FATIGUE DEBOND GROWTH IN SANDWICH STRUCTURES LOADED IN MIXED MODE BENDING (MMB) ABSTRACT

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1 FATIGUE DEBOND GROWTH IN SANDWICH STRUCTURES LOADED IN MIXED MODE BENDING (MMB) * Amilcar Quispitupa, * Christian Berggreen and Leif A. Carlsson * Department of Mechanical Engineering, Technical University of Denmark Nils Koppels Allé, Building 43, DK-8 Kgs. Lyngby, Denmark cbe@mek.dtu.dk Department of Mechanical Engineering, Florida Atlantic University 777 Glades Road, Boca Raton, FL 33431, USA carlsson@fau.edu ABSTRACT Static and cyclic debond growth in sandwich specimens loaded in mixed mode bending (MMB) is examined. The MMB sandwich specimens were manufactured using H PVC foam core and E-glass/polyester non-crimp quadro-axial [/45/9/-45] s DBLT-85 face sheets. Static test were performed to determine the fracture toughness of the debonded sandwich specimens at different mixed mode loadings. The mixed mode ratio (mode I to mode II) was controlled by changing the lever arm distance of the MMB test rig. Compliance technique and visual inspection was employed to measure the crack length during fatigue. Fatigue tests were performed at 9% of the static fracture toughness at a loading ratio of R=.1. Fatigue results revealed higher debond crack growth rates when the lever arm distance was increased. For some specimens, the crack propagated just below the face/core interface in the foam core and for others the crack kinked into the face sheet. 1. INTRODUCTION Sandwicomposites have a superior stiffness/weight ratio compared to monolithic metallic materials making sandwicomposites very attractive for wind turbine blades, and aerospace and marine structural applications [1,]. Sandwich specimens may contain a number of various defects introduced during the manufacturing process or inherent material imperfections in the core, face sheet and/or face/core interfaces. The most common cause of these defects is poor or bonding due to careless manufacturing of sandwicomponent [1-3]. It is well know that these types of structures are subjected to cyclic loading whican lead to fatigue failure. Debonds in sandwich structures subjected to static or cyclic loads can cause a reduction in the load bearing capacity of the structure, since tensile and shear loads cannot be transferred efficiently between core and the face sheets [3-5]. As a result the overall strength and fatigue lifetime of the sandwich structure will be compromised. A small number of fatigue studies of debonded sandwicomposites have been reported in the literature [3-5]. Pure mode I and pure mode II fatigue tests of debonded sandwich beams showed higher fatigue crack growth rates under mode I than mode II loadings; however, no consistent methodology to analyze the fatigue crack growth has been proposed. Analysis of cyclic debonding in sandwich structures is complex due to the presence of multiple crack growth scenarios and the mode-mixity effect at the crack tip [1,6,7]. The development of lifetime or fatigue crack growth models for mixed mode fatigue loading is an important task. Fatigue crack growth behavior in debonded sandwich structures under well controlled mixed mode loading conditions remains uncharted territory. The objective of this paper is to develop a consistent test procedure for fatigue crack growth in debonded sandwicomposites. Experimental fatigue crack growth rates results are reported as function of the cyclic energy release rate and mode ratio. 1

2 . EXPERIMENTAL PROCEDURE.1 Materials Sandwich specimens were manufactured using Divinycell H foam core bonded to GFRP DBLT-85 face sheets made from glass/polyester non-crimp multi-axial (/45/9/-45) weave. The face sheet and core material were assumed to be isotropic and linear elastic with mechanical properties provided in Table 1. Properties H Compressive Strength (MPa) Compressive Modulus (MPa) 135 Tensile Strength (MPa) 3.5 Tensile Modulus (MPa) 13 Shear Strength (MPa) 1.6 Shear Modulus (MPa) 35 Shear Strain (%) 4 Fracture Toughness G IC (J/m ) 31 Face DBLT-85 (/45/9/-45) Young's modulus (E), GPa 16.4 Shear modulus (G), GPa 6.3 Poisson's modulus (ν).36 Table 1: Mechanical properties of H PVC foam and face sheets [1,9]. P Saddle c a Hinge L L Figure 1: Debonded sandwich specimen in the MMB test rig.. Specimens The sandwich specimen and the MMB test rig are shown in Figure 1. Two sandwich geometries were used with 1 and 9 mm core thickness. The MMB specimen consist of a rectangular beam type specimen, width of 35 mm, span length of 15 mm (L), crack length of 5 mm and face sheet thickness of mm. The initial face/core interface debonds in these specimens were created using a razor blade of.35 mm thickness. The initial crack was 5 mm for all specimens. The sandwich specimen is similar to the well known DCB [1] and CSB [11] sandwich specimens used for static debond fracture studies under mode I and mode II.

3 .3 Static testing The test procedure utilizes a modification of the MMB specimen which is an ASTM standard (ASTM D 6671 [1]) for the static mixed mode fracture testing of unidirectional laminated composites, as shown in Figure 1. The load (P) was introduced through a steel loading joke and saddle, and transferred to the sandwich specimen via rollers and steel hinges, see Figure 1. The steel hinges were specially manufactured to avoid nonlinear rotations and/or friction forces during testing. In principle, the MMB test rig subjects the crack front to tensile normal (mode I) and sliding shear (mode II) loadings. The ratio between mode II/mode I is controlled by varying the distance of the lever arm position, c. Three c values were used, i.e. 3, 4 and 5 mm in order to evaluate the effect of c on the fracture toughness of the face/core interface. The MMB specimens were designed following the methodology presented in [7] in order to promote debond failure as controlling failure mechanism..4 Fatigue testing The fatigue tests were designed based on the static tests results. The fatigue testing was performed at 9% of the static fracture toughness at a fixed lever arm distance c. A loading ratio of R=.1 (P min /P max or δ min / δ max ), and a sinusoidal waveform witonstant displacement amplitude was used. Displacement control testing is associated with reduced stress intensity as well as energy release rate at the tip of the growing crack. However, displacement control test is an advantageous technique when conducting comparative fatigue crack growth studies. This type of test was chosen because the testing time can be greatly reduced and better control can be exercised in obtaining stable crack growth (corresponding to region II in the conventional load control testing). Since the R-ratio employed for the fatigue testing was small, there is no significant distinction in the current tests between G and G max, as shown in Eq. (1), thus, G max can be used instead of G, as will be presented in the results for crack propagation. (.1P ) ΔP dcmmb Pmax Pmin dcmmb Pmax min dcmmb.99pmax dcmmb Δ G = = = = G (1) max b da b da b.5 Crack length measurement Special care was exercised in measuring crack length. Crack length was, therefore, calculated using a novel compliance technique based on Eq. (), which was recently developed and presented in [6,7], and by direct measurement. c c L c c + L c + L CMMB = CDCB _ upper + CDCB _ lower + CCSB L L α () L L L Where, c is the lever arm distance, L is the span length, and α measures the asymmetry between the upper and lower sub-beams at the debonded region of the sandwich specimen. Expressions for the compliances C DCB-upper, C DCB-lower and C CSB for upper DCB sub-beam, lower DCB sub-beam and CSB specimens respectively are provided in [6,7,1,11]. The visual crack length measurement was carried out using a caliper with an accuracy of ±.5 mm. However, the manual measurement is difficult which might cause uncertainty in the correct crack tip position. The MMB compliance expression (Eq. ()) is a function of the crack length, material properties, load and displacement applied to the specimen. Then, knowing load (P) and displacement (δ) from the testing machine, the compliance C MMB =δ/p can be calculated. Then rearranging Eq. (), the crack lengtan be determined for any load, displacement and given time during fatigue testing. The crack length measurement from the compliance technique is more accurate, since it uses the actual load and displacement applied to the specimen. Therefore, the compliance based crack lengtan be considered more reliable for crack length da b da 3

4 measurements and allows the automation and reduction in data collection. The crack length measurement based compliance technique and via visual inspection is presented in Figure Compliance Technique Visual N (cycles) = 1mm = 1mm Compliance Technique Visual 4 3 N (cycles) Figure : Crack length obtained from MMB compliance and visual inspection (initial crack length = 5 mm). The validation of the compliance base crack length measurements showed good agreement with the physical crack measurements, as shown in Figure. 3. RESULTS 3.1 Static tests An analysis of the debonded sandwich specimens loaded statically under mixed mode bending was performed in order to determine the static fracture toughness and to ensure debond failure rather than core shear, crushing or indentation [7]. Results from the static tests provided the critical failure loads to propagate an interfacial crack at a given mixed mode ratio (mode II/mode I). Load versus displacement curves for various testing conditions are presented in Figures 3 and 4 for specimens with 9 and 1 mm core thickness. Linear elastic behavior is observed before the initiation of crack propagation for all specimens tested. Thus, the critical strain energy release rate, based on the assumption that linear elastic fracture mechanics is valid, can be used to characterize the fracture toughness of the face/core sandwich interface. As shown in Figure 3 and 4, the onset of crack propagation is marked with an open circle. In addition, it can also be observed that the load required to propagate the face/core debond is higher for small c values. This behavior can be attributed to the fact that at small c values the mixed mode applied to the specimen become dominated by mode II and at larger c values mode I is dominant. For instance, for the specimens with 9 mm core thickness, the critical failures load for c=3 mm was approximately 35 N and 175 N for c=5 mm, see Figure 3. The same trend can be observed in Figure 4 which shows the results for specimens with 1 mm core thickness, the maximum failure load for c=3 mm was approximately 5 N and 14 N for c=5 mm. 4

5 =9mm c = 3mm =9mm =9mm Figure 3: MMB experimental for load vs. displacement ( Onset of crack growth, =9 mm, h f = mm) =1mm c = 3mm 15 =1mm =1mm Figure 4: MMB experimental for the load vs. displacement ( Onset of crack growth, =1 mm, h f = mm). 5

6 For the static test results (Figures 3-4), the crack path for all tested specimens was located beneath the resin-rich foam cell region [3,13]. Based on the static failure loads presented in Figures 3 and 4, the fracture toughness (critical energy release rate) calculation was performed for the specimens tested. The results of these calculations are shown in Figure 5. Figure 5a shows the fracture toughness for crack initiation for specimens with 1 mm core thickness and Figure 5b the fracture toughness for specimens with 9 mm core thickness. 8 8 Fracture Toughness (J/m ) 6 4 Fracture Toughness (J/m ) 6 4 =1mm =9mm c (mm) Figure 5: Debond fracture toughness for sandwich specimens with a) =1 mm and b) =9 mm. It can be observed for Figures 5a and 5b that the fracture toughness decreases when the distance c increases, whiconsistent with the findings reported in [6,7]. A relatively large deviation in the fracture toughness values for the specimens with 9 mm core thickness compared to the ones with 1 mm is observed in Figure 5. This could be caused by the presence of manufacturing defects in the specimens due to the manually created starter crack. However, due to the small amount of tested specimens and an expected large scatter in fracture toughness measurements for sandwich interface, the deviations are within an acceptable magnitude. A finite element analysis by use of the commercial software package, ANSYS, was performed for the testing conditions presented above in order to determine the mode-mixity in terms of the phase angle between the mode II and mode I at the crack tip. The CSDE method present in [1,14] was used to extract the mode-mixity at the crack tip and a J-integral calculation was used to determine the energy release rate. To determine the mode-mixity, the reduced formulation was employed assuming that the oscillatory index at the crack tip, ε, is equal to zero. The mode-mixity for the specimens with 1 mm core thickness evaluated at c values of 3, 4 and 5 mm were -14, -7,8 and -3.9 respectively For the specimens with 9 mm core thickness, the mode-mixity was 3.5 for c=3 mm, 5.3 for c=4 mm and 6.4 for c=5 mm. The latter values can be considered to be within the region of mode I dominance. An additional finite element analysis was performed in order to determine if the mode-mixity at the crack tip is independent of the crack length. The results of that analysis are presented in Figure 6a. It can be observed that the mode-mixity at the crack tip remains approximately constant as function of an increasing crack length, which is important for fatigue tests. Furthermore, the comparison between the energy release rates calculated analytically [6] and from FEA are in excellent agreement, as shown in Figure 6b. c (mm) 6

7 Phase Angle ( o ) G (J/m ) -5 FEA: Phase Angle FEA Figure 6: a) Phase angle (mode-mixity) at the crack tip as function of the crack length and b) energy release rate as function of the crack length. 3. Fatigue Under fatigue loading, a debond may possibly propagate through at the face/core interface, into the core or into the face sheet, and propagate further as an interlayer delamination. The crack path depends on the stress condition at the crack tip and the cyclic energy release rate level applied to the specimen. In the current tests, cyclic debond growth tests revealed two crack paths, in the foam and face sheet, as shown in Figure 7. As reported previously in [3] for sandwich specimens with H foam core, the fatigue crack path was in the foam core underneath the resin-ricells. In the current tests, for the majority of specimens the crack grew mainly in the core and for few specimens kinked into the face sheet. In addition, faster fatigue crack growth rates were observed for specimens where kinking was present. The crack kinking could be attributed to the high stress intensity factor as well as high energy release rate at the outset of the tests which was close to the static fracture toughness (9% of the static fracture toughness). Furthermore, the sign of the shear stresses at the crack tip determines the direction of the kinking [13]. Thus, since the shear stresses acting on the face/core interface for the tested specimens are negative, the kinking will be towards the upper face sheet, as shown in Figure 7b. crack increment crack increment Figure 7: Crack path during fatigue testing, a) crack growth in the foam core and b) crack kinked into the face sheet (Both specimens tested at the same loading conditions and modemixity) The crack length as function of the number of cycles and different loading conditions are presented in Figure 8. Since the crack growth rate was higher in specimens where kinking was 7

8 present, the crack lengths were longer. For instance, in Figure 8a, the specimens tested at c=4 ( ) and 5 mm ( ) kinking of the crack into the face sheet was observed. The crack kinked after approximately 1 mm of growth and remained in the face until the end of the test. For the specimen wit=3 mm ( and, see Figure 8a) the crack grew slowly in the foam core material, and after approximately cycles the crack did not extend significantly which might be due to the near-threshold crack growth rate values, approximately 1-6 mm/cycle [3]. However, further investigation needs to be performed in order to establish a threshold crack growth rate value as function of the R-ratio used. Slow crack propagation is believed to be due to the ductility and density of the H PVC foam core material. On the other hand, for the results presented in Figure 8b, the crack grew primarily in the foam, however, for one specimen tested at c=3 mm ( ) the crack kinked into the face sheet and a larger crack growth rate was measured. A clear trend cannot be established regarding the findings presented in Figure 8 since two crack paths were observed. More experimental studies need to be performed in order to establish a more consistent tendency x1 3 x1 3 3x1 3 4x1 3 5x1 3 6x1 3 N (cycles) c = 3mm c = 3mm -FS -FS hc = 1mm hf = mm hc = 9mm hf = mm 4 x1 3 4x1 3 6x1 3 N (cycles) c = 3mm-FS c = 3mm Figure 8: Crack length as function of number of cycles for specimens with: a) 1 mm core thicknesses and b) 9 mm core thicknesses (FS indicates that crack propagated in the face sheet, otherwise in the foam). For some specimens, post-mortem, inspection revealed uneven crack growth. In one side of the specimen, the crack grew in the foam core material below the resin-ricells, whereas on the other side of the specimen, the crack kinked into the face sheet. If the variation from the two crack fronts was greater than mm, the specimen was discarded following the recommendation by ASTM D-6671 [1] because of non-uniform growth. The uneven crack growtould be attributed to the fact that the starter crack was created manually using a razor blade which does not guarantee uniformity of the crack front. The proportion of mode I and mode II applied to the MMB specimen is controlled by the lever arm distance. Faster crack growth rates are expected for specimens evaluated at larger c values since the mode I become dominant. Experimental fatigue crack growth results for different loading conditions and sandwich specimens (1 and 9 mm core thickness) are shown in Figure 9. Faster crack propagation rates were encountered at the beginning of the tests (approximately within the first cycles for specimens with 1mm core thickness and cycles for specimens with 9 mm core thickness) and followed by a slow crack increment after this period, see Figure 9a. In Figure 9a, faster crack growth rates can be observed for the specimen wit=5 mm (steeper slope) compared to c=4 mm. However, in the test at c=3 mm, during the experiments the crack was arrested after approximately 4-5 mm (see Figure 8a) growth. 8

9 Furthermore, there was no significant drop in the load and as a result the energy release rate remains roughly constant. Additionally, the crack growth rate relation versus the cyclic energy release became very erratic and was therefore not included in Figure 9a. In Figures 9b-d, a dependence of the fatigue crack growth rate on the distance c can be observed. As the distance c, increases the fatigue crack growth rate also increases. da/dn (mm/cycle) = 1mm h f = mm C = 1x1-14 m = 4.3 da/dn (mm/cycle) c = 3mm = 9mm h f = mm C = 3x1-11 m = 3.1 C = 1x1-16 m = 5.15 ΔG (J/m ) ΔG (J/m ) da/dn (mm/cycle) = 9mm h f = mm C = 3x1-11 m = da/dn (mm/cycle) = 9mm h f = mm C = 8x1-4 m = (c) ΔG (J/m ) ΔG (J/m ) (d) Figure 9: Crack growth rate versus energy release rate for a) =1 mm and b)-d) =9 mm (C and m (slope of the curve) are curve fitting parameters). The fatigue crack growth rates presented in Figure 9 agrees well with the reported values in [3] for a similar combination of materials evaluated under mode I. The large scatter in the experimental results presented in Figure 9 is expected since sandwich composites are inherently inhomogeneous. Hence it is difficult to get a high degree of reproducibility. In addition, some manufacturing defects can also introduce scatter in the fatigue crack growth rate results. More experimental fatigue crack propagation studies are underway and will be presented in a forthcoming paper using the methodology described here. 4. CONCLUSIONS The MMB specimen has been applied in the study of cyclic crack growth in sandwich structures. It was demonstrated that the compliance based crack length measurement technique is very accurate and can be used for automation and data reduction, thus avoiding the difficulty of crack measurements during testing. Furthermore, fatigue testing revealed kinking of the crack into the face sheet for a few specimens which promoted faster fatigue 9

10 crack growth rates compared to specimens where the crack grew mainly in the core (under the resin-rich foam cells). The fatigue crack growth rate in debonded sandwicomposites is highly dependent on the lever arm distance, c, whicontrols the applied global mixed mode ratio. Finally, the viability to use the MMB sandwich specimen and tests rig for fracture toughness characterization and fatigue crack growth studies has been proved. ACKNOWLEDGEMENTS This work is carried out as an integrated part of the research project Growth of Debonds in Foam Cored Sandwich Structures under Cyclic Loading (SANTIGUE) funded by the Danish Research Agency (Grant nr ). Furthermore, the sponsoring of test specimens by LM Glasfiber A/S is highly appreciated. REFERENCES 1. Berggreen C., Damage Tolerance in Debonded Sandwich Structures, PhD. Thesis, Department of Mechanical Engineering, Technical University of Denmark, 4.. Zenkert D., An introduction to sandwiconstruction, London, EMAS, Shipsha, A., Burman, M. and Zenkert, D., Interfacial fatigue crack growth in foam core sandwich structures, Fatigue and Fracture of Engineering Materials and Structures, Vol., pp , Quispitupa, A. and Shafiq B., Fatigue characteristics of foam core sandwich composites, International Journal of Fatigue, Vol. 8, No.1, pp 96-1, Berkowitz, K.C. and Johnson, W., Fracture and fatigue tests and analysis of composite sandwich structure, Journal of Composite Materials, Vol. 39, No.16, , Quispitupa, A., Berggreen, C. and Carlsson L.A., On the analysis of a mixed mode bending (MMB) sandwich specimen for debond fracture characterization, Engineering Fracture Mechanics, Submitted, Quispitupa, A., Berggreen, C. and Carlsson, L.A., A debonded sandwich specimen under mixed mode bending (MMB), 8th International Conference on Sandwich Structures ICSS 8, Porto, May 3-6, Sriram, P., Khourchid, Y., Hooper, S.J. and Martin R.H., Experimental development of a mixed-mode fatigue delamination criterion, Composite Materials: Fatigue and Fracture-Fifth Volume, ASTM STP 13, R.H. Martin Ed., pp. 3-18, DIAB. Technical Manual. Divinycell H, Denmark, Avilés, F. and Carlsson, L.A., Analysis of the Sandwich DCB Specimens for Debond Characterization, Engineering Fracture Mechanics, Vol. 75, , Carlsson, L.A., Sendlein, L.S. and Merry S.L., Characterization of Face/Core Shear Fracture of Composite Sandwich Beams, Journal of Composite Materials, Vol.5, No.1, pp , ASTM D6671/D 6671M-6, Standard Test Method for Mixed Mode I-Mode II Interlaminar Fracture Toughness of Unidirectional Fiber Reinforced Polymer Matrix Composites, ASTM International, Carlsson, L.A., Matteson, R.C., Aviles, F. and Loup D.C., Crack path in foam cored DCB sandwich fracture specimens, Composites Science and technology, Vol. 65, 61-61, Berggreen, C., Simonsen, B.C. and Borum, K.K., Experimental and Numerical Study of Interface Crack Propagation in Foam Cored Sandwich Beams, Journal of Composite Materials, 41(4), 493-5, 7. 1