Tensile elongation of unidirectional or laminated composites combining a brittle reinforcement with a ductile strain and strain-rate hardening matrix

Abstract

We use the long-wavelength model of Hutchinson and Neale (Hutchinson JW, Neale KW. Acta Metall 1977;25:839) and Ghosh (Ghosh AK. Acta Metall 1977;25:1413) to estimate the uniform tensile elongation of two-phase composites deforming quasistatically according to the equistrain rule of mixtures, in which one phase is ductile while the other fractures progressively according to twoparameter Weibull statistics. We use shear-lag models in the literature to quantify load transfer from the ductile phase to the fractured brittle phase, to estimate the influence of matrix strain and strain-rate hardening, of brittle phase fracture characteristics, and of phase volume and strength ratios, on the composite strain to failure as dictated by the onset of unstable necking. Calculations show that strain and strain-rate hardening of the ductile phase do relatively little to increase the ductility of the composite. Two parameters play a dominant role, namely the brittle phase Weibull modulus and a dimensionless parameter describing load transfer across the two phases. The main practical implication of this analysis is that, to produce reasonably ductile two-phase composites, the best strategy is to aim for small layer thicknesses. IntroductionMany composite materials combine a ductile matrix with a brittle reinforcement: ceramic or carbon fibre reinforced metals fall in this category, as do some laminated metal composites and many other layered materials (such as thin film structures or ceramic-coated metals) [1][2][3][4]. When such composites are strained in tension the brittle phase develops cracks that cut its fibres or layers in two along a plane normal to the applied load; in laminated composites these are known as "tunnel cracks". Final fracture of the material may then happen in one of two ways. One is sudden brittle failure, caused by a propagative localization of internal damage that cuts abruptly the entire specimen in two; many strongly bonded ceramic or carbon fibre reinforced composites fail in this way [5][6][7], as do some particle reinforced composites [8]. Alternatively, internal damage accumulates stochastically throughout the material, in gradual and uncorrelated fashion. The composite is then likely to fail by strain localization, reaching its ultimate tensile strength at a smooth maximum along its stress-strain curve, and sometimes deforming significantly thereafter, while deformation concentrates in a portion of the sample's gauge length. Weakly bonded fibre reinforced composites (e.g., [5]), ceramic particle reinforced metals (e.g., [8,9]), two-phase metal alloys [10] or laminated metal composites [11] can all fail in this way. Strain hardening and strain-rate hardening then both play an important role: even small increases in a ductile material's strain hardening rate, or in its strain-rate sensitivity, can noticeably increase the tensile elongation when it is governed by the onset of strain localization.

The Deformation Characteristics, Fracture Behavior and Strengthening-Toughening Mechanisms of Laminated Metal Composites: A Review

“…The fracture elongation of multilayer metal matrix composites should be located in the intermediate value of the constitute metals if neglected of m value. However, the actual tensile ductility of laminated metal matrix composites is always lower or higher than the constitute metals [61,62]. That is to say, the fracture elongation of multilayer metal matrix composites heavily depends on the strain rate sensitivity factor (m).…”

“…ε r is the reference strain rate, high strain hardening exponent (n) represents high uniform plastic deformation capacity, and high strain rate sensitivity factor (m) reveals superior tensile deformation behavior [61,62]. The m value does not delay localized necking, but also retains a series of diffuse necking.…”

Multiscale Hierarchical Structure and Laminated Strengthening and Toughening Mechanisms

“…The laminated composites with superior tensile ductility can be obtained by adjusting the values of n and m of constitute layer [80]. Figure 18 shows the fracture elongation map of many power-law hardening monolithic materials [80,81]. It is interesting to note that a low ductility material laminated with another material that can coax the laminated composites toward higher elongation.…”

A metallic glass syntactic foam with enhanced energy absorption performance

“…In addition, compared with syntactic Al and high strength alloy foams, the existing metallic glass foams have no significant advantage in energy absorption [18][19][20][21][22]. Fortunately, it is shown that the addition of non-metallic such as brittle ceramic particles and fibers is an effective way to produce materials with attractive engineering attributes [23][24][25][26]. The high content of brittle second phases can increase both the strength and ductility of composites [25,26].…”

“…Fortunately, it is shown that the addition of non-metallic such as brittle ceramic particles and fibers is an effective way to produce materials with attractive engineering attributes [23][24][25][26]. The high content of brittle second phases can increase both the strength and ductility of composites [25,26]. In this paper, using hollow ceramic microspheres as a reinforcer that are also effective in avoiding crystallization, we fabricate a BMG syntactic foam through pressure infiltration, which was previously applied to make metal matrix composites with monolithic (non-hollow) ceramic reinforcement [27].…”