A numerical approach for predicting the failure locus of fiber reinforced composites under combined transverse compression and axial tension

https://doi.org/10.1016/j.commatsci.2011.07.039Get rights and content

Abstract

A computational model based on the finite element method is presented for the estimation of strength of a fiber-reinforced lamina subjected to a combination of the transverse compression and axial tension. A complex damage mechanism including fiber breakage, fiber/matrix debonding and matrix plastic deformation is reproduced in the proposed model by using appropriate constitutive equations. The numerical simulation of mechanical response of the unidirectional lamina under biaxial loading is used to obtained the failure locus. Subsequently, the model is verified against an analytical solution and experimental data. It was found that the numerical calculations agree better with experimental results than analytical predictions.

Highlights

Micromechanics model predicted the biaxial failure locus of unidirectional lamina. ▸ Successful simulation of failure mechanisms based on a regular unit cell. ▸ Transverse contraction affected the interaction between transverse and axial loading.

Introduction

The ability to predict deformation and ultimate strength of unidirectional lamina under biaxial loading is a key aspect in the successful design of a composite laminate structure. Since, in most cases, the damage process in unidirectional composites begins at the constituent level, a realistic failure analysis should start at the same level. Unfortunately, an accurate measurement of the local strain and stress distributions throughout the microstructure is practically impossible through the use of experimental methods. Also, an applicability of empirical formulas to the analysis of ultimate failure in practical laminates is limited because they do not provide useful information for estimating a softening response of the material. Therefore, a development of micromechanics models that, on the one hand, take into account microstructural effects, and on the other hand, link the macroscopic behavior of unidirectional composite to the microstructural phenomena occurring inside it is essential. An efficient way to analyze the microstructural influences on the load bearing behavior of such materials is through the use of numerical techniques of homogenization based on the unit cell approach and the finite element method. According to this technique, different phases in a composite such as the matrix, fibers, interphase, and interfaces are explicitly modeled by finite elements and their material properties are directly assigned to the elements. Recently, this technique was successfully employed in the analysis of the effect of damage on the mechanical behavior of fiber-reinforced lamina subjected to a combination of the transverse compression and out-of plane shear [1], transverse tension and out-of plane shear [2] as well as transverse compression and longitudinal shear [3]. A common feature of all the works mentioned above is the use of multi-fiber unit cells containing a random distribution of fibers. To the author’s knowledge, no attempt has been made to obtain a solution for the combined transverse compression and axial tension, probably due to the high computational cost associated with generating a large number of potential fracture planes. Composite specimens subjected to this kind of biaxial loading may fail according to two distinct mechanisms. Tensile deformation along the fibers leads to fiber fracture (FF) while compressive deformation perpendicular to the fibers results in inter-fiber fracture (IFF) by the localization of the matrix plastic strain along shear bands and the fiber/matrix decohesion [4], [5].

The main objective of this paper is to develop a simple and efficient micromechanics model for the simulation of mechanical response and fracture behavior of unidirectional lamina subjected to a combination of the transverse compression and axial tension. The use of a regular unit cell that includes a small number of the damageable planes makes it possible to find a solution to this problem. To illustrate the capability of the proposed model, first, the failure locus of a unidirectional glass/epoxy composite subjected to this kind of biaxial loading was computed. Then, the predictions of biaxial strength were compared with experimental results chosen for use in the World Wide Failure Exercise [6], [7] and theoretical results obtained from the Puck criterion [8]. Nonlinear effects associated with damage evolution were taken into account through an application of appropriate constitutive equations. The pressure-dependent, elasto-plastic behavior of matrix was simulated by the Drucker–Prager yield criterion [9], [10]. The fiber fracture and the fiber/matrix debonding were controlled by the cohesive zone model [11].

Section snippets

Micromechanics model

One micromechanical unit cell model is considered independently from the type of load and the biaxial loading ratio. For simplicity, it was assumed that a random microstructure of fiber reinforced composite material can be approximated by a periodic arrangement of fibers for which a hexagonal unit cell can be isolated. Using ANSYS finite element code, a three-dimensional finite element model made of isoparametric brick elements with eight nodes (Solid185) was generated as shown in Fig. 1. An

Results and discussion

The presented model is now used to simulate both uniaxial loading responses and biaxial loading responses. The nonlinear material behavior of unidirectional lamina under pure transverse compression (κ = 0) and pure axial tension (κ = ∞) is illustrated by the stress–strain curves shown in Figs. 3 and 4. The transverse compressive response differs from the longitudinal tensile response. It can be observed that the transverse stiffness of lamina is gradually decreasing after the peak value of stress

Conclusions

A computational micromechanics model was developed in order to predict the failure locus of fiber reinforced composites under combined transverse compression and axial tension. The most important feature of the presented approach is that failure behavior of unidirectional composite is affected by fracture properties of the constituent materials and interface. Nonlinear effects due to fiber breakages, fiber–matrix debonding and plastic deformation of matrix are included in order to reconstruct a

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