C. K. L. Davies

Interfacial Shear Stress Distribution in Model Composites Part 2: Fragmentation Studies on Carbon Fibre/Epoxy Systems

The micromechanics of reinforcement of a model composite system con sisting of a continuous high-modulus (HM) carbon fibre embedded in an epoxy resin have been investigated. The composite was subjected to incremental tensile loading up to full fibre fragmentation, while the strain in the fibre was monitored at each level of load using a laser Raman spectroscopic (LRS) technique. The average strain in the fibre increased linearly with applied matrix strain up to a value of 0.8 %, when the first fibre fracture oc curred. After fracture, the strain in the fibre was found to build from the tips of the fibre breaks, reaching a maximum value in the middle of each fragment. The shape of the load transfer profiles at the locality of the fibre tips indicated that the stress transfer efficiency had been affected by the fracture process. The length of interfacial debonding at the point of fibre fracture was found to be driven by the strain energy of the fractured fragments. The interfacial shear stress (ISS) distributions at various levels of applied load along in dividual fragments, have been derived from the load transfer profiles using a balance of forces analysis. The shape of the ISS profiles confirmed that interfacial debonding initiated from the tips of the fibre breaks, whereas good fibre/matrix adhesion was retained around the mid-length of each fragment. By increasing the applied strain to 1.8%, the maximum ISS values also increased in spite of the presence of debonding at the fibre tips. An upper ISS limit of 42 MPa was calculated at this point. Further increases of the applied strain to 5% resulted in significant reductions in the values of the maximum ISS, as well as an in crease, of the frictional slip towards the middle of each fragment. Finally, by employing the assumptions of the conventional fragmentation test, the calculated value of the nominal interfacial shear strength at the point of full fragmentation was lower by a factor of 2 than the value measured by the LRS method.

Effect of materials variables on the tear behaviour of a non-crystallising elastomer

Crack growth rates (r) were measured in pure shear test specimens as a function of strain energy release rate (G) for a non-crystallising SBR elastomer. Measurements were made as a function of: extent of swelling with Dibutyl Adipate; carbon black content; and crosslink density. In some cases experiments were carried out over a range of temperatures. In most cases the resulting G versus r plots showed a clear transition from rough to smooth crack surface behaviour with increasing crack growth rate, with an intervening slip/stick region. In the high speed/steady tear/smooth region the value of G necessary to drive a crack at a given rate was determined largely by the magnitude of the visco-elastic losses in the crack tip region, increasing with: decreasing temperature; increasing molar mass between crosslinks; decreasing extent of swelling; and increasing carbon black content. However G was independent of specimen thickness in this region suggesting that crack tip effects were minimal. In the low speed/rough region changes in the magnitude of G with materials and temperature/rate variables could not be explained by changes in visco-elastic loss alone. Furthermore the magnitude of G increased significantly with increasing specimen thickness. This suggested that in this region cavitation ahead of the growing crack tip resulting from dilatational stresses determined the crack tip diameter, and hence the magnitude of G.

Monitoring the micromechanics of reinforcement in carbon fibre/epoxy resin systems

The technique of laser Raman spectroscopy (LRS) was employed to obtain the interfacial shear stress (ISS) distribution along a short high-modulus carbon fibre embedded in epoxy resin at different levels of applied stress. Up to 0.6% applied strain, the ISS reached a maximum at the bonded fibre ends and decayed to zero at the middle of the fibre. At higher applied strains, the maximum value of the ISS distribution shifted away from the fibre ends towards the middle of the fibre. At the point of fibre fracture, fibre/matrix debonding was found to initiate at the fibre breaks. Further increase of applied strain resulted also in debonding initiation at the fibre ends. Current analytical stress-transfer models are reviewed in the light of the experimental data.

Precipitation in Ni-Co-Al alloys

Etude de la precipitation entre 673 et 973 K par microscopie optique et microscopie electronique en transmission

Morphology oftrans-1, 4-polyisoprene crystallized in thin films

The development of melt-grown crystalline morphology in thin films of trans-1,4-polyisoprene (TPI) was studied by optical and electron microscopy. The crystalline morphologies observed are explained in terms of thin chainfolded lamellar crystals which would grow (if unrestricted) to a diamond shape. The electron diffraction patterns obtained can be indexed using the unit cells proposed by Fisher [3]. The preferred growth faces for the low melting form crystals (LMF) are the (120) planes and probably the (110) planes for the high melting form crystals (HMF). LMF crystals are exclusive to LMF spherulites and HMF crystals are exclusive to HMF spherulites. At large supercoolings both LMF and HMF spherulites nucleate as bundles of lamellar crystals and grow by extensive, twisting, branching and spawning. LMF spherulites grown at small supercoolings develop as hedrites/axialites, or as splayed groups of large crystals differing in orientation with respect to the electron beam. The frequency of twisting, branching and spawning being minimal at these supercoolings. Row nucleated structures are observed in strained films. They consist of long wavy backbone crystals (5 to 25 nm thick) lying in the direction of strain, overgrown by lamellar crystals (5 to 10 nm thick) oriented at right angles to the strain direction. At some temperatures both LMF and HMF crystals nucleate in the same row. The morphologies observed in thin films are compared with and discussed in terms of the observations made of bulk-grown and solution-grown crystals.

Interfacial shear stress distribution in model composites: the effect of fibre modulus

Abstract The micromechanics of reinforcement have been investigated for a continuous intermediate-modulus (IM) carbon fibre embedded in an epoxy resin (MY-750). The embedded single-fibre (fragmentation) geometry was employed as the loading configuration. A laser Raman spectroscopic method was used to obtain the fibre strain distribution along the embedded fibre fragments, at various levels of applied strain. The interfacial shear stress distribution along the fibre was derived through a balance of forces analysis. A number of parameters, such as the maximum interfacial shear stress at each level of applied strain and the fibre debonded length, were evaluated. The maximum interfacial shear stress of the IM fibre system was found to increase by 80%, compared with the high-modulus fibre system examined previously, while the distance from the fibre end where the interfacial shear stress maximizes was significantly shorter. The debonded length was found to increase only marginally up to an applied strain of 1.8%, followed by a dramatic rate of increase between 1.8% and 2.5% of applied strain.

Contributions of time dependent and cyclic crack growth to the crack growth behavior of non strain-crystallizing elastomers

Engineering components are observed to fail more rapidly under cyclic loading than under static loading. This reflects features of the underlying crack growth behavior. This behavior is characterized by the relation between the tearing energy. T, and the crack growth per cycle, dc/dn. The increment of crack growth during each cycle is shown here to result from the sum of time dependent and cyclic crack growth components. The time dependent component represents the crack growth behavior that would be present in a conventional constant T erack growth test. Under repeated stressing additional crack growth, termed the cyclic crack growth component, occurs. For a non-crystallizing elastomer, significant effects of frequency have been found on the cyclic crack growth behavior, reflecting the presence of this cyclic element of crack growth. The cyclic crack growth behavior over a wide range of frequencies was investigated for unfilled and swollen SBR materials. The lime dependent crack growth component was calculated from constant T crack growth tests and the cyclic contribution derived from comparison with the observed cyclic growth. It is shown that decreasing the frequency or increasing the maximum tearing energy during a cycle results in the cyclic crack growth behavior being dominated by time dependent crack growth. Conversely at high frequency and at low tearing energy, cyclic crack growth is dominated by the cyclic crack growth component. A large effect of frequency on cyclic crack growth behavior was observed for highly swollen SBR. The cyclic crack growth behavior was dominated by the time dependent crack growth component over the entire range of tearing energy and/or crack growth rate. The origin of the cyclic component may be the formation/melting of quasi crystals at the crack tip, which is absent at fast crack growth rates in the unswollen SBR and is absent at all rates in the swollen SBR.

Kinetics of crystallization of trans-1, 4-polyisoprene crystallized in thin films

The lamellar thickness and crystal growth rates of both high melting form and low melting form trans-1,4-polyisoprene crystals growing from the same melt in thin films, have been determined by transmission electron microscopy. Values of the fold surface energy (σe) have been determined and compare well with values for solution grown and bulk melt grown crystals. It is suggested that the crystals have a similar form in all three cases. The crystal growth rate data can be described by equations derived from secondary nucleation theory and the product of the surface energies (σeσs) is calculated. The value of the product is compared with recalculated values determined by using previously published optical growth rate data.

Silicon nitride-nickel compatibility: the effects of environment

The effect of gaseous environment on the high temperature stability of nickel-coated silicon nitride whiskers has been investigated. Under vacuum conditions above 900°C, the nickel coatings broke up to form spheroidal particles, which subsequently became faceted (activation energy = 26 kcal/mol) and wetted the whiskers (activation energy=74 kcal/mol) In addition, at 1100° C, whisker disintegration occurred rapidly due to the formation of a nickel suicide reaction product. Under similar conditions in a nitrogen atmosphere the whiskers remained coherent and in an argon atmosphere the whiskers developed side growths. These results are correlated with variations in the nitrogen and oxygen partial pressures between the various conditions.

Self-consistent forms of the chemical rate theory of Ostwald ripening

The chemical rate theory of Ostwald ripening introduced by A. D. Brailsford and P. Wynblatt (Act. Metall.27 (1979) 498) determines the mean growth rate of particles of a particular size class by solving the diffusion equations for a representative particle (radius r) surrounded by a shell of matrix (the averaging sphere, radius rA) outside which there is a homogeneous effective medium averaging the emission and absorption of solute atoms by the remainder of the particles. Brailsford and Wynblatt set r = rA, in effect removing the matrix shell. It is argued herein that the feature of the theory so omitted is a very important one and we therefore use it to develop and extend the theory to make it self-consistent in the sense that the mean ratio of the particle and averaging sphere volumes is equal to the volume fraction of particles. Three self-consistent versions are developed, two of which have rA relatively constant for small particles and slowly increasing for particles greater than approximately average size. These were motivated by the observation from numerical simulations that small particles are little influenced by their neighbours whereas larger particles are much more strongly affected by the environment. Analytical expressions in terms of experimentally observable variables are given for the probability distributions for particle sizes, and tables of the parameters required to evaluate the distribution functions as a function of volume fraction are provided. It is concluded that the properties of the Brailsford and Wynblatt effective medium are closely reproduced by the alternative analytical theories, but that the idea of a matrix shell round the representative particle is unique to the chemical rate theory. It is argued that this feature makes the theory flexible and adaptable. This adaptability could be used to reproduce the results of sophisticated numerical simulations in a form which would be computationally efficient to include in wider simulations involving, say, the effect of particle growth on long term mechanical properties.