Results of many experimental and numerical studies indicate that, in unidirectionally reinforced composites, plastic deformations do not arise in tension along the reinforcing fibers. CFRPs and boron-aluminum composites with rectilinear fibers deform elastically up to fracture. However, unlike homogeneous materials, such composites deform plastically in hydrostatic loadings. In order to rationally reflect these features, this work proposes a plasticity model for, unidirectionally reinforced composites based on the concept of materials with imposed constraints. The yield criterion and the plasticity function derived do not depend on the normal stresses in areas perpendicular to fibers. For a composite with a hexagonal packing of fibers, a micromechanical simulation of the representative element is performed, and all material parameters of the model are determined. It is known that, with respect to the elastic properties, the equivalent homogeneous material for such composites is transversely isotropic. However, a micromechanical analysis showed that, for the characteristics of plasticity, the isotropy in the plane perpendicular to fibers is violated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Eksi and K. Genel, “Comparison of mechanical properties of unidirectional and woven carbon, glass and aramid fiber reinforced epoxy composites,” Acta Phys. Polonica A, 132, No. 3-II, 879-882 (2017).
M. R. Nedele and M. R. Wisnom, “Finite element micromechanical modelling of a unidirectional composite subjected to axial shear loading,” Composites, 25, No. 4, 263-272 (1994).
A. Wongsto and S. Li, “Micromechanical FE analysis of UD fibre-reinforced composites with fibres distributed at random over the transverse cross-section,” Composites: Part A, 36, 1246-1266 (2005).
X. Wanga, J. Zhang, Z. Wang, S. Zhou, and X. Sun, “Effects of interphase properties in unidirectional fiber reinforced composite material,” Mater. Des., 32, 3486-3492 (2011).
L. Yang, Y. Yan, Y. Liu, and Z. Ran, “Microscopic failure mechanisms of fiber-reinforced polymer composites under transverse tension and compression,” Compos. Sci. Technol., 72, 1818-1825 (2012).
L. Yang, Z. Wu, Y. Cao, and Y. Yan, “Micromechanical modelling and simulation of unidirectional fibre-reinforced composite under shear loading,” J. Reinf. Plast. Compos., 34, Iss. 1, 72-83 (2015).
R. Cai and T. Jin, “The effect of microstructure of unidirectional fibre-reinforced composites on mechanical properties under transverse loading: A review,” J. Reinf. Plast. Compos., 37, Iss. 22, 1360-1377 (2018).
T. Laux, K. W. Gan, J. M. Dulieu-Barton, and O. T. Thomsen, “A simple nonlinear constitutive model based on nonassociative plasticity for UD composites: development and calibration using a modified arcan fixture,” Int. J. Solids Struct. (2018). URL: doi: 10.1016/j.ijsolstr.2018.12.004 (ref. date 15.02.2021)
K. W. Gan, T. Laux, S. T. Taher, J. M. Dulieu-Barton, and O. T. Thomsen, “A novel fixture for determining the tension/compression-shear failure envelope of multidirectional composite laminates,” Compos. Struct., 184, 662-673 (2018).
W. Chen, Y. Liu, Z. Jiang, L. Tang, Z. Liu, and L. Zhou, “Modeling of compressive strength for unidirectional fiber reinforced composites with nanoparticle modified epoxy matrix,” Materials., 12, 3897 (2019).
S. G. Nagaraja, M. Pletz, and C. Schuecker, “Constitutive modeling of anisotropic plasticity with application to fiberreinforced composites,” Int. J. Solids Struct., 180-181, 84-96 (2019).
X. Wang, Z. Guan, S. Du, G. Han, and Z. Li, “An accurate and easy to implement method for predicting matrix crack and plasticity of composites with an efficient search algorithm for LaRC05 criterion,” Composites: Part A., 131, 10580 (2020).
L. Jia, L. Yu, K. Zhang, M. Li, Y. Jia, and B. R. K. Blackman, “Combined modelling and experimental studies of failure in thick laminates under out-of-plane shear,” Composites: Part B., 105, 8-22 (2016).
W. Tan and B. G. Falzon, “A crystal plasticity phenomenological model to capture the non-linear shear response of carbon fibre reinforced composites,” Int. J. Lightweight Materials and Manufacture, 4, 99-109 (2021).
A. I. Lurie, Nonlinear Theory of Elasticity [in Russian], Moscow, Nauka (1980).
A. Spencer, “Plasticity theory for fibre-reinforced composites,” J. Eng. Math., 26, 107-118 (1992).
J. Małachowski, G. L’vov, and S. Daryazadeh, “Numerical prediction of the parameters of a yield criterion for fibrous composites,” Mech. Compos. Mater., 53, No. 5, 589-600 (2017).
R. Hill, The Mathematical Theory of Plasticity, Oxford: Oxford Univ. Press (1950).
G. I. Lvov and O. A. Kostromitskaya, “Two-level computation of elastic characteristics of woven composites,” Mech. Compos. Mater., 54, No. 5, 577-590 (2018).
S. Darya Zadeh and G. I. Lvov, “Numerical procedure of determining the effective mechanical characteristics of an aligned fiber composite,” Strength Mater., 47, No. 4, 636-643 (2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Mekhanika Kompozitnykh Materialov, Vol. 57, No. 3, pp. 481-500, May-June, 2021.
Rights and permissions
About this article
Cite this article
Lvov, G.I. Using the Concept of Imposed Constraints in the Plasticity Theory of Composites. Mech Compos Mater 57, 337–348 (2021). https://doi.org/10.1007/s11029-021-09958-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11029-021-09958-x