A statistical approach to strength evaluation incorporating porosity effect for porous ceramics

ABSTRACT It has not been clear whether the conventional effective volume proposed for dense brittle materials can be applied satisfactorily to the strength evaluation of porous ceramics. In the present study, a modified effective volume was proposed by incorporating the porosity effect in the statistical evaluation of strength properties of porous ceramics. The modified effective volume was derived as the conventional effective volume multiplied by a function of porosity p. In this work, a power function of (1 + p)^a was adopted as the simplest porosity function. To clarify the applicability of the modified effective volume, bending tests were conducted using smooth and notched specimens of 3 wt% MgO partially stabilised zirconia with six different porosities. The porosity dependence appeared in the relation between the conventional effective volume and the mean strength of various zirconia ceramics with different porosities. The exponent a of the porosity function was determined from experimental data obtained by using identically shaped specimens with distinct porosities, and the modified effective volume was calculated for several types of specimens used in the experiments. It was revealed that the mean strength was almost uniquely correlated with the modified effective volume independent of porosity. The experimental correlation verified the applicability of the modified effective volume to strength evaluation of porous ceramics.     

Progress in engineering high strain lead-free piezoelectric ceramics

Abstract

Environmental concerns are strongly driving the need to replace the lead-based piezoelectric materials currently employed as multilayer actuators. The current review describes both compositional and structural engineering approaches to achieve enhanced piezoelectric properties in lead-free materials. The review of the compositional engineering approach focuses on compositional tuning of the properties and phase behavior in three promising families of lead-free perovskite ferroelectrics: the titanate, alkaline niobate and bismuth perovskites and their solid solutions. The ‘structural engineering’ approaches focus instead on optimization of microstructural features including grain size, grain orientation or texture, ferroelectric domain size and electrical bias field as potential paths to induce large piezoelectric properties in lead-free piezoceramics. It is suggested that a combination of both compositional and novel structural engineering approaches will be required in order to realize viable lead-free alternatives to current lead-based materials for piezoelectric actuator applications.     

10CrNi3MoV钢焊接热影响区组织和晶粒度研究

采用焊接热模拟技术研究了590MPa级船用高强度结构钢焊接热影响区组织和晶粒度的变化规律．研究结果表明：10CrNi3MoV钢热影响区粗晶区(CGHAZ)经峰值温度在临界相变点Ac1和Ac3温度范围二次热循环后，具有粗大组织或粗大晶粒遗传现象．焊接线能量(t8/5时间)对粗大晶粒遗传没有影响，但对粗大组织遗传具有显著影响．当t8/5较小时，能够产生粗大组织遗传．当t8/5较大时，仅仅产生粗大晶粒遗传．并且，随着t8/5值增加，产生粗大组织遗传的温度区间减小。     

Modeling the dependence of strength on grain sizes in nanocrystalline materials

Abstract

A model was developed to describe the grain size dependence of hardness (or strength) in nanocrystalline materials by combining the Hall–Petch relationship for larger grains with a coherent polycrystal model for nanoscale grains and introducing a log-normal distribution of grain sizes. The transition from the Hall–Petch relationship to the coherent polycrystal mechanism was shown to be a gradual process. The hardness in the nanoscale regime was observed to increase with decreasing grain boundary affected zone (or effective grain boundary thickness, Δ) in the form of Δ^?1/2. The critical grain size increased linearly with increasing Δ. The variation of the calculated hardness value with the grain size was observed to be in agreement with the experimental data reported in the literature.     

铜箔抗拉强度及延伸率的尺寸效应研究

为了研究尺寸参数对金属箔材的抗拉强度和延伸率的影响规律,采用不同厚度和晶粒尺寸的铜箔进行室温单向拉伸试验.试验结果表明:铜箔的抗拉强度和延伸率同时受厚度和晶粒尺寸的影响,这种尺寸效应的描述必须引入无量纲的厚度晶粒尺寸比(T/D)作为比较参数.抗拉强度在不同厚度晶粒尺寸比区间内的变化规律不同;而延伸率在厚度晶粒尺寸比相同时都随厚度的减小而降低.拉伸断口的扫描电镜分析显示箔材的延伸率随着厚度的减小出现的突降和断裂机制的变化有关.     

Maximum strength for intermolecular adhesion of nanospheres at an optimal size

Previous studies have emphasized that the adhesion strength between solid objects tends to increase as the characteristic size of the objects decreases and eventually saturates at the theoretical adhesion strength below a critical size scale. Here we show that the adhesion strength between two spheres or between a sphere and a solid half-space actually exhibits a peak value at an optimal size. This optimal size arises owing to a transition between surface- and bulk-dominated interaction regimes at the nanoscale.     

Assessment of defect size in brittle fibers

Fiber defects, modeled as inner circular or part-circular surface cracks in planes normal to the fiber axis, are analyzed for computing the relationship between the maximum defect size and the fiber fracture stress. Linear elastic fracture mechanics is applied to compute the critical tensile stress for both surface and inner cracks, taking into account that when an inner crack reaches the surface it can stop growing or become unstable. The minimum critical tensile stress is correlated with defect size when defects are randomly located, and the numerical computations are compared with some available experimental results.     

Effects of porosity and pore size distribution on mechanical strength reliability of industrial-scale catalyst during preparation and catalytic test steps

This paper investigates the effects of porosity and pore size distribution on crushing strength reliability of industrial-scale catalysts during their preparation and after reactor tests. Six supports, fabricated from two types of γ-alumina (type A, 119?m²/g; and type B, 343?m²/g), were used as starting materials. The supports were impregnated using a copper/zinc nitrate solution. The supports and catalysts, before and after the reactor tests, were characterized using XRD, ICP, SEM, and BET methods and were subjected to single particle crushing strength tests. The results revealed that the strength and Weibull modulus of all samples were decreased after the impregnation process due to the emergence of new flaws. In contrast, the partial sintering/necking of the interparticles during the reaction led to an increase of the crushing strength of the used catalysts. Furthermore, the porosity of the supports and catalysts from type A to type B γ-alumina were increased, leading to the strength decrease. Nevertheless, their Weibull modulus and strength reliability were increased due to the narrowing of pore size distribution in the range of mesopores.     

A finite fracture mechanics approach to structures with sharp V-notches

Criteria assuming that failure of quasi-brittle materials is affected by the stresses acting over a finite distance from the crack tip are widely used inside the scientific community. For instance, they have been applied to predict the failure load of specimens containing sharp V-notches, assuming as a critical parameter the average stress ahead the notch tip. However, this kind of approaches disregards energy balance considerations, which, as well known, are the basis of linear elastic fracture mechanics (LEFM). In order to overcome these drawbacks, the present paper uses a recently introduced finite fracture mechanics (FFM) criterion, i.e. a fracture criterion assuming that crack grows by finite steps. The length of this finite extension is determined by a condition of consistency of both energy and stress requirements; as a consequence, the crack advancement is not a material constant but a structural parameter. The criterion is applied to structures with sharp V-notches. The expression of the generalized fracture toughness, which is a function of material tensile strength, fracture toughness and notch opening angle, is given analytically. Finally, we provide comparisons with: (i) the experimental data we obtained from testing Polystyrene specimens under three point bending; (ii) some experimental data available in the literature. The agreement between theoretical predictions and experimental results is generally satisfactory and, for most of the cases analyzed, the FFM predictions are better than the ones provided by the simple average stress approach.     

Phase field simulation of abnormal grain growth mediated by initial particle size distribution

The uniform initial particle size distribution was considered to be an important condition for the preparation of dense ceramics. With the rapid development of templated grain growth method, it is necessary to add large template particles into small matrix to promote the epitaxial growth of grains. However, abnormal grain growth will inevitably occur in this process. In this work, a phase field method was employed to study the growth behavior of the large grains into the small matrix. The effect of initial particle size distribution on the grain growth kinetics was investigated. Our simulations revealed that the growth rate of large grains slowed down as the initial grain size distribution widened. Regulating the initial grain size distribution will be an effective way to control abnormal growth of grain. It was found that the growth rate of a large grain was proportional to the number of surrounding grains. These results have implications for the design of the functional ceramics with a target grain microstructure.     

A unification of small- and large-crack growth laws

A generalized model enhancement is proposed to link small- and large-crack growth laws. The enhancement is based on crack growth rate laws with crack tip plastic zone size formulations. Transition functions are used to transform small-crack plastic zone sizes and crack growth law exponents to those predicted by linear-elastic fracture mechanics. In doing so, influences on crack growth, e.g. constraint, crack aspect ratio and specimen geometry are accounted for. The applicability of the enhancement is directed toward instances where small cracks start from geometric features and grow through stress gradients to eventually become large cracks under nominal LEFM conditions. The enhancement is applied to the Wang model, and crack growth rate and fatigue lifetime predictions are made. The enhancement is shown to provide a good correlation to experimental results for Ti–6Al–4V under various maximum stresses at a stress ratio of R = 0.4.     

Application of size effect to compressive strength of concrete members

It is important to consider the effect of size when estimating the ultimate strength of a concrete member under various loading conditions. Well known as the size effect, the strength of a member tends to decrease when its size increases. Therefore, in view of recent increased interest in the size effect of concrete this research focuses on the size effect of two main classes of compressive strength of concrete: pure axial compressive strength and flexural compressive strength. First, fracture mechanics type size effect on the compressive strength of cylindrical concrete specimens was studied, with the diameter, and the height/diameter ratio considered as the main parameters. Theoretical and statistical analyses were conducted, and a size effect equation was proposed to predict the compressive strength specimens. The proposed equation showed good agreement with the existing test results for concrete cylinders. Second, the size, length, and depth variations of a flexural compressive member have been studied experimentally. A series of C-shaped specimens subjected to axial compressive load and bending moment were tested. The shape of specimens and the test procedures used were similar to those by Hognestad and others. The test results are curve-fitted using Levenberg-Marquardt’s least squares method (LSM) to obtain parameters for the modified size effect law (MSEL) by Kim and co workers. The results of the analysis show that the effect of specimen size, length, and depth on ultimate strength is significant. Finally, more general parameters for MSEL are suggested.     

An approach to size effect in fatigue of metals using fractal theories

ABSTRACT As was experimentally observed by several authors, the fatigue strength of metallic materials decreases with increasing the specimen size. Such a decrease can be remarkable for very large structures like, for example, big cargo ships (some hundred meters long) transporting oil or other goods. Size effect in fatigue is herein explained by considering the fractal nature of the reacting cross sections of structures, that is, the renormalized fatigue strength is represented by a force amplitude acting on a surface with a fractal dimension lower than 2, where such a dimensional decrement depends on a self‐similar weakening of the material ligament, owing to the presence of cracks, defects, voids and so forth (microscopic level). However, this decrement tends to progressively disappear with increasing the structure size (macroscopic level), i.e. the effect of the material microstructure on the macroscopic fatigue behaviour gradually vanishes for structures large enough with respect to a characteristic microstructural size, this phenomenon being defined as multifractality. A multifractal scaling law for fatigue limit of metals is proposed, and some experimental results are examined in order to show how to apply the theoretical approach presented.     

A study of microstructural variations in BSCCO Ag-clad tapes and a method to improve grain alignment

The microstructural variations in BSCCO Ag-clad tapes obtained by a conventional fabrication procedure were studied by SEM and microhardness tester. A method to improve grain alignment in the tape by treatment of the magnetic field with mechanical vibration was developed and investigated.     

The effect of grain size on small fatigue crack growth in pure titanium

The growth behaviour of small fatigue cracks has been studied in both fine- and coarse-grained versions of a pure titanium under axial loading at stress ratio, R, of −1. The growth behaviour and its statistical properties in a coarse-grained version of a different pure titanium have also been investigated under rotating bending (R = −1), and the results obtained were compared with those of a fine-grained version of this titanium in a previous report. Under both loading conditions, small cracks grew faster than large cracks. As the growth data were plotted in terms of the effective stress intensity factor range ΔK_eff (after allowing for crack closure, the growth rates could be well correlated with large-crack data in a large-crack regime. In a small-crack regime, however, small cracks still grew faster than large cracks. Small cracks in coarse-grained material showed higher growth rates than those in fine-grained material owing to a much smaller effect of microstructure such as grain boundaries and crack deflection. Stage I facets were observed in all the specimens tested, and their depths were less than the maximum grain size estimated by the statistics of the extreme values, but the distribution of stage I facet depths approximately corresponded to the maximum value distributions of grain size of the materials. The growth rates of small cracks followed log-normal distributions independent of grain size. The coefficients of variation, η, of growth rate in coarse-grained material were smaller than those in fine-grained material. The η values were significantly large at a/d 3 (a = crack depth, D = grain size), indicating that the relative size of microstructurally small cracks was not dependent on grain size.     

Residual strength at −40 °C of a precracked cold‐formed rectangular hollow section made of ultra‐high‐strength steel – an engineering approach

This study investigated the residual strength of a precracked cold‐formed rectangular hollow section made of novel ultra‐high‐strength steel. The primary goal was to experimentally discover the residual strength of the structure when used in low temperature service conditions. The secondary goal was to predict the residual strength by using a J‐integral approach with nonlinear finite element calculations and to compare these predictions with measured results. The experimental tests were carried out with a beam in four‐point bending loading. The test specimens were taken from a cold‐formed rectangular hollow section fabricated from direct quenched (untempered) ultra‐high‐strength steel S960 QC omitting the annealing in the fabrication process. The tests for final failure were carried out at ?40 °C, with the exception of the first pilot test. There were two kinds of tests: (1) the beam was cyclically loaded until the final fracture or the fatigue precrack was first introduced and (2) the specimen was then subjected to a quasistatic bending loading condition until it failed. The new experimental results matched well with our predictions, and both confirmed the high toughness of ultra‐high‐strength steel in beam construction studied, even at a low ambient temperature.     

Effect of particle size distribution on pile tip resistance in calcareous sand in the geotechnical centrifuge

Until recently, the micro mechanical origins of soil behaviour have remained illusive, but it is now known that that the constitutive behaviour of a soil is largely determined by its particle size distribution. This paper examines the specific boundary problem associated with the penetration of a model pile into two different gradings of dry calcareous sand in a geotechnical centrifuge, in order to establish the effect of the inclusion of fine particles on the pile end bearing resistance. The first grading of sand comprised particles smaller than 0.5 mm; the second grading contained particles of nominal size d such that 0.15 mm < d < 0.5 mm. Each test was performed on each of two samples of each grading. Tip resistance was observed to rise to a peak at shallow depths, and then fall; a micro mechanical explanation is presented for this instability. Following the centrifuge tests, particles were retrieved from the centres of the soil samples, where the pile had previously been driven, for subsequent particle size analysis. It was found that insignificant crushing had occurred in the sand retrieved from depths less than the depth of peak resistance, but that significant crushing had occurred in the sand retrieved from greater depths. The peak in tip resistance was a factor of two larger for the well-graded sand, but the ultimate tip resistance at greater depths was found to be approximately independent of the initial particle size distribution for all four tests. A micro mechanical explanation is also proposed for this observation. Received: 11 November 1999     

A design-centered approach in developing Al-Si-based light-weight alloys with enhanced fatigue life and strength

Material heterogeneities and discontinuities such as porosity, second phase particles, and other defects at meso/micro/nano scales, determine fatigue life, strength, and fracture behavior of aluminum castings. In order to achieve better performance of these alloys, a design-centered computer-aided renovative approach is proposed. Here, the term “design-centered” is used to distinguish the new approach from the traditional trial-and-error design approach by formulating a clear objective, offering a scientific foundation, and developing a computer-aided effective tool for the alloy development. A criterion for tailoring “child” microstructure, obtained by “parent” microstructure through statistical correlation, is proposed for the fatigue design at the initial stage. A dislocations pileup model has been developed. This dislocation model, combined with an optimization analysis, provides an analytical-based solution on a small scale for silicon particles and dendrite cells to enhance both fatigue performance and strength for pore-controlled castings. It can also be used to further tailor microstructures. In addition, a conceptual damage sensitivity map for fatigue life design is proposed. In this map there are critical pore sizes, above which fatigue life is controlled by pores; otherwise it is controlled by other mechanisms such as silicon particles and dendrite cells. In the latter case, the proposed criteria and the dislocation model are the foundations of a guideline in the design-centered approach to maximize both the fatigue life and strength of Al-Si-based light-weight alloy.     

A size effect law for notched tensile strength of woven carbon/epoxy laminates

Specimen-size effect and notch-size effect on the tensile strength of woven fabric carbon/epoxy laminates are evaluated and modeled. For two different layups of [(0/90)₁₂] and [(±45)₂/(0/90)₅]_S, respectively, static tension tests were performed on two-dimensional geometrically similar unnotched and double-edge notched specimens scaled to three different sizes. Experimental results demonstrate that the notched strength of the woven CFRP laminates depend on the size of specimen as well as the size of notch. The ratio of notched strength to unnotched strength decreases as the length of notch increases, regardless of the size of specimen. For a given size of notch, the notch strength ratio becomes larger with decreasing size of specimen. A notch-size effect law is derived by means of the Neuber interpolation method. A specimen-size effect is embedded into the notch sensitivity parameter involved by the notch-size effect law to establish a size effect law that can cope with these two kinds of size effect. The engineering size effect law proposed can adequately describe the specimen-size effect as well as notch-size effect on the tensile strength of the woven CFRP laminates. It is also demonstrated that the size effect law allows determining the size independent fracture toughness on the basis of notched strengths of small specimens that fail in a quasi-brittle manner.     

复合材料层合板单钉双剪连接挤压强度的一种工程估算方法

将上限理论应用到复合材料层合板单钉双剪连接挤压强度分析中, 把连接结构的位移场划分为动态区域(层合板)和静态区域(紧固件), 并认为失效发生在位移可动场和不动场之间的钉孔边受挤压部分。由于受挤压孔孔边各层应力状态不一样, 受挤压孔边各层的失效区域和失效模式也各不相同。从宏观上研究复合材料层合板单钉连接孔边的失效区域和失效模式, 结合上限理论提出了一种估算复合材料单钉连接挤压强度的工程算法。通过与试验结果对比, 发现该方法能较好地预测出复合材料单钉双剪连接挤压强度。