Sivasambu Mahesh

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 δ-bundles of length δ, which is the length-scale of fiber load transfer. Within each δ-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 δ-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 ρ and σδ, respectively. Under Weibull fiber strength, failure simulations for 2D δ-bundles, reveal two regimes: When fiber strength variability is low (roughly ρ>2) the dominant failure mode is by growing clusters of fiber breaks, one of which becomes catastrophic. When this variability is high (roughly 0<ρ<2) cluster formation is suppressed by a dispersed failure mode due to the blocking effects of a few strong fibers. For 1D δ-bundles or for 2D δ-bundles under power-law fiber strength, the transitional value of ρ 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 δ-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 δ-bundles with up to 1500 fibers.

On the influence of fiber shape in bone-shaped short-fiber composites

Abstract Composite materials reinforced by bone-shaped short (BSS) fibers enlarged at both ends are well-known to have significantly better strength and toughness than those reinforced by conventional, short, straight (CSS) fibers with the same aspect ratio. Comparing the fracture characteristics of double-cantilever-beam specimens made of BSS and CSS fiber composites reveals the distinct mechanisms responsible for the toughness enhancement provided by the BSS fiber reinforcement. Enlarged BSS fiber ends anchor the fiber in the matrix and lead to a significantly higher stress to pull out than that required for CSS fibers, altering crack propagation characteristics. To study BSS fiber-bridging capability further, we examine the effects of increasing the size of the enlarged fiber end on the pull-out characteristics and identify the sequence of failure mechanisms involved in the pull-out process. However, large microcracks initiated at the enlarged ends can potentially mask the toughening enhancements provided by BSS fibers. To understand the influence of fiber-end geometry on debond initiation at the fiber ends, we analyze the interfacial stresses around fiber ends varying in geometry using an elastic finite-element model. We note a bound to these in terms of the Eshelby and Kelvin elastic solutions.

Size and heterogeneity effects on the strength of fibrous composites

Abstract Probabilistic fiber composite strength distributions and size scalings depend heavily on both the stress redistribution mechanism around broken fibers and properties of the fiber strength distribution. In this study we perform large scale Monte Carlo simulations to study the fracture process in a fiber composite material in which fibers are arranged in parallel in a hexagonal array and their strengths are given by a two-parameter Weibull distribution function. To calculate the stress redistribution due to several broken fibers, a realistic 3D shear-lag theory is applied to rhombus-shaped domains with periodic boundary conditions. Empirical composite strength distributions are generated from several hundred Monte Carlo replications, particularly for much lower values of fiber Weibull modulus γ , and larger composite sizes than studied previously. Despite the localized stress enhancements due to fiber failures, predicted by the shear-lag model, composite response displays a transition to equal load sharing like behavior for approximately γ ≤1. Accordingly, the results reveal distinct alterations in size effect, failure mode, and weak-link scaling behavior, associated with a transition from stress-driven to fiber strength-driven breakdown.

Deformation banding under arbitrary monotonic loading in cubic metals

We present a Taylor-based theory of deformation of an aggregate of rigid-plastic crystals that allows for heterogeneity of grain deformation, and use it to model macroscopic subdivision of grains into mutually misoriented volumes, a process termed deformation banding. Each grain is assumed to accommodate the macroscopically imposed deformation such that the power of its plastic deformation is minimized. This minimization may involve the formation of deformation bands. The theory is applied to tension, compression and rolling of fcc aluminium and bcc α-iron polycrystals, and used to predict the macroscopic mechanical response, the polycrystal texture, the orientation of deformation bands, and the misorientations across them. These predictions are compared with experimental observations available in the literature, and good qualitative agreement is found.

Deformation Twinning in Zirconium: Direct Experimental Observations and Polycrystal Plasticity Predictions

Deformation twinning was directly observed in three commercial zirconium alloy samples during split channel die plane-strain compression. One pair of samples had similar starting texture but different grain size distributions, while another pair had similar grain size distribution but different starting textures. Extension twinning was found to be more sensitive to the starting texture than to the grain size distribution. Also, regions of intense deformation near grain boundaries were observed. A hierarchical binary tree-based polycrystal plasticity model, implementing the Chin-Hosford-Mendorf twinning criterion, captured the experimentally observed twinning grains’ lattice orientation distribution, and the twin volume fraction evolution, provided the critical resolved shear stress for extension twinning,

Orientation preferences of extended sub-granular dislocation boundaries

\tau_{0} ,

Strength distribution of large unidirectional composite patches with realistic load sharing

τ0, was assumed much larger than any of the values reported in the literature, based on the viscoplastic self-consistent model. A comparison of the models suggests that