Failure of Composite Materials by Kink Band Formation
Nøgleord:
Kink band formation, Localisation, Plasticity, Propagating instability, Instabilitiy, Fibre compositesSynopsis
Fibre-reinforced composites and layered materials have a heterogeneous composition of two or more constituents and have anisotropic material behaviour. This heterogeneous structure enables numerous failure mechanisms. One of the dominant compressive failure mechanisms of the latter composites is composed of so-called kink bands. These are bands of material where the fibres inside the band have rotated relative to the fibres outside.
This dissertation mainly concerns the examination of kink band formation in fibre composites and layered materials using several different methodologies. Five publications on the latter topic have arisen based on the work done in this project. The four introductory chapters in the dissertation are devoted to explanations and elaborations of the methods used and developed during the project. Several finite element models are developed specifically to examine either the peak strength of the composite or the post-buckling kink band behaviour. Two novel constitutive formulations are developed that can be used in a general framework to investigate the elastic-plastic behaviour of composites, including the study of kink bands.
The following results and conclusions are drawn from the project results. Compressive kinking strength is affected by:
• Fibre-misalignments
• Insufficient fibre-to-matrix bonding
• Matrix yield strength
• Multi-axial loading
The stress at steady-state kink band broadening can be seen as the lower bound of the compressive strength and is lowered by:
• Increasing band inclinations to a certain limit
• Decreasing matrix Poisson’s ratio
• Decreasing maximum tangent modulus of the matrix
As part of my visit to the Department of Engineering at the University of Cambridge, contributions are made to the field of joint mechanics, particular regarding composites made from ultra-high molecular weight polyethylene. The latter study is a secondary focus of this dissertation. The research questions, problems, methodologies, results and conclusions appear in an attached article.
Referencer
Argon, A. S. (1972). Fracture of composites, volume 1. ACADEMIC PRESS, INC.
Ashby, M., Evans, T., Fleck, N., Hutchinson, J., Wadley, H., and Gibson, L. (2000). Metal
Foams: A Design Guide. Elsevier Science.
Attwood, J. P., Fleck, N. A.,Wadley, H. N. G., and Deshpande, V. S. (2015). The compressive
response of ultra-high molecular weight polyethylene fibres and composites. International
Journal of Solids and Structures, 71:141–155.
Beuth, J. L. (1992). Cracking of thin bonded films in residual tension. International Journal
of Solids and Structures, 29(13):1657–1675.
Budiansky, B. (1983). Micromechanics. Computers & Structures, 16(1-4):3–12.
Budiansky, B. and Fleck, N. (1993). Compressive failure of fibre composites. Journal of the
Mechanics and Physics of Solids, 41(I):183–211.
Chater, E. and Hutchinson, J. W. (1984). On the Propagation of Bulges and Buckles. Journal
of Applied Mechanics.
Christoffersen, J. and Jensen, H. M. (1996). Kink band analysis accounting for the microstructure
of fiber reinforced materials. Mechanics of Materials, 24(4):305–315.
Corneliussen, A. H. and Shield, R. T. (1961). Finite deformation of elastic membranes
with application to the stability of an inflated and extended tube. Archive for Rational
Mechanics and Analysis, 7(1):273–304.
Ericksen, J. L. (1975). Equilibrium of bars. Journal of Elasticity, 5(3):191–201.
Evans, A. G. and Adler, W. F. (1978). Kinking as a mode of structural degradation in carbon
fiber composites. Acta Metallurgica, 26(5):725–738.
Fleck, N. (1997). Compressive failure of fibre composites.
Fleck, N. A. and Budiansky, B. (1991). Compressive failure of fibre composites due to
microbuckling. Proc. 3rd Symp. on Inelastic Deformation of Composite Materials, pages
235–273.
Fleck, N. A. and Shu, J. Y. (1995). Microbuckle initiation in fibre composites : A finite
element study. Journal of the Mechanics and Physics of Solids, 43(12):1887–1918.
Guggenheim, E. A. (1959). Thermodynamics, Classical and Statistical, pages 1–118.
Springer Berlin Heidelberg, Berlin, Heidelberg.
Hsu, S.-Y., Vogler, T., and Kyriakides, S. (1999). On the axial propagation of kink bands
in fiber composites : Part II analysis. International Journal of Solids and Structures,
36:575–595.
Hsu, S.-Y., Vogler, T. J., and Kyriakides, S. (1998). Compressive Strength Predictions for
Fiber Composites. Journal of Applied Mechanics, 65(1):7.
Huang, Z.-M. (2018). On micromechanics approach to stiffness and strength of unidirectional
composites. Journal of Reinforced Plastics and Composites, page 073168441881193.
Hutchinson, J. W. and Koiter, W. T. (1970). Postbuckling theory. Applied mechanics reviews,
23(12):1353–1366.
Hutchinson, J. W. and Neale, K. W. (1978). Sheet Necking-II. Time-Independent Behavior.
Hutchinson, J. W. and Neale, K. W. (1983). Neck propagation. Journal of the Mechanics
and Physics of Solids, 31(5):405–426.
Hutchinson, J.W. and Suo, Z. (1991). Mixed Mode Cracking in Layered Materials. Advances
in Applied Mechanics.
Jäger, J., Sause, M. G., Burkert, F., Moosburger-Will, J., Greisel, M., and Horn, S. (2015).
Influence of plastic deformation on single-fiber push-out tests of carbon fiber reinforced
epoxy resin. Composites Part A: Applied Science and Manufacturing, 71:157–167.
Jensen, H. M. (1988). Collapse of hydrostatically loaded cylindrical shells. International
Journal of Solids and Structures, 24(1):51 – 64.
Jensen, H. M. (1999a). Analysis of compressive failure of layered materials by kink band
broadening. International Journal of Solids and Structures, 36(23):3427–3441.
Jensen, H. M. (1999b). Models of failure in compression of layered materials. Mechanics of
Materials, 31:553–564.
Jensen, H. M. and Christoffersen, J. (1997). Kink band formation in fiber reinforced materials.
Journal of the Mechanics and Physics of Solids, 45(7):1121–1136.
Jensen, H. M. and Thouless, M. D. (1995). Buckling Instability of Straight Edge Cracks.
Journal of Applied Mechanics, 62(3):620–625.
Ji, W., Waas, A. M., and Bazant, Z. P. (2013). On the Importance of Work-Conjugacy and
Objective Stress Rates in Finite Deformation Incremental Finite Element Analysis. Journal
of Applied Mechanics, 80(4):041024.
Jones, R. (1975). Mechanics of Composite Materials. International student edition. Scripta
Book Company.
Kyriakides, S. (1993). Propagating Instabilities in Structures. Advances in Applied Mechanics,
30:67 – 189.
Kyriakides, S. (1998). Propagating Instabilities in Solids. APS March Meeting Abstracts.
Kyriakides, S., Arseculeratne, R., Perry, E. J., and Liechti, K. M. (1995). On the compressive
failure of fiber reinforced composites. International Journal of Solids and Structures,
32(6-7):689–738.
Kyriakides, S. and Yu-Chung, C. (1991). The initiation and propagation of a localized
instability in an inflated elastic tube. International Journal of Solids and Structures,
27(9):1085 – 1111.
Lager, J. R. and June, R. R. (1969). Compressive Strength of Boron-Epoxy Composites.
Journal of Composite Materials, 6:48–56.
Liu, G., Thouless, M. D., Deshpande, V. S., and Fleck, N. A. (2014). Collapse of a composite
beam made from ultra high molecular-weight polyethylene fibres. Journal of the Mechanics
and Physics of Solids, 63(1):320–335.
Liu, X. H., Moran, P. M., and Shih, C. F. (1996). The mechanics of compressive kinking in
unidirectional fiber reinforced ductile matrix composites. Composites Part B: Engineering,
27(6 SPEC. ISS.):553–560.
Mesloh, R. E., Sorenson, J. E., and Atterbury, T. J. (1973). Buckling–and offshore pipelines.
Gas, 49(7):40 – 43.
Moran, P. M., Liu, X. H., and Shih, C. F. (1995). Kink band formation and band broadening in
fiber composites under compressive loading. Acta Metallurgica Et Materialia, 43(8):2943–
2958.
Naya, F., Herraez, M., Gonzalez, C., Lopes, C., der Veen, S. V., and Pons, F. (2017).
Computational micromechanics of fiber kinking in unidirectional FRP under different
environmental conditions. Composites Science and Technology, 144:26–35.
Nizolek, T., Begley, M., McCabe, R., Avallone, J., Mara, N., Beyerlein, I., and Pollock, T.
(2017). Strain fields induced by kink band propagation in Cu-Nb nanolaminate composites.
Acta Materialia, 133:303–315.
Palmer, A. C. and Martin, J. H. (1972). Buckle propagation in submarine pipelines. Nature,
254:46 – 48.
Paterson, M. S. and Weiss, L. E. (1966). Experimental deformation and folding in phyllite.
Bulletin of the Geological Society of America, 77(4):343–374.
Poulios, K. and Niordson, C. F. (2016). Homogenization of long fiber reinforced composites
including fiber bending effects. Journal of the Mechanics and Physics of Solids, 94:433–
452.
Prabhakar, P. and Waas, A. M. (2013). Interaction between kinking and splitting in the
compressive failure of unidirectional fiber reinforced laminated composites. Composite
Structures, 98:85–92.
Rice, J. R. (1976). The Localization of plastic deformation. Theoretical and Applied
Mechanics, pages 207–220.
Rosen, B. W. (1965). Mechanics of composite strengthening. Fiber Composite Seminar of
the American Society for Metals, pages 37–75.
Sammis, C. G. and Ashby, M. F. (1986). The failure of brittle porous solids under compressive
stress states. Acta Metallurgica, 34(3):511–526.
Schreyer, S. L. and Masur, E. F. (1966). Buckling of shallow arches. Journal of the
Engineering Mechanics Division, 92:1 – 20.
Shaffer, G. D. (2006). An Archaeomagnetic Study of a Wattle and Daub Building Collapse.
Journal of Field Archaeology.
Skovsgaard, S. P. H. and Jensen, H. M. (2018a). Constitutive model for imperfectly bonded
fibre-reinforced composites. Composite Structures, 192(February):82–92.
Skovsgaard, S. P. H. and Jensen, H. M. (2018b). International Journal of Solids and Structures
Three-dimensional constitutive model for elastic-plastic behaviour of fibre-reinforced
composites. International Journal of Solids and Structures, 139-140:150–162.
Skovsgaard, S. P. H. and Jensen, H. M. (2018c). Steady-State Kink Band Propagation in
Layered Materials. Journal of Applied Mechanics, 85(6):061005.
Skovsgaard, S. P. H. and Jensen, H. M. (2019). A general approach for the study of kink band
broadening in fibre composites and layered materials. European Journal of Mechanics -
A/Solids, 74(September 2018):394–402.
Slaughter, W. S., Fleck, N. A., and Budiansky, B. (1993). Compressive failure of fibre
composites: the roles of multi-axial loading and creep. Journal of Engineering Materials
and Technology, 115(3):308 – 313.
Sørensen, K. D., Mikkelsen, L. P., and Jensen, H. M. (2009). User subroutine for compressive
failure of composites. 2009 Simulia Customer Conference, (1965):618–632.
Sutcliffe, M. and Fleck, N. (1997). Microbuckle propagation in fibre composites. Acta
Materialia, 45(3):921–932.
Timoshenko, S. and Young, D. (1962). Elements of Strength of Materials. Fourth Edition. D.
Van Nostrand Company.
Tojaga, V., Skovsgaard, S. P. H., and Jensen, H. M. (2018). Micromechanics of kink band
formation in open-hole fi bre composites under compressive loading. Composites Part B,
149(March):66–73.
Vogler, T. and Kyriakides, S. (1997). Initiation and axial propagation of kink bands in fiber
composites. Acta Materialia, 45(6):2443–2454.
Wind, J. L., Steffensen, S., and Jensen, H. M. (2014). Comparison of a composite model and
an individually fiber and matrix discretized model for kink band formation. International
Journal of Non-Linear Mechanics, 67:319–325.
Ashby, M., Evans, T., Fleck, N., Hutchinson, J., Wadley, H., and Gibson, L. (2000). Metal
Foams: A Design Guide. Elsevier Science.
Attwood, J. P., Fleck, N. A.,Wadley, H. N. G., and Deshpande, V. S. (2015). The compressive
response of ultra-high molecular weight polyethylene fibres and composites. International
Journal of Solids and Structures, 71:141–155.
Beuth, J. L. (1992). Cracking of thin bonded films in residual tension. International Journal
of Solids and Structures, 29(13):1657–1675.
Budiansky, B. (1983). Micromechanics. Computers & Structures, 16(1-4):3–12.
Budiansky, B. and Fleck, N. (1993). Compressive failure of fibre composites. Journal of the
Mechanics and Physics of Solids, 41(I):183–211.
Chater, E. and Hutchinson, J. W. (1984). On the Propagation of Bulges and Buckles. Journal
of Applied Mechanics.
Christoffersen, J. and Jensen, H. M. (1996). Kink band analysis accounting for the microstructure
of fiber reinforced materials. Mechanics of Materials, 24(4):305–315.
Corneliussen, A. H. and Shield, R. T. (1961). Finite deformation of elastic membranes
with application to the stability of an inflated and extended tube. Archive for Rational
Mechanics and Analysis, 7(1):273–304.
Ericksen, J. L. (1975). Equilibrium of bars. Journal of Elasticity, 5(3):191–201.
Evans, A. G. and Adler, W. F. (1978). Kinking as a mode of structural degradation in carbon
fiber composites. Acta Metallurgica, 26(5):725–738.
Fleck, N. (1997). Compressive failure of fibre composites.
Fleck, N. A. and Budiansky, B. (1991). Compressive failure of fibre composites due to
microbuckling. Proc. 3rd Symp. on Inelastic Deformation of Composite Materials, pages
235–273.
Fleck, N. A. and Shu, J. Y. (1995). Microbuckle initiation in fibre composites : A finite
element study. Journal of the Mechanics and Physics of Solids, 43(12):1887–1918.
Guggenheim, E. A. (1959). Thermodynamics, Classical and Statistical, pages 1–118.
Springer Berlin Heidelberg, Berlin, Heidelberg.
Hsu, S.-Y., Vogler, T., and Kyriakides, S. (1999). On the axial propagation of kink bands
in fiber composites : Part II analysis. International Journal of Solids and Structures,
36:575–595.
Hsu, S.-Y., Vogler, T. J., and Kyriakides, S. (1998). Compressive Strength Predictions for
Fiber Composites. Journal of Applied Mechanics, 65(1):7.
Huang, Z.-M. (2018). On micromechanics approach to stiffness and strength of unidirectional
composites. Journal of Reinforced Plastics and Composites, page 073168441881193.
Hutchinson, J. W. and Koiter, W. T. (1970). Postbuckling theory. Applied mechanics reviews,
23(12):1353–1366.
Hutchinson, J. W. and Neale, K. W. (1978). Sheet Necking-II. Time-Independent Behavior.
Hutchinson, J. W. and Neale, K. W. (1983). Neck propagation. Journal of the Mechanics
and Physics of Solids, 31(5):405–426.
Hutchinson, J.W. and Suo, Z. (1991). Mixed Mode Cracking in Layered Materials. Advances
in Applied Mechanics.
Jäger, J., Sause, M. G., Burkert, F., Moosburger-Will, J., Greisel, M., and Horn, S. (2015).
Influence of plastic deformation on single-fiber push-out tests of carbon fiber reinforced
epoxy resin. Composites Part A: Applied Science and Manufacturing, 71:157–167.
Jensen, H. M. (1988). Collapse of hydrostatically loaded cylindrical shells. International
Journal of Solids and Structures, 24(1):51 – 64.
Jensen, H. M. (1999a). Analysis of compressive failure of layered materials by kink band
broadening. International Journal of Solids and Structures, 36(23):3427–3441.
Jensen, H. M. (1999b). Models of failure in compression of layered materials. Mechanics of
Materials, 31:553–564.
Jensen, H. M. and Christoffersen, J. (1997). Kink band formation in fiber reinforced materials.
Journal of the Mechanics and Physics of Solids, 45(7):1121–1136.
Jensen, H. M. and Thouless, M. D. (1995). Buckling Instability of Straight Edge Cracks.
Journal of Applied Mechanics, 62(3):620–625.
Ji, W., Waas, A. M., and Bazant, Z. P. (2013). On the Importance of Work-Conjugacy and
Objective Stress Rates in Finite Deformation Incremental Finite Element Analysis. Journal
of Applied Mechanics, 80(4):041024.
Jones, R. (1975). Mechanics of Composite Materials. International student edition. Scripta
Book Company.
Kyriakides, S. (1993). Propagating Instabilities in Structures. Advances in Applied Mechanics,
30:67 – 189.
Kyriakides, S. (1998). Propagating Instabilities in Solids. APS March Meeting Abstracts.
Kyriakides, S., Arseculeratne, R., Perry, E. J., and Liechti, K. M. (1995). On the compressive
failure of fiber reinforced composites. International Journal of Solids and Structures,
32(6-7):689–738.
Kyriakides, S. and Yu-Chung, C. (1991). The initiation and propagation of a localized
instability in an inflated elastic tube. International Journal of Solids and Structures,
27(9):1085 – 1111.
Lager, J. R. and June, R. R. (1969). Compressive Strength of Boron-Epoxy Composites.
Journal of Composite Materials, 6:48–56.
Liu, G., Thouless, M. D., Deshpande, V. S., and Fleck, N. A. (2014). Collapse of a composite
beam made from ultra high molecular-weight polyethylene fibres. Journal of the Mechanics
and Physics of Solids, 63(1):320–335.
Liu, X. H., Moran, P. M., and Shih, C. F. (1996). The mechanics of compressive kinking in
unidirectional fiber reinforced ductile matrix composites. Composites Part B: Engineering,
27(6 SPEC. ISS.):553–560.
Mesloh, R. E., Sorenson, J. E., and Atterbury, T. J. (1973). Buckling–and offshore pipelines.
Gas, 49(7):40 – 43.
Moran, P. M., Liu, X. H., and Shih, C. F. (1995). Kink band formation and band broadening in
fiber composites under compressive loading. Acta Metallurgica Et Materialia, 43(8):2943–
2958.
Naya, F., Herraez, M., Gonzalez, C., Lopes, C., der Veen, S. V., and Pons, F. (2017).
Computational micromechanics of fiber kinking in unidirectional FRP under different
environmental conditions. Composites Science and Technology, 144:26–35.
Nizolek, T., Begley, M., McCabe, R., Avallone, J., Mara, N., Beyerlein, I., and Pollock, T.
(2017). Strain fields induced by kink band propagation in Cu-Nb nanolaminate composites.
Acta Materialia, 133:303–315.
Palmer, A. C. and Martin, J. H. (1972). Buckle propagation in submarine pipelines. Nature,
254:46 – 48.
Paterson, M. S. and Weiss, L. E. (1966). Experimental deformation and folding in phyllite.
Bulletin of the Geological Society of America, 77(4):343–374.
Poulios, K. and Niordson, C. F. (2016). Homogenization of long fiber reinforced composites
including fiber bending effects. Journal of the Mechanics and Physics of Solids, 94:433–
452.
Prabhakar, P. and Waas, A. M. (2013). Interaction between kinking and splitting in the
compressive failure of unidirectional fiber reinforced laminated composites. Composite
Structures, 98:85–92.
Rice, J. R. (1976). The Localization of plastic deformation. Theoretical and Applied
Mechanics, pages 207–220.
Rosen, B. W. (1965). Mechanics of composite strengthening. Fiber Composite Seminar of
the American Society for Metals, pages 37–75.
Sammis, C. G. and Ashby, M. F. (1986). The failure of brittle porous solids under compressive
stress states. Acta Metallurgica, 34(3):511–526.
Schreyer, S. L. and Masur, E. F. (1966). Buckling of shallow arches. Journal of the
Engineering Mechanics Division, 92:1 – 20.
Shaffer, G. D. (2006). An Archaeomagnetic Study of a Wattle and Daub Building Collapse.
Journal of Field Archaeology.
Skovsgaard, S. P. H. and Jensen, H. M. (2018a). Constitutive model for imperfectly bonded
fibre-reinforced composites. Composite Structures, 192(February):82–92.
Skovsgaard, S. P. H. and Jensen, H. M. (2018b). International Journal of Solids and Structures
Three-dimensional constitutive model for elastic-plastic behaviour of fibre-reinforced
composites. International Journal of Solids and Structures, 139-140:150–162.
Skovsgaard, S. P. H. and Jensen, H. M. (2018c). Steady-State Kink Band Propagation in
Layered Materials. Journal of Applied Mechanics, 85(6):061005.
Skovsgaard, S. P. H. and Jensen, H. M. (2019). A general approach for the study of kink band
broadening in fibre composites and layered materials. European Journal of Mechanics -
A/Solids, 74(September 2018):394–402.
Slaughter, W. S., Fleck, N. A., and Budiansky, B. (1993). Compressive failure of fibre
composites: the roles of multi-axial loading and creep. Journal of Engineering Materials
and Technology, 115(3):308 – 313.
Sørensen, K. D., Mikkelsen, L. P., and Jensen, H. M. (2009). User subroutine for compressive
failure of composites. 2009 Simulia Customer Conference, (1965):618–632.
Sutcliffe, M. and Fleck, N. (1997). Microbuckle propagation in fibre composites. Acta
Materialia, 45(3):921–932.
Timoshenko, S. and Young, D. (1962). Elements of Strength of Materials. Fourth Edition. D.
Van Nostrand Company.
Tojaga, V., Skovsgaard, S. P. H., and Jensen, H. M. (2018). Micromechanics of kink band
formation in open-hole fi bre composites under compressive loading. Composites Part B,
149(March):66–73.
Vogler, T. and Kyriakides, S. (1997). Initiation and axial propagation of kink bands in fiber
composites. Acta Materialia, 45(6):2443–2454.
Wind, J. L., Steffensen, S., and Jensen, H. M. (2014). Comparison of a composite model and
an individually fiber and matrix discretized model for kink band formation. International
Journal of Non-Linear Mechanics, 67:319–325.
Downloads
Publiceret
5 september 2019
Serier
Kategorier
Detaljer om denne monografi
ISBN-13 (15)
978-87-7507-456-3
