A micro/macro approach to fracture in composites

The results of an integrated microscopic/macroscopic finite element analysis of fracture in fiber-reinforced composites are presented. A macroscopic analysis of a composite double-cantilever-beam (DCB) fracture toughness test specimen was carried out using a singular finite element method. The effects of fiber layup angle on strain energy release rate are discussed. Results from this analysis were input as boundary conditions to a microscopic model used to calculate J-integral values in the crack tip region. Nonhomogeneity in this region causes the elastic strain energy release rate to vary with crack tip location and geometry. Elastic-plastic calculations showed that significant matrix plasticity occurs near fibers away from the crack tip region. The constitutive equation chosen for the matrix plasticity was shown to have an important effect on the J-integral value. The results show how the microscopic J-integral is related to the macroscopic strain energy release rate.     

Polyacrylamide gels filled with ferromagnetic anisotropic powder: A model of a magnetomechanical device

The concept of a magnetomechanical system able to show permanent magnetization if compressed or to deform in a uniform magnetic field, is presented. The system design is based on polyacrylamide gel filled with demagnetized hard ferrite particles. The ferrite filled gel is deformed by plane strain compression and magnetized while compressed. The orientation of individual magnetized particles was randomized upon compression release. Such samples exhibit no magnetic moment if decompressed and produce magnetic field intensity from 3 to 30 G if compressed. The samples exposed to external uniform magnetic field show macroscopic contraction or expansion of up to 40% of the initial dimensions. The most efficient ferrite was neodymium ferrite in the form of flakes. © 1995 John Wiley & Sons, Inc.     

The mechanical properties of poly(ether-ether-ketone) (PEEK) with emphasis on the large compressive strain response

The mechanical properties of PEEK 450G have been extensively investigated. The compressive properties were measured at strain rates between 1 × 10⁻⁴ and 3000 s⁻¹ and temperatures between −85 and 200 °C. The tensile properties were measured between the strain rates of 2.7 × 10⁻⁵ and 1.9 × 10⁻² s⁻¹ and at temperatures between −50 and 150 °C. The Taylor impact properties were investigated as a function of velocity and various large-strain compression tests were undertaken to explain the results. The fracture toughness was investigated as a function of temperature and compared with previous literature. Additionally, the fracture surfaces were studied by microscopy. As with all semi-crystalline polymers the mechanical response is a strong function of the strain rate and testing temperature. A previously reported phenomenon of darkening observed in Taylor impacted samples is shown to be due to reduced crystallinity brought about by large compressive strain. For samples deformed to large compressive strains using a variety of techniques and strain-rates the measured Vickers hardness was found to decrease in accordance with reduced crystallinity measured by other techniques.     

Experimental characterisation and constitutive modelling of RTM-6 resin under impact loading

The response to mechanical loading of the thermosetting resin system RTM-6 has been investigated experimentally as a function of strain rate and a constitutive model has been applied to describe the observed and quantified material behaviour. In order to determine strain rate effects and to draw conclusions about the hydrostatic stress dependency of the material, specimens were tested in compression and tension at strain rates from 10⁻³ to 10⁴ s⁻¹. A Standard screw-driven tensile machine was used for quasi-static testing, with an ‘in house’ hydraulic rig and Hopkinson bars for medium and high strain rates, respectively. At all rates appropriate photography and optical metrology have been used for direct strain measurement, observation of failure and validation of experimental procedures. In order to enable the experimental characterisation of this brittle material at very high rates in tension, a novel pulse shaping technique has been applied. With the help of this device, strain rates of up to 3800 s⁻¹ have been achieved while maintaining homogeneous deformation state until specimen fracture in the gauge section of the tensile specimens. The yield stress and initial modulus increased with increasing strain rate for both compression and tension, while the strain to failure decreased with strain rate in tension. An existing constitutive model, the Goldberg model has been extended in order to take into account the nonlinear strain rate dependence of the elastic modulus. The model has been validated against 3-point impact bending tests of prismatic RTM-6 beams.     

Compression and deformation of soft spherical particles

In order to model geometric property variation and investigate different compression behaviors between compressible (variable volume) and incompressible (invariable volume) soft spherical particles, two compression models based on different shapes of the lateral surface (non-contacted surface of the particle) of the compressed particles are proposed. The shape profiles in various compression degrees calculated by the models showed good agreement with the experimental data. The models can be also used to estimate the surface area and volume of the soft particles. Additionally, according to particle shape profiles, the particle structures, porous or dense, show great influences on the compression behavior for both compressible and incompressible soft particles, where the dense incompressible particle performs a higher degree of lateral extension during compression. This is because its volume can be transferred more completely from the compressed portion to the lateral surface, which is without loading contact on it.     

Electrorheological response of swollen silicone gels containing barium titanate

We have investigated storage moduli of silicone gels containing barium titanate in the presence of dc electric fields. The gels containing barium titanate swollen by silicone oil showed a storage modulus reduction, i.e. negative electrorheological effect. Contrary, no negative electrorheological effect was observed in the unswollen gels and silicon gels without barium titanate. Swollen silicone gels and most of silicone/BaTiO₃ gels obeyed empirical quadratic dependence in electric field strength. Although an apparent phase separation was not observed in the swollen gel, microscopic phase separation may occur due to the difference in electric conductivity between particles (∼10⁻¹⁰ S/cm) and silicone oil (10⁻⁹ S/cm), as a result, the negative electrorheological effect appears. The effects of frequency, degree of swelling, and the field strength have been discussed.     

The effects of carbonaceous inclusions and their distributions on dynamic failure processes in boron carbide ceramics

Commercially available boron carbide ceramics typically have heterogeneous microstructures that contain distributions of processing-induced inclusions. The inclusions that are rich in carbon (i.e., carbonaceous) govern the underlying mechanisms of brittle fracture through wing crack formation, and thus dictate the mechanical response of the ceramic. In this study, we investigate the dynamic failure of five boron carbide ceramic materials with different inclusion populations. All of the materials were prepared by hot-pressing; four of these boron carbides contained different sizes and concentrations of carbonaceous inclusions, while one contained no carbonaceous inclusions. The heterogeneity distributions were characterized in some detail for statistical analysis using scanning electron microscopy and quantitative image analysis. A modified compression Kolsky bar setup with in situ ultra-high-speed microscopic imaging (10 million frames per second) was then used to study the influence of the inclusion distributions on the dynamic failure processes in these materials, at nominal high strain rates of 10²–10³ s⁻¹. The in situ ultra-high-speed microscopy highlighted the link between micro and macroscale failure processes and demonstrated that the carbonaceous inclusions are indeed the preferential sites for nucleation of wing cracks, as previously hypothesized based on post-mortem observations. The relative orientation of an inclusion with respect to the compression axis was shown to affect the likelihood that it would participate in crack nucleation. All of the ceramics were also found to have orientation-dependent peak compressive stress, regardless of the presence of carbonaceous inclusions, suggesting that grain orientation distributions are also important.     

Compressive behavior of C/SiC composites over a wide range of strain rates and temperatures

The mechanical behavior of two-dimensional (2D) carbon fiber reinforced silicon carbide (C/SiC) composites is investigated at both quasi-static and dynamic uniaxial compression under temperatures ranging from 293 to 1273 K. Experimental results show that temperature and strain rate dramatically affect the compressive behavior of 2D C/SiC composites. If the temperature is below 873 K, the compressive strength increases with rising temperature. The reason is that the release of thermal residual stress enhances the compressive strength and this enhancement is more significant than the strength degradation due to the high temperature induced oxidation. In contrast, when the temperature rises above 873 K, the compressive strength decreases as temperature rises due to the stronger effect of oxidation induced strength degradation. Moreover, the degradation of compressive strength at strain rate of 10⁻⁴/s and temperatures above 873 K is much more obvious than those at higher strain rates, and the strain rate sensitivity factor of compressive strength increases remarkably at temperature above 873 K. Post-deformation observation shows that failure angles and fracture surfaces are also strongly dependent on testing temperature and strain rate. The change of interfacial strength at high strain rate or high temperature is responsible for the variations.     

Plastic deformation of polyethylene crystals as a function of crystal thickness and compression rate

Plastic deformation of polyethylene (PE) samples with crystals of various thickness was studied during uniaxial compression with initial compressive strain rates of 5.5×10⁻⁵, 1.1×10⁻³ and 5.5×10⁻³ s⁻¹. Samples with a broad range of crystals thickness, from usual 20 up to 170 nm, were obtained by crystallization under high pressure. The samples underwent recoverable compression below the compression ratio of 1.05-1.07. Following yield, plastic flow sets in above a compression ratio of 1.12. At a compression rate of 5.5×10⁻⁵ s⁻¹ the yield stress increases with the increase of crystal thickness up to 40 nm. For crystals thicker than 40 nm the yield stress levels off and remains constant. This experimental dependence was compared with the model developed on the basis of classical crystal plasticity and the monolithic nucleation of screw dislocations from polymer crystals. In that model contrary to the experimental evidence, the yield stress does not saturate with increase of crystal thickness. The activation volumes determined from strain rate jump experiments and from stress relaxation for crystals thicker than 40 nm are nearly constant at a level of 8.1 nm³. This activation length agrees very well with 40 nm for crystal thickness above which the yield stress levels off. It is proposed, as shown in a companion communication, that for PE crystals thicker than 40 nm two other modes of dislocation emission in the form of half loops of edge and screw dislocations begin to govern the strain rate, which no longer depend on lamella thickness.     

Structure, anisotropy and fractals in compressed cohesive powders

Correlation functions are commonly used to characterise the microstructure of materials. The correlation function is then related to other properties or phenomenology connected to the investigated material. In this paper, we investigate the bulk microstructure in two cohesive powders — a silica powder containing spherical grains and a carbon nanotube powder, by means of Spin-echo Small-angle Neutron Scattering technique. We show that, for the silica powder, the typical size of the heterogeneities decreases with increasing strain, thus linking microscopic deformations with the macroscopic ones. Measurements also show that the compressed silica powder is isotropic in terms of its density distribution. On the compressed nanotube powder we are able to conclude that the applied uniaxial stress induces anisotropy in the density distribution. We are able to link the compressive strain with the measured anisotropy, thus creating the link between macroscopic and microscopic behaviours. Both powders are shown to have a fractal structure, and are characterised in terms of a fractal dimension.     

Mechanical performance of highly compressible multi-walled carbon nanotube columns with hyperboloid geometries

Multi-walled carbon nanotube (MWCNT) columns are formed from the frit compression of a random distribution of MWCNTs in a casting solvent; its drying led to the formation of hyperboloid geometry. Uniaxial loading of MWNT columns mimics an open-cell foam behaviour and possesses an expansion rate in excess of 250 mm min⁻¹ and an elastic modulus of 10-12 MPa, thus superior to conventional low-density flexible foams. Successive compression-expansion cycling within the Hookean region reveals a hysteresis loop in the stress-strain curve that stabilises at a final value of ε_F = 18%, but on contact with its casting solvent and subsequent drying, the sample can be regenerated to within ε_R = 6% according to a memory effect and is repeatable in successive stress cycles and solvent regeneration. The system was modelled for the macroscopic stress-strain behaviour of the MWCNT column to reveal the contributions of linear dependence, elasticity-plasticity and elasticity-plasticity with hardening, revealing good agreement with the stress-strain data. MWCNT columns should prove useful as an energy adsorbing device.     

Effect of plating mode, thiourea and chloride on the morphology of copper deposits produced in acidic sulphate solutions

The influence of plating mode, chloride and thiourea (TU) on morphology of copper deposits has been studied. All experiments were conducted on disc electrodes rotating at 500 rpm and an average current density of 4 A dm⁻² to produce 10 μm thick deposits. In additive-free solutions, the use of pulsed current (PC) improved deposit morphology and brightness over DC plating. In the presence of thiourea (no Cl⁻), the deposits obtained by DC and PC plating were similar under most plating conditions. The presence of thiourea generally improved deposit quality over that obtained in additive-free solutions, but caused the formation of microscopic nodules and the deposits to appear slightly cloudy, resulting in lower reflectances than that of a polished uncoated copper surface. The addition of Cl⁻ to thiourea-containing solutions strongly influenced deposit morphology at both microscopic and macroscopic scales depending on chloride concentration and pulse conditions. It prevented nodule formation and created microscopically bright and reflective deposits, but caused extreme macroscopic roughness. Nevertheless, PC plating at 50 Hz in solutions containing appropriate amounts of thiourea and Cl⁻ was found to yield macroscopically and microscopically smooth deposits with reflectance similar to that of a polished uncoated copper substrate.     

Dynamic fracture of C/SiC composites under high strain-rate loading: microstructures and mechanisms

We investigate dynamic fracture of C/SiC composites under high strain-rate compression or tension with split Hopkinson pressure bar (SHPB) and gas gun loading. Components of the as-fabricated composites are mapped and quantified with X-ray computed tomography, including C fibers and fiber bundles, SiC matrix, and inter- and intrabundle voids. Compression loading is applied along the out-of- and in-plane directions by SHPB at strain rates of 10²–10³ s⁻¹ along with in situ X-ray phase contrast imaging. Out-of-plane direction compression and tension are examined with gas gun impact at strain rates 10⁴–10⁵ s⁻¹. For the out-of-plane loading, compression induces fracture via void collapse and shear damage banding, while delamination dominates fracture for the in-plane direction compression. With increasing strain rates, the compression failure modes transit from interbundle to intrabundle fracture of SiC, and then to fiber and bundle breaking. Tensile failure involves delamination, fiber pullout and fiber breaking. In contrary to normal solids, dynamic tensile or spall strength decreases with increasing impact velocities, owing to compression-induced predamage before subsequent tensile loading.     

Feldspar and firing cycle effects on the evolution of sanitary-ware vitreous body

This work is focused on the study of macroscopic and microscopic properties of traditional sanitary-ware vitreous bodies as a function of feldspar flux and firing time-temperature profile, using a fixed slip formulation (50 wt.% clay, 25 wt.% quartz and 25 wt.% feldspar). Two flux particle sizes (45 and 75 μm), three flux compositions (Na-based feldspar, K-based feldspar and a mix of them) and three firing cycles with the same soaking temperature (i.e. 1240 °C) have been combined to evaluate their effects on the relevant industrial properties of water absorption and thermal expansion. The micro-scale observables, phase composition and micro-morphology, have also been investigated. Despite a general similarity exhibited by the ceramic samples, qualitative and quantitative differences in terms of feldspar dissociation temperature, phase-composition and densification trends have been observed. In particular, for a fixed firing cycle, the combination of the sodium based feldspar with the smallest flux particle size leads systematically to a water absorption value that is below the 0.5 target value and to a glass amount that approaches 70 wt.%. Thermal expansion coefficients below the quartz α–β transition are found in the 6.2–6.9×10⁻⁶ °C⁻¹ range; the highest values seem to be favoured by incorporation of potassium based.     

The properties of poly(tetrafluoroethylene) (PTFE) in compression

Samples of DuPont 7A and 7C Teflon (PTFE, poly(tetrafluoroethylene)) were tested in compression at strain-rates between 10⁻⁴ and 1 s⁻¹ and temperatures between −198 and 200 °C. Additionally, using a Split-Hopkinson pressure bar, a temperature compression series was undertaken between −100 and 150 °C at a strain rate of 3200 s⁻¹. To investigate the small-strain response, strain gauges were used to measure axial and transverse strain allowing the Poisson ratio to be quantified. As expected, the mechanical properties were found to be strongly affected by strain-rate and temperature. Moduli were found by several methods and the trend, with respect to temperature, lends weight to the suggestion that the glass-transition temperature of PTFE is ≈−100 °C. The physical properties of the sintered PTFE were measured and the crystallinities measured by several techniques.     

Macroscopic analysis of polyvinyl chloride (PVC) fracture modes under impact loads

In this paper, the PVC impact fracture modes and processes were analyzed via the technique of successively increasing impact energies. Force-displacement and microscopic analyses were employed at macroscopic level to study PVC fracture modes. The fracture modes were classified as: ductile, brittle, and mixed. The mixed mode was separated into: semi-ductile and semi-brittle. In the semi-ductile mode, radial cracks were initiated and propagated, but were ultimatley arrested. For the semi-brittle mode, the fracture was characterized by connected radial and circumferential cracks. It was verified that the primary elements which governed the fracture modes and impact resistance of PVC were the crack initiation and propagation processes.     

Multi-wall carbon nanotubes coated with polyaniline

Multi-wall carbon nanotubes (CNT) were coated with protonated polyaniline (PANI) in situ during the polymerization of aniline. The content of CNT in the samples was 0-80 wt%. Uniform coating of CNT with PANI was observed with both scanning and transmission electron microscopy. An improvement in the thermal stability of the PANI in the composites was found by thermogravimetric analysis. FTIR and Raman spectra illustrate the presence of PANI in the composites; no interaction between PANI and CNT could be proved. The conductivity of PANI-coated CNT has been compared with the conductivity of the corresponding mixtures of PANI and CNT. At high CNT contents, it is not important if the PANI coating is protonated or not; the conductivity is similar in both cases, and it is determined by the CNT. Polyaniline reduces the contact resistance between the individual nanotubes. A maximum conductivity of 25.4 S cm⁻¹ has been found with PANI-coated CNT containing 70 wt% CNT. The wettability measurements show that CNT coated with protonated PANI are hydrophilic, the water contact angle being ∼40°, even at 60 wt% CNT in the composite. The specific surface area, determined by nitrogen adsorption, ranges from 20 m² g⁻¹ for protonated PANI to 56 m² g⁻¹ for neat CNT. The pore sizes and volumes have been determined by mercury porosimetry. The density measurements indicate that the compressed PANI-coated CNT are more compact compared with compressed mixtures of PANI and CNT. The relaxation and the growth of dimensions of the samples after the release of compression have been noted.     

Strain-rate-dependent compressive and compression-shear response of an alumina ceramic

This paper assessed the microstructure and properties of CeramTec ALOTEC 98 SB alumina ceramic through microscopic characterization and mechanical experiments. The rate-dependent strength and failure response of an alumina ceramic were studied under both uniaxial compression and compression-shear loading. Under quasi-static uniaxial compression at rates of 10^?5 to 10³ s^?1, the strength had an average of 3393 ± 306 MPa, and at dynamic strain rates of 10² to 10³ s^?1, the strength ranged from 3763 to 4645 MPa. The CeramTec ALOTEC 98 SB alumina ceramic was found to have greater mechanical properties than other commercial alumina ceramics from the literature (i.e., AD-995). To monitor the strain field and the failure process of the alumina ceramic during testing, an ultra-high-speed camera coupled with digital image correlation (DIC) was used to visualize crack initiation and propagation processes, and obtain quantitative stress-strain information. A new data processing method was then proposed in this study to calculate the shear components for the compression-shear tests. Validation of the proposed method was confirmed by the shear strain obtained from the DIC analysis with the ultra-high-speed camera. Using the results obtained by the proposed model and the DIC analysis, new observations and understandings of failure mechanisms are obtained. (1) In compression-shear tests, the shear failure happens before complete failure, and shear behavior plays an important role during the failure process. (2) The equivalent peak stress (strength) of compression-shear test is smaller than the uniaxial compression one. (3) The directional cracks have weak influence on the compressive stiffness, but have a strong influence on the shear response.     

Dehumidifier-Assisted Drying Characteristics of Nutrient Enriched Gellan and Agar Gels

The characteristics of moisture removal and selected physical properties during the dehumidifier-assisted drying of model food gel systems like agar and gellan gels were studied. The effect of gel forming ingredients/nutrients like FeSO₄ (0.05%), whey protein concentrate (WPC; 5%), and flaxseed powder (FSP; 5%) were investigated with an overall intention of developing a delivery system for nutrients as a convenience food. Gellan and agar gels were prepared at concentrations of 1, 2, and 3% (w/w) and subjected to drying at a low temperature of 40°C in a dehumidifier-assisted dryer up to 12 h. The different quality parameters that were determined included the extent of shrinkage, moisture content, textural parameters, and the diffusion coefficient. Agar gels possessed higher moisture ratios compared to corresponding gellan samples. The diffusion coefficients for agar and gellan gels were 0.83 × 10^?7 ? 2.38 × 10^?7 m²s^?1. The gellan gels were much harder than their corresponding agar gels. The addition of WPC, FeSO₄, and FSP increased the textural indices like fracture force, fracture strain, fracture energy, and total energy for 50% compression for all the gels. Gellan and agar gels showed volume shrinkage; the lowest shrinkages were with WPC added gels followed by the FSP and FeSO₄ incorporated samples. Dehumidifier-assisted dried food gels can serve as a delivery system for nutrients.     

High strain rate mechanical behavior of polyurea

Stress-strain measurements are reported for an elastomeric polyurea in uniaxial tension over a range of strain rates from 0.06 to 573 s⁻¹. The experiments were carried out on a new drop weight test instrument, which provides mechanical data at strain rates up to 1000 s⁻¹, filling the gap between conventional low speed instruments and split Hopkinson bar tests. The tensile data obtained herein are compared with recent high strain rate compression data on the same material [Yi et al. Polymer 2006;47:319-29]. Advantages of the present measurements include a more uniform strain rate and the ability to ensure homogeneous strain.