Stress Transfer In Fiber Reinforced Composites Research Articles

The plastic behavior of matrix and its effect on the interface stress transfer in fiber-reinforced composites

ABSTRACT Existing shear-lag models for fiber-reinforced elasto-plastic composites always assume a rectangular-shaped plastic zone in the matrix, which is not consistent with numerical simulations. In this paper, a shear-lag model considering a more realistic parabolic shape of the plastic zone in an elasto-plastic matrix is proposed, in order to investigate the effect of matrix plasticity on the interface stress transfer. A closed-form solution to the profile of parabolic shape related to the applied stress is obtained so that the plastic zone evolution can be analytically characterized. Compared with the case with a purely elastic matrix, a plastic matrix could lead to a decrease in the interfacial shear stress (ISS) and an increase in the fiber stress. The smaller the plastic tangent modulus of the matrix, the lower the ISS is and the larger the fiber stress becomes, and the ISS and fiber stress keep being on same magnitudes of yielding strength and Young’s modulus of matrix, respectively. The present model with a parabolic plastic shape is more accurate to describe the mechanical behaviors of plasticity in matrix, which is of guiding value for the design of elasto-plastic composites used in vehicle accessories, medical devices, civil engineering and so on.

Study of the effect of interfacial damage and friction on stress transfer in short fiber-reinforced composites

The purpose of this study is to investigate the influence of different stages of different interfaces evolution under external forces on stress transfer within composite materials, which is crucial for analyzing reinforcement mechanisms in composite materials. Analytical solutions are derived to explore the impact of these distinct phases, both at the interfaces along the fiber length direction and at the fiber ends, on the complex stress distribution profiles within composite materials. Furthermore, the frictional effect at the interface serves to impede the debonding process in the composite. Under the same load, the debonding length of the interface decreases as the frictional effect increases. The increase in fiber aspect ratio (AR) effectively reduces the length of the damage and debonding interface and increases the axial fiber stress. Additionally, the theoretical results agree well with numerical simulation and experimental results. In essence, this model provides analytical solutions that are instrumental for analyzing stress transfer in fiber-reinforced composites during different stages of interface evolution.

The effect of a graded interphase on the mechanism of stress transfer in a fiber-reinforced composite

Based on an improved shear-lag model, the effect of an inhomogeneous interphase on the mechanism of stress transfer in fiber-reinforced composites is investigated. The inhomogeneity of the interphase is represented by the graded feature of the Young’s modulus varying according to a power law or a linear one in the radius direction, while the Poisson’s ratio and thermal expansion coefficient are assumed to be constants. Considering the effects of the inhomogeneous interphase as well as the Poisson’s contraction and thermal residual stress, closed-form solutions to the axial fiber stress and interfacial shear stress are obtained analytically. Comparing the case with a power law to that with a linear one, we find that the fiber stress increases significantly in the former case, while it decreases slightly in the latter one with an increasing interphase thickness. With the same external tensile load and interphase thickness, it is found that the fiber in the power law case is subjected to a larger tensile stress than that in the linear variation one. However, the interfacial shear stress is not sensitive to the interphase thickness in both cases, except that near the two ends of fiber. Under the same external load, the maximum shear stress in the interphase is much smaller in the latter than that in the former. All the phenomena can be characterized by one parameter, i.e., the average Young’s modulus of interphase, and denote that an interphase with a power variation law is more effective for stress transfer while the linearly graded one is more advantageous to avoid shear failure. The results should be helpful for engineers to properly design the interphase in novel composites, e.g. a carbon-fiber reinforced epoxy one.

Shear-lag versus finite element models for stress transfer in fiber-reinforced composites

The stress transfer from broken to unbroken fibers in fiber-reinforced polymer-matrix (PMC) and aluminum-matrix (AMC) composites is studied using a detailed 3D finite element model (FEM) and using the standard shear-lag model (SLM). The stress transfer predicted by the SLM is in good agreement with the FEM results for the PMC at high fiber volume fractions but not at low volume fractions. For the AMC with an elastic/plastic matrix, the FEM results depend on whether the fiber is broken initially (pre-break) or after loading (post-break), while the SLM is independent of the fiber break load. Compared to the pre-break FEM, the stress transfer in the SLM is too low at high volume fractions and fairly accurate at low volume fractions while the reverse trend obtains when the SLM is compared to the post-break FEM. These results suggest that the SLM is generally accurate for high fiber/matrix stiffness ratios and high fiber volume fractions, and/or when global matrix yielding proceeds fiber breaking such that the tangent stiffness of the matrix is small. At low volume fractions, matrix load carrying capacity accounts for much of the discrepancy between the SLM and the FEM, which can be rectified by more sophisticated SLMs. A simple elastic model demonstrates that neglect of the finite fiber dimensions and fiber shear deformation in the SLM can also affect the stress transfer. It is concluded that although the standard SLM cannot generally be used for simulations of composite deformation and failure, it is reasonably accurate for an important range of composite constituent material properties.

Interfacial Effects on Stress Transfer in Fiber-Reinforced Composites

A three-dimensional solution for a fiber-reinforced circular cylinder is presented for axisymmetric force and displacement boundary conditions. The solution, which can satisfy all the boundary conditions prescribed on the curved and end surfaces of the cylinder, can be used directly in the micromechanical analysis of fiber-reinforced composites to investigate the typical representative volume element (RVE). The element consists of a combined circular cylinder composed of a solid inner circular cylinder of transversely isotropic fiber, a concentric outer circular cylinder of isotropic matrix material, and an interface layer between the fiber and the matrix. The radial and tangential flexural compliances of the interfacial material are considered, and their effects on the stress transfer at the interface are studied parametrically. The numerical results presented show that the material properties of the interfacial layer have significant influences on the stress distribution within the RVE, particularly at the cross sections near the ends of the cylinder, where external loads are applied.

A modified analysis for stress transfer in fibre-reinforced composites with bonded fibre ends

The elastic stress transfer from the matrix to the embedded fibre in fibre-reinforced composites has been analysed previously when the loading direction is parallel to the fibre axis and the fibre is bonded to the matrix. Stress transfer occurs both at the interface along the fibre length and at the ends of the fibre. However, the boundary condition at the bonded ends is ambiguous, and various assumptions have been made to obtain solutions for this stress transfer problem. To satisfy more rigorously the boundary condition for the bonded ends, a new technique of assuming imaginary fibres in the composite is proposed in the present study. Compared to the previous analytical solution, the present analytical solution bears more physical meaning and is in better agreement with numerical and experimental results

On the stress transfer in fibre-reinforced composites with bonded fibre ends

In the conventional shear lag model [1], the fibre end stress is usually assumed to be negligible. This assumption is apparently not justified when the fibre ends are perfectly bonded. The exact condition can only be determined, however, as part of full solutions to a three-dimensional axisymmetrical elasticity problem. This problem is too difficult to be handled by any analytical means. On the other hand, if we assume that the shape of the fibre is prolate ellipsoidal, then Eshelby's famous solution [2] can be used to determine the stress in the fibre. The uniform stress state of the Eshelby solution does not allow the variation of the stress in the fibre to be investigated, particularly near the fibre ends. Recent publications [3, 4] have indicated that a simple but reasonably accurate solution is desirable. The purpose of this letter is to communicate some results regarding this problem. Consider a fibre with radius r0 and length 2I embedded in an infinite matrix. The Young's moduli of the fibre and the matrix are denoted by Ef and Era, respectively. The applied stress at infinity in the direction of the fibre is uniform and is denoted by am. It has been found [5] that the fibre stress along the fibre axis is ( + 1 O" m E m K m + K f

Analytical analyses of stress transfer in fibre-reinforced composites with bonded and debonded fibre ends

The elastic stress transfer from the matrix to the fibre is analysed analytically for fibre-reinforced composites when the loading direction is parallel to the fibre axis. The fibres with bonded lateral interfaces and (1) debonded and (2) bonded ends are considered in the present study. For the case of debonded ends, the present solutions contain refinements of the previously derived analytical solutions. For the case of bonded ends, unlike the numerical solutions derived previously, the present analytical solutions are ready to be used for further analyses. The results show that the stress transfer is more effective when the fibre has higher Young's modulus or longer length. Also, compared to the debonded ends case, the stress transfer is more effective and the stress distribution is more uniform when the ends are bonded to the matrix.