A nonlinear constitutive model of unidirectional natural fiber reinforced composites considering moisture absorption

Moisture absorption in natural fiber reinforced composites causes remarkable degradation of mechanical properties. A nonlinear constitutive model is proposed to study the effect of the water uptake on the mechanical properties of unidirectional natural fiber reinforced composites. Accompanying the water absorption in the composites, there are several irreversible thermodynamic processes such as fiber degradation and interface damage. The energy dissipation induced by these processes is described by an internal variable, and two degradation parameters representing interface damage and fiber degradation are introduced to reflect the modulus reduction of the composite. Particularly, the model is used to derive the evolution of elastic moduli influenced by the moisture absorption. The predictions from the present model show a good agreement with experiment results of sisal fiber unidirectional reinforced composites.     

Nonlinear shear behavior and interlaminar shear strength of unidirectional polymer matrix composites: A numerical study

Detailed finite element implementation is presented for a recently developed technique (He et al., 2012) to characterize nonlinear shear stress–strain response and interlaminar shear strength based on short-beam shear test of unidirectional polymeric composites. The material characterization couples iterative three-dimensional finite element modeling for stress calculation with digital image correlation for strain evaluation. Extensive numerical experiments were conducted to examine the dependence of the measured shear behavior on specimen and test configurations. The numerical results demonstrate that consistent results can be achieved for specimens with various span-to-thickness ratios, supporting the accurate material properties for the carbon/epoxy composite under study.     

A variational method for unidirectional fiber-reinforced composites with matrix creep

A variational method is developed for analyzing the matrix creep induced time-dependent change in fiber stress profiles in unidirectional composites. A functional of admissible profiles of fiber stress rate is presented by supposing a fiber broken in matrix as well as a fiber pulled out from matrix. The functional is shown to have the stationary function satisfying an incremental differential equation based on the shear lag assumption. Then, the stationary function is approximately determined by assuming bilinear profiles of fiber stress and a power law of matrix creep, leading to analytical solutions for the time-dependent change in fiber stress profiles. The solutions are verified on the basis of an energy balance equation and a finite difference computation. Moreover, it is shown that the solution for the fiber pull-out model agrees well with an experiment on a single carbon fiber/acrylic model composite if the initial slip at fiber/matrix interface is taken into account. In addition, the solution for the fiber breakage model is used for evaluating the characteristic time in long-term creep rupture of unidirectional composite.     

Thermal stress investigation in unidirectional composites under the hyperbolic energy model

The hyperbolic energy model is applied in this paper for determining transient temperature variation across a unidirectional composite plate subjected to different temperature changes at the boundaries. Thermal stresses developed are then analyzed for different material properties. Governing equations are solved numerically using implicit methods. The results are presented over a wide range of variables commonly found in most composite materials. The transient thermal stresses generated inside the plate were found to fluctuate between compressive and tensile quantities, a result that was not predicted using the classical heat model. Consequently, this will lead to an earlier crack initiation and failure of the material.     

Stress relaxation in broken fibers in unidirectional composites: modeling and application to creep rupture analysis

This paper describes a model of stress relaxation in broken fibers in unidirectional metal matrix composites reinforced with long brittle fibers. A cylindrical cell with a broken fiber embedded in a power law creeping matrix is employed, and the broken fiber is assumed to have a bilinear distribution of axial stress. Then, on the basis of energy balance in the cell under constant overall strain, a relaxation equation of interfacial shear stress acting on stress recovery segments is derived in a simple form. The relaxation equation is approximated rationally and integrated to obtain an analytical solution, which is shown to agree fairly well with the numerical analysis of Du and McMeeking. (Du, Z.-Z., McMeeking, R.M., 1995. Creep models for metal matrix composites with long brittle fibres. J. Mech. Phys. Solids 43, 701–726.) Moreover, the relaxation equation is combined with Curtin's model (Curtin, W.A., 1991. Theory of mechanical properties of ceramic-matrix composites. J. Am. Ceram. Soc. 74, 2837–2845.), so that rupture time in long term creep is evaluated analytically and explicitly on the assumption of global load sharing. It is shown that the resulting relation represents well the dependence of creep rupture time on applied stress observed experimentally on a unidirectional metal matrix composite.     

Modeling long-term creep rupture by debonding in unidirectional fibre-reinforced composites

Delayed fracture due to debonding can be observed in many unidirectional fibre-reinforced composites when the fibre/matrix interface experiences creep. The aim of this work is to describe such a phenomenon within the recently proposed modeling framework of transverse isotropy that allows for a neat decomposition of the mechanical behavior into fibre-directional, transverse, and pure shear parts. Specifically, debonding is here chosen to be governed by the tension transverse to the fibres. One can then speak of a mode-I debonding if use is made of the terminology adopted in fracture mechanics. On another hand, the time-dependent response is attributed to the matrix constituent. As the role of this latter is to deform and support stresses primarily in shear, a viscoelastic behavior is introduced that affects solely the pure shear part of the behavior. We show that both characteristics can be easily embedded into the aforementioned formulation. Among others, the occurrence of tertiary creep is made possible to predict. It is otherwise found that the predicted debonding path always propagates along the direction of the fibres in agreement with many experimental observations found in the literature. On the numerical side, the algorithmic treatment of debonding is independent of the one for viscoelasticity. This renders the implementation within the context of the finite element method very easy.     

Fatigue reliability based on residual strength model with hybrid uncertain parameters

The aim of this paper is to evaluate the fatigue reliability with hybrid uncertain parameters based on a residual strength model. By solving the non-probabilistic setbased reliability problem and analyzing the reliability with randomness, the fatigue reliability with hybrid parameters can be obtained. The presented hybrid model can adequately consider all uncertainties affecting the fatigue reliability with hybrid uncertain parameters. A comparison among the presented hybrid model, non-probabilistic set-theoretic model and the conventional random model is made through two typical numerical examples. The results show that the presented hybrid model, which can ensure structural security, is effective and practical.     

一种基于区间过程模型的时变可靠性分析方法

本文提出了一种基于区间过程模型的时变可靠性分析方法来处理涉及区间变量和区间过程的问题.首先,定义一种基于极值响应的可靠性指标来度量区间变量和区间过程不确定性下结构的可靠性.其次,建立并求解一双层优化模型以获得可靠性指标.在内层中,使用EGO方法计算功能函数关于时间的极值响应;在外层中,对极值响应关于原始区间变量和区间过...     

A plane stress formulation for elastic-plastic deformation of unidirectional composites

A plane stress analysis of the elastic-plastic deformation of unidirectional composites is presented. A continuum model based on the solid-mixture concept is selected as the basis for the analysis. Model parameters, including process-dependent variables, are deduced from experiments performed on unidirectional composites. A computer program MET1MAT has been developed accordingly and tested for a few simple in-plane loading cases. Experimental data for uniaxial tests performed in longitudinal and transverse directions and for a few biaxial tests are presented to substantiate the analysis. And, finally, application of the results to laminated metal matrix composites is discussed.     

Shear characterization of unidirectional composites with the off-axis tension test

The influence of end constraints on accurate determination of the intralaminar shear modulusG ₁₂ from an off-axis tension test is examined both analytically and experimentally. The Pagano-Halpin model is employed to illustrate that, when the effect of end constraints is properly considered, the exact expression forG ₁₂ is obtained. When the effect of end constraints is neglected, expressions for the apparent shear modulusG ₁₂ ^* and apparent Young's modulusE _xx ^* are obtained. Numerical comparison for various off-axis configurations and aspect ratios is carried out using typical material properties for graphite/polyimide unidirectional composites. It is demonstrated that the end-constraint effect influences accurate determination ofG ₁₂ more adversely than it affects the laminate Young's modulusE _xx in the low off-axis range. Experimental results obtained from off-axis tests on unidirectional Gr/Pi specimens confirm the above. Based on the presented analytical and experimental evidence, the 45-deg off-axis coupon is proposed for the determination of the intralaminar shear modulusG ₁₂.     

Brush-like modes of fatigue fracture in unidirectional fibre composites

Fatigue fracture of unidirectional fibre composites under tension along the fibres is discussed with account of the interaction between various mechanisms of damage such as single and multiple fibre ruptures, matrix cracking, and matrix-fibre debonding. The case of brittle fibres and a comparatively weak and ductile matrix is considered that exposes non-conventional modes of fracture, named “brush-like” cracks. Growth of such cracks under cyclic quasistatic loading is studied, and the effect of various factors on the crack growth rate is investigated.     

Fracture mechanics of unidirectional fibrous composites with metal matrix under compression

Two different approaches are used to evaluate the critical loads of the unidirectional fiber composites. They are based on the three-dimensional linearized elasticity theory. The constituents of the composite are assumed to have elastoplastic behavior. In the first approach, the composite is assumed to be homogeneous and orthotropic at the continuum level while the second approach assumes piecewise homogeneity where the fiber and matrix interaction at the interfaces are accounted for. For different ratios of the fiber and matrix moduli, critical loads and deformations are obtained and compared with experimental values.     

三维编织复合材料渐进损伤的非线性模型及强度分析

建立了考虑周期性位移边界条件的细观体胞模型,对三维编织复合材料的渐进损伤过程进行数值模拟。采用Eshelby-Mori—Tanaka方法计算含损伤裂纹的材料的剐度矩阵,并将有限元网格尺寸和单元裂纹尺寸引入损伤演化方程,有效地降低了模拟结果对有限元网格的依赖程度。通过计算得到了材料应力应变的非线性关系和失效时的极限强度,并分析了材料的破坏机理。结果表明,大编织角材料的破坏模式主要是基体失效与纤维横向拉剪破坏,模拟计算结果与文献中的实验值吻合较好。     

Shock propagation in regular wetted arrays of fibers

We present results of shock propagation in a wetted foam modeled as a regular staggered row lattice of parallel cylinders in two-dimensions immersed in a background of different density. Both media are perfect mono-atomic gases. We show that shock velocity increases due to the heterogeneity of wetted foams in comparison to the velocity of shock in a homogeneous medium with the same average density. The post-shock medium is characterized by turbulence and multiple vortices. Destructive or constructive interactions between vortices appear in the downstream fluid depending on the fiber alignment. We show that the shock velocity increase is related to the kinetic energy stored in the downstream fluid in the turbulence and the vortices. A turbulent model is used to analytically relate the turbulent kinetic energy to the shock velocity increase.