Analytical theories were developed for studying post-local buckling-driven delamination of thin layer materials under in-plane compressive stresses which can arise from externally applied mechanical loads, thermal stresses due to mismatch of coefficients of thermal expansion between the thin layer
material and the thick substrates, the intercalation stresses due to electrochemical lithiation and delithiation, and etc. The development was based on three mixed mode partition theories. They are Euler beam or classical plate, Timoshenko beam or shear deformable plate [1-5] and 2D-elasticity [6-8] theories. Independent experimental tests [9] show that, in general, the analytical partitions based on the Euler beam or classical plate theory predicts the propagation behaviour very well and much better than the partitions based on the Timoshenko beam and 2D-elasticity theories

Andrew Watson (1251807)

Bin Wang (30851)

Christopher Harvey (1256223)

Qiusheng Li (4612561)

Simon Wang (1250952)

English

Loughborough University Institutional Repository

21ST International Conference on Composite Materials Xi’an, 20‐25th August 2017 THE MECHANICS OF INTERFACE FRACTURE IN LAYERED COMPOSITE MATERIALS: (4) BUCKLING DRIVEN DELAMINATION OF THIN LAYER MATERIALS  Simon S. Wang1, 2, Christopher M. Harvey1, Qiusheng Li2, Bin Wang1 and Andrew Watson1  1 Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom E-mails: s.wang@lboro.ac.uk, c.m.harvey@lboro.ac.uk, b.wang2@lboro.ac.uk, a.watson@lboro.ac.uk  2 School of Mechanical and Equipment Engineering,  Hebei University of Engineering, Handan, China E-mail: Lqs59@126.com  Keywords: Buckling, Composite materials, Delamination, Fracture toughness, Thin films  ABSTRACT Analytical theories were developed for studying post-local buckling-driven delamination of thin layer materials under in-plane compressive stresses which can arise from externally applied mechani-cal loads, thermal stresses due to mismatch of coefficients of thermal expansion between the thin layer material and the thick substrates, the intercalation stresses due to electrochemical lithiation and deli-thiation, and etc. The development was based on three mixed mode partition theories. They are Euler beam or classical plate, Timoshenko beam or shear deformable plate [1-5] and 2D-elasticity [6-8] the-ories. Independent experimental tests [9] show that, in general, the analytical partitions based on the Euler beam or classical plate theory predicts the propagation behaviour very well and much better than the partitions based on the Timoshenko beam and 2D-elasticity theories. 1 INTRODUCTION Thin layer/substrate composite material systems are commonly seen in many engineering applica-tions, such as thermal barrier coating system in aero engines, erosion resistance coating system in oil transportation pipes, thin film electrodes in batteries, and etc. The thin layer is often sustain substantial in-plane residual stresses in service condition, such as mechanical stresses due to release of pre-strains in the substrate, thermal stresses due to mismatch of thermal expansion coefficients, intercalation stresses in thin film electrodes [10] due to electrochemical lithiation and delithiation, and other diffu-sion induced stresses. The compressive residual stresses can cause buckling-driven delamination which has to be considered for reliable design of such thin layer/substrate composite material systems. The study aims to develop analytical theories to predict the buckling driven delamination behaviour of thin layer/substrate composite material systems under in-plane compressive stresses. 2 THEORY Fig. 1 illustrates two typical buckling driven delaminations of thin layer materials, which are often used in experimental tests to determine the fracture toughness of the film/substrate interfaces and also often occur in practice. The thin layer materials are under in-plane compressive stresses which can arise from externally applied mechanical stresses, thermal stresses due to mismatch of coefficients of thermal expansion between the thin layer material and the thick substrates, the intercalation stresses due to electrochemical lithiation and delithiation, and etc. The present work focuses at the buckling driven delamination with straight edges as shown in Fig. 1(a), which can be readily extended to study the buckling driven delamination with circular edge as shown in Fig. 1(b).  Simon S. Wang, Christopher M. Harvey, Qiusheng Li, Bin Wang and Andrew Watson      (a) (b) Figure 1: Buckling driven delamination of thin layer materials (a) with straight edges and (b) with cir-cular edge. The buckled mode shape of the delamination with straight edges in Fig. 1 (a) is assumed to be [11]        coscos2 BRxAxw  (1) where   is the correction factor for the quality of the clamped end condition at the crack tip B, which equals to 1 when the thickness h  of the thin layer material is very small in comparison with the thick-ness of the substrate, and A , BR  are the amplitude and half buckling width, respectively. The energy release rates (ERR) IG  and IIG  at the crack tip B are determined in the following as they control the delamination propagation behaviour. 2.1 Euler beam or classical plate partitions  According to Euler beam or classical plate partition theory [1-5], the ERR partitions are given as    BeBBeBIEIENMNMcG 1111  (2)    BeBBeBIIEIIENMNMcG 1111  (3) where   ,  and   ,  are the two sets of orthogonal pure modes which are    hh 2,6,  (4)      ,0,  (5) and   36EhcIE   (6) BM1  and BeN1  are the crack tip bending moment and effective axial force per unit width, respectively. The parameter   is given as  hhEE ss   ,,1 (7) E , h , sE and sh are the Young’s modulus of the thin layer materials, the thickness of the thin layer, 21ST International Conference on Composite Materials Xi’an, 20‐25th August 2017 the Young’s modulus of the substrate material and the thickness of the substrate, respectively. When hhs /  is very big, the parameter   approaches to 1. For convenience, the partitions are also given below in terms of the critical buckling strain c  and the residual compressive strain 0 .   acacIE cEhcG   32   (8)   acaIIE cEhG   21323   (9) where the critical local-buckling strain c  is   2212 Bc Rh  (10) and the additional compressive strain beyond c  is   ca   0  (11) 0  is residual compressive strain. It can be produced by externally applied mechanical strain, thermal strain due to mismatch of coefficients of thermal expansion between the thin layer material and the thick substrates, the intercalation stain due to electrochemical lithiation and delithiation, and etc. The parameter c  is close to 1 for large hhs / . Note that when      32 ca c , the crack tip normal stress becomes compressive, and so IEG  is taken to be zero with GGIIE  . 2.2 Timoshenko beam or shear deformable plate partitions According Timoshenko beam or shear deformable plate partition theory [1-5], the ERR partitions are  211   BeBITITNMcG  (12)  211   BeBIITIITNMcG  (13) where  3)31(6EhcIT   (14)    3)3/(116EhcIIT   (15) In terms of the critical buckling strain c  and the additional compressive strain a , they become     232312 1 acaIT cEhG     (16)     232312 acaIIT cEhG     (17) Again note that when      32 ca c , the crack tip normal stress becomes compressive, and  Simon S. Wang, Christopher M. Harvey, Qiusheng Li, Bin Wang and Andrew Watson so ITG  is taken to be zero with GGIIT  . 2.3 2D elasticity partitions By ignoring the material mismatch the 2D elasticity partition theory [6-8] gives the following parti-tions  221122  DBeBDIDINMcG   (18)  221122  DBeBDIIDIINMcG   (19) where    hhDD 450.4,697.2, 22  (20)     322226697.2450.412697.212450.4Ehc DI   (21)     322226697.2450.412450.412697.2Ehc DII   (22) In terms of the critical buckling strain c  and the additional compressive strain a , they become     2222 3450.4697.2450.46697.212acaDI cEhG    (23)      2222 3697.2697.2450.46450.412acaDII cEhG    (24) Again note that when      3450.4 ca c , the crack tip normal stress becomes compressive, and so the DIG 2  is taken to be zero and GG DII 2 . 3 EXPERIMENTAL ASSESSMENTS In this Section experimental results are used to assess which above ERR partitions gives the best predictions for the mechanical behaviour of buckling driven delamination. A linear failure criterion was used for the relatively low interface fracture toughness in consideration. Fig. 2 shows the compar-ison between the analytical predictions and experimental test [9] for case 1 specimen. The thickness of the thin layer is 0.518 mm and the thickness of the substrate is 2.072 mm. It is seen that the two beam partition theories predict the propagation behavior very well and much better than the 2D elasticity partition theory does. The delamination propagation is indeed the pure mode II propagation predicted by the two beam partition theories. It is now clear that the 2D elasticity partition theory does not pro-vide the right partition for predicting the propagation behaviour of buckling-driven delamination for Case 1. The question of which beam partition theory provides the right partitions when the propaga-tion is not pure mode II, however, still needs to be answered. Fig. 3 shows the comparison between the analytical predictions and experimental test [9] for case 2 specimen. The thickness of the thin layer is 0.508 mm and the thickness of the substrate is 2.032 mm. It is observed that the analytical theory based on the classical partition theory predicts the propagation behaviour very well and much better than the analytical theories based on the shear deformable and 2D-elasticity partition theories. 21ST International Conference on Composite Materials Xi’an, 20‐25th August 2017  Figure 2: Compression force per unit width F  vs. upper-surface mid-span strain sc  for case 1 speci-men.  Figure 3: Compression force per unit width F  (N/mm) vs. upper-surface mid-span strain sc . 4 CONCLUSIONS Mechanical models have been developed for studying buckling driven delamination of thin layer materials under in plane compressive stress arising from mechanical, thermal and electrochemical ac-tions. In both test cases, the thin layers have macroscopic thicknesses. The Euler beam or classical plate partition theory [1-5] predicts the delamination behaviour very well due to the global nature of the theory. Whilst the Timoshenko beam or shear deformable plate and 2D elasticity partition theories perform less well due to their local nature.    Simon S. Wang, Christopher M. Harvey, Qiusheng Li, Bin Wang and Andrew Watson REFERENCES [1] S. Wang S and C.M. Harvey, A theory of one-dimensional fracture. Composite Structures, 94, 2012, pp.758–767 (doi: 10.1016/j.compstruct.2011.09.011).  Also a plenary lecture at the 16th International Conference on Composite Structures (ICCS16), 28–30 June 2011, Porto, Portugal. [2] S. Wang and C.M. Harvey, Mixed mode partition theories for one dimensional fracture, Engi-neering Fracture Mechanics, 79, 2012, pp. 329-352 (doi: 10.1016/j.engfracmech.2011.11.013). [3] C.M. Harvey and S. 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Watson, A novel method for the partition of mixed-mode fractures in 2D elastic laminated unidirectional composite beams, Composite Structures 116, 2014, pp. 589-594 (doi: 10.1016/j.compstruct.2014.05.041). [8] J.D. Wood, C.M. Harvey and S. Wang, Partition of mixed-mode fractures in 2D elastic ortho-tropic laminated beams under general loading, Composite Structures, 149, 2016, pp. 239-246 (doi: 10.1016/j.compstruct.2016.04.016). [9] Z. Kutlu and F.K. Chang, Composite panels containing multiple through-the-width delamina-tions and subjected to compression: Part II: experiments and verification, Composite Structures, 31, 1995, pp. 297-314 (doi: 10.1016/0263-8223(95)00093-3) [10] V.A. Sethuraman, M.J. Chon, M. Shimshak, V. Srinivasan and P.R. Guduru, In situ measure-ments of stress evolution in Silicon thin films during electrochemical lithiation and delithiation, 195, 2010, pp. 5062-5066 (doi: 10.1016/j.jpowsour.2010.02.013). [11] S. Wang, C.M. Harvey, B. Wang and A. 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The mechanics of interface fracture in layered composite materials: (4) buckling driven delamination of thin layer materials

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The mechanics of interface fracture in layered composite materials: (4) buckling driven delamination of thin layer materials

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