Intermediate Volume Fractions Research Articles

The Role of Particle Strength and Filler Volume Fraction in the Fracture of Alumina Trihydrate Filled Epoxy Resins

The critical strain energy release rate, Glc, and the critical stress intensity factor or fracture toughness, Klc, of alumina trihydrate (ATH) filled epoxy resin have been determined as a function of filler volume fraction, using tapered double cantilever beam and single edge notch geometries respectively. GIc showed a maximum at a filler volume fraction of approximately 0.18. The fracture toughness increased linearly up to a filler volume fraction of 0.55. It is proposed that the predominant toughening mechanism depends on the volume fraction of filler and that ATH particles are strong enough for crack pinning to constitute the main toughening mechanism in the intermediate volume fraction region. At low volume fractions and with unstable crack propagation, crack blunting is also important. When the volume fraction is very high, ductile responses by the resin matrix are less easy and particle fracture becomes common, reducing the scope for crack pinning. The value of the breakaway parameter in the crack pinning model of Green was estimated in terms of the particle size.

Computer Modelling for the Yield Strength of the Mixed Micro-Structures of Bainite and Martensite

The strength of mixed microstructures of bainite and martensite can peak at an intermediate volume fraction of martensite has been published by recently experimental studies. A quantitative interpretation of these observations is achieved by modelling the mechanical properties of mixed microstructures of bainite and martensite. The peak in the curve of the strength as a function of the volume fraction of martensite can be attributed to two factors. It enriches the residual austenite with carbon when bainite forms, so that the strength of the subsequent martensite increases. In addition, the strength of the bainite is enhanced via plastic constraint by the surrounding stronger martensite. This means the bainite is under a tri-axial stress state. Taking these effects into consideration for the computer modelling, it is possible to predict accurately both the trends and the absolute values of published experimental data on the strength of mixed microstructures.

Nanophase Separation in Monodisperse Rodcoil Diblock Polymers

The authors have observed nanophase-separated structures in rodcoil polymers synthesized in their laboratory. Each polymer consists of a perfectly monodisperse, rodlike segment covalently bonded to a coil like segment of polyisoprene such that both rod and coil share the same molecular backbone. The polyisoprene was prepared by living anionic polymerization, and thus the rodcoil diblock molecules in the systems studied are of fairly uniform molar mass. Annealing of solution-cast thin films approximately 5--10 nm thick leads to ordered nanoscale morphologies that depend upon the volume fraction of rod segments in these diblock molecules. The authors find by transmission electron microscopy that the morphology varies from alternating strips of rod- and coil-rich domains to discrete aggregates of rods arranged in a hexagonal superlattice as rod volume fraction is decreased. At an intermediate volume fraction the authors see a coexistence of strips and aggregates. This breakup of rod domains may be the result of entropic coil stretching penalties analogous to those postulated recently by Williams and Fredrickson in lamellar assemblies of rodcoils.

Finite element micromechanical modelling of a unidirectional composite subjected to axial shear loading

Abstract A micromechanical model is presented which predicts the behaviour of a unidirectional composite subjected to axial shear load using standard finite elements. Only a three-dimensional model can handle the necessary shear loading boundary conditions when using such elements. These boundary conditions give shear stress components but no direct stress components within the composite. A parametric study is carried out on unidirectional carbon fibre/epoxy within the linear elastic regime of both constituents. The study reveals that the most critical parameters controlling the axial shear modulus of the composite are matrix modulus and fibre volume fraction whilst the stress state in the composite is mainly controlled by geometrical features of the composite, i.e., fibre volume fraction and fibre spacing. Comparison between the predicted axial shear modulus based on the concentric cylinder model and the current finite element model shows good agreement for low and intermediate fibre volume fractions. Both predictions lie within the Hashin bounds and the finite element prediction tends to be closer to the upper Hashin bound for fibre volume fractions greater than 60%. The initial tangent shear modulus predicted with the finite element model and that measured differ by less than 2.5%. The non-linear shear stress/strain response of the composite material is also predicted and agreement with the experimental results is good.

Strength of mixtures of bainite and martensite

Recently published experimental data demonstrate that the strength of mixed microstructures of tempered bainite and martensite can peak at an intermediate volume fraction of martensite. In the present work, a quantitative interpretation of these observations is achieved by modelling the mechanical properties of bainite and martensite in their tempered states. It is found that the peak in the curve of the strength as a function of the volume fraction of martensite can be attributed to two factors. When bainite forms it enriches the residual austenite with carbon, so that the strength of the subsequent martensite increases. In addition, during its deformation, the strength of the bainite is enhanced via plastic constraint by the surrounding stronger martensite. Taking these effects into account, it is possible to predict accurately both the trends and the absolute values of published experimental data on the strength of mixed microstructures.MST/1901

Prediction of steady state creep behavior of two phase composites

A simple continuum mechanics-based model has been developed to predict the steady state creep rates of composites containing coarse and rigid reinforcements from the matrix creep behavior. The model has been derived on the basis of a unit cell, representative of the composite microstructure, which is idealized to a pattern of periodic, cubic inclusions distributed uniformly in a continuous creeping matrix. Comparisons of the predicted creep rates are made with the experimental data of a number of two phase systems as well as transversely loaded continuous fiber reinforced composites. A good agreement between the predicted and measured creep rates is seen for most of the systems. However, for some composites, the calculations overestimate the creep rates significantly at intermediate volume fractions, typically, 0.3–0.4. It is suggested that factors such as the differences between the microstructure of the matrix in the composite and that of the monolithic matrix could be responsible for the differences in the predicted and experimentally measured creep behavior. Finally, an assessment of the predictions of the model proposed in this study with rigorous, self-consistent calculations as well as finite element simulations has been made.

Morphological Effect on the Mechanical Behavior of a Two-Phase Ti3Al-Nb Alloy

A study has been made on the deformation and fracture behavior of a two-phase (α2 + β) Ti3Al-Nb alloy, with particular emphasis on the effect of morphologies. The coarse colony structure obtained by continuously annealing in the two-phase region directly from the β region results in poor elongation ductility. The fine colony structure obtained by two-phase annealing the β-quenched specimen also results in poor elongation ductility. However, upon obtaining fine equiaxed or basket-weave structures by following different transformation paths, improvements occur in elongation ductility without any sacrifice in strength. For the fine equiaxed structure, maximum elongation is obtained at the intermediate volume fraction of a2, while for the basket-weave structure, an increase in the volume fraction of α2 increases the elongation. Detailed fracture analysis shows that different fracture mechanisms operate for different morphologies, and the critical microstructural unit for arresting fracture also varies, depending on the morphologies.

Structure-property relations in duplex materials

A two-dimensional micromechanical model to determine the plastic flow properties of two phase alloys with coarse microstructures is presented. In the analysis special attention is devoted to the correct representation of the geometrical features of the real microstructure in the model. The model microstructures are characterized by stereological parameters also applied to real materials. Microstructures are of inclusion-matrix topology at low and high volume fractions of the second phase. At intermediate volume fractions duplex-microstructures are formed. The calculation of the plastic flow properties of a solid consisting of two elastic-perfectly plastic constituents is conveniently done by a unit cell approach with the finite element method. The limit flow stress of the composite is calculated for microstructures covering the whole range of possible volume fractions. The incorporation of the microstructural informations in the analysis of the computed results leads to an improved understanding of the plastic flow properties of the model composite. Results from the present model calculations are compared to results obtained from other micromechanical models.

The effects of convection on Ostwald ripening in solid-liquid mixtures

The effects of convection on Ostwald ripening in solid-liquid mixtures have been studied using a SnPb alloy over a wide range of volume fraction solid. The convection was induced by a slow rotation of a disk shaped sample with the axis of rotation perpendicular to the gravity vector. At low volume fractions of solid the experiments show that convection can alter the exponent of the temporal power law for the average intercept length from its classical value of 1 3 to 0.37. For intermediate volume fractions of solid the temporal exponent is 1 3 , but the amplitude of the temporal power law for the average particle radius depends on the rate of rotation. At very high volume fractions of solid, where a stable skeletal structure was present, rotation had no effect on the kinetics of the ripening process. A theoretical analysis of Ostwald ripening in the low Peclet number limit was undertaken in an effort to understand the experimental results. The analysis showed that temporal power law solutions to the equations describing ripening do not exist when the particles move in the fluid with either a constant velocity or according to Stokes law. However, if the magnitude of the fluid flow scales with time in the proper way, temporal power law solutions can be found which are qualitatively consistent with the experiments.

Structure, tensile deformation, and fracture of a Ti3Al-Nb alloy

The development of Ti3Al-Nb alloys is an excellent example of the recent resurgence of interest in the use of intermetallics for high-temperature applications. We examine, in this contribution, the structure of a typical alloy Ti-24A1-11Nb and show it to consist primarily of the ordered α2 phase (based on Ti3Al, DO19) and βo, (based on Ti2NbAl, B2) phases, with small amounts of a third phase, which is distorted slightly to an orthorhombic symmetry from the D019 (hexagonal) structure. Tensile properties have been examined on samples heat-treated to vary the size, shape, and volume fraction of α2 phase and the deformation and fracture behavior of the ordered, two-phase mixture established. The tensile ductility is seen to maximize at intermediate volume fractions of the α2 and βo phases (∼30 pct) at values of 6 to 10 pct elongation to fracture, depending on the grain size of the βo phase. A rationale incorporating the failure modes of the two phases—cleavage of α2 and slipband decohesion of βo—has been evolved to explain the trends in ductility with heat treatment.

Toughening due to crack-front interaction with a second-phase dispersion

A model for the restraining effect of second-phase inclusions on an advancing crack front in a brittle matrix is presented which incorporates a parameter characterizing the relative ease of cutting through or circumventing the second phase, compared with matrix cracking. The model predicts a rapid increase in toughness with volume fraction of the second phase at dilute concentrations, and a maximum toughness at intermediate volume fraction, in agreement with available experimental results.

Rheological properties of mixtures of protein-polysaccharide-dynamic viscoelasticity of blend gels of acylated gelatin, kappa-carrageenan, and agarose.

Complex Young's modulus of blend gels of gelatin and kappa-carrageenan or agarose has been measured in order to clarify the protein-polysaccharide interaction in biological systems. The mixture of gelatin and kappa-carrageenan showed phase separation in the intermediate volume fraction of gelatin, and it formed a homogeneous gel when the volume fraction of gelatin is very large or very small. Since the dynamic Young's modulus for blend gels of kappa-carrageenan and gelatin was larger than the calculated one from a theory for dispersed systems, some structural reinforcing must occur. The mixture of agarose and gelatin showed the inverse tendency. It was concluded that the role of electrolytic groups was dominant in dilute gels, while molecular entanglement became more important in concentrated gels.

Variation of mitochondrial volume fraction along multiply innervated fibers in rabbit extraocular muscle

Mitochondrial volume fraction was compared among three regions along the length of six multiply innervated fibers (MIFs) in the orbital surface layer of rabbit superior rectus. These MIFs are of about 5 μm diameter toward the middle of their length, and of about 15 μm diameter toward their proximal and distal ends. The region of highest volume fraction (26%) was located toward the proximal end of their segment of minimal diameter, in apparent association with endplate-like nerve junctions. The region of lowest volume fraction (8%) was located at their distal segment of maximal diameter. The region toward the distal end of their segment of minimal diameter displayed an intermediate volume fraction (15%). These mitochondrial volume fractions were further analyzed in terms of the relative contributions of the I-band, the A-band, and the subsarcolemmal mitochondrial clusters. Comparable changes in mitochondrial content occur in both the I-band and A-band: in the fibers' distal segment of maximal diameter, however, the mitochondrial volume fraction in the A-band (5%) is lower than in the I-band (11%). These modifications of mitochondrial content along the fibers' length occur irrespective of the contributions of the subsarcolemmal mitochondrial clusters.

Crack propagation in metal-matrix/ metal-fibre composites: I. Strength and toughness

The strength and toughness of composites consisting of an aluminium-4% copper alloy reinforced with tungsten wires has been studied by conventional mechanical testing methods and with the aid of fracture mechanics techniques. The effects of fibre volume fraction and of the plastic deformation behaviour of the matrix alloy are shown. Values of the fracture energy, measured in a variety of ways, are compared with each other and with the predictions of existing theoretical models. One of these, modified to take account of the actual shape of the plastic zone developed during crack propagation, has been found to agree reasonably satisfactorily with the experimental results for intermediate fibre volume fractions - ie for composites in which Vf is not sufficiently high to cause splitting and not so low as to permit matrix plasticity to control the composite behaviour. The effect of the matrix work-hardening rate is found to be insignificant in composites containing more than about 12 volume% of fibres.