Strength distributions and size effects for 2D and 3D composites with Weibull fibers in an elastic matrix

Monte Carlo simulation and theoretical modeling are used to study the statistical failure modes in unidirectional composites consisting of elastic fibers in an elastic matrix. Both linear and hexagonal fiber arrays are considered, forming 2D and 3D composites, respectively. Failure is idealized using the chain-of-bundles model in terms of -bundles of length , which is the length-scale of fiber load transfer. Within each -bundle, fiber load redistribution is determined by local load-sharing models that approximate the in-plane fiber load redistribution from planar break clusters, as predicted from 2D and 3D shear-lag models. As a result the -bundle failure models are 1D and 2D, respectively. Fiber elements have random strengths following either a Weibull or a power-law distribution with shape and scale parameters and , respectively. Under Weibull fiber strength, failure simulations for 2D -bundles, reveal two regimes: When fiber strength variability is low (roughly >2) the dominant failure mode is by growing clusters of fiber breaks, one of which becomes catastrophic. When this variability is high (roughly 0<<2) cluster formation is suppressed by a dispersed failure mode due to the blocking effects of a few strong fibers. For 1D -bundles or for 2D -bundles under power-law fiber strength, the transitional value of drops to 1 or lower, and overall, it may slowly decrease with increasing bundle size. For the two regimes, closed-form approximations to the distribution of -bundle strength are developed under the local load-sharing model and an equal load-sharing model of Daniels, respectively. The results compare favorably with simulations on -bundles with up to 1500 fibers.     

A fast algorithm for the elastic fields due to a single fiber break in a periodic fiber-reinforced composite

The stress state in a shear-lag model of a unidirectional fiber composite with an arbitrary configuration of fiber breaks is obtained by the weighted superposition of the stress state due to a single broken fiber. In a periodic patch comprised of N fibers located at the points of a regular lattice, a method to determine the stress state due to a single break was proposed by Landis et al. (J Mech Phys Solids 48(3):621–648, 2000). This method entails the determination of the eigenspace of an \(N\times N\) matrix, at a computational cost of \(O(N^3)\). In the present work, an alternative algorithm is proposed. This algorithm exploits the circulant structure of the matrix describing the inter-fiber interactions. The asymptotic computational complexity of the present algorithm equals that of the discrete Fourier transform: \({O}(N \log N)\). Run times of the present method with the eigensolution based method are compared, and shown to be very favorable for the present method, even for small N. Power-law scaling of the overloads due to a single break to much larger distances than previously possible has been verified using the present method.     

A fast algorithm for the elastic fields due to interacting fibre breaks in a periodic fibre composite

Monte Carlo simulations of the failure of unidirectional fibre composites typically require numerous evaluations of the stress-state in partially damaged composite patches. In a simulated composite patch comprised of N fibres, of which \(N_b\) fibres are broken in a common cross-sectional plane transverse to the fibre direction, the stress overloads in the intact fibres are given by the weighted superposition of the unit break solutions associated with each of the breaks. Determining the weights involves solving \(N_b\) linear equations, and determining overloads in the intact fibres requires matrix-vector multiplication. These operations require \(O(N_b^3)\), and \(O(N N_b)\) floating point operations, respectively. These costs become prohibitive for large N, and \(N_b\); they limit Monte Carlo failure simulations to composite patches of only a few thousand fibres. In the present work, a fast algorithm to determine the overloads in a partially damaged composite, requiring \(O( N_b^{1/3} N \log N)\) floating point operations, is proposed. This algorithm is based on the discrete Fourier transform. The efficiency of the proposed method derives from the computational simplicity of weighted superposition in Fourier space. Computations of the stress state ahead of large circular clusters of breaks in composite patches comprised of about one million fibres are used to demonstrate the efficiency of the proposed algorithm.     

Tough–brittle transition in unidirectional composites with fibre breakage and fibre–matrix interfacial failure

International Journal of Fracture - Fracture of three-dimensional unidirectional composites is studied through Monte Carlo fracture simulations on model composites. Fracture develops in the model...     

Failure mechanisms and fracture energy of hybrid materials

A shear-lag model of hybrid materials is developed. The model represents an alternating arrangement of two types of aligned linear elastic fibres, embedded in a linear elastic matrix. Fibre and matrix elements are taken to fail deterministically when the axial and shear stresses in them reach their respective strengths. An efficient solution procedure for determining the stress state for arbitrary configurations of broken fibre and matrix elements is developed. Starting with a single fibre break, this procedure is used to simulate progressive fibre and matrix failure, up to composite fracture. The effect of (1) the ratio of fibre stiffnesses, and (2) the ratio of the fibre tensile strength to matrix shear strength, on the composite failure mechanism, fracture energy, and failure strain is characterised. Experimental observations, reported in the literature, of the fracture behaviour of two hybrid materials, viz., hybrid unidirectional composites, and double network hydrogels, are discussed in the framework of the present model.     

Sub-zero Temperature Dependence of Tensile Response of Friction Stir Welded Al-Cu-Li (AA2198) Alloy

Mechanical properties at ambient and cryogenic temperatures of Al-Cu-Li alloy are required for design and fabrication of liquid hydrogen and liquid oxygen tanks of satellite launch vehicles. In the present work, bead-on-sheet, friction stir welding was carried out with three different rotation speeds. The yield and strain hardening behaviors of the welds were evaluated in temperature range of 20 K to 298 K. Both yield stress and strain hardening ability in the specimen increased with decrease in testing temperature. The dependence of yield stress on temperature was modeled on the basis of thermally activated dislocation mobility, while that of strain hardening was modeled on the temperature dependence of dynamic recovery rate parameter. The recovery parameter followed an Arrhenius-type relationship with temperature. The model parameters determined from the experimental data were further used to simulate the stress–strain curves at different sub-zero temperatures for the friction stir welds.

     

Comparison of Continuum Damage Laws Under Uniaxial Creep for an AISI 316 Stainless Steel

Parameters of five popular continuum damage models are fit to match their creep rate and time to rupture predictions with that of a validated micro-mechanisms based model at a high nominal stress for an austenitic stainless steel. Their predictions are then compared with that of the micro-mechanisms based model at lower stress levels. The creep-strain rate and time to failure predictions of the model due to Wen et al. (Eng Fract Mech 98:169–184, 2013) best agrees with that of the micro-mechanisms based model in the regime of dominance of creep deformation processes. At still lower stress levels, where cavitation-rate is determined by diffusion processes, the Wen et al. model predictions of creep lifetimes become excessively non-conservative. A correction based on a formula due to Cocks and Ashby (Prog Mater Sci 27:189–244, 1982) has been proposed for this regime.     

The Defining Role of Local Shear on the Development of As-Rolled Microstructure and Crystallographic Texture in Steel

Metallurgical and Materials Transactions A - This study involved laboratory unidirectional (UDR) and reverse (RR) cold rolling of steel, and corresponding direct (and indirect) observations of...