Some comments about “Comment on hardness definitions”, by J. Malzbender [J. Eur. Ceram. Soc. 23 (2003) 1355–1359]

Malzbender has suggested a model to determine hardness and elastic modulus as a function of the mechanical energies involved during tip penetration in instrumented indentations tests. However, the values obtained with these expressions are not consistent with the ones determined by the well-accepted Oliver and Pharr method. After revision, based on Malzbender's study itself, equations were rewritten and then, the obtained indentation hardness (H) for soda-lime glass was in agreement with the literature data. However, the reduced elastic modulus (E_r) was still about 20% higher than the values in the literature. Developing Malzbender's proposal by the inclusions of additional mechanical energy assumptions, a new expression for E_r is now suggested. Using the new expression, the hardness and reduced elastic modulus agreed very well with the Oliver and Pharr method.     

Analysis of the nanoindentation load–displacement curves measured on high-purity fine-grained alumina

This paper conducted a preliminary examination on the effect of microstructural inhomogeneity on the reproducibility of the nanoindentation data. Nanoindentation tests were conducted on a high-purity, fine-grained alumina ceramic. It was found that the reproducibility of the nanoindentation data were somewhat poor. The nanoindentation data were then analyzed with the widely employed Oliver–Pharr method to yield the hardness, H, and the Young’s modulus, E. Large scatters were observed in the resultant H and E. These experimental findings revealed that microstructural inhomogeneity may play an important role in the material response to nanoindentation.     

Enhanced mechanical properties of yttrium doped ZnO nanoparticles as determined by instrumented indentation technique

Yttrium doped (1, 3 and 5?wt%) zinc oxide nanoparticles were synthesized via sol-gel process. The phase, structural and mechanical properties were investigated using X-ray diffraction, scanning electron microscopy, energy dispersive X-ray spectroscopy and micro hardness based on indentation technique. The lattice parameters and grain sizes of the samples were calculated from the XRD data. As the lattice parameters increased, the grain sizes decreased dramatically, resulting in more grain boundaries and strong grain connectivity in the ZnO microstructure. Load-depth curves were obtained by applying indentation loads in the range from 400 to 2000?mN at room temperature. As the Y concentration increased, a significant increase was observed in the hardness values computed from loading-unloading curves using the Oliver and Pharr method. The indentation modulus of the samples reached a saturation value for 3% Y and then decreased as the doping rate increased. Moreover, the crack formation around the indent on the sample surface was examined by electron microscopy and was identified as radial/median type. The fracture toughness of the samples was calculated using the Vickers indentation fracture method. Increased fracture toughness values confirm that ZnO nanoparticles are mechanically strengthened by Y doping.     

Weld‐line sensitivity of injected amorphous polymers

The effects of the processing parameters on the weld‐line mechanical properties of polystyrene (PS) and polycarbonate (PC) were investigated. PS was very sensitive to the presence of a weld line, showing property reductions of up to 70%. However, this sensitivity was mainly connected to the surface notch at the weld line. When this notch was removed, behavior close to that of unwelded specimens was obtained. The injection temperature was the main processing parameter because it affected the macromolecular diffusion speed and, therefore, influenced the weld quality. A direct relationship between the distance of molecular diffusion and the fracture mechanism was established. PC had a low weld‐line sensitivity, despite being an amorphous polymer like PS. The difference between these materials was connected to the different sizes of the surface defects and to the different entanglement densities, which influenced the relaxation time and the global behavior (brittle–ductile). © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 644–650, 2004     

A phenomenological constitutive model for foams under large deformations

A nonlinear phenomenological constitutive model applicable to structural foams subjected to large deformations is proposed. The five‐parameter model can fully capture the three fundamental features of stress‐strain response, i.e., linearity, plasticity‐like stress plateau, and densification phases, when subjected to compressive loads. Moreover, the parameters of the model can be systematically varied to capture the influence of initial density of foams that may be responsible for changes in yield stress and hardening‐like or softening‐like behavior under various confinement conditions. The model was successfully applied to capture the stress‐strain response of two structural foams of different initial densities when subjected to uniaxial compression without lateral confinement and unixial compression under rigid confinement. Polym. Eng. Sci. 44:463–473, 2004. © 2004 Society of Plastics Engineers.     

Effects of molecular weight distribution on the spinodal temperature of polymer mixtures

The effects of molecular weight distribution on the phase stability of polymer mixtures were explored theoretically and experimentally. Based on the lattice‐fluid theory and volume‐fluctuation thermodynamics, the spinodal conditions for a lattice‐fluid mixture of two polymers with molecular weight distribution were derived. The results indicated that the phase stability of a polymer mixture decreases by increasing the molecular weight distribution of polymers in the blend. To confirm the theoretical results with experiments, the changes in the spinodal temperatures of poly(ethyl methacrylate)/polystyrene (PEMA/PS) blends and tetramethyl polycarbonate/polystyrene (TMPC/PS) blends were examined when each component has a different molecular weight distribution. When the weight‐average molecular weight of each component is the same, a blend composed of polymers having broad molecular weight distribution always exhibited lower phase separation than that composed of polymers having narrow molecular weight distribution at the same blend composition. Copyright © 2004 Society of Chemical Industry     

Free‐radical bulk polymerization of styrene with a new trifunctional cyclic peroxide initiator

The bulk free‐radical polymerization of styrene in the presence of a new cyclic trifunctional initiator, 3,6,9‐triethyl‐3,6,9‐trimethyl‐1,4,7‐triperoxonane, was studied. Full‐conversion‐range experiments were carried out to assess the effects of the temperature and initiator concentration on the polymerization kinetics, molecular weight, and polydispersity. Gel permeation chromatography was used to measure the molecular weight and the molecular weight distribution of polystyrene. When this multifunctional initiator was used for styrene polymerization at higher temperatures, it was possible to produce polymers with higher molecular weights and narrower molecular weight polydispersity at a higher rate. This showed that the molecular weight and polydispersity were influenced by the initiator concentration and the polymerization temperature in an unusual manner. Moreover, polystyrene, obtained with trifunctional peroxide, had O? O bonds in the molecular chains and was investigated with differential scanning calorimetry and gel permeation chromatography. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 1035–1042, 2004     

Low molecular weight block copolymers as plasticizers for polystyrene

Polystyrene‐b‐alkyl, polystyrene‐b‐polybutadiene‐b‐polystyrene, and polystyrene‐b‐poly(propylene glycol)monotridecyl ether were synthesized using macro initiators and atom transfer radical polymerization or by esterifications of homopolymers. The aim was a maximum molecular weight of 4 kg/mol and minimum polystyrene content of 50 w/w %, which by us is predicted as the limits for solubility of polystyrene‐b‐alkyl in polystyrene. DSC showed polystyrene was plasticized, as seen by a reduction in glass transition temperature, by block copolymers consisting of a polystyrene block with molecular weight of approximately 1 kg/mol and an alkyl block with a molecular weight of approximately of 0.3 kg/mol. The efficiency of the block copolymers as plasticizers increases with decreasing molecular weight and polystyrene content. In addition, polystyrene‐b‐alkyl is found to be an efficient plasticizer also for polystyrene‐b‐polyisoprene‐b‐polystyrene (SIS) block copolymers. The end use properties of SIS plasticized with polystyrene‐b‐alkyl, measured as tensile strength, is higher than for SIS plasticized with dioctyl adipate. The polystyrene‐b‐polybutadiene‐b‐polystyrene and polystyrene‐b‐poly(propylene glycol)monotridecyl ether series were only partially soluble in polystyrene and insoluble in the polystyrene phase of SIS. For the lowest molecular weight samples, this leads to measurable plasticization of polystyrene but no plasticization of SIS. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 95: 981–991, 2005     

A method to predict triaxial residual stresses in plastic pipes

Significant hoop and longitudinal stresses are present in medium‐density polyethylene (MDPE) pipe, arising from differential cooling from the inner and the outer surfaces of a pipe during production. Owing to the difficulty of directly measuring deformations, these stresses have hitherto been almost exclusively estimated indirectly from deflection measurements on large samples cut from the pipe wall. Furthermore, because of procedural problems, only uniaxial hoop or longitudinal stresses are normally attempted, and these are known to be specimen size–dependent. Similar problems are experienced with other polymeric pipes. In this paper, based on direct biaxial strain measurements on small samples cut from the pipe wall, a method to predict triaxial residual stress distributions through the pipe wall is presented. Thermal effects that generate residual stresses in plastic pipe were considered in the theory. The analytical solutions satisfy the self‐equilibrating conditions for both the hoop and the longitudinal stresses. Also, the radial stress is shown to be insignificant through the wall thickness of a mildly thick pipe. Polym. Eng. Sci. 44:1828–1838, 2004. © 2004 Society of Plastics Engineers.     

Double torsion tests for studying slow crack growth of portland cement mortar

For studying slow crack growth in portland cement mortar 32″ (812.8 mm) long double torsion specimens were tested. During testing, the loading and reloading compliances, permanent (or inelastic) deformations and crack growth were measured. It was observed that the strain energy release rates calculated from elastic, secant or reloading compliances do not accurately represent the fracture behavior of this material. A modified definition of the strain energy release rate is developed here to include both the elastic and the inelastic strain energy absorbed during crack extension. For this method, in addition to the reloading compliance, the knowledge of the rate of change of permanent deformations with crack growth is necessary. Details of the analytical and experimental procedure are described in this paper.     

Statistical fatigue strength evaluation and inelastic deformation generated during static and cyclic loading in Ce-TZP/alumina nanocomposite: Part 1—in air environment

The statistical fatigue strength evaluations of an intragranular type Ce-TZP/Al₂O₃ nanocomposite (Ce-TZP/A-N), such as its initial strength, static and cyclic fatigue lives, and its dispersion, were investigated in comparison to 3Y-TZP. The strength degradations during static and cyclic loading of Ce-TZP/A-N were fairly small, and the dispersions of the fatigue life were also quite small compared to those of 3Y-TZP, especially for the case of cyclic loading. In addition, fairly large inelastic deformations (converted strain ≈0.1–0.3%) were observed in the non-failure fatigued specimens after both static and cyclic loading. The amount of inelastic deformations was generally higher under the static loading than under cyclic loading, and increased with increasing the applied stress. In contrast, no inelastic deformation was identified for 3Y-TZP. By means of X-ray diffraction analysis, a good correlation between the amount of inelastic strain and the transformed monoclinic content was recognized for both static and cyclic loading.     

Residual orientation in injection‐moulded plaques of atactic‐polystyrene I: The effect of processing conditions

Injection moulded polymer articles often have residual macromolecular or crystalline orientation which can have a significant impact on the optical and mechanical properties of the moulded article. Small angle neutron scattering (SANS) was used to measure the molecular shape and orientation of deuterated blends of injection moulded polystyrene. For ～1‐mm‐thick mouldings of uniform rectangular cross‐section, the eccentricity in the SANS pattern gave a direct measure of the residual molecular orientation over the length scale ～100–1,500 Å. The residual orientation was found to vary significantly with injection moulding conditions with comparative residual orientation decreasing with decreasing mould fill‐time, and increasing with mould thickness and moulding temperatures. The orientation was found to be a minimum in the centre of the mould and highest near the surface and the average orientation at a particular position in the mould was found to be strongly correlated with the volume of material deposited as a solid skin layer during injection moulding. POLYM. ENG. SCI., 58:1322–1331, 2018. © 2017 Society of Plastics Engineers     

Solvent-Crazing criteria

Craze initiation in amorphous thermoplastics can be regarded as a transition from the safe to the unsafe state and, as such, can constitute a rational engineering design limit. A critical appraisal is made of three different criteria for initiation, which are of current interest. From this, it is concluded that the approach presented in this article, which is based upon the concept of inelastic strain, is to be preferred to the two other criteria, which are based upon an asymptotic total strain or constant inelastic strain energy criterion. The inelastic strain criterion is not only capable of modeling high stress/strain crazing in air but also satisfies the case of low stress/strain crazing in solvents. Furthermore, it offers an accurate method of extrapolating data to long times and, thus, satisfies a fundamental requirement for a parameter that can be used in engineering design.     

Pre‐necking and post‐necking relaxation and creep behavior of polycarbonate: A phenomenological study

Experiments have been performed to investigate the mechanical response of unfilled polycarbonate vis‐à‐vis the influence of prior deformation on stress relaxation and creep. Piecewise linear deformation histories, which involve strain‐controlled tensile loading of a specimen to a maximum load and partial unloading to a target strain/stress point as prologue to a relaxation test, have been shown to qualitatively influence the recorded stress‐time behavior. In particular, the stress magnitude during relaxation first increases and is then followed by a decrease. Analogously, in creep tests during unloading, the strain might decrease and then increase. Time characteristics for this U‐turn in the deformation response are influenced by the placement of the test. The influence of prior specimen conditioning on this phenomenon is investigated by comparing test data from virgin samples to that of specimens having high (～85%) inelastic strain from prior tensile elongation. Findings suggest that the observed persistence in the occurrence of this reversal effect for both types of specimens is evidence of the need to incorporate this behavior into the fold of material modeling. Additionally, this novel relaxation and creep behavior has been observed in other amorphous (poly(phenylene oxide)) and crystalline (high‐density polyethylene) polymers. Polym. Eng. Sci. 44:1783–1791, 2004. © 2004 Society of Plastics Engineers.     

Development of elastic and plastic properties of polyoxymethylene during bending fatigue

The development of the plastic and viscoelastic properties and the corresponding failure limits of the acetal homopolymer polyoxymethylene were studied in unidirectional cyclic fatigue. Samples with molecular weights (MWs) ranging from 90 to 142 kg/kmol were tested in displacement‐controlled conditions, resulting in maximum stress amplitudes between 30 and 59 MPa and strain amplitudes between 35.8 and 92.6 με. The zero‐hour material properties and the cycle‐dependent property development were predominantly dictated by deformations in the crystalline regions and showed a negligible dependence on MW. However, the final failure limits were found to be primarily dependent on the length of the amorphous tie chains that connect the crystallites. As such, fatigue life analysis showed a strong dependence on MW. Results are interpreted in light of the primary mechanical failure mechanisms and the corresponding molecular deformations. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40762.     

Strain‐rate and temperature effects on the deformation of polypropylene and its simulation under monotonic compression and bending

Monotonic compressive loading and bending tests are conducted for solid polypropylene (PP) under constant or time‐varying strain‐rates and temperatures of 10, 25, 40°C. The observed compressive stress‐strain responses under constant conditions have revealed that the inelastic deformation behavior is remarkably dependent on loading rates and temperatures of normal use. The examination of such inelastic behavior has indicated that the strain‐rate effects correspond with the temperature effects based on the concept of time‐temperature equivalence. The viscoplastic constitutive theory based on overstress (VBO) has successfully reproduced the experimental responses with stress‐jumping phenomena using the equivalent time. Four‐point bending tests are performed under monotonic loading and holding for PP beams at three different temperatures. The observed deformation behavior has shown that the Bernoulli‐Euler hypothesis is valid. The VBO model and beam bending theory has generated the basic equations for PP beams, showing an analogy with the uniaxial one. In the numerical analysis, the equations are transformed into nonlinear ordinary differential equations with use of Gaussian quadrature for the spatial integrals. The comparison of numerical and experimental results has suggested some modifications for actually loaded moment taking the effect of deflection and friction into consideration. Finally, the numerical calculation has simulated the experimental time‐histories of curvatures fairly well.     

A new PDMS macromonomer stabilizer for dispersion polymerization of styrene in supercritical carbon dioxide

Free radical polymerization of styrene in supercritical CO₂ requires addition of a surfactant to produce polystyrene (PS) in high conversion and molecular weight with well‐defined particle sizes. In this work, we examined a new stabilizer that can provide effective stabilization for the polymerization of styrene. A commercially available poly(dimethylsiloxane) macromonomer has been employed as a stabilizer for dispersion polymerization of PS in scCO₂. The reactions were conducted in a 225‐mL stainless steel autoclave over the temperature range 60–80°C and under pressures of 1,500 to 3,000 psi. After 2–12 h of polymerization, the conversion determined by gravimetrical method was between 20 and 80%. These preliminary results suggest that this macromonomer offers satisfactory stabilization for the styrene system. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 545–549, 2004     

Development of discrete nanopores I: Tension of polypropylene/ polyethylene copolymer blends

Porous polymeric materials can be prepared by using micromechanical deformations. The development of porous structures in the tension of polyolefin blends are studied with the goal of developing a novel technique to make porous films. It is found in polypropylene/polyethylene copolymer blends of near 50/50 weight ratio that a metallocene polymer pair can produce stable nanopores throughout a wide range of strain, ～50–700%. Its strain‐to‐break was relatively high, although its continuous phase is a brittle polypropylene. The typical size of nanopores is 10–300 nm; they start to develop at approximately 50% strain. The disruption of craze‐like structures into discrete nanopores seems to be the key mechanism in stabilizing pore development. Varying stretching direction and speed controls the pore morphology. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 91: 3642–3650, 2004     

Development of a constitutive relation for elastomers exhibiting self‐reinforcement

A constitutive relation was developed to describe the mechanical behavior of elastomers that exhibit self‐reinforcement, or elastic strain‐hardening behavior, such as most polyurethane elastomers and some hydrogels. A number of constitutive relations based on both molecular network theory and phenomenological behavior were evaluated. Generally, molecularly based constitutive relationships work well for small deformations, but demonstrate gross deviations from actual behavior at large deformations. Phenomenological relations often predict behavior well but employ mathematical functions based on strain invariants that may cause difficulty in identifying and consistently predicting material properties. The constitutive relation developed here has an exponential functional form. The argument of the exponential is a general fourth order tensor reduced to the isotropic case. The tensor coefficients used in the exponential function are sensitive to variations in molecular weight and can be related to the shear modulus. This exponential constitutive relation is relatively simple to implement, and the two material parameters can be predicted from the maximum extension ratio, the molecular weight between crosslinks, and the experimentally determined shear modulus in the high strain region. POLYM. ENG. SCI., 46:919–929, 2006. © 2006 Society of Plastics Engineers     

Meso‐scale simulations of solid–liquid flow and strategies for meso–macro coupling

Solid–liquid flows span a large parameter space, with dimensionless coordinates such as Stokes numbers, the solids volume fraction, the density ratio between the phases, and Reynolds numbers (e.g., associated with the continuous phase flow). We are interested in systems with appreciable inertia effects—that is, nonzero Stokes and Reynolds numbers—having density ratios of the order of one and solids volume fractions of order 0.1. In such flows, direct numerical simulations are desired to reveal the relevant interactions. The resolution required for DNS limits the size of the systems that we are able to simulate to the meso‐scale. In this article, examples of direct simulations based on the lattice‐Boltzmann method of dense solid–liquid flows are presented, along with suggestions as to how to use their results at the macro‐scale. © 2011 Canadian Society for Chemical Engineering