Shear lag models for discontinuous composites: fibre end stresses and weak interface layers

Abstract

A new shear lag (SL) type model for stress transfer in a composite with cylindrical fibres is derived. It accounts for fibre end stresses in an approximate yet realistic manner, and leads to a new formula for predicting the Young's modulus of the composites. The predictions of this model were found to agree well with data for metal matrix composites (MMCs) with fibres of various aspect ratios. The accuracy and relative simplicity of the new model have been exploited in the development of an approximate analytical model for the stress transfer and macroscopic yield stress of a composite that contains a weak layer in the matrix adjacent to the reinforcement. With the aid of the latter model, the proof stress of MMCs which contain a precipitate free zone (PFZ) around the reinforcement, can be studied; experimental data obtained for aged 8090 MMCs is consistent with the model predictions.

Predicting the Structural Performance of Heat-Treatable Al-Alloys

“…Hence, there exists a considerable body of work on modelling independent contributions of strength in alloys and composites but predictive modelling of properties of complex alloys and composites requires superposition of these contributions. This type of complex strength modelling has been performed, to a varying degree of detail, for several monolithic precipitation hardened alloys [3,4,5,25,52,54,55], and recently a detailed model of strengthening in precipitation hardened metal matrix composites (MMCs) has been reported by the present authors [56,57,58]. In the strength modelling approach adopted in the present paper, the strengthening of MMCs and monolithic alloys are ascribed to five mechanisms: i. Precipitation strengthening, which involves strengthening of grains due to GPB zones, δ' (Al 3 Li) phase and S′ (Al 2 CuMg) phase [59,60], with a small contribution due to β′ (Al 3 Zr) dispersoids.…”

“…This indicates that the elements of the physically-based model presented are sound and that, in general, strength modelling of complex alloys can be successfully pursued using a physicallybased approach. It must however be emphasised that the amount of data for the NF and SVM model training was clearly well below that which may be expected to reasonably represent a problem of this complexity and the physically-based model required extensive experimental [58,59,60] and analytical [56,57] [59] and the physically based model.…”

A Novel “Fiber-Spacing” Model of Tensile Modulus Enhancement by Shortening Fibers to Sub-Millimeter in an Injection-Molded Glass Fiber Reinforced Polymer Bulk Molding Compound (GFRP-BMC)

“…In the BMC, the CTE of the cured polyester resin matrix (55 to 100 © 10 ¹6 /K) 10) is about an order of magnitude higher than that of E-glass fibers (5.4 © 10 ¹6 /K), 17) therefore thermal residual stresses will be generated by the matrix on the fibers during cool-down and shrink. Within the matrix itself, the third phase of CaCO 3 particle dispersion appears to assist in this process.…”

Size dependent strengthening in particle reinforced aluminium

“…This concept of "load-sharing" is central to composite continuum mechanics, which proposes models like the unit-cell, modified shearlag theory and different homogenization models [6,[9][10][11][12][13], to predict strengthening in particle reinforced composites based on knowledge of the bulk metal matrix properties and the volume fraction, aspect ratio, and spatial arrangement of the particles.…”