Elastic stress field model and micro-crack evolution for isotropic brittle materials during single grit scratching

An analytical model for the elastic stress field in isotropic hard and brittle materials during scratching is presented. The model considers the entire elastic stress field and the effect of material densification that was ignored in past studies, and is developed under a cylindrical coordinate system to make the modeling process simpler. Based on the model's predictions, the location and sequence of crack nucleation are estimated and the associated mechanisms are discussed. A single grit scratching experiment with an increasing scratch depth up to 2 µm is conducted for two types of optical glasses representing isotropic brittle materials: fused silica and BK7 glasses. It is found that the model's predictions correlate well with experimental data. Median cracks are found to be formed first during scratching, and the corresponding depth of the scratch sets the basis for determining the critical depth for brittle to ductile machining. Lateral cracks are initiated in the plastic yielding region and deflect to the work surface to cause material removal, while Hertzian cracks interact with lateral cracks to help remove lateral-cracked material. Furthermore, it is found that, owing to its open network molecular structure, fused silica has a much worse ductile machinability than the BK7 glass.     

Charge density dependence of elastic modulus of strong polyelectrolyte hydrogels

The mechanical behavior of a series of strong polyelectrolyte hydrogels based on acrylamide and 2-acrylamido-2-methylpropane sulfonic acid sodium salt (AMPS) was investigated. The hydrogels were prepared at a fixed crosslinker ratio and monomer concentration, but at various charge densities, i.e. AMPS contents between 0 and 100 mol%. The elastic modulus of the hydrogels after their preparation first increases with increasing charge density but then decreases continuously. Investigation of the swollen state properties of the hydrogels shows existence of a large number of ionic groups inside the gel that are ineffective in gel swelling. The results indicate two opposite effects of charged groups on the elastic modulus of the hydrogels: formation of multiplets acting as additional crosslinks in the gel increases the elastic modulus of ionic hydrogels, whereas the effect of the electrostatic interaction of charged groups on elastic free energy decreases the modulus.     

Drying-induced stresses in elastic and viscoelastic saturated materials

The paper presents a theoretical analysis of stresses generated during convective drying of kaolin, based on elastic and viscoelastic models. The equations of these models were solved analytically for a cylindrically shaped sample; the distribution and evolution of the radial and circumferential stresses are illustrated in diagrams. The acoustic emission method was used in experimental tests for identification on line of the time period during which the stresses reach their maximal values. A better correlation has been found between the experimental tests and the theoretical predictions obtained on the basis of the viscoelastic model.     

X-ray structure analysis and elastic properties of a fabric reinforced carbon/carbon composite

The effect of heat treatment on microstructure of a plain-weave carbon fabric reinforced carbon-carbon composite with phenolformaldehyde-derived carbon matrix was investigated by X-ray diffraction. The diffraction patterns were analysed by the least-square fitting program Carbonxs. After heat treatment from 1000 to 2800 °C the interplanar distance of (002) planes decreased from 3.488 to 3.420 Å and the lattice parameter in basal plane increased from 2.440 to 2.464 Å, respectively. Simultaneously, the coherent block size in the basal plane directions increased from 18 to 54 Å, which was accompanied by an increase of the fraction of organised carbon atoms from 0.50 to 0.85. The 002 diffraction profile of the composite was much narrower than the sum of peaks of the matrix and fabric alone. This can probably be caused by a better crystallographic ordering (or by a partial graphitisation) of the matrix in the composite. On the other hand, the composite Young’s modulus slightly decreased with the treatment temperature increasing from 2200 to 2800 °C in spite of the established strong improvement of fibre crystallinity and, therefore, fibre modulus. The mechanisms diminishing the modulus of composite (e.g. partial matrix graphitisation at the fibre/matrix interface and decreasing fibre/matrix contact area) probably prevailed over the increasing contribution of the fibre modulus.     

CONTACT BETWEEN A SMOOTH MICROSPHERE AND AN ANISOTROPIC ROUGH SURFACE

This article discusses the effects of asperities on elastic and adhesive contact between a smooth sphere and a rough surface. Two numerical methods are introduced: an asperity-superposition method and a direct-simulation method. In the first method, geometric parameters such as asperity heights, orientations, and radii of curvature are identified by a least-squares regression of neighboring surface heights measured using an atomic force microscope. The rough surface is reconstructed by the superposition of these asperities. The modeling of adhesive and elastic contacts begins with the modeling of a single parabolic-shaped asperity contact. A generalized JKR model for an arbitrary parabola is developed to suit this purpose. The contact between the rough surface (represented by the supposition of parabolic-shaped asperities) and the sphere consequently is modeled bythe mapping and integration of individual asperity contacts. In the second method, pure-elastic contact is modeled by half-space elastic theory. A contact-search algorithm is used to find solutions on the displacement and the contact-pressure distribution that satisfy both the load-displacement equation and the contactboundary conditions. Results from both methods are compared to reveal the effects of asperities on adhesion and elastic-contact pressure.     

A multiscale model for effective moduli of concrete incorporating ITZ water-cement ratio gradients, aggregate size distributions, and entrapped voids

This paper develops a model for the effective elastic properties of concrete, which is a function of the volume fractions, size distributions, and elastic properties of fine aggregate (FA) and coarse aggregate (FA) and entrapped voids. Furthermore, the model is a function of the overall water-cement ratio and specific gravity of cement. Explicitly modeled are the water-cement ratio gradients through the interfacial transition zone (ITZ), which, in turn, affect the variation of the cement paste elastic properties through the ITZ, while maintaining the total fractions of cement and water consistent with the overall water-cement ratio. The ITZ volume is also conserved.     

Segmented blockcopolymers with uniform amide segments

Segmented blockcopolymers based on poly(tetramethylene oxide) (PTMO) soft segments and uniform crystallisable tetra-amide segments (TxTxT) are made via polycondensation. The PTMO soft segments, with a molecular weight of 1000 g/mol, are extended with terephthalic groups to a molecular weight of 6000 g/mol. The crystallisable segment is uniform of length and is based on a tetra-amide with terephthalamide groups. The length of the aliphatic diamine (x) in the tetra-amide segment is varied from x=2 to 8. The thermal properties of the blockcopolymers were studied with dynamic mechanical analysis (DMA) and differential scanning calorimetry (DSC). Due to the use of uniform TxTxT segments a fast and almost complete crystallization of the hard segments is obtained. The melting temperature of the blockpolymers increases with decreasing diamine length and the well-known odd-even effect is observed. The elastic behavior of the blockcopolymer was studied by compression set. All the blockcopolymers had a low compression set and were highly elastic.     

Effect of temperature and age on the relationship between dynamic and static elastic modulus of concrete

This study investigates the effects of cement type, curing temperature, and age on the relationships between dynamic and static elastic moduli or compressive strength. Based on the investigation, new relationship equations are proposed. The impact-echo method is used to measure the resonant frequency of specimens from which the dynamic elastic modulus is calculated. Types I and V cement concrete specimens with water-cement ratios of 0.40 and 0.50 are cured isothermally at 10, 23, and 50 °C and tested at 1, 3, 7, and 28 days.Cement type and age do not have a significant influence on the relationship between dynamic and static elastic moduli, but the ratio of static to dynamic elastic modulus approaches 1 as temperature increases. The initial chord elastic modulus, which is measured at low strain level, is similar to the dynamic elastic modulus. The relationship between dynamic elastic modulus and compressive strength has the same tendency as the relationship between dynamic and static elastic moduli for various cement types, temperatures, and ages.     

The effect of two types of C-S-H on the elasticity of cement-based materials: Results from nanoindentation and micromechanical modeling

It has long been recognized, in cement chemistry, that two types of calcium-silicate-hydrate (C-S-H) exist in cement-based materials, but less is known about how the two types of C-S-H affect the mechanical properties. By means of nanoindentation tests on nondegraded and calcium leached cement paste, the paper confirms the existence of two types of C-S-H, and investigates the distinct role played by the two phases on the elastic properties of cement-based materials. It is found that (1) high-density C-S-H are mechanically less affected by calcium leaching than low density C-S-H, and (2) the volume fractions occupied by the two phases in the C-S-H matrix are not affected by calcium leaching. The nanoindentation results also provide quantitative evidence, suggesting that the elastic properties of the C-S-H phase are intrinsic material properties that do not depend on mix proportions of cement-based materials. The material properties and volume fractions are used in a novel two-step homogenization model, that predicts the macroscopic elastic properties of cement pastes with high accuracy. Combined with advanced physical chemistry models that allow, for a given w/c ratio, determination of the volume fractions of the two types of C-S-H, the model can be applied to any cement paste, with or without Portlandite, Clinker, and so on. In particular, from an application of the model to decalcified cement pastes, it is shown that that the decalcification of the C-S-H phase is the primary source of the macroscopic elastic modulus degradation, that dominates over the effect of the dissolution of Portlandite in cement-based material systems.     

ANALYTICAL SOLUTIONS FOR PEELING USING BEAM-ON-FOUNDATION MODEL AND COHESIVE ZONE

When fibrillation occurs during peeling, the normal stress in the adhesive may gradually reduce to zero at the peel front. The shear stress also reduces to zero. Classical beam-spring (or beam-on-elastic-foundation) models do not yield solutions that have these properties. With the use of a beam-on-foundation model combined with a cohesive zone in the neighborhood of the peel front, these properties can be satisfied. In order to obtain analytical solutions, peel tests are considered in which the backing has a small slope and is linearly elastic in the adhered region, and the traction law is assumed to be piecewise linear. Cases are considered with only normal stresses in the adhesive (mode I), only shear stresses (mode II), and both stresses coupled (mixed-mode behavior). Analytical solutions are obtained for displacements of the backing, forces in the backing, and stresses between the adhesive and the backing.