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Review
. 2018 Oct 9;11(10):1919.
doi: 10.3390/ma11101919.

Analytical Micromechanics Models for Elastoplastic Behavior of Long Fibrous Composites: A Critical Review and Comparative Study

Yanchao Wang  1 , ZhengMing Huang  2
Affiliations
Review

Analytical Micromechanics Models for Elastoplastic Behavior of Long Fibrous Composites: A Critical Review and Comparative Study

Yanchao Wang et al. Materials (Basel). .

Abstract

Elasto-plastic models for composites can be classified into three categories in terms of a length scale, i.e., macro scale, meso scale, and micro scale (micromechanics) models. In general, a so-called multi-scale model is a combination of those at various length scales with a micromechanics one as the foundation. In this paper, a critical review is made for the elastoplastic models at the micro scale, and a comparative study is carried out on most popular analytical micromechanics models for the elastoplastic behavior of long fibrous composites subjected to a static load, meaning that creep and dynamic response are not concerned. Each model has been developed essentially following three steps, i.e., an elastic homogenization, a rule to define the yielding of a constituent phase, and a linearization for the elastoplastic response. The comparison is made for all of the three aspects. Effects of other issues, such as the stress field fluctuation induced by a high contrast heterogeneity, the stress concentration factors in the matrix, and the different approaches to a plastic Eshelby tensor, are addressed as well. Correlation of the predictions by different models with available experimental data is shown.

Keywords: analytical models; elastoplastic behavior; fibrous composites; micromechanics.

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Conflict of interest statement

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

Figures

Figure 1
Figure 1
Schematic of a multi-scale framework: (a) macro-scale model; (b) meso-scale model; (c) micro-scale model.
Figure 2
Figure 2
Schematic of a representative volume element RVE and a repeating unit cell (RUC) (solid line-undeformed, dash line-deformed). (a) An RVE for a unidirectional (UD) composite with randomly distributed fibers; (b) an RUC for a UD composite with periodically distributed fibers.
Figure 3
Figure 3
Establishment of elastoplastic models for composites.
Figure 4
Figure 4
Imperfect interface phenomenon in fibrous composites. (a) Crack growth in a SiC/SiC woven composite under cyclic load [242]; (b) Ear-hole formation in a SiC/Ti-6Al-4V composite [243]; (c) Interphase produced by chemical reaction in a SiC/Ti-6Al-4V composite [244]; (d) BN coated T300 fiber [245].
Figure 5
Figure 5
Schematic of an RUC for a UD composite.
Figure 6
Figure 6
Schematic of a multi-fiber model and a single fiber model. (a) Multi-fiber model; (b) single fiber model.
Figure 7
Figure 7
Schematic for generalized self-consistent method (GSCM).
Figure 8
Figure 8
Illustration of a typical elastoplastic stress-strain curve.
Figure 9
Figure 9
Comparison between elastoplastic models (IM7/8551-7 UD composite). (a) Transverse compression; (b) In-plane shear.
Figure 10
Figure 10
Comparison between elastoplastic models (E-Glass/Epoxy UD composite). (a) Transverse compression; (b) In-plane shear.
Figure 11
Figure 11
Comparison between elastoplastic models (AS4/Peek UD composite). (a) 30° off-axis tension; (b) 45° off-axis tension; (c) 60° off-axis tension.
Figure 12
Figure 12
Short fiber reinforced polyamide composite under uniaxial tension [280]. (a) Longitudinal tension; (b) Transverse tension.
Figure 13
Figure 13
Finite element analysis (FEA) strain contour for short fiber reinforced polyamide composite [280].
Figure 14
Figure 14
Comparison between the first and second-moment approach. (a) Ceramic reinforced aluminum composite (aspect ratio = 1, plastic parameter n = 0.05); (b) Ceramic reinforced aluminum composite (aspect ratio = 3, plastic parameter n = 0.05); (c) Ceramic reinforced aluminum composite (aspect ratio = 3, plastic parameter n = 0.4); (d) two-phase steel with martensite inclusions (aspect ratio = 3, plastic parameter n = 0.31).
Figure 15
Figure 15
Comparison of models with/without stress concentration factors (SCFs)—IM7/8551-7 UD composite. (a) Transverse compression; (b) In-plane shear.
Figure 16
Figure 16
Comparison of models with/without stress concentration factors (SCFs)—E-glass/Epoxy UD composite. (a) Transverse compression; (b) In-plane shear.
Figure 17
Figure 17
Comparison of models with/without SCFs—AS4/Peek UD composite. (a) 30° Off-axis tension; (b) 45° Off-axis tension; (c) 60° Off-axis tension.
Figure 17
Figure 17
Comparison of models with/without SCFs—AS4/Peek UD composite. (a) 30° Off-axis tension; (b) 45° Off-axis tension; (c) 60° Off-axis tension.
Figure 18
Figure 18
Schematic of linearization theories.
Figure 19
Figure 19
Schematic of the incremental-secant linearization [112].
Figure 20
Figure 20
Comparison among linearizations–IM7/8551-7 UD composite. (a) Transverse compression; (b) In-plane shear.
Figure 21
Figure 21
Comparison among linearizations–E-Glass/Epoxy UD composite. (a) Transverse compression; (b) In plane shear.
Figure 22
Figure 22
Comparison among linearizations–AS4/Peek UD composite. (a) 30° off-axis tension; (b) 45° off-axis tension; (c) 60° off-axis tension.
Figure 23
Figure 23
Comparison among the four approaches to determine an Eshelby tensor. (a) Longitudinal tension—(IM7/8551-7 UD composites); (b) Transverse compression—(IM7/8551-7 UD composites); (c) In-plane shear—(IM7/8551-7 UD composites); (d) 30° off-axis tension—(AS4/Peek UD composite); (e) 45° off-axis tension—(AS4/Peek UD composite); (f) 60° off-axis tension—(AS4/Peek UD composite).
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