基于虚拟裂缝模型求解混凝土等效断裂韧度的实用解析方法

主裂缝亚临界扩展所形成的虚拟裂缝区的粘聚力是影响混凝土断裂韧度尺寸相关性的重要因素。根据混凝土准脆性材料的断裂特性,建立了一种基于虚拟裂缝模型的求解混凝土等效断裂韧度的实用解析方法。首先根据复合材料力学和线弹性断裂力学的基本原理,将虚拟裂缝的粘聚力作为相应的边界条件,运用修正的剪滞理论,分区引入变异层,建立了分层剪滞模型;然后根据能量法则,推导出求解混凝土等效断裂韧度的解析计算模式;最后针对相关试验的数值解,得到了混凝土等效断裂韧度的解析解。结果表明,对于不同的子层数,体积系列试件的混凝土等效断裂韧度均方差和变异系数分别低于0.0398和0.0384,高度系列试件的混凝土等效断裂韧度均方差和变异系数分别低于0.0394和0.0363,从而证明了混凝土等效断裂韧度是与试件尺寸无关的断裂参数;且与数值解相比,解析解的均方差和变异系数更小,证明了本文解析方法具有更好的鲁棒性。由此得出结论,基于虚拟裂缝模型所建立的解析模式为求解混凝土等效断裂韧度提供了一种可靠的、实用的解析方法。     

Mechanical properties of silicate glass–ceramics containing tricalcium phosphate

The flexural strength, elastic moduli, Vickers hardness and fracture toughness for silicate glass-ceramics (anorthite and diopside) containing tricalcium phosphate (TCP) were measured. The microstructures of the silicate glass–ceramics containing TCP were shown to consist of a complex structure of rod-like silicate and TCP crystals. The flexural strengths of glass–ceramics containing 32 wt% TCP for anorthite and 38 wt% TCP for diopside corresponding to a eutectic composition in the phase diagram were 236 and 226 MPa. The Youngs modulus and fracture toughness of the eutectic compositions were 89.4 GPa and 2.5 MPa·m1/2 for anorthite and 126 GPa and 2.3 MPa·m1/2 for diopside, respectively. The anorthite glass–ceramic containing TCP has a lower Youngs modulus in spite of a high strength as compared to other silicate glass–ceramics containing apatite or TCP.     

The effect of SiO2 on high-temperature deformation and strength of zirconia-toughened alumina

At room temperature, SiO₂ additions may increase the fracture toughness, K _IC, by diminishing the tetragonal phase contents to about 50%, but with ground surfaces the influence on strength is small. A pronounced decrease in strength is observed with rising temperature in the high toughness region from 20°C to M _s, the starting temperature for martensitic transformation. Beyond M _s at lower toughness, the strength behaviour is very similar to nontransforming alumina ceramics, and an even modest increase of the silicate concentration intensively promotes propagation-controlled failure in the brittle creep region (> 900°C) and inelastic deformation. With less than 1% amorphous grain boundary phases, damage-free superplasticity is restricted to small strains of less than 10%. The significance of high-temperature data for tool applications is considered by cutting tests with high feeding rates.     

Surface microroughness of optical glasses under deterministic microgrinding

Deterministic microgrinding of precision optical components with rigid, computer-controlled machining centers and high-speed tool spindles is now possible on a commercial scale. Platforms such as the Opticam systems at the Center for Optics Manufacturing produce convex and concave spherical surfaces with radii from 5 mm to ∞, i.e., planar, and work diameters from 10 to 150 mm. Aspherical surfaces are also being manufactured. The resulting specular surfaces have a typical rms microroughness of 20 nm, 1 μm of subsurface damage, and a figure error of less than 1 wave peak to valley. Surface roughness under deterministic microgrinding conditions (fixed infeed rate) with bound abrasive diamond ring tools with various degrees of bond hardness is correlated to a material length scale, identified as a ductility index, involving the hardness and fracture toughness of glasses. This result is in contrast to loose abrasive grinding (fixed nominal pressure), in which surface microroughness is determined by the elastic stiffness and the hardness of the glass. We summarize measurements of fracture toughness and microhardness by microindentation for crown and flint optical glasses, and fused silica. The microindentation fracture toughness in nondensifying optical glasses is in good agreement with bulk fracture toughness measurement methods.     

Strength and fracture surface energy of phase-separated glasses

Flexural strength and fracture surface energy were determined for lead borate glasses whose compositions lie in the immiscible region of the PbO-B₂O₃ system. The microstructural characterization indicated that the glasses are typical particulate composites which consist of two immiscible phases. For the glasses whose microstructure consists of PbO-rich particles/B₂O₃-rich matrix (B₂O₃-rich side of the miscibility gap), the fracture surface energy was found to decrease with increasing second-phase particles. To explain this behaviour, a crack propagation model in a brittle composite containing penetrable particles was proposed. On the other hand, for the glasses whose microstructure consists of B₂O₃-rich particles/PbO-rich matrix (PbO-rich side of the miscibility gap), an increase in fracture surface energy with volume fraction of dispersed particles was observed. This phenomenon could be best explained by Lange-Evans theory of fracture in brittle composites containing impenetrable particles. It was concluded that, when the critical crack size in a non-dispersed host glass is much larger than the particle size, the crack size in particulate composites is invariant with microstructure and also that the variation of strength results entirely from the variation of fracture toughness.     

Influence of poly(acrylic acid) molar mass on the fracture properties of glass polyalkenoate cements

The failure behaviour of glass polyalkenoate cements was investigated using a linear elastic fracture mechanics (LEFM) approach. Cements were based on four model glasses with varying reactivity and four poly(acrylic acid)s (PAA)s with number average molar masses (Mn) ranging from 3.25 × 104 to 1.08 × 105. Cement properties were studied at time intervals of one, seven and twenty eight days. Compressive strengths (c) of the cements increased with increasing fluorine content of the glass, with increased molar mass of the PAA and with ageing time. The Young's moduli increased with time, but were lower for cements based on the fluorine free glass. Moduli values were independant of PAA molar mass. The un-notched fracture strength (f) of the cement increased with the molar mass of the PAA and with ageing time. Glass composition did not appreciably influence the un-notched fracture strength. The fracture toughness (KIC) increased with the molar mass of the PAA and with ageing time, but reduced with increasing fluorine content of the glass. The toughness (GIC) was dependant on molar mass. The influence of molar mass was not as great as predicted by the reptation chain pull-out model for fracture. The molar mass dependence of toughness was greatest with the lower fluorine content glasses. The plastic zone size at the crack tip increased with the molar mass of the PAA. However the plastic zone size decreased with ageing time for all the cements studied and was smaller for the more reactive higher fluorine content glasses.     

Synthesis, microstructure and mechanical properties of ceria stabilized tetragonal zirconia prepared by spray drying technique

Ceria stabilized zirconia powders with ceria concentration varying from 6 to 16 mol% were synthesized using spray drying technique. Powders were characterized for their particle size distribution and specific surface area. The dense sintered ceramics fabricated using these powders were characterized for their microstructure, crystallite size and phase composition. The flexural strength, fracture toughness and microhardness of sintered ceramics were measured. High fracture toughness and flexural strength were obtained for sintered bodies with 12 mol% of CeO₂. Flexural strength and fracture toughness were dependent on CeO₂ concentration, crystallite size and phase composition of sintered bodies. Correlation of data has indicated that the transformable tetragonal phase is the key factor in controlling the fracture toughness and strength of ceramics. It has been demonstrated that the synthesis method is effective to prepare nanocrystalline tetragonal ceria stabilized zirconia powders with improved mechanical properties. Ce-ZrO₂ with 20 wt% alumina was also prepared with flexural strength, 1200 MPa and fracture toughness, 9.2 MPa√m.     

求解混凝土等效断裂韧度的小波基无单元方法

考虑混凝土主裂缝亚临界扩展长度及虚拟裂缝区粘聚力,利用,积分与应力强度因子的解析关系,建立基于小波基无单元方法求解混凝土等效断裂韧度的数值方法,研究不同基底小波分辨率对混凝土等效断裂韧度计算值的影响。对8个带裂缝试件的混凝土等效断裂韧度的计算结果表明:在相同小波基分辨率下,4根体积系列试件的计算值的均方差和变异系数分别小于0.0244和0.0231,4根高度系列试件的计算值的均方差和变异系数分别小于0.0384和0.0362,计算结果的一致性好;与解析解相比,8个试件的计算值的最大相对误差均在5%左右,计算结果的精度高;且不同小波基分辨率对计算结果影响不大。由此得出结论,小波基无单元方法是求解混凝土等效断裂韧度的一种可靠的高精度数值方法,可以作为混凝土断裂力学的一种有力的计算工具。     

基于连续球压痕法的45钢强度与韧性测试研究

为研究在役设备的材料强度与韧性测试评价问题,针对工程中常用材料45钢,采用连续球压痕方法,获取了材料的屈服强度、抗拉强度与断裂韧性,通过与常规力学性能试验结果比较,对该方法的可靠性进行了验证。通过研究球压头下压产生的塑性功,与冲击启裂能及断裂韧性之间的关联关系,建立基于仪器化球压痕测试技术的冲击韧性估算评估方法。试验结果表明,利用连续球压痕方法获取的屈服强度、抗拉强度与实际结果的偏差均小于10%,断裂韧性值与试验结果的偏差为12.3%,计算结果在试验值偏差数据范围内。利用连续球压痕技术,建立的断裂韧性与冲击韧性之间的关联公式,所预测的冲击韧性结果与仪器化冲击试验值具有较好的一致性,为在役设备材料的韧性快速评价提供了有效的测试方法。      

Development and mechanical properties of metal–particulate glass matrix composites from recycled glasses

The great number of glasses available from recycling activity and vitrification treatment of industrial wastes leads to the need for new applications, with the development of new materials, such as low-cost composite materials from a powder technology route. In the present work a variety of recycled glasses is investigated, in order to obtain aluminium reinforced glass matrix composites via cold-pressing and viscous flow sintering. A good compatibility between lead silicate glasses from cathode ray tubes dismantling and aluminium reinforcement is found to be effective. Composites exhibiting good mechanical properties were developed from these materials. A particular attention was due to fracture toughness (K_IC) determination. The absolute K_IC of glass matrix composites value remains low, but a notable increment in relation to unreinforced matrix is observed.     

Composition and size dependent torsion fracture of metallic glasses

The fracture of metallic glasses(MGs)of different compositions and sizes down to micrometers under torsion loading were systematically investigated.Contrary to the flat shear fracture along the circumfer-ential plane as commonly supposed under torsion,we find that the torsion fracture of metallic glasses can deviate from flat shear plane,and the fracture angle is closely dependent on the composition and the size of MG samples.With a conversion method,we show that the torsion fracture of both millimeter-and micrometer-sized MGs can be described by the ellipse fracture criterion as originally proposed for the tension fracture.The deviation from the circumferential shear plane under torsion is further shown to intrinsically relate to the fracture toughness of MGs.The tougher MG tends to have a smaller fracture angle with respect to the maximum shear plane,and vice versa,indicating a correlation between the fracture toughness and pressure/normal stress sensitivity in MGs.Our results provide new insights on the fracture mechanism and are helpful to design and control the deformation and fracture behavior of MGs under torsion loading.     

Near net-shape fabrication of hydroxyapatite glass composites

Near net-shape fabrication of hydroxyapatite (HA) glass composites has been attempted by infiltrating a glass into porous HA performs. Main efforts were put to develop glasses that are chemically compatible with HA at elevated temperatures. After extensive investigations in the phosphate and borosilicate systems, glasses of (50-55)SiO₂-(20-25)B₂O₃-(10-20)Li₂O-(0-6)CaO (wt%) composition were successfully developed. The glass shows good chemical compatibility with HA at elevated temperatures. Dense HA/glass composites can be fabricated at 850–950 C by the melt infiltration process. Investigations demonstrated a good near net-shape capability of the process, where the linear shrinkage induced by the infiltration process is less than 0.1%. Preliminary mechanical tests showed that the fracture strength and toughness of the infiltrated HA/glass composite are comparable with dense HA.     

Designing metallic glasses with optimal combinations of glass-forming ability and mechanical properties

It is a long-standing challenge to search for metallic glasses(MGs)with optimal combinations of glassforming ability(GFA),strength and toughness in the vast compositional space.By taking into account both recently developed ellipse criterion and temperature-based GFA criterion,here we established quantitative correlations among compositions,elastic constants,GFA and mechanical properties of MGs,which enable to predict the GFA,fracture strength and fracture surface simultaneously in advance once the compositions of MGs are determined.Experimental data confirm the validity of this approach in prediction.Finally,a strategy for designing MGs with optimal combinations of strength,toughness and GFA is proposed,which allows for high-throughput discovering glass formers with excellent mechanical properties.     

Grain size and porosity dependence of ceramic fracture energy and toughness at 22 °C

A review of the fracture energy and toughness data for dense ceramics at 22 °C shows maxima commonly occurring as a function of grain size. Such maxima are most pronounced for non-cubic materials, where they are often associated with microcracking and R-curve effects, especially in oxides, but often also occur at too fine a grain size for association with microcracking. The maxima are usually much more limited, but frequently definitive, for cubic materials. In a few cases only a decrease with increasing grain size at larger grain size, or no dependence on grain size is found, but the extent to which these reflect lack of sufficient data is uncertain. In porous ceramics fracture toughness and especially fracture energy commonly show less porosity dependence than strength and Young's modulus. In some cases little, or no, decrease, or possibly a temporary increase in fracture energy or toughness are seen with increasing porosity at low or intermediate levels of porosity in contrast to continuous decreases for strength and Young's modulus. It is suggested that such (widely neglected) variations reflect bridging in porous bodies. The above maxima as a function of grain size and reduced decreases with increased porosity are less pronounced for fracture toughness as opposed to fracture energy, since the former reflects effects of the latter and Young's modulus, which usually has no dependence on grain size, but substantial dependence on porosity. In general, tests with cracks closer to the natural flaw size give results more consistent with strength behaviour. Implications of these findings are discussed.     

Influence of reprocessing on properties of short fibre-reinforced polycarbonate

The influence of reprocessing by injection moulding on properties of polycarbonate has been studied. It was found that reprocessing reduces the mean fibre length and increases the melt flow index. There was no variation in tensile or flexural properties with the number of reprocessing cycles. Fracture toughness, K _c, measured via notched tensile and flexural bars indicated that the material toughness is affected by the number of reprocessing cycles. The effect was more pronounced in bending than in tension. Strain energy release rate, G _c, was found not to be affected significantly by the number of reprocessing cycles. Although, as the material was reprocessed, fracture parameters were always lower than that of the virgin unprocessed material.The influence of reprocessing on weld-line properties was also investigated using notched tensile specimens. It was found that whereas tensile strength is not affected by the presence of the weld-line, fracture toughness deteriorated significantly, giving a weld-line integrity factor, F, of 0.75. The value of F was not affected significantly by the number of reprocessing cycles.     

Fracture toughness correlation with microstructure and other mechanical properties in near-eutectoid steel

The variation of yield strength and fracture toughness was investigated for four different heat treatments attempted on specimens of a near-eutectoid steel. The aim of this study was to optimize the microstructure for simultaneous improvements in strength and toughness. Further, the fracture toughness deduced through empirical relations from tensile and charpy impact tests was compared with those measured directly according to ASTM Designation: E 399. Among the four different heat treatments attempted in this study, the plane strain condition was valid in the fracture toughness tests for (i) normalized and (ii) hardened and tempered (500°C for 1 h) treatments only. The latter of the two heat treatments resulted in simultaneous improvement of strength and plane strain fracture toughness. The finely-dispersed carbides seem to arrest the crack propagation and also increase the strength. The pearlitic microstructure of the former leads to easy crack propagation along cementite platelets and/or cementite/ferrite interfaces. The nature of variation of empirically determined toughness values from tensile tests for different heat treatments is similar to that measured directly through fracture toughness tests, although the two sets of values do not match quantitatively. On the other hand, the toughness data deduced from charpy impact test is in close agreement with that evaluated directly from fracture toughness tests.     

Implication of peritectic composition in historical high-tin bronze metallurgy

Bronze alloys of varying tin contents from 0% to 28% were cast and then heated at elevated temperatures followed by quenching to examine the variation of microstructure, hardness and fracture characteristics. The results show that hardness increases with tin content and almost reaches the upper limit at 22% tin. Evidence has been found that the small-scale α dendrites spanning across the former β grains that were transformed to martensite serve as interlocking micro-bridges and thereby substantially reinforce the boundary strength to enhance fracture toughness. This effect is extremely sensitive to the α fraction and can best be obtained in alloys of near 22% tin. This specific composition, termed peritectic, seems optimal for sufficient strength without serious brittleness, and allows objects for a similar purpose to be made with less material. The choice of near peritectic composition in historical high-tin bronze metallurgy constitutes an excellent example of human adaptation to harsh environments where access to tin was limited and material cost had to be minimized.     

The conflicts between strength and toughness

The attainment of both strength and toughness is a vital requirement for most structural materials; unfortunately these properties are generally mutually exclusive. Although the quest continues for stronger and harder materials, these have little to no use as bulk structural materials without appropriate fracture resistance. It is the lower-strength, and hence higher-toughness, materials that find use for most safety-critical applications where premature or, worse still, catastrophic fracture is unacceptable. For these reasons, the development of strong and tough (damage-tolerant) materials has traditionally been an exercise in compromise between hardness versus ductility. Drawing examples from metallic glasses, natural and biological materials, and structural and biomimetic ceramics, we examine some of the newer strategies in dealing with this conflict. Specifically, we focus on the interplay between the mechanisms that individually contribute to strength and toughness, noting that these phenomena can originate from very different lengthscales in a material's structural architecture. We show how these new and natural materials can defeat the conflict of strength versus toughness and achieve unprecedented levels of damage tolerance within their respective material classes.     

Fracture and physical properties of carbon anodes for the aluminum reduction cell

An experimental study with total 504 specimens has been carried out to investigate the fracture and physical properties of the carbon anode materials. The specimens were sampled from anodes produced with machined stub holes. From normal-and Weibull analysis the fracture toughness and the tensile strength showed a clear temperature dependency and orthotropic behavior. It has been found that both the fracture toughness and tensile strength increases with the temperature and are larger for the specimens directed in the horizontal direction than in the vertical direction. The variation in the tensile strength within an anode decreased with the temperature but the variation in the fracture strain increased. The tensile strain appears to be only dependent on the temperature and insensitive to the routine anode properties of the anode material. A multivariate linear regression analyses of the fracture toughness and tensile strength has been conducted and a typical correlation of R² = 0.5 (R is the Coefficient of Determination) to the measured routine anode properties was found. The thermal expansion coefficient is also larger in the vertical anode direction which makes the crack initiation more sensitive to temperatures. The orthotropic studies also showed that the air permeability has a tendency to be larger in the horizontal direction in the upper part of the anode which can induce unnecessary burning from the anode sides. The influence of the processing parameters in the paste plant and baking furnace has not been presented in this paper.     

Comparison of failure mechanisms for cements used in skeletal luting applications

Glass Polyalkenoate Cements (GPCs) based on strontium calcium zinc silicate (Sr–Ca–Zn–SiO₂) glasses and low molecular weight poly(acrylic acid) (PAA) have been shown to exhibit suitable compressive strength (65 MPa) and flexural strength (14 MPa) for orthopaedic luting applications. In this study, two such GPC formulations, alongside two commercial cements (Simplex^® P and Hydroset?) were examined. Fracture toughness and tensile bond strength to sintered hydroxyapatite and a biomedical titanium alloy were examined. Fracture toughness of the commercial Poly(methyl methacrylate) cement, Simplex^® P, (3.02 MPa m^1/2) was superior to that of the novel GPC (0.36 MPa m^1/2) and the commercial calcium phosphate cement, Hydroset?, for which no significant fracture toughness was obtained. However, tensile bond strengths of the novel GPCs (0.38 MPa), after a prolonged period (30 days), were observed to be superior to commercial controls (Simplex? P: 0.07 MPa, Hydroset?: 0.16 MPa).