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2012 | OriginalPaper | Buchkapitel

6. Fiber Composites

verfasst von : Prof. Fabrice Pierron, Michel Grédiac

Erschienen in: The Virtual Fields Method

Verlag: Springer New York

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Abstract

The objective of this chapter is to present a number of examples of application of the Virtual Fields Method (VFM) to polymer matrix fiber composites. Historically, composites have been the first materials considered for the VFM. Such composites possess two main features as far as their mechanical behavior is concerned: they are elastically anisotropic and they are prone to damage in the form of cracks, delamination, and/or fiber breakage. The first part of the chapter deals with the measurements of anisotropic stiffness components of composites. In-plane and through-thickness properties are first addressed and then bending properties for thin plates. Then, two applications related to damage are presented. The first one concerns the identification of a damage model when damage develops under loading. The second one deals with the detection and evaluation of a pre-existing damage caused, for instance, by some impact event on a thin panel. Finally, a recent application in the field of high strain rate testing is also presented.

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Literatur
2.
Zurück zum Zitat Grédiac M, Vautrin A (1990) A new method for determination of bending rigidities of thin anisotropic plates. J Appl Mech 57:964–968. Transactions of the American Society of Mechanical Engineers Grédiac M, Vautrin A (1990) A new method for determination of bending rigidities of thin anisotropic plates. J Appl Mech 57:964–968. Transactions of the American Society of Mechanical Engineers
3.
Zurück zum Zitat Grédiac M, Vautrin A (1993) Mechanical characterization of anisotropic plates: experiments and results. Eur J Mech/A Solids 12(6):819–838 Grédiac M, Vautrin A (1993) Mechanical characterization of anisotropic plates: experiments and results. Eur J Mech/A Solids 12(6):819–838
4.
Zurück zum Zitat Grédiac M, Pierron F, Vautrin A (1994) The Iosipescu in-plane shear test applied to composites: a new approach based on displacement field processing. Compos Sci Technol 51(3):409–417CrossRef Grédiac M, Pierron F, Vautrin A (1994) The Iosipescu in-plane shear test applied to composites: a new approach based on displacement field processing. Compos Sci Technol 51(3):409–417CrossRef
5.
Zurück zum Zitat Grédiac M, Fournier N, Paris P-A, Surrel Y (1998) Direct identification of elastic constants of anisotropic plates by modal analysis: experiments and results. J Sound Vibration 210(5):645–659CrossRef Grédiac M, Fournier N, Paris P-A, Surrel Y (1998) Direct identification of elastic constants of anisotropic plates by modal analysis: experiments and results. J Sound Vibration 210(5):645–659CrossRef
6.
Zurück zum Zitat Surrel Y, Fournier N, Grédiac M, Paris P-A (1999) Phase-stepped deflectometry applied to shape measurement of bent plates. Exp Mech 39(1):66–70CrossRef Surrel Y, Fournier N, Grédiac M, Paris P-A (1999) Phase-stepped deflectometry applied to shape measurement of bent plates. Exp Mech 39(1):66–70CrossRef
7.
Zurück zum Zitat Grédiac M, Pierron F, Surrel Y (1999) Novel procedure for complete in-plane composite characterization using a single T-shaped specimen. Exp Mech 39(2):142–149CrossRef Grédiac M, Pierron F, Surrel Y (1999) Novel procedure for complete in-plane composite characterization using a single T-shaped specimen. Exp Mech 39(2):142–149CrossRef
9.
Zurück zum Zitat ASTM D5379 / D5379M 05. Standard test method for shear properties of composite materials by the V-notched beam method. ASTM International, West Conshohocken, PA, 2003, 2005. DOI: 10.1520/D5379_D5379M-05 ASTM D5379 / D5379M 05. Standard test method for shear properties of composite materials by the V-notched beam method. ASTM International, West Conshohocken, PA, 2003, 2005. DOI: 10.1520/D5379_D5379M-05
17.
Zurück zum Zitat Hendricks MAN (1991) Identification of the mechanical properties of solid materials. Doctoral dissertation, Eindhoven University of Technology Hendricks MAN (1991) Identification of the mechanical properties of solid materials. Doctoral dissertation, Eindhoven University of Technology
18.
Zurück zum Zitat LeMagorou L, Bos F, Rouger F (2002) Identification of constitutive laws for wood-based panels by means of an inverse method. Compos Sci Technol 62(4):591–596CrossRef LeMagorou L, Bos F, Rouger F (2002) Identification of constitutive laws for wood-based panels by means of an inverse method. Compos Sci Technol 62(4):591–596CrossRef
28.
Zurück zum Zitat Claire D, Hild F, Roux S (2004) A finite element formulation to identify damage fields: The equilibrium gap method. Int J Numer Meth Eng 61(2):189–208MATHCrossRef Claire D, Hild F, Roux S (2004) A finite element formulation to identify damage fields: The equilibrium gap method. Int J Numer Meth Eng 61(2):189–208MATHCrossRef
38.
Zurück zum Zitat Grédiac M, Pierron F (2004) Numerical issues in the virtual fields method. Int J Numer Meth Eng 59(10):1287–1312MATHCrossRef Grédiac M, Pierron F (2004) Numerical issues in the virtual fields method. Int J Numer Meth Eng 59(10):1287–1312MATHCrossRef
39.
Zurück zum Zitat Avril S, Grédiac M, Pierron F (2004) Sensitivity of the virtual fields method to noisy data. Comput Mech 34(6):439–452MATHCrossRef Avril S, Grédiac M, Pierron F (2004) Sensitivity of the virtual fields method to noisy data. Comput Mech 34(6):439–452MATHCrossRef
40.
Zurück zum Zitat Avril S, Pierron F (2007) General framework for the identification of elastic constitutive parameters from full-field measurements. Int J Solids Struct 44:4978–5002MATHCrossRef Avril S, Pierron F (2007) General framework for the identification of elastic constitutive parameters from full-field measurements. Int J Solids Struct 44:4978–5002MATHCrossRef
62.
Zurück zum Zitat ISO 527-4:1997. Plastics – determination of tensile properties – part 4: Test conditions for isotropic and orthotropic fibre-reinforced plastic composites. International Standards Organization ISO 527-4:1997. Plastics – determination of tensile properties – part 4: Test conditions for isotropic and orthotropic fibre-reinforced plastic composites. International Standards Organization
63.
Zurück zum Zitat ISO 527-5:2009. Plastics – determination of tensile properties – part 5: Test conditions for unidirectional fibre-reinforced plastic composites. International Standards Organization ISO 527-5:2009. Plastics – determination of tensile properties – part 5: Test conditions for unidirectional fibre-reinforced plastic composites. International Standards Organization
64.
Zurück zum Zitat ISO 14129:1997. Fibre-reinforced plastic composites – determination of the in-plane shear stress/shear strain response, including the in-plane shear modulus and strength, by the plus or minus 45 degree tension test method. International Standards Organization ISO 14129:1997. Fibre-reinforced plastic composites – determination of the in-plane shear stress/shear strain response, including the in-plane shear modulus and strength, by the plus or minus 45 degree tension test method. International Standards Organization
65.
Zurück zum Zitat ISO 15310:1999. Fibre-reinforced plastic composites – determination of the in-plane shear modulus by the plate twist method. International Standards Organization ISO 15310:1999. Fibre-reinforced plastic composites – determination of the in-plane shear modulus by the plate twist method. International Standards Organization
66.
Zurück zum Zitat Lecompte D, Smits A, Sol H, Vantomme J, Van Hemelrijck D (2007) Mixed numerical-experimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens. Int J Solids Struct 44(5):1643–1656CrossRef Lecompte D, Smits A, Sol H, Vantomme J, Van Hemelrijck D (2007) Mixed numerical-experimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens. Int J Solids Struct 44(5):1643–1656CrossRef
67.
Zurück zum Zitat Pierron F, Vautrin A (1994) Accurate comparative determination of the in-plane shear modulus of T300/914 using the Iosipescu and 45 ∘  off-axis tests. Compos Sci Technol 52(1):61–72CrossRef Pierron F, Vautrin A (1994) Accurate comparative determination of the in-plane shear modulus of T300/914 using the Iosipescu and 45 ∘  off-axis tests. Compos Sci Technol 52(1):61–72CrossRef
68.
Zurück zum Zitat Pierron F (1998) Saint-Venant effects in the Iosipescu specimen. J Compos Mater 32(22):1986–2015CrossRef Pierron F (1998) Saint-Venant effects in the Iosipescu specimen. J Compos Mater 32(22):1986–2015CrossRef
69.
Zurück zum Zitat Prabhakaran R, Sawyer W (1986) A photoelastic investigation of asymmetric four point bend shear test for composite materials. Compos Struct 5(3):217–231CrossRef Prabhakaran R, Sawyer W (1986) A photoelastic investigation of asymmetric four point bend shear test for composite materials. Compos Struct 5(3):217–231CrossRef
70.
Zurück zum Zitat Romano AJ, Shirron JJ, Bucaro JA (1998) On the noninvasive determination of material parameters from a knowledge of elastic displacements: Theory and numerical simulation. IEEE Trans Ultrasonics, Ferroelectrics Freq Control 45(3):751–759CrossRef Romano AJ, Shirron JJ, Bucaro JA (1998) On the noninvasive determination of material parameters from a knowledge of elastic displacements: Theory and numerical simulation. IEEE Trans Ultrasonics, Ferroelectrics Freq Control 45(3):751–759CrossRef
71.
Zurück zum Zitat Romano AJ, Bucaro JA, Ehman RL, Shirron JJ (2000) Evaluation of a material parameter extraction algorithm using MRI-based displacement measurements. IEEE Trans Ultrasonics, Ferroelectrics Freq Control 47(6):1575–1581CrossRef Romano AJ, Bucaro JA, Ehman RL, Shirron JJ (2000) Evaluation of a material parameter extraction algorithm using MRI-based displacement measurements. IEEE Trans Ultrasonics, Ferroelectrics Freq Control 47(6):1575–1581CrossRef
72.
Zurück zum Zitat Pierron F, Grédiac M (2000) Identification of the through-thickness moduli of thick composites from whole-field measurements using the Iosipescu fixture. Compos Part A: Appl Sci Manufac 31(4):309–318CrossRef Pierron F, Grédiac M (2000) Identification of the through-thickness moduli of thick composites from whole-field measurements using the Iosipescu fixture. Compos Part A: Appl Sci Manufac 31(4):309–318CrossRef
73.
Zurück zum Zitat Grédiac M, Toussaint E, Pierron F (2002) Special virtual fields for the direct determination of material parameters with the virtual fields method. 1- Principle and definition. Int J Solids Struct 39(10):2691–2705 Grédiac M, Toussaint E, Pierron F (2002) Special virtual fields for the direct determination of material parameters with the virtual fields method. 1- Principle and definition. Int J Solids Struct 39(10):2691–2705
74.
Zurück zum Zitat Grédiac M, Toussaint E, Pierron F (2002) Special virtual fields for the direct determination of material parameters with the virtual fields method. 2- Application to in-plane properties. Int J Solids Struct 39(10):2707–2730 Grédiac M, Toussaint E, Pierron F (2002) Special virtual fields for the direct determination of material parameters with the virtual fields method. 2- Application to in-plane properties. Int J Solids Struct 39(10):2707–2730
75.
Zurück zum Zitat Chalal H, Meraghni F, Pierron F, Grédiac M (2004) Direct identification of the damage behaviour of composite materials using the virtual fields method. Compos Part A: Appl Sci Manuf 35(7-8):841–848CrossRef Chalal H, Meraghni F, Pierron F, Grédiac M (2004) Direct identification of the damage behaviour of composite materials using the virtual fields method. Compos Part A: Appl Sci Manuf 35(7-8):841–848CrossRef
76.
Zurück zum Zitat Chalal H, Avril S, Pierron F, Meraghni F (2006) Experimental identification of a nonlinear model for composites using the grid technique coupled to the virtual fields method. Compos Part A: Appl Sci Manuf 37(2):315–325CrossRef Chalal H, Avril S, Pierron F, Meraghni F (2006) Experimental identification of a nonlinear model for composites using the grid technique coupled to the virtual fields method. Compos Part A: Appl Sci Manuf 37(2):315–325CrossRef
77.
Zurück zum Zitat Surrel Y (1994) Moiré and grid methods: a signal-processing approach. In: Pryputniewicz RJ, Stupnicki J (eds) Interferometry ’94: Photomechanics, vol 2342, pp 213–220 Proc Soc Photo-Opt Instrum Eng Surrel Y (1994) Moiré and grid methods: a signal-processing approach. In: Pryputniewicz RJ, Stupnicki J (eds) Interferometry ’94: Photomechanics, vol 2342, pp 213–220 Proc Soc Photo-Opt Instrum Eng
78.
Zurück zum Zitat Moulart R, Rotinat R, Pierron F, Lerondel G (2007) On the realization of microscopic grids for local strain measurement by direct interferometric photolithography. Opt Lasers Eng 45(12):1131–1147CrossRef Moulart R, Rotinat R, Pierron F, Lerondel G (2007) On the realization of microscopic grids for local strain measurement by direct interferometric photolithography. Opt Lasers Eng 45(12):1131–1147CrossRef
79.
Zurück zum Zitat Piro J-L, Grédiac M (2004) Producing and transferring low-spatial-frequency grids for measuring displacement fields with moiré and grid methods. Exp Tech 28(4):23–26CrossRef Piro J-L, Grédiac M (2004) Producing and transferring low-spatial-frequency grids for measuring displacement fields with moiré and grid methods. Exp Tech 28(4):23–26CrossRef
80.
81.
Zurück zum Zitat Pierron F, Vert G, Burguete R, Avril S, Rotinat R, Wisnom M (2007) Identification of the orthotropic elastic stiffnesses of composites with the Virtual Fields Method: sensitivity study and experimental validation. Strain 43(3):250–259CrossRef Pierron F, Vert G, Burguete R, Avril S, Rotinat R, Wisnom M (2007) Identification of the orthotropic elastic stiffnesses of composites with the Virtual Fields Method: sensitivity study and experimental validation. Strain 43(3):250–259CrossRef
82.
Zurück zum Zitat ASTM D2344 / D2344M 00(2006). Standard test method for short-beam strength of polymer matrix composite materials and their laminates. ASTM International, West Conshohocken, PA, 2003, 2006. DOI: 10.1520/D2344_D2344M-00R06. ASTM D2344 / D2344M 00(2006). Standard test method for short-beam strength of polymer matrix composite materials and their laminates. ASTM International, West Conshohocken, PA, 2003, 2006. DOI: 10.1520/D2344_D2344M-00R06.
83.
Zurück zum Zitat Genovese K, Lamberti L, Pappalettere C (2004) A new hybrid technique for in-plane characterization of orthotropic materials. Exp Mech 44(6):584–592CrossRef Genovese K, Lamberti L, Pappalettere C (2004) A new hybrid technique for in-plane characterization of orthotropic materials. Exp Mech 44(6):584–592CrossRef
84.
Zurück zum Zitat Grédiac M, Pierron F (1998) A T-shaped specimen for the direct characterization of orthotropic materials. Int J Numer Meth Eng 41:293–309MATHCrossRef Grédiac M, Pierron F (1998) A T-shaped specimen for the direct characterization of orthotropic materials. Int J Numer Meth Eng 41:293–309MATHCrossRef
85.
Zurück zum Zitat Broughton WR, Sims GD (1994) An overview of through-thickness test methods for polymer matrix composites. Technical report, DMMA(A) 148, National Physics Laboratory, UK, 1994 Broughton WR, Sims GD (1994) An overview of through-thickness test methods for polymer matrix composites. Technical report, DMMA(A) 148, National Physics Laboratory, UK, 1994
86.
Zurück zum Zitat Mespoulet S (1998) Through-thickness test methods for laminated composite materials. PhD thesis, Imperial College of Science, Technology and Medecine Mespoulet S (1998) Through-thickness test methods for laminated composite materials. PhD thesis, Imperial College of Science, Technology and Medecine
87.
Zurück zum Zitat Broughton WR (2000) Mechanical testing of advanced fibre composites. Hodgkinson JM (ed) chapter 8. Through-thickness testing, pp 143–170. Woodhead Publishing, Delhi, India Broughton WR (2000) Mechanical testing of advanced fibre composites. Hodgkinson JM (ed) chapter 8. Through-thickness testing, pp 143–170. Woodhead Publishing, Delhi, India
88.
Zurück zum Zitat Pierron F, Zhavoronok S, Grédiac M (2000) Identification of the through-thickness properties of thick laminates using the virtual fields method. Int J Solids Struct 37(32):4437–4453MATHCrossRef Pierron F, Zhavoronok S, Grédiac M (2000) Identification of the through-thickness properties of thick laminates using the virtual fields method. Int J Solids Struct 37(32):4437–4453MATHCrossRef
89.
Zurück zum Zitat Moulart R, Avril S, Pierron F (2006) Identification of the through-thickness rigidities of a thick laminated composite tube. Compos Part A: Appl Sci Manuf 37(2):326–336CrossRef Moulart R, Avril S, Pierron F (2006) Identification of the through-thickness rigidities of a thick laminated composite tube. Compos Part A: Appl Sci Manuf 37(2):326–336CrossRef
90.
Zurück zum Zitat Pierron F (1998) Saint-Venant effects in the Iosipescu specimen. J Compos Mater 32(22):1986–2015CrossRef Pierron F (1998) Saint-Venant effects in the Iosipescu specimen. J Compos Mater 32(22):1986–2015CrossRef
91.
Zurück zum Zitat Pannier Y, Avril S, Rotinat R, Pierron F (2006) Identification of elasto-plastic constitutive parameters from statically undetermined tests using the virtual fields method. Exp Mech 46(6):735–755CrossRef Pannier Y, Avril S, Rotinat R, Pierron F (2006) Identification of elasto-plastic constitutive parameters from statically undetermined tests using the virtual fields method. Exp Mech 46(6):735–755CrossRef
92.
Zurück zum Zitat Nunio F, Aubert G, Berriaud C, Schild T, Védrine P (2008) Full resolution structural finite element analysis of the CEA/Iseult 11.75T MRI coil. IEEE Trans Appl Superconduct 18(2):916–919. art. no. 4497225 Nunio F, Aubert G, Berriaud C, Schild T, Védrine P (2008) Full resolution structural finite element analysis of the CEA/Iseult 11.75T MRI coil. IEEE Trans Appl Superconduct 18(2):916–919. art. no. 4497225
93.
Zurück zum Zitat Nunio F, Aubert G, Berriaud C, Schild T, Védrine P (2010) Mechanical design of the Iseult 11.7 T whole body MRI magnet. IEEE Trans Appl Superconduct 20(3):916–919. art. no. 5422888. Nunio F, Aubert G, Berriaud C, Schild T, Védrine P (2010) Mechanical design of the Iseult 11.7 T whole body MRI magnet. IEEE Trans Appl Superconduct 20(3):916–919. art. no. 5422888.
94.
Zurück zum Zitat Kim J-H, Nunio F, Pierron F, Védrine P (2010) Identification of the mechanical properties of superconducting windings using the Virtual Fields Method. IEEE Trans Appl Superconduct 20(3):1993–1997CrossRef Kim J-H, Nunio F, Pierron F, Védrine P (2010) Identification of the mechanical properties of superconducting windings using the Virtual Fields Method. IEEE Trans Appl Superconduct 20(3):1993–1997CrossRef
95.
Zurück zum Zitat Pierron F (2009) A novel method for measuring the through-thickness shear moduli of anisotropic plates from surface deformation measurements. Compos Part A: Appl Sci Manuf 40(12):1815–1825CrossRef Pierron F (2009) A novel method for measuring the through-thickness shear moduli of anisotropic plates from surface deformation measurements. Compos Part A: Appl Sci Manuf 40(12):1815–1825CrossRef
96.
Zurück zum Zitat Avril S, Feissel P, Pierron F, Villon P (2010) Comparison of two approaches for controlling the uncertainty in data differentiation: application to full-field measurements in solid mechanics. Meas Sci Technol 21(015703):11 Avril S, Feissel P, Pierron F, Villon P (2010) Comparison of two approaches for controlling the uncertainty in data differentiation: application to full-field measurements in solid mechanics. Meas Sci Technol 21(015703):11
97.
Zurück zum Zitat Kim J-H, Pierron F, Grédiac M, Wisnom M (2007) A procedure for producing reflective coatings on plates to be used for full-field slope measurements by a deflectometry technique. Strain 43(2):138–144CrossRef Kim J-H, Pierron F, Grédiac M, Wisnom M (2007) A procedure for producing reflective coatings on plates to be used for full-field slope measurements by a deflectometry technique. Strain 43(2):138–144CrossRef
98.
Zurück zum Zitat Kim J-H, Pierron F, Wisnom M, Syed-Muhammad K (2007) Identification of the local stiffness reduction of a damaged composite plate using the virtual fields method. Compos Part A: Appl Sci Manuf 38(9):2065–2075CrossRef Kim J-H, Pierron F, Wisnom M, Syed-Muhammad K (2007) Identification of the local stiffness reduction of a damaged composite plate using the virtual fields method. Compos Part A: Appl Sci Manuf 38(9):2065–2075CrossRef
99.
Zurück zum Zitat Lekhnitskii SG (1968) Anisotropic plates. Gordon and Breach Science, New York. Translated from the second Russian edition by Tsai SW and Cheron T Lekhnitskii SG (1968) Anisotropic plates. Gordon and Breach Science, New York. Translated from the second Russian edition by Tsai SW and Cheron T
100.
Zurück zum Zitat Tsai SW, Hahn HT (1980) Introduction to composite materials. Technomic Publishing Tsai SW, Hahn HT (1980) Introduction to composite materials. Technomic Publishing
101.
Zurück zum Zitat Grédiac M, Vautrin A, Verchery G (1993) A general method for data averaging of anisotropic elastic constants. J Appl Mech 60:614–618. Trans Am Soc Mech Eng Grédiac M, Vautrin A, Verchery G (1993) A general method for data averaging of anisotropic elastic constants. J Appl Mech 60:614–618. Trans Am Soc Mech Eng
102.
Zurück zum Zitat Grédiac M (1996) On the direct determination of invariant parameters governing the bending of anisotropic plates. Int J Solids Struct 33(27):3969–3982MATHCrossRef Grédiac M (1996) On the direct determination of invariant parameters governing the bending of anisotropic plates. Int J Solids Struct 33(27):3969–3982MATHCrossRef
103.
Zurück zum Zitat Bruno L, Furgiuele FM, Pagnotta L, Poggialini A (2002) A full-field approach for the elastic characterization of anisotropic materials. Opt Lasers Eng 37(4):417–431CrossRef Bruno L, Furgiuele FM, Pagnotta L, Poggialini A (2002) A full-field approach for the elastic characterization of anisotropic materials. Opt Lasers Eng 37(4):417–431CrossRef
104.
Zurück zum Zitat Avril S, Grédiac M, Pierron F, Surrel Y, Toussaint E (2004) Deflectometry and virtual fields for identification of static plate bending stiffnesses. In: Xth International Congress of the Society for Experimental Mechanics, Costa Mesa Avril S, Grédiac M, Pierron F, Surrel Y, Toussaint E (2004) Deflectometry and virtual fields for identification of static plate bending stiffnesses. In: Xth International Congress of the Society for Experimental Mechanics, Costa Mesa
105.
Zurück zum Zitat Grédiac M, Toussaint E, Pierron F (2003) Special virtual fields for the direct determination of material parameters with the virtual fields method. 3- Application to the bending rigidities of anisotropic plates. Int J Solids Struct 40:2401–2419MATHCrossRef Grédiac M, Toussaint E, Pierron F (2003) Special virtual fields for the direct determination of material parameters with the virtual fields method. 3- Application to the bending rigidities of anisotropic plates. Int J Solids Struct 40:2401–2419MATHCrossRef
106.
Zurück zum Zitat Syed Muhammad K, Toussaint E, Grédiac M, Avril S, Kim JH (2008) Characterization of composite plates using the Virtual Fields Method using optimized loading conditions. Compos Struct 85(1):70–82CrossRef Syed Muhammad K, Toussaint E, Grédiac M, Avril S, Kim JH (2008) Characterization of composite plates using the Virtual Fields Method using optimized loading conditions. Compos Struct 85(1):70–82CrossRef
107.
Zurück zum Zitat Kim J-H, Pierron F, Wisnom M, Avril S (2009) Local stiffness reduction in impacted composite plates from full-field measurements. Compos Part A: Appl Sci Manuf 40(12):1961–1974CrossRef Kim J-H, Pierron F, Wisnom M, Avril S (2009) Local stiffness reduction in impacted composite plates from full-field measurements. Compos Part A: Appl Sci Manuf 40(12):1961–1974CrossRef
108.
Zurück zum Zitat Grédiac M, Paris P-A (1996) Direct identification of elastic constants of anisotropic plates by modal analysis: theoretical and numerical aspects. J Sound Vibration 195(3):401–415CrossRef Grédiac M, Paris P-A (1996) Direct identification of elastic constants of anisotropic plates by modal analysis: theoretical and numerical aspects. J Sound Vibration 195(3):401–415CrossRef
109.
Zurück zum Zitat Swanson SR, Messick M, Toombes GR (1985) Comparison of torsion tube and Iosipescu in-plane shear test results for a carbon epoxy composite. Composites 16(3):220–224CrossRef Swanson SR, Messick M, Toombes GR (1985) Comparison of torsion tube and Iosipescu in-plane shear test results for a carbon epoxy composite. Composites 16(3):220–224CrossRef
110.
Zurück zum Zitat Ho H, Morton J, Farley GL (1993) Nonlinear numerical analysis of the Iosipescu specimen for composite materials. Compos Sci Technol 50(3):355–65CrossRef Ho H, Morton J, Farley GL (1993) Nonlinear numerical analysis of the Iosipescu specimen for composite materials. Compos Sci Technol 50(3):355–65CrossRef
111.
Zurück zum Zitat Ladevèze P, Le Dantec E (1992) Damage modeling of the elementary ply for laminated composites. Compos Sci Technol 43(3):257–267CrossRef Ladevèze P, Le Dantec E (1992) Damage modeling of the elementary ply for laminated composites. Compos Sci Technol 43(3):257–267CrossRef
112.
Zurück zum Zitat Grédiac M, Auslender F, Pierron F (2001) Using the virtual fields method to identify the through-thickness moduli of thick composites with a nonlinear shear response. Compos Part A: Appl Sci Manuf 32(12):1713–1725CrossRef Grédiac M, Auslender F, Pierron F (2001) Using the virtual fields method to identify the through-thickness moduli of thick composites with a nonlinear shear response. Compos Part A: Appl Sci Manuf 32(12):1713–1725CrossRef
113.
Zurück zum Zitat Périé JN, Leclerq H, Roux S, Hild F (2009) Digital image correlation and biawial test on composite material for anisotropic damage law identification. Int J Solids Struct 46:2388–2396MATHCrossRef Périé JN, Leclerq H, Roux S, Hild F (2009) Digital image correlation and biawial test on composite material for anisotropic damage law identification. Int J Solids Struct 46:2388–2396MATHCrossRef
114.
Zurück zum Zitat Claire D, Hild F, Roux S (2007) Identification of a damage law by using full-field displacement measurements. Int J Damage Mech 16(2):179–197CrossRef Claire D, Hild F, Roux S (2007) Identification of a damage law by using full-field displacement measurements. Int J Damage Mech 16(2):179–197CrossRef
115.
Zurück zum Zitat Crouzeix L, Périé JN, Collombet F, Douchin B (2009) An orthotropic variant of the equilibrium gap method applied to the analysis of a biaxial test on a composite material. Compos Part A: Appl Sci Manuf 40(11):1732–1740CrossRef Crouzeix L, Périé JN, Collombet F, Douchin B (2009) An orthotropic variant of the equilibrium gap method applied to the analysis of a biaxial test on a composite material. Compos Part A: Appl Sci Manuf 40(11):1732–1740CrossRef
116.
Zurück zum Zitat Kim J-H (2008) Identification of the local stiffness reduction of damaged composite plates using the virtual fields method. PhD thesis, Arts et Métiers ParisTech, 2008. www.lmpf.net. Kim J-H (2008) Identification of the local stiffness reduction of damaged composite plates using the virtual fields method. PhD thesis, Arts et Métiers ParisTech, 2008. www.​lmpf.​net.
117.
Zurück zum Zitat Moulart R, Pierron F, Hallett SR, Wisnom MR (2011) Full-field strain measurement and identification of mechanical properties at high strain rate. Exp Mech 51(4):509–536CrossRef Moulart R, Pierron F, Hallett SR, Wisnom MR (2011) Full-field strain measurement and identification of mechanical properties at high strain rate. Exp Mech 51(4):509–536CrossRef
118.
Zurück zum Zitat Pierron F, Green B, Wisnom MR, Hallett SR (2007) Full-field assessment of the damage process of laminated composite open-hole tensile specimens. Part II: experimental results. Compos Part A: Appl Sci Manuf 38:2321–2332CrossRef Pierron F, Green B, Wisnom MR, Hallett SR (2007) Full-field assessment of the damage process of laminated composite open-hole tensile specimens. Part II: experimental results. Compos Part A: Appl Sci Manuf 38:2321–2332CrossRef
Metadaten
Titel
Fiber Composites
verfasst von
Prof. Fabrice Pierron
Michel Grédiac
Copyright-Jahr
2012
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-1824-5_6

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