulation rule prediction for block loading (LO-HI).

4 of 5 American Institute of Aeronautics and Astronautics

19

VII.

Expected Results and Conclusions

A new model capable of predicting the crack growth of FMLs’ under VA loading has been introduced. Supporting experiments have been performed and the results of the experiments are used to compare with the prediction model. It has been shown that the model sufficiently resembles the experimental trends of the crack growth. The conditions under which the principal assumption of the model, linear damage accumulation is valid are discussed. For example, the errors in the LDA predictions will be small if the difference between the load peaks and the remaining load sequence is less or if the retardation and acceleration effects are compensated within the sequence. But, in case of a large difference between the peaks and the baseline level loading the predictions can be seriously in error, with very conservative or very unconservative results being possible.

References 1

Khan, S., Alderliesten, R., Schijve, J., and Benedictus, R., “On the fatigue crack growth prediction under variable amplitude loading,” Computational and experimental analysis of damaged materials, edited by P. D. Pavlou, Research Signpost, 1st ed., 2007, To be published. 2 Elber, W., “The Significance of Fatigue Crack Closure,” Tech. rep., ASTM STP 486, 1971. 3 Sander, M. and Richard, H., “Fatigue crack growth under variable amplitude loading Part II: Analytical and numerical investigations,” Fatigue & Fracture of Engineering Materials & Structures, Vol. 29, 2006, pp. 303–319. 4 Vlot, A. and Gunnink, J., Fibre Metal Laminates-An introduction, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001. 5 Wanhill, R. and Schijve, J., “Current status of flight simulation fatigue crack growth concepts,” Fatigue crack growth under variable amplitude loading, edited by J. Petit, D. Davidson, S. Suresh, and R. Rabbe, Elsevier applied science,England, 1988, pp. 326–339. 6 Marissen, R., “Fatigue crack growth in ARALL - A hybrid aluminium-aramid composite material,” Tech. rep., Delft University of Technology, Delft,LR-574, 1988. 7 Vlot, A., Vogelesang, L., and Vries, T., “Toward application of fibre metal laminates in large aircraft,” Aircraft Engineering & Aerospace Technology, Vol. 71, 1999, pp. 558–570. 8 Skorupa, M., “Load interaction effects during fatigue crack growth under variable amplitude loading-A literature review. Part I: Empirical trends,” Fatigue & Fracture of Engineering Materials and Structures, Vol. 21, 1998, pp. 987–1006. 9 Alderliesten, R., Fatigue crack propagation and delamination growth in Glare, Ph.D. thesis, Delft University of Technology, Delft, 2005.

5 of 5 American Institute of Aeronautics and Astronautics

This paper presents the experimental and analytical research on the applicability of Linear Damage Accumulation Rule for fatigue crack growth in Fibre reinforced Metal Laminates under variable amplitude loading. A recently developed constant amplitude analytical prediction model has been extended to predict fatigue crack growth under variable amplitude loading using a linear damage accumulation rule. The modified model has been compared with crack growth tests on Fibre reinforced Metal Laminates centre-cracked tension specimen. In the end it is discussed to what extent or under what conditions the linear damage accumulation predictions are sufficiently accurate for Fibre reinforced Metal Laminates structures.

I.

Introduction

I

n reality, the mechanical and structural components are often loaded under variable amplitude (VA) loading. The majority of structural failures happen due to the mechanical fatigue. For fatigue crack growth predictions under VA loading a number of prediction models have been developed.1 These models range from simple models like linear damage accumulation (LDA) to the more complex yield zone, crack closure and strip yield models. This variety of prediction models is the result of the required prediction accuracy and integration of physical phenomena like plastic zone and crack closure2 in the formulation of the models. It has been observed that the fatigue crack growth predictions of LDA rule are not accurate in metallic structures.3 Fibre reinforced Metal Laminates (FML) being a hybrid material of metal and composite, have both metallic as well as composite properties.4 It is assumed that linear damage accumulation predictions for VA loading are more accurate than in metals due to the existence of fibre bridging restraining crack opening similar to crack closure. ∗

PhD Student, Faculty of Aerospace Engineering, [email protected] Astt. Professor, Faculty of Aerospace Engineering, [email protected] ‡ Professor, Faculty of Aerospace Engineering, [email protected]

†

1 of 5 American Institute of Aeronautics and Astronautics

II.

Linear Damage Accumulation

The linear damage accumulation model is based on a cycle-by-cycle analysis independent of previous load history. It is an integration of calculated crack growth increments ∆ai using crack growth laws 5 ,after every load cycle to obtain a prediction for the full load spectrum. As a result, it is the simplest model to predict the crack growth rate under VA loading. The advantage of LDA rule is computational efficieny. In general, this rule can be presented mathematically as: a = a0 +

n X

f (∆K, r, ..) = a0 +

i=1

III.

N X

∆ai

(1)

i=1

Fibre Reinforced Metal Laminates

After ARALL,6 GLARE (GLAss-REinforced) is the second member of the FML material family. Like its predecessor, Glare also has very favourable fatigue crack growth properties. FML’s are built up of alternating metal- and fiber layers as shown in figure 1. For standard GLARE, aluminium (alloy) 2024-T3 sheets and S2-glass fibres are bonded together with FM94 epoxy adhesive to form a laminate. This stack is cured in an autoclave at 120 ◦ C and 6 bar for 1 21 hour. The fibre orientation is defined with respect to the rolling direction of the aluminium layers and each orientation represents a prepreg layer of 0.133mm thickness. Detailed description of Glare grades are shown in table 1.

Glare

Sub

Glare 1

Glare 2A

Prepreg OriMetal Sheet entation in Thickeach fiber ness[mm] layer 0.3-0.4 0/0 0.2-0.4 0/0

Glare 2B Glare 4A

0.2-0.5 0.2-0.5 0.2-0.5

90/90 0/90 0/90/90

Glare 4B Glare 6A

0.2-0.5 0.2-0.5 0.2-0.5

90/0/90 0/90/90/0 +45/-45

Glare 6B

0.2-0.5

-45/+45

Glare 2 Glare 3 Glare 4 Glare 5 Glare 6 Figure 1. GLARE

Table 1. Standard Glare grades

Since 1980, the FML concept has been investigated, developed and tested especially at Delft University of Technology. This development was speeded up in 1996 after the decision of Airbus to apply GLARE on Airbus A380.7 In April 2005 this newly-build aircraft with GLARE on major structural fuselage parts, performed its first maiden flight.

2 of 5 American Institute of Aeronautics and Astronautics

IV.

Selective Variable Amplitude

A selective variable amplitude load spectrum (figure 28 ) is defined as a constant amplitude spectrum with few load variations like single overload/underlod, multiple overload/underload and their combinations. These selective load variations are the building blocks of the (aircraft) service spectrum. The selective variable amplitude spectrum has been utilized to get the basic understanding of crack growth behaviour of FMLs’ under aircraft spectra.

V.

(a)

(b)

(g)

(f)

(j)

k(i)

(e)

(d)

(c)

(h)

k(ii)

(i)

k(iii)

Figure 2. (a)single OL;(b)block of OL;(c)period blocks of OL;(d) single UL; (e)block of UL;(f ) period blocks of UL;(g) single OL-UL;(h)single UL-OL;(i)periodic OL-UL blocks;(j)periodic ULOL blocks; and (k)two-level block loading.k(i)HILO;k(ii)LO-HI; and k(iii)both maximum and minimum load.

Research Approach

A model has been developed using the LDA rule (equation (1)), in order to investigate the prediction accuracy of LDA rules for FML under VA loading. The CA model of Alderliesten9 has been used as the basis for development of this VA prediction model using LDA rule for FMLs’. The flow diagram of the LDA prediction model is shown in figure 3(a). Matlab is used for the programming and simulation tasks. In order to make the code functional for all sort of variable spectra, an input file system is programmed. The model is validated with fatigue crack growth experiments on Glare 3-4/3-0.3 with cross-ply fibre orientation. Load variations were applied on a CA baseline spectrum with a maximum stress Smax of 120 MPa and a stress ratio R of 0.1. The single overload spectrum has an overload Sol of 175 MPa at 100 kcycles. The multiple overload spectrum has three overloads i.e. Sol1 = 175M P a, Sol2 = 158M P a and Sol3 = 139M P a at 100, 160 and 220 kcycles respectively. Block loading spectra are constituted of two stress levels Smax1 = 100M P a, Smax2 = 140M P a and vice-versa with 0.1 stress ratio. Apart from these selective VA loading spectra, representative complex flight spectra are also used for the model validation. The fatigue crack growth tests have been performed on centre-cracked tension (CCT) specimens, illustrated in figure 3(b). The starter notches are made by drilling a hole of 3 mm diameter with two saw cuts, directing perpendicular to the loading direction. The total length of the starter notch (2a0 )is approximately 5 mm.

VI.

Simulation Example

One of the simulations performed using block load spectrum LO-HI sequence (LO: Smin = 10M P a, Smax = 100M P a; HI: Smin = 14M P a, Smax = 140M P a) is shown in figure 4. In this figure, plots are shown comparing the test results with LDA predictions. From the plot, it is clear that the predictions are close to the test results. However, it has been observed that the predictions made from LDA depend on the nature of spectrum.

3 of 5 American Institute of Aeronautics and Astronautics

Ø 10

3

580 370 5

210 25 All dimensions in mm

25 25 25 25

70

(a) Flow diagram for the crack growth prediction model

70

(b) Centred-cracked Specimen geometry

Figure 3. Research Approach

Crack Length -a Vs. Number of Cycles - N

Crack Growth Rate - da/dN Vs. Crack Length -a 0.001

25

Experimental Measurements

Experimental Measurements

Transition of Smax

Transition of Smax

LDA Predicition

Crack Growth Rate - da/dN [mm/cycle]

LDA Predicitions

Crack Length - a [mm]

20

15

10

0.0001

5

0 0

50

100

150

200

250

300

0.00001 3

5

Number of Cycles - N [cycle]

7

9

11

13

15

17

Crack Length - a [mm]

(a) Crack length vs. number of cycles

(b) Crack growth rate vs. crack length

Figure 4. Comparison of test results with linear damage accumulation rule prediction for block loading (LO-HI).

4 of 5 American Institute of Aeronautics and Astronautics

19

VII.

Expected Results and Conclusions

A new model capable of predicting the crack growth of FMLs’ under VA loading has been introduced. Supporting experiments have been performed and the results of the experiments are used to compare with the prediction model. It has been shown that the model sufficiently resembles the experimental trends of the crack growth. The conditions under which the principal assumption of the model, linear damage accumulation is valid are discussed. For example, the errors in the LDA predictions will be small if the difference between the load peaks and the remaining load sequence is less or if the retardation and acceleration effects are compensated within the sequence. But, in case of a large difference between the peaks and the baseline level loading the predictions can be seriously in error, with very conservative or very unconservative results being possible.

References 1

Khan, S., Alderliesten, R., Schijve, J., and Benedictus, R., “On the fatigue crack growth prediction under variable amplitude loading,” Computational and experimental analysis of damaged materials, edited by P. D. Pavlou, Research Signpost, 1st ed., 2007, To be published. 2 Elber, W., “The Significance of Fatigue Crack Closure,” Tech. rep., ASTM STP 486, 1971. 3 Sander, M. and Richard, H., “Fatigue crack growth under variable amplitude loading Part II: Analytical and numerical investigations,” Fatigue & Fracture of Engineering Materials & Structures, Vol. 29, 2006, pp. 303–319. 4 Vlot, A. and Gunnink, J., Fibre Metal Laminates-An introduction, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001. 5 Wanhill, R. and Schijve, J., “Current status of flight simulation fatigue crack growth concepts,” Fatigue crack growth under variable amplitude loading, edited by J. Petit, D. Davidson, S. Suresh, and R. Rabbe, Elsevier applied science,England, 1988, pp. 326–339. 6 Marissen, R., “Fatigue crack growth in ARALL - A hybrid aluminium-aramid composite material,” Tech. rep., Delft University of Technology, Delft,LR-574, 1988. 7 Vlot, A., Vogelesang, L., and Vries, T., “Toward application of fibre metal laminates in large aircraft,” Aircraft Engineering & Aerospace Technology, Vol. 71, 1999, pp. 558–570. 8 Skorupa, M., “Load interaction effects during fatigue crack growth under variable amplitude loading-A literature review. Part I: Empirical trends,” Fatigue & Fracture of Engineering Materials and Structures, Vol. 21, 1998, pp. 987–1006. 9 Alderliesten, R., Fatigue crack propagation and delamination growth in Glare, Ph.D. thesis, Delft University of Technology, Delft, 2005.

5 of 5 American Institute of Aeronautics and Astronautics