Bridging Stress Modeling of Composite Materials Reinforced by Fibers Using Discrete Element Method
The problem of toughening in brittle materials
reinforced by fibers is complex, involving all of the mechanical
properties of fibers, matrix and the fiber/matrix interface, as well as
the geometry of the fiber. Development of new numerical methods
appropriate to toughening simulation and analysis is necessary. In
this work, we have performed simulations and analysis of toughening
in brittle matrix reinforced by randomly distributed fibers by means
of the discrete elements method. At first, we put forward a
mechanical model of toughening contributed by random fibers. Then
with a numerical program, we investigated the stress, damage and
bridging force in the composite material when a crack appeared in the
brittle matrix. From the results obtained, we conclude that: (i) fibers
of high strength and low elasticity modulus are beneficial to
toughening; (ii) fibers of relatively high elastic modulus compared to
the matrix may result in substantial matrix damage due to spalling
effect; (iii) employment of high-strength synthetic fibers is a good
option for toughening. We expect that the combination of the discrete
element method (DEM) with the finite element method (FEM) can
increase the versatility and efficiency of the software developed. The
present work can guide the design of ceramic composites of high
performance through the optimization of the parameters.
[1] C. Wang, L. F. Friedrich, “Computational model of effective fibers on
toughening in fiber reinforced composites at an early stage of crack
formation,” in Proc. 20th Annual International Conference on
Composites or Nano Engineering, Beijing, 2012.
[2] Y. Wang, V. C. Li, S. Backer, “Modelling of fibre pull-out from a
cement matrix,” Int. J. Cement Composites Lightweight Concrete, vol.
10, pp. 143-149, 1988.
[3] V. C. Li, Y. Wang, S. Backer, “A micromechanical model of tension
softening and bridging toughening of short random fiber reinforced
brittle matrix composites,” J. Mech. Phys. Solids, vol. 39, pp. 607- 625,
1991.
[4] V. C. Li, “A simplified micromechanical model of compressive strength
of fiber-reinforced cementitious composites,” Cement & Concrete
Composites, vol. 14, pp. 131-141, 1992.
[5] Z. Lin, V. C. Li, “Crack bridging in fiber reinforced cementitious
composites with slip-hardening interfaces,” J. Mech. Phys. Solids, vol.
45, pp. 763-787, 1997.
[6] X. Chen, I. J. Beyerlein, L. C. Brinson, “Bridged crack models for the
toughness of composites reinforced with curved nanotubes,” J. Mech.
Phys. Solids, vol.59, pp. 1938-1952, 2011.
[7] J. A. Mohandesi, A. Sangghaleh, A. Nazari, N. Pourjavad, “Analytical
modeling of strength in randomly oriented PP and PPTA short fiber
reinforced gypsum composites,” Computational Materials Science, vol.
50, pp. 1619-1624, 2011.
[8] J. D. Riera, “Local effects in impact problems on concrete structures,” in
Proc. Conference on Structural Analysis and Design of Nuclear Power
Plants, Porto Alegre, Brazil, 1984, Vol. 3, CDU
264.04:621.311.2:621.039.
[9] J. D. Riera, I. Iturrioz, “Discrete element dynamic response of
elastoplastic shells subjected to impulsive loading,” Communications in
Num. Meth. in Eng., vol. 11, pp. 417-426, 1995.
[10] J. D. Riera, I. Iturrioz, “Discrete element model for evaluating impact
and impulsive response of reinforced concrete plates and shells
subjected to impulsive loading,” Nuclear Engineering and Design, vol.
179, pp. 135-144, 1998.
[11] L. E. Kosteski, J. D. Riera, I. Iturrioz, R. K. Singh, T. Kant, “Analysis of
reinforced concrete plates subjected to impact employing the truss-like
discrete element method,” Fatigue & Fracture of Engineering Materials
& Structures, doi: 10.1111/ffe.12227, to be published.
[12] F. Schnaid, L. Spinelli, I. Iturrioz, M. Rocha, “Fracture mechanics in
ground improvement design,” Ground Improvement, vol. 8, pp. 7-15,
2004.
[13] L. F. F. Miguel, I. Iturrioz, J. D. Riera, “Size effects and mesh
independence in dynamic fracture analysis of brittle materials,”
Computer Methods Modeling in Engineering & Sciences, vol. 56, pp. 1-
16, 2010.
[14] L. A. Dalguer, K. Irikura, J. D. Riera, H. C. Chiu, HC, “The importance
of the dynamic source effects on strong ground motion during the 1999
Chi-Chi, Taiwan, earthquake: brief interpretation of the damage
distribution on buildings,” Bulletin of the Seismological Society of
America, vol. 91, pp. 1112-1127, 2001.
[15] A. Dalguer, K. Irikura, J. D. Riera, “Generations of New Cracks
Accompanied by Dynamic Shear Rupture Propagation of the 2000
Tottori (Japan), Earthquake,” Bulletin of the Seismological Society of
America, vol. 93, pp. 2236-2252, 2003.
[16] R. D. Rios, J. D. Riera, “Size effects in the analysis of reinforced
concrete structures,” Engineering Structures, vol. 26, pp.1115-1125,
2004.
[17] L. F. F. Miguel, J. D. Riera, I. Iturrioz, “Influence of size on the
constitutive equations of concrete or rock dowels,” International Journal
for Numerical and Analytical Methods in Geomechanics, vol. 32, pp.
1857-1881, 2008.
[18] I. Iturrioz, L. F. F. Miguel, J. D. Riera JD, “Dynamic fracture analysis of
concrete or rock plates by means of the Discrete Element Method,” Latin
American Journal of Solids and Structures, vol. 6, pp. 229-245, 2009.
[19] L. E. Kosteski, I. Iturrioz, R. G. Batista, A. P. Cisilino, “The truss-like
discrete element method in fracture and damage mechanics,”
Engineering Computations, vol. 28, pp. 765-787, 2011.
[20] L. E. Kosteski, R. L. Barrios D'Ambra, I. Iturrioz, “Crack propagation in
elastic solids using the truss-like discrete element method,” International
Journal of Fracture, vol. 174, pp. 139-161, 2012.
[21] R. L. Barrios D`Ambra, I. Iturrioz, H. Coceres, L. E. Kosteski, T. W.
Tech, A. Cisilino, “Cálculo del factor de intensidad de tensiones
utilizando el método de los elementos discretos,” Revista Sul-Americana
de Engenharia Estrutural, vol. 4, pp. 7-20, 2007.
[22] L. E. Kosteski, R. Barrios, I. Iturrioz, “Determinación de Parámetros
Fractomecánicos Estáticos y Dinámicos utilizando el Método de los
Elementos Discretos compuestos por barras,” Revista Internacional
Métodos numéricos para cálculo y diseño en ingeniería, vol. 24, pp.
323-343, 2008.
[23] L. E. Kosteski, R. Barrios, I. Iturrioz, “Fractomechanics parameter
calculus using the Discrete Element Method with bars,” Latin American
Journal of Solids and Structures, vol. 6, pp. 301-321, 2009.
[24] M. A. Caravaca, L. E. Kosteski, J. C. Miño, R. L. Barrios D'ambra, B.
Uberti, R. A. Casali, “Model for Vickers microhardness prediction
applied to SnO2 and TiO2 in the normal and high pressure phases,”
Journal of the European Ceramic Society, vol. 34, pp. 3791–3800, 2014.
[1] C. Wang, L. F. Friedrich, “Computational model of effective fibers on
toughening in fiber reinforced composites at an early stage of crack
formation,” in Proc. 20th Annual International Conference on
Composites or Nano Engineering, Beijing, 2012.
[2] Y. Wang, V. C. Li, S. Backer, “Modelling of fibre pull-out from a
cement matrix,” Int. J. Cement Composites Lightweight Concrete, vol.
10, pp. 143-149, 1988.
[3] V. C. Li, Y. Wang, S. Backer, “A micromechanical model of tension
softening and bridging toughening of short random fiber reinforced
brittle matrix composites,” J. Mech. Phys. Solids, vol. 39, pp. 607- 625,
1991.
[4] V. C. Li, “A simplified micromechanical model of compressive strength
of fiber-reinforced cementitious composites,” Cement & Concrete
Composites, vol. 14, pp. 131-141, 1992.
[5] Z. Lin, V. C. Li, “Crack bridging in fiber reinforced cementitious
composites with slip-hardening interfaces,” J. Mech. Phys. Solids, vol.
45, pp. 763-787, 1997.
[6] X. Chen, I. J. Beyerlein, L. C. Brinson, “Bridged crack models for the
toughness of composites reinforced with curved nanotubes,” J. Mech.
Phys. Solids, vol.59, pp. 1938-1952, 2011.
[7] J. A. Mohandesi, A. Sangghaleh, A. Nazari, N. Pourjavad, “Analytical
modeling of strength in randomly oriented PP and PPTA short fiber
reinforced gypsum composites,” Computational Materials Science, vol.
50, pp. 1619-1624, 2011.
[8] J. D. Riera, “Local effects in impact problems on concrete structures,” in
Proc. Conference on Structural Analysis and Design of Nuclear Power
Plants, Porto Alegre, Brazil, 1984, Vol. 3, CDU
264.04:621.311.2:621.039.
[9] J. D. Riera, I. Iturrioz, “Discrete element dynamic response of
elastoplastic shells subjected to impulsive loading,” Communications in
Num. Meth. in Eng., vol. 11, pp. 417-426, 1995.
[10] J. D. Riera, I. Iturrioz, “Discrete element model for evaluating impact
and impulsive response of reinforced concrete plates and shells
subjected to impulsive loading,” Nuclear Engineering and Design, vol.
179, pp. 135-144, 1998.
[11] L. E. Kosteski, J. D. Riera, I. Iturrioz, R. K. Singh, T. Kant, “Analysis of
reinforced concrete plates subjected to impact employing the truss-like
discrete element method,” Fatigue & Fracture of Engineering Materials
& Structures, doi: 10.1111/ffe.12227, to be published.
[12] F. Schnaid, L. Spinelli, I. Iturrioz, M. Rocha, “Fracture mechanics in
ground improvement design,” Ground Improvement, vol. 8, pp. 7-15,
2004.
[13] L. F. F. Miguel, I. Iturrioz, J. D. Riera, “Size effects and mesh
independence in dynamic fracture analysis of brittle materials,”
Computer Methods Modeling in Engineering & Sciences, vol. 56, pp. 1-
16, 2010.
[14] L. A. Dalguer, K. Irikura, J. D. Riera, H. C. Chiu, HC, “The importance
of the dynamic source effects on strong ground motion during the 1999
Chi-Chi, Taiwan, earthquake: brief interpretation of the damage
distribution on buildings,” Bulletin of the Seismological Society of
America, vol. 91, pp. 1112-1127, 2001.
[15] A. Dalguer, K. Irikura, J. D. Riera, “Generations of New Cracks
Accompanied by Dynamic Shear Rupture Propagation of the 2000
Tottori (Japan), Earthquake,” Bulletin of the Seismological Society of
America, vol. 93, pp. 2236-2252, 2003.
[16] R. D. Rios, J. D. Riera, “Size effects in the analysis of reinforced
concrete structures,” Engineering Structures, vol. 26, pp.1115-1125,
2004.
[17] L. F. F. Miguel, J. D. Riera, I. Iturrioz, “Influence of size on the
constitutive equations of concrete or rock dowels,” International Journal
for Numerical and Analytical Methods in Geomechanics, vol. 32, pp.
1857-1881, 2008.
[18] I. Iturrioz, L. F. F. Miguel, J. D. Riera JD, “Dynamic fracture analysis of
concrete or rock plates by means of the Discrete Element Method,” Latin
American Journal of Solids and Structures, vol. 6, pp. 229-245, 2009.
[19] L. E. Kosteski, I. Iturrioz, R. G. Batista, A. P. Cisilino, “The truss-like
discrete element method in fracture and damage mechanics,”
Engineering Computations, vol. 28, pp. 765-787, 2011.
[20] L. E. Kosteski, R. L. Barrios D'Ambra, I. Iturrioz, “Crack propagation in
elastic solids using the truss-like discrete element method,” International
Journal of Fracture, vol. 174, pp. 139-161, 2012.
[21] R. L. Barrios D`Ambra, I. Iturrioz, H. Coceres, L. E. Kosteski, T. W.
Tech, A. Cisilino, “Cálculo del factor de intensidad de tensiones
utilizando el método de los elementos discretos,” Revista Sul-Americana
de Engenharia Estrutural, vol. 4, pp. 7-20, 2007.
[22] L. E. Kosteski, R. Barrios, I. Iturrioz, “Determinación de Parámetros
Fractomecánicos Estáticos y Dinámicos utilizando el Método de los
Elementos Discretos compuestos por barras,” Revista Internacional
Métodos numéricos para cálculo y diseño en ingeniería, vol. 24, pp.
323-343, 2008.
[23] L. E. Kosteski, R. Barrios, I. Iturrioz, “Fractomechanics parameter
calculus using the Discrete Element Method with bars,” Latin American
Journal of Solids and Structures, vol. 6, pp. 301-321, 2009.
[24] M. A. Caravaca, L. E. Kosteski, J. C. Miño, R. L. Barrios D'ambra, B.
Uberti, R. A. Casali, “Model for Vickers microhardness prediction
applied to SnO2 and TiO2 in the normal and high pressure phases,”
Journal of the European Ceramic Society, vol. 34, pp. 3791–3800, 2014.
@article{"International Journal of Earth, Energy and Environmental Sciences:69687", author = "Chong Wang and Kellem M. Soares and Luis E. Kosteski", title = "Bridging Stress Modeling of Composite Materials Reinforced by Fibers Using Discrete Element Method", abstract = "The problem of toughening in brittle materials
reinforced by fibers is complex, involving all of the mechanical
properties of fibers, matrix and the fiber/matrix interface, as well as
the geometry of the fiber. Development of new numerical methods
appropriate to toughening simulation and analysis is necessary. In
this work, we have performed simulations and analysis of toughening
in brittle matrix reinforced by randomly distributed fibers by means
of the discrete elements method. At first, we put forward a
mechanical model of toughening contributed by random fibers. Then
with a numerical program, we investigated the stress, damage and
bridging force in the composite material when a crack appeared in the
brittle matrix. From the results obtained, we conclude that: (i) fibers
of high strength and low elasticity modulus are beneficial to
toughening; (ii) fibers of relatively high elastic modulus compared to
the matrix may result in substantial matrix damage due to spalling
effect; (iii) employment of high-strength synthetic fibers is a good
option for toughening. We expect that the combination of the discrete
element method (DEM) with the finite element method (FEM) can
increase the versatility and efficiency of the software developed. The
present work can guide the design of ceramic composites of high
performance through the optimization of the parameters.
", keywords = "Bridging stress, discrete element method, fiber
reinforced composites, toughening.", volume = "8", number = "11", pages = "782-6", }
