Após a realização do presente trabalho, verifica-se que algumas das metodologias utilizadas podem ser melhoradas. Neste contexto, sugerem-se as seguintes tarefas a desenvolver em trabalhos futuros:
Iniciação da pré-fenda através de um inserto de Teflon®, (método explicado no presente trabalho) em vez da iniciação da pré-fenda através da utilização de uma lâmina;
Utilização de uma pré-força no ensaio dos provetes DCB em modo I, na medição do COD através do método de correlação digital de imagem;
Utilização da mesma frequência no registo dos valores e medidos experimentalmente e das imagens do padrão speckle capturadas durante o ensaio pela camara do sistema ARAMIS;
Utilização de um veio retificado ( 3 mm) com bainhas separadoras na colagem dos cubos metálicos, que impeçam o escorregamento dos cubos na direção transversal aos bordos do provete, aquando do aperto dos grampos.
Utilização de uma metodologia diferente na análise de resultados. Este aspeto é de particular importância dado que se constatou que o polinómio de 6º grau apresenta algumas dificuldades na reprodução completa das curvas . Sugere-se em alternativa o método dos polinómios de menor grau por tramos da curva , que terá de ser otimizado neste contexto.
69
Bibliografia
1 Harris, J. A. and Adams, R. D. Strength prediction of bonded single-lap joints by nonlinear finite element methods. In International Journal of Adhesion & Adhesives ( 1984), 4: 65- 78.
2 Towse, A., Davies, R. G. H., Clarke, A., Wisnom, M. R., Adams, R. D., and Potter, K. D. The design and analysis of high load intensity adhesively bonded double lap joints. In
International conference on deformation and fracture of composites ( 1997), 479-488.
3 Whitney, J.M. and Nuismer, R.J. Stress Fracture Criteria for Laminated Composites. In
Journal of Composite Materials ( 1974), 8: 253-265.
4 Griffith, A. A. The Phenomena of Rupture and Flow in Solids. In Philosophical
Transactions of the Royal Society ( 1921), A221: 163-198.
5 Esteves, V. H. C. Determinação da Tenacidade de um Adesivo em Solicitações de Modo
Misto (I+II). Faculdade de Engenharia da Universidade do Porto, ( 2010).
6 Kinloch, A. J. Adhesion and Adhesives. Champman & Hall 441, ( 1987).
7 de Moura, M. F. S. F., Goncalves, J. P. M., Chousal, J. A. G., and Campilho, R. D. S. G. Cohesive and Continuum Mixed-Mode Damage Models Applied to the Simulation. In
International Journal of Adhesion and Adhesives ( 2008), 28: 419-426.
8 Liljedahl, C. D. M., Crocombe, A. D., Wahab, M. A., and Ashcroft, I. A. Damage modeling of adhesive bonded joints. In International Journal of Fracture ( 2006), 141:147-161. 9 Turon, A., Dávila, C. G., Camanho, P. P., and Costa, J. An engineering solution for mesh
size effects in the simulation of delamination using cohesive zone models. In Engineering
Fracture Mechanics ( 2007), 74:1665-1682.
10 Campilho, R. D. S. G., de Moura, M. F. S. F., and Domingues, J. J. M. Modelling single and double-lap repairs on composite materials. In Composites Science and Technology (2005), 65:1948-1958.
11 Yang, Q. D., Thouless, M. D., and Ward, S. M. Numerical simulations of adhesively- bonded beams failing with extensive plastic deformation. In Journal of the Mechanics and
70
12 Campilho, R. D. S. G., de Moura, M. F. S. F., and Domingues, J. J. M. Using a cohesive damage model to predict the tensile behaviour of CFRP single-strap repairs. In
International Journal of Solids and Structures ( 2008), 45:1497-1512.
13 Campilho, R. D. S.G., deMoura, M. F. S. F. Pinto, A. M.G., Morais, J. J. L., and Domingues, J. J. M. S. Modelling the tensile fracture behaviour of CFRP scarf repairs. In
Composites: Part B – Engineering ( 2009), 40:149-157.
14 de Moura, M. F. S. F. and Chousal, J. A. G. Cohesive and Continuum Damage Models Applied to Fracture Characterization of Bonded Joints. In International Journal of
Mechanical Sciences ( 2006), 48: 493–503.
15 de Moura, M. F. S. F., Gonçalves, J. P. M., de Magalhães, A. G., and de Castro, P. M.S.T. Elementos Finitos de Interface Aplicados ao Estudo do Comportamento Mecânico das Juntas Coladas. In Revista Iberoamericana de Ingenharía Mecânica ( 2006), 10: 69- 79.
16 Andersson, T. and Stigh, U. The stress-elongation relation for an adhesive layer loaded in pell using equilibrium of energetic forces. In International Journal of Solids and Structures ( 2004), 41: 413-434.
17 Cavalli, M. N. and Thouless, M. D. The effect of damage nucleation on the toughness of an adhesive joint. In Journal of adhesion ( 2001), 76: 75-92.
18 Leffler, K., Alfredsson, K. S., and Stigh, U. Shear behaviour of adhesive layers. In
International Journal of Solids and Structures ( 2007), 44:530-545.
19 Stigh, U. Damage and crack growth analysis of the double cantilever beam specimen. In
International Journal of Fracture ( 1988), 37: 13-18.
20 Edlund, U. Mechanical analysis of adhesive joints: models and computational methods.
Linköping Studies in Science and Technology. Linköping University, Linköping, Sweden,
(1992).
21 Yang, Q. D., Thouless, M. D., and Ward, S. M. Mixed-mode fracture analyses of plastically-deforming adhesive joints. In International Journal of Fracture ( 2001), 110: 175-187.
22 Sørensen, B. F. Cohesive law and notch sensitivity of adhesive joints. In Acta. Materialia (2002), 50: 1053–1061.
23 Andersson, T. and Biel, A. on the effective constitutive properties of a thin adhesive layer loaded in peel. In International Journal of Fracture ( 2006), 141: 227-246.
71
24 de Moura, M. F. S. F., Campilho, R. D. S. G., and Gonçalves, J. P. M. Crack equivalent concept applied to the fracture characterization of bonded joints under pure mode I loading. In Composites Science and Technology ( 2008), 68: 2224-2230.
25 de Moura, M. F. S. F., Morais, J. J. L., and Dourado, N. A new data reduction scheme for mode I wood fracture characterization using the double cantilever beam test. In
Engineering Fracture Mechanics ( 2008), 75:3852–3865.
26 Olsson, P. and Stigh, U. On the determination of the constitutive properties of thin interphase layers–an exact solution. In International Journal of Fracture ( 1989), 41: 71- 76.
27 Stigh, U. and Andersson, T. An experimental method to determine the complete stress- elongation relation for a structural adhesive layer loaded in peel. In European Structural
Integrity Society ( 2000), 27: 297-306.
28 Jacobsen, T. K. and Sørensen, B. F. Mode I intra-laminar crack growth in composites–– modelling of R-curves from measured bridging laws. In Composites Part A ( 2001), 32: 1– 11.
29 Fernberg, S. P. and Berglund, L. A. Bridging law and toughness characterisation of CSM and SMC composites. In Composites Science and Technology ( 2001), 61: 2445–2454. 30 Biel, Anders. Constitutive behaviour and fracture toughness of an adhesive layer.
Chalmers University of Technology, ( 2005).
31 Post, D. Moiré Interferometry at VPI and SU. In Experimental Mechanics ( 1983), 23: 203- 210.
32 Fottenburg, W. G. Some Applications of Holographic Interferometry. In Experimental
Mechanics ( 1969), 8: 281-285.
33 Wang, Y. Y., Chen, D. J., and Chiang, F. P. Material testing by computer aided speckle interferometry. In Experimental Techniques ( 1993), 17: 30-32.
34 Brillaud, J. and Lagattu, F. Limits and possibilities of laser speckle and white-light image- correlation methods: theory and experiments. In Applied Optics ( 2002), 41:6603–6613. 35 Sutton, M. A., Wolters, W. J., Peters, W. H., Ranson, W. F., and McNeil, S. R.
Determination of Displacements Using an Improved Digital Correlation Method. In Image
72
36 Sutton, M. A., Cheng, M. Q., Peters, W. H., Chao, Y. J., and McNeill, S. R. Application of an Optimized Digital Correlation Method to Planar Deformation Analysis. In Image and
Vision Computing ( 1986), 4: 143-151.
37 Sutton, M. A., Turner, J. L., Bruck, H. A., and Chae, T. A. Full-field Representation of Discretely Sampled Surface Deformation for Displacement and Strain Analysis. In
Experimental Mechanics ( 1991), 31: 168-177.
38 Bruck, H. A., McNeil, S. R., Sutton, M. A., and Peters, W. H. Digital Image Correlation Using Newton-Raphson Method of Partial Differential Correction. In Experimental
Mechanics ( 1989), 29: 261-267.
39 Sutton, M. A., McNeill, S. R., Helm, J. D., and Chao, Y. J. Advances in two-dimensional and three-dimensional computer vision. In Topics in Applied Physics ( 2000), 323–372. 40 Schreier, H. W. Investigation of two and three-dimensional image correlation techniques
with applications in experimental mechanics. University of South Carolina, ( 2003).
41 Marcellier, H., Vescovo, P., Varchon, D., Vacher, P., and Humbert, P. Optical analysis of displacement and strain fields on human skin. In Skin Research and Technology ( 2001), 7: 246-253.
42 Ribeiro, J. E., Martins, P., Monteiro, J., Vaz, M. A. P., and Lopes, H. Caracterização do campo de deslocamentos em tecidos hiperelásticos. Bragança: Instituto Politécnico, (2009).
43 Pan, B., Asundi, A., Xie, H. M., and Gao, J. X. Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements. In Optics and Lasers in Engineering ( 2009), 47: 865-874.
44 Pan, B. Reliability-guided digital image correlation for image deformation measurement. In
Applied Optics ( 2009), 48: 1535-1542.
45 Pan, B., Wang, Z. Y., and Lu, Z. X. Genuine full-field deformation measurement of an object with complex shape using reliability-guided digital image correlation. In Optics
Express ( 2010), 18: 1011-1023.
46 Vendroux, G. and Knauss, W. G. Submicron deformation field measurements: Part 2. Improved digital image correlation. In Experimental Mechanics ( 1998), 38: 86-92.
47 Chousal, J. A. G. and de Moura, M. F. S. F. Validação da medição de deformações por correlação digital de imagem em compósitos laminados de matriz polimérica. In Revista
73
48 Chen, D. J., Chiang, F. P., Tan, Y. S., and Don, H. S. Digital speckle-displacement measurement using a complex spectrum method. In Applied Optics ( 1993), 32: 1839- 1849.
49 Sutton, M. A., McNeill, S. R., Helm, J. D., and Chao, Y. J. Advances in 2-D and 3-D computer vision for shape and deformation measurements. In Applied Physics ( 2000), 77: 323–372.
50 Chu, T. C., Ranson, W. F., and Sutton, M. A. Applications of digital-image-correlation techniques to experimental mechanics. In Experimental Mechanics ( 1985), 25: 232-244. 51 Mguil-Touchal, S., Morestin, F., and Brunet, M. Various Experimental Applications of
Digital Image Correlation Method. In Computer Methods and Experimental Measurements ( 1997), 45–58.
52 Chen, J., Zhang, X., Zhan, N., and Hu, X. Deformation measurement across crack using two-step extended digital image correlation method. In Optics Lasers Engineering ( 2010), 48:1126–1131.
53 Yates, J. R., Zanganeh, M., and Tai, Y. H. Quantifying crack tip displacement fields with DIC. In Engineering Fracture Mechanics ( 2010), 77:2063–76.
54 Ferreira, M. D. C., Venturini, W. S., and Hild, F. On the analysis of notched concrete beams: from measurement with digital image correlation to identificationwith boundary element method of a cohesive model. In Engineering Fracture Mechanics ( 2011), 78: 71– 84.
55 Zhang, R. and He, L. Measurement of mixed-mode stress intensity factors using digital image correlation method. In Optics and Lasers in Engineering ( 2012), 50: 1001-1007. 56 Mekky, W. and Nicholson, P. S. The fracture toughness of Ni/Al2O3 laminates by digital
image correlation I: experimental crack opening displacement and R-curves. In
Engineering Fracture Mechanics ( 2006), 73: 571–82.
57 Nunes, L. C. S. and Reis, J. M. L. Estimation of crack-tip-opening displacement and crack extension of glass fiber reinforced polymer mortars using digital image correlation method. In Materials and Design ( 2012), 33:248–253.
58 de Moura, M. F. S. F. Numérical simulation of the ENF test for the mode II fracture characterization of bonded joints. In Journal of Adhesion Science and Technology (2006), 20: 37.52.
59 Bader, M. G., Hamerton, I., Hay, J. N., Kemp, M., and Winchester, S. Double cantilever beam testing of repaired carbon fibre composites. In Composites Part A ( 2000), 31: 603– 8.
74
60 Banea, M. D., da Silva, L. F. M., and Campilho, R. D. S. G. Mode I fracture toughness of adhesively bonded joints as a function of temperature: Experimental and numerical study. In International Journal of Adhesion & Adhesives ( 2011), 31: 273-279.
61 Ducept, F., Davies, P., and Gamby, D. Mixed mode failure criteria for a glass/epoxy composite and an adhesively bonded composite/composite joint. In International Journal
of Adhesion and Adhesives ( 2000), 20: 233–44.
62 Kanninen, M. F. and Popelar, C. H. Advanced Fracture Mechanics. In Oxford University
Press ( 1985).
63 Marques, E. A. S. and da Silva, L. F. M. Joint strength optimization of adhesively bonded patches. In The Journal of Adhesion ( 2008), 84: 917-936.
64 Lee, D. B., Ikeda, T., Miyazaki, N., and Choi, N. S. Effect of Bond Thickness on Fracture Toughness of Adhesive Joints. In Journal of Engineering Materials and Technology
Transactions of the Asme ( 2004), 126: 14–18.
65 Carbas, R. J. C. Estudo paramétrico de juntas adesivas pelo método de Taguchi. Tese de Mestrado, Faculdade de Engenharia da Universida do Porto, ( 2008).
66 da Silva, L. F., de Moura, M. F. S. F, and de Magalhães, A. G. Juntas Adesivas
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Anexos
Anexo A
A equação (26) pode ser expressa como,
(A1)
onde os coeficientes , e são, respectivamente
(A2)
Usando o software MATLAB e considerando apenas a parte real da solução, obtém-se
(A3)
sendo
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Anexo B
Equações dos polinómios de 6º grau ajustados às curvas
Curva numérica (Figura 24)
Curva experimental do provete T_1 (Figura 65)
Curva experimental do provete T_2 (Figura 67)
Curva experimental do provete L_2 (Figura 69)
Curva experimental do provete L_3 (Figura 71)
Curva numérica do provete T_1 (Figura 77)
77 Curva numérica do provete T_2 (Figura 81)
Curva numérica do provete L_2 (Figura 85)
Curva numérica do provete L_3 (Figura 89)
78
Anexo C
Figura 93 – Rutura coesiva do provete L_2 Figura 94 - Rutura coesiva do provete L_3 Figura 91 – Rutura coesiva do provete T_1 Figura 92 - Rutura coesiva do provete T_2