Bonded particle modeling of grain size effect on tensile and compressive strengths of rock under static and dynamic loading

The effect of grain (particle) size on the strength is an interesting subject in the rock engineering. Some investigations about the impact of particle size on static strength of rock have been conducted and reported in the literature. However, this issue has not received enough attention when high loading rates are involved. In this work, by utilizing the CA3 bonded particle - finite element computer program, the combined influence of loading rate and particle size on the compressive and tensile strengths of rock is examined. The bonded particle model is used to simulate the crack initiation and failure of the rock specimen and the finite element is utilized to model the elastic bars in the Split Hopkinson Pressure Bar (SHPB) apparatus employed for the dynamic testing. Specimens with four different particle sizes were prepared. The results suggest that the particle size does not affect the rock strength under static and dynamic loading. However, the particle size modifies the nominal tensile strength of the notched Brazilian specimens. For the intact Brazilian specimens under high stress rates, the particle size contributes to the tensile strength and this contribution can be justified based on the principles of fracture mechanics. The theoretical reason for these observations is derived for a 3D bonded particle system and discussed.     

Use of Tablet Tensile Strength Adjusted for Surface Area and Mean Interparticulate Distance to Evaluate Dominating Bonding Mechanisms

In this study, tablet tensile strength has been adjusted for tablet surface area and the average distance between particles in compacts of different materials. The aim of the study was to evaluate the feasibility of using this concept to assess the dominating interparticulate bonding mechanisms. Adjustment of the tensile strength for both tablet surface area and mean pore radius gave similar bonding strength values for materials bonding mainly by weak distance forces (crystalline lactose, sucrose, and microcrystalline cellulose) almost independently of compaction pressure. However, particle size and other factors may still affect the compensated strength values. The bond strength was much higher and more varied for materials bonding also with solid bridges (potassium chloride, sodium chloride, and possibly also sodium bicarbonate and amorphous lactose). For these materials, particle size and compaction pressure had a substantial effect on the bond strength. It is probably the formation of continuous bridges between adjacent particles that is important in these materials rather than the surface properties and the average distance between particles positioned at some distance from each other. Hence, adjusting the tensile strength of compacts does not necessarily reflect all the dominating factors responsible for interparticulate bonding. Nonetheless, adjustment for tablet surface area and mean pore radius allowed discrimination between different dominating interparticulate bonding mechanisms in these compacted materials.     

Use of Tablet Tensile Strength Adjusted for Surface Area and Mean Interparticulate Distance to Evaluate Dominating Bonding Mechanisms

In this study, tablet tensile strength has been adjusted for tablet surface area and the average distance between particles in compacts of different materials. The aim of the study was to evaluate the feasibility of using this concept to assess the dominating interparticulate bonding mechanisms. Adjustment of the tensile strength for both tablet surface area and mean pore radius gave similar bonding strength values for materials bonding mainly by weak distance forces (crystalline lactose, sucrose, and microcrystalline cellulose) almost independently of compaction pressure. However, particle size and other factors may still affect the compensated strength values. The bond strength was much higher and more varied for materials bonding also with solid bridges (potassium chloride, sodium chloride, and possibly also sodium bicarbonate and amorphous lactose). For these materials, particle size and compaction pressure had a substantial effect on the bond strength. It is probably the formation of continuous bridges between adjacent particles that is important in these materials rather than the surface properties and the average distance between particles positioned at some distance from each other. Hence, adjusting the tensile strength of compacts does not necessarily reflect all the dominating factors responsible for interparticulate bonding. Nonetheless, adjustment for tablet surface area and mean pore radius allowed discrimination between different dominating interparticulate bonding mechanisms in these compacted materials.     

Tensile strength degradation of ceramic fibres due to cyclic loading

Interfacial strength of Ti β 21S/SCS 6 composite was increased via ageing. Composite specimens with a_o/W ratios of 0.24 and 0.07 were prefatigued in three point bending at ambient and at 500 °C both in the air and vacuum. Bridging fibres were extracted from the pre-fatigued specimens and tested in tensile loading to monitor the strength degradation due repeated opening and closing of the fatigue crack. A tri-modal Weibull distribution was employed to express strength distribution of the SCS 6 fibres. Results have shown that cyclic loading of the composites lower the mean tensile strength of the fibres by 20%, compared to the unfatigued composite. A marked effect of initial unbridged defect size was observed, when the tensile strength data were divided into two sub-population using the fatigue crack length values. Compared to unfatigued composite, tensile strength reductions of 41 and 22% were measured from the prefatigued composites with a_o/W of 0.24 and 0.07, respectively.     

On the calculation of deformation curves for two-phase cermets

Analytical algorithms for the construction of tensile and compression stress-strain diagrams of two-phase cermets are proposed, which are based on the concept of mean stresses in the phase volume and physical equations of the theory of small elastoplastic strains. The deformation properties and strength of cermet are supposed to depend on such parameters of its microstructure as mean size and coefficient of variation of solid phase grain-size distribution, contiguity coefficient of solid phase grains, and mean thickness of the metal phase inter-layers. A numerical analysis of the characteristic parameters of deformation curves for WC-Co hard metals has been carried out over a wide range of cobalt concentration and carbide grain size. A good agreement between the theoretical values of ultimate tensile and compression strength and known experimental values has been established. The constructed model deformation curves for hard metals may be regarded as alternatives to the corresponding experimental curves of stress against relative change in specimen length. __________ Translated from Problemy Prochnosti, No. 3, pp. 99–111, May–June, 2006.     

Investigations into the mechanical strength anisotropy of Sorbitol Instant compacts made by uniaxial compression

Powder compacts manufactured by the pharmaceutical industry are usually produced by uniaxial compression of powders or granules. This process results in compacts that are anisotropic in their mechanical strength, but this hypothesis has received little attention in the past. In this work, compacts were produced from sorbitol granules using two distinctively different particle size fractions, two compaction speeds and a range of different tablet porosities. The compact tensile strength was assessed by diametral and biaxial compression and by flexural bending. Fracture mechanics, i. e. the critical stress intensity factors in mode I and II loading, and the construction of the fracture envelope were used to investigate failure mechanisms and strength anisotropy. The strength results were also analyzed statistically employing Weibull analysis and analysis of variance. Granule size and compaction speed were identified as major influence factors on tensile strength. The magnitude of the effects found, however, varied between the individual test configurations. Further processing of the Weibull moduli obtained from the different tests confirmed the anisotropy of powder compacts made by uniaxial compression. They also showed that the commonly used diametral compression test to obtain tensile strength values is the least sensitive measure to assess the influence of particle properties on mechanical strength. Biaxial testing was found to be able to detect small changes in crack and flaw structure as a result of small changes in the particle characteristics of sorbitol.     

Mechanical testing of directionally solidified eutectic ceramics (DSECs): specific problems and limitations

The specific problems of DSECs mechanical testing result from the particularities of these 3-D interconnected eutectic ceramics. First of all, 4-point bending tests ensure pure bending loading, whereas 3 PB tests only lead to a tensile and shear stress combination. Consequently, due to the 3-D microstructure of DSECs, interfaces between the various phases are subjected to a mixed (tensile and shear) loading which makes the interpretation of the results (strength) and of the fracture surfaces, rather difficult. For usual ceramics, biaxial flexure testing offers many advantages over 3- or 4-point beam-bending testing. The coaxial-ring test is free of edge influences (flaws): cracks initiate in the central area and propagate outwardly. However, in the case of DSECs, due to the presence of high internal thermal stresses (especially for ternary eutectics), interfaces can be subjected to a strong radial tensile and shear (near the free surface) stress combination. In the presence of the radial tensile stress resulting from biaxial loading, this internal thermal stress combination can lead to premature crack initiation leading to failure. Specimen machining through grinding leads to the formation of a strongly damaged layer. Annealing of this layer leads to the formation of a rough surface: slightly protruding phases and stress concentrations at the interfaces. The measured strength is ≈20% lower after annealing than that directly after grinding. Concerning the effect of the microstructure size, four representative sizes have been selected in the ≈10 µm to submicrometre range. A classical crack propagation criterion has allowed explaining the corresponding strength values.     

Characterization of strength properties of thin polycrystalline silicon films for MEMS applications

The aim of this work is to characterize the strength properties of polycrystalline silicon (polysilicon) with the use of tensile and bending test specimens. The strength of thin polysilicon films with different geometry, size and stress concentrations has been measured and correlated with the effective size of the specimen and its stress distribution. The test results are evaluated using a probabilistic strength approach based on the weakest link theory with the use of STAU software. The use of statistic methods of strength prediction of polysilicon test structures with a complex geometry and loading based on test values for standard material tests specimen has been evaluated.     

Sr effect on the microstructure and tensile properties of A357 aluminum alloy and Al2O3/SiC-A357 cast composites

The effect of strontium as a modifier on the microstructures and tensile properties of two castable particulate metal matrix composites has been studied. The particulate metal matrix composites had similar matrix alloy (A357) but different reinforcing fine particles (silicon carbide and alumina). Results showed that the addition of 0.03% strontium makes a modest improvement to the yield strength, ultimate tensile strength and elongation percentage values, and the scatter of these properties, but makes a significant improvement to minimum strength and elongation results. Microstructural examinations by scanning electron microscope and energy dispersive spectroscopy analysis of metal matrix composites showed segregation of strontium on both the silicon carbide and alumina particles. Further results showed that the addition of higher strontium levels contributes to the over-modification of the eutectic silicon and promotes the formation of an Al–Si–Sr intermetallic compound on the particle/matrix interface.     

Relationship between tensile strength and porosity for foamed metals under equal speed biaxial tension

Abstract

A preliminary experimental investigation has been carried out on an isotropic three dimensional reticulated foamed metal with high porosity under biaxial tensile loading. The approximate relationship between tensile strength of these materials and their porosity has been evaluated under equal-speed biaxial tension loading. The mathematical formula is proved to be in a good agreement with the experimental data for nickel foam.     

Mechanical and Electrical Properties of Cryo-worked Cu

For manufacturing the magnets of fusion machines pure copper of both high mechanical resistance and electrical conductivity is required. Though high purity copper guarantees high electrical conductivity, its mechanical properties may be not suitable for the applications in tokamaks. In this view, a new procedure developed for obtaining high purity copper with excellent mechanical strength is described in this work. Samples of oxygen free copper (OFC) have been worked by pressing in liquid nitrogen (77 K). It has been verified that the mechanical properties of the worked metal are strongly dependent on the strain rate. Very low strain rates permitted to attain values of tensile yield strength (550 MPa) significantly higher than those obtained by traditional cold-working at room temperature (450 MPa). The electrical conductivity of the cryo-worked Cu decreases with the tensile yield strength even though the hardest samples of tensile yield strength of 550 MPa exhibit still acceptable values of conductivity (about 94 % IACS at room temperature).     

The influence of particle size on the tensile strength of particulate — filled polymers

The tensile strengths of a particulate-filled rigid polyurethane resin are presented at varying volume fractions and a wide range of particle sizes. These results are compared with exisiting theories of the strength of particulate-filled composite systems. A linear relationship is proposed to exist between the mean particle diameter and the tensile strength at a given volume fraction. A method of normalizing data is presented which removes the stress-concentration effects of finite particle sizes and allows comparison of the data with a simple equation relating tensile strength and volume fraction. The effects of particle size and volume fraction in relation to crack propagation are discussed, and the proposed method of analysis is shown to give similar results when applied to published data.     

Effect of stress ratio on fatigue behaviour in SiC particulate-reinforced aluminium alloy composite

Axial fatigue tests have been performed at three different stress ratios, R, of ?1, 0 and 0.4 using smooth specimens of an aluminium alloy composite reinforced with SiC particulates of 20 μm particle size. The effect of stress ratio on fatigue strength was studied on the basis of crack initiation, small crack growth and fracture surface analysis. The stress ratio dependence of fatigue strength that has been commonly observed in other materials was obtained, in which fatigue strength decreased with increasing stress ratio when characterized in terms of stress amplitude. At R=?1, the fatigue strength of the SiC_p/Al composite was the same as that of the unreinforced alloy, but at R= 0 and 0.4 decreased significantly, indicating a detrimental effect of tensile mean stress in the SiC_p/Al composite. The modified Goodman relation gave a fairly good estimation of the fatigue strength at 10⁷ cycles in the unreinforced alloy, but significantly unconservative estimation in the SiC_p/Al composite. At R= 0 and 0.4, cracks initiated at the interfaces between SiC particles and the matrix or due to particle cracking and then grew predominantly along the interfaces, because debonding between SiC particles and the matrix occurred easily under tensile mean stress. Such behaviour was different from that at R=?1. Therefore, it was concluded that the decrease in fatigue strength at high stress ratios and the observed stress ratio dependence in the SiC_p/Al composite were attributed to the different fracture mechanisms operated at high stress ratios.     

Effects of sandblasting metal bracket base on the bond strength of a resin-modified glass ionomer cement: an in vitro study

The introduction of air abrasion (sandblasting) technology to orthodontics may allow reaching optimum bond strength between the metal bracket and resin-modified glass ionomer cement. This study examined the effects of sandblasting metal bracket bases on the in vitro tensile bond strength of a resin-modified glass ionomer cement. Two-hundred foil-mesh based brackets were divided into ten groups and combinations of three sizes of aluminum oxide powder (25, 50 and 110 μm) and three sandblasting times (3, 6 and 9 seconds) were tested. One group was not sandblasted and used as control. Analysis of variance showed that bond strength was significantly affected by the sandblasting time (p < 0.001) and size of the aluminum oxide powder (p < 0.001). Only the group (SO₂₅) sandblasted with 25 μm aluminum oxide powder for 3 seconds yielded higher mean bond strength than that of the control group. The bond strength values were also analyzed using a Weibull analysis, which showed the most favorable size (25 μm) and time combination (3 seconds), and the 5% and 90% probabilities of failures. This study suggests that sandblasting time and particle size have and important effect on the bond between the metal bracket and resin-modified glass ionomer cement.     

Effect of prestrain on tensile properties and ratcheting behaviour of Ti-stabilised interstitial free steel

Effect of prestrain ranging between 2.5 and 15 percent on tensile properties, and ratcheting behaviour of an interstitial free steel has been studied at two different stress combinations. It is found that while yield strength increases in two distinctly different stages, the increase of tensile strength follows perfect linear relationship with increase in the amount of prestrain. The ratcheting strain accumulation direction during initial stage of asymmetric cyclic loading at constant tensile mean stress depends upon imposed maximum stress and the amount of prestrain. Number of cycles for accumulation of 16.30 pct true ratcheting strain increases with the amount of prestrain following perfect exponential relationships for both the stress combinations; but it increases in a perfectly bilinear manner with tensile yield strength of prestrained specimens. With 16.30 pct accumulated ratcheting strain the amount of back stress is found as 110 MPa irrespective of the amount of prestrain. Marginal variation in post-ratcheting tensile properties as a function of tensile prestrain has been observed.     

Plane thermal transpiration of a rarefied gas in the presence of gravitation

Plane thermal transpiration of a rarefied gas that flows horizontally in the presence of gravitation is studied based on the Boltzmann equation. Assuming that the temperature gradient along the walls is small, the asymptotic analysis for a slow variation in the flow direction is conducted. The semi-analytical solution that is valid for arbitrary values of the mean free path and the gravitational strength is derived, and the problem is reduced to solving the spatially one-dimensional Boltzmann equation. This reduced problem is solved numerically for a hard-sphere molecular gas for small values of gravitational strength, and the behavior of the flow is studied based on the numerical solution. The effect of weak gravitation is no longer negligible when the gas is so rarefied that the mean free path is comparable to the maximum range that the molecules travel along the parabolic path within the channel. This phenomenon has been observed in the plane Poiseuille flow of a highly rarefied gas, and a similar phenomenon also occurs in the plane thermal transpiration considered in the present paper.     

Effects of particle size and distribution on the mechanical properties of SiC reinforced Al-Cu alloy composites

This paper studied the combined effects of particle size and distribution on the mechanical properties of the SiC particle reinforced Al-Cu alloy composites. It has been shown that small ratio between matrix/reinforcement particle sizes resulted in more uniform distribution of the SiC particles in the matrix. The SiC particles distributed more uniformly in the matrix with increasing in mixing time. It has also been shown that homogenous distribution of the SiC particles resulted in higher yield strength, ultimate tensile strength and elongation. Yield strength and ultimate tensile strength of the composite reinforced by 4.7 μm sized SiC particles are higher than those of composite reinforced by 77 μm sized SiC particles, while the elongation shows opposite trend with yield strength and ultimate tensile strength. Fracture surface observations showed that the dominant fracture mechanism of the composites with small SiC particle size (4.7 μm) is ductile fracture of the matrix, accompanied by the “pull-out” of the particles from the matrix, while the dominant fracture mechanism of the composites with large SiC particle size (77 μm) is ductile fracture of the matrix, accompanied by the SiC particle fracture.     

Development and characterization of novel EPDM/NR prophylactic waste composites

Ethylene propylene diene rubber (EPDM) is a well-known versatile polymer, which is frequently used in the production of rubber goods based on conventional and specialty polymers. The present paper investigates the role of recycled natural rubber prophylactic waste compared to virgin natural rubber in the development of novel ethylene propylene diene rubber composites. The processing characteristics have been evaluated using a Monsanto rheometer at three different temperatures 150, 160 and 170°C. The cure curves of EPDM compounds have been found to be the resultant of slow curing or marching cure curve of EPDM and that of fast curing S shaped cure curve of natural rubber. The curing properties such as optimum cure time, scorch time and induction time have been found to be decreasing with the loading of prophylactic filler. For most of the cases, the values obtained for compositions with virgin natural rubber (ISNR-5) have been found to be lower than that with prophylactic filler.The cure activating nature of the prophylactic waste in EPDM is higher at higher temperatures. The unaged tensile strength has been increased with the loading of prophylactic filler up to 30 phr. The aged tensile strength and unaged/aged elongation at break have been found to be a maximum at 20 phr prophylactic filler loading. The tear strength has been found to be a maximum at 40 phr. Better performance has been noted in the case of virgin natural rubber filled samples for unaged/aged tensile strength, elongation break and tear strength except at 40 phr loading. The diffusion process in EPDM vulcanizates is found to be anomalous. Crosslink density values determined using Mooney-Rivlin equation agree with the tensile strength values for most of the cases. An increase in the crosslink density has been noted with the thermal aging of the samples.     

考虑加载速度影响的沥青混合料疲劳方程

为了建立沥青混合料强度与疲劳行为之间的联系,通过不同加载速率下的沥青混合料直接拉伸强度试验,揭示了强度随加载速率的幂函数变化规律;基于不同加载速率下的强度值,得到了与疲劳加载速率对应的沥青混合料疲劳真实应力比;通过疲劳试验,创建了基于名义应力比和真实应力比的沥青混合料疲劳方程,基于名义应力比的疲劳方程后延后与横坐标的交点远比1 大,不具有后延性,而基于真实应力比的疲劳方程可以后延到疲劳寿命为1 的强度破坏点,统一了强度破坏与疲劳破坏行为;据此推导了沥青路面抗拉强度结构系数计算新方法;研究结果可为我国公路沥青路面设计规范的修订提供理论依据.     

Analytical study of strength and failure behaviour of plain weave fabric composites made of twisted yarns

A two-dimensional analytical method is presented for the failure behaviour of plain weave fabric composites made of twisted yarns. The studies have been carried out on laminates with different configurations under on-axis uni-axial tensile loading. The cross-sectional area of the yarn was taken to be elliptical and the yarn path was taken to be sinusoidal. Different stages of failure are considered in the analysis. It has been observed that there is no significant reduction in tensile strength properties of plain weave fabric composites as a result of twisting of yarns. For E-glass yarns, twisting of yarns up to 5°, can facilitate ease of fabrication without significantly compromising the strength properties of the woven fabric composites.