On Micro-Buckling of Unidirectional Fiber-Reinforced Composites by Means of Computational Micromechanics

Abstract

Micro-buckling of unidirectional fiber-reinforced composites is investigated in this paper by means of an explicit representation of a geometrically imperfect fiber within the context of kinematical and material non-linear behavior. Two types of fiber imperfections are considered: a helicoidal shape, identified as 3D imperfection; and a sinusoidal plane shape (2D imperfection). Both imperfection models are characterized by a maximum misalignment angle of the fiber with respect to the ideal or perfect configuration, as is usually considered in this field. A total of 816 cases were computed in terms of imperfection type (either 2D or 3D), fiber volume fraction, fiber arrangement (square or hexagonal array), orientation for 2D models, matrix yield stress, and misalignment angle. Two load cases, with constrained and unconstrained transverse strain, were considered. Assuming periodic boundary conditions, homogenization was carried out to obtain macroscopic stresses. Numerical results are compared with an analytical model available in the literature. The results show a high imperfection-sensitivity for small misalignment angles; on the other hand, the type of imperfection and the fiber arrangement do not have a large influence on the results. In addition, it was found that this problem is governed by fiber volume fraction and matrix yield stress only for small imperfections, whereas for large misalignment angles, a change in fiber volume fraction produces small changes in micro-buckling stress. column which is laterally supported on an elastic matrix. This problem has attracted a number of researchers, starting from the pioneer work of Rosen (1965). There are two general ways in which such instability can occur: either due to elastic buckling of the fiber involving deformations of the matrix (a problem which is usually called micro-buckling), or by plastic deformations (called kinking), as reported by Budiansky and Fleck (1993). Comparison between both modes has been made by Sun and Tsai (2001) among others: both are seen to be different problems and involve different assumptions; however, these authors concluded that the loads (stress fields) found at buckling or kinking are not very different.Micro-buckling may occur in mainly two modes: in a periodic (or "in-phase") mode there are periodic deformations of the fibers and shear of the matrix but no significant transverse deformation occurs. Micro-buckling can also occur in a non-periodic (or "out-of-phase") mode, in which shear is negligible and buckling is dominated by transverse deformations, much in the form of a beam on an elastic foundation. Both cases were discussed by Rosen (1965) and were reviewed in the classical text by Jones (1975). Regarding stability of the post-critical path, Maewal (1981) anticipated a stable post-buckling behavior for the in-phase problem. On the other hand, Yurgartis and Sternstein (1994) performed tests that showed the detrimental influence of fiber misalignment on the microbuckling process, a behavior that is typical of uns...

A Review on Mechanical Performance of Hybrid Natural Fiber Polymer Composites for Structural Applications

“…Microbuckling refers to the buckling of the fibers involving transverse displacement under compression in the direction of the 3cdevg [ 117 ]. The microbuckling of fiber composite laminates initiates at the open hole, and this microbuckle grows from the edge of the hole [ 118 ].…”

Micromechanical analysis of longitudinal and shear strength of composite laminae

“…Barulich et al. 14 included 3 D misalignment, concluding that the 2 D representation has a good accuracy.…”

“…Some authors assume a fiber sinusoidal misalignment. 14 Here, the fiber misaligned is assumed to have a following cubic form (see Figure 11): …”

“…Regarding the compressive strength, the fiber misalignment is included in the criterion, assuming a polynomial form model that allows the use of simple equations. 14 Due to curvature effect, the misalignment decreases lamina compressive strength and the proposed model is able to quantify it.…”

A unit-cell approach to prediction of the microbuckling strength of composites with non-uniform fiber imperfections under combined axial compression and in-plane shear

“…The model with periodic boundary conditions usually consists of one fiber embedded in the matrix. The concept of the periodic unit cell model has been employed for studying compressive failure in unidirectional composites in papers by Guynn et al (1992), Morais (1996), Hsu et al (1999), Pansart et al (2009), Gutkin et al (2010a), Barulich et al (2016), Naya et al (2017). Both types of boundary conditions have advantages and limitations.…”