Dynamic Fracture and Strain Rate Behavior of Aggregates Used in Transportation

The static and dynamic uniaxial compressive strengths of coarse aggregate materials used in portland cement concrete (PCC) were determined under dry and saturated conditions for three blast furnace slags, three limestones, four dolomites, and two mafic igneous rocks. The slag aggregates exhibited the lowest compressive strength, followed by the carbonates (limestones and dolomites), and the mafic igneous rocks. Both the dry and saturated aggregates revealed a higher compressive strength under dynamic loads compared to the static loads. Based on the experimental data, a rate sensitivity parameter was defined to describe the increase in compressive strength as a function of strain rate. This parameter is deemed to have considerable relevance in evaluating the ability of a specific aggregate to resist dynamic loads such as in aggregate interlock in PCC cracks and joints, friction in asphalt, and also in the development of microfracture during rock blasting. Comparison of the compressive strength data to density and LA abrasion values revealed that the dynamic data have a better correlation to the above properties than the static data.     

静载荷与循环冲击组合作用下岩石损伤本构模型研究

建立合理的损伤本构模型,对研究岩石在静载荷与循环冲击组合作用下的动态力学性能具有重要的意义. 首先,基于静载荷与循环冲击组合作用下岩石的损伤累积演化模型,结合岩石弹性模量与累积损伤变量的关系,将循环冲击次数引入岩石损伤本构关系中. 接着,假设岩石微元体强度服从Weibull分布,将统计损伤模型和黏弹性模型相结合,并根据Drucker-Prager破坏准则,建立有轴压有围压时循环冲击作用下岩石的动态损伤本构模型.进而,利用岩石动静组合加载试验数据验证损伤本构模型的正确性和可行性. 最后,研究模型中参数对循环冲击过程中应力-应变曲线的影响规律.结果表明,建立的岩石损伤本构模型较好地与试验数据吻合,能较好地反映具有静载荷的岩石在循环冲击过程中的本构关系.岩石的弹性模量、黏性系数等参数对循环冲击时岩石的应力-应变曲线影响较大;而岩石的摩擦角和泊松比等对具有三维静载岩石的冲击疲劳应力-应变曲线影响较小. 循环冲击过程中,岩石的非均匀度逐渐增加. 研究结果有益于完善静载荷与循环冲击组合作用下岩石动态疲劳力学理论体系.      

A theory of size reduction involving fracture mechanics

Abstract

A theoretical study was made to derive an energy equation for 'the size reduction process. The stress and deformation experienced by an irregularly shaped rock particle, which is subjected to the action of a pair of concentrated loads directed in compression towards the loading point at the shortest distance, were analyzed by the theory of elasticity. Then, based on the experimental fact that fracture is possible only when the tensile stress excéeds the tensile strength of rock, the strain energy required for size reduction was found to be proportional to the third power of particle size and the square of tensile strength, as well as inversely proportional to Young's modulus.

Since the tensile strength of a rock particle is a function of particle size, Weibull's concept applied to the size reduction problem, requires that the energy for size reduction is now proportional to the 3[1-(2/β)]th order of the particle size, β being the coefficient of uniformity of the rock.

The energy equation derived in this study is the same as Kick's theory when β=∞ Bond's theory when β= 12 and Rittinger's theory when β= 6. This theory may permit an accurate energy calculation for a selected size reduction operation from laboratory test information on rock specimen, such as tensile tests yielding Young's modulus and fracture stress.

Résumé

Une étude théorique a été entreprise pour obtenir une expression énergétique dans le procédé de réduction des dimensions de particules. Les contraintes et les déformations engendrées sur une particule rocheuse de forme irrégulière et sujette à des charges concentrées, en compression et dirigées vers le point de mise en charge à la plus courte distance, ont été analysées par la théorie de l' élasticite. En se basant sur le fait, vérifié expérimentalement, que la rupture n'est possible que si la contrainte de tension dépasse la charge de traction de la roche. l' énergie de deformation requise pour réduire les dimensions est alors proportionnelle au cube de la taille de la particule et au carré de la résistance a la traction et inversement proportionnelle au module d'Young.

Comme la résistance à la traction d 'une particule de roche est fonction de sa taille, le concept de Weibull appliqué à ce problème, implique que l' énergie pour la réduction est proportionnelle à la puissance 3 (1? 2/β de la taille de la particule (β est un coefficient d'uniformité de la roche).

L'équation d' énergie obtenue par cette étude est semblable à la théorie de Kick quand β=∞, à la theorie de Bond quand β= 12 et à celle de Rittinger quand β = 6. Cette theorie peut permettre une évaluation précise de l'energie pour une opération de réduction de taille déterminée à partir de données obtenues au laboratoire sur des échantillons de roches, comme un essaie de traction, le module d'Young et la contrainte de rupture.     

钢锭模用灰口铸铁热循环载荷下的微观组织与服役特性

应用马弗炉对灰口铸铁试样进行热循环处理,并通过Gleeble-1500、光学显微镜、电子显微镜和能谱仪等手段重点分析了灰口铸铁拉伸性能、基体组织、化学成分与热历程的相关性。发现铸态试样珠光体片层间距较大,石墨片较厚,且其周围存在铁素体,这是其拉伸性能较差的根本原因。经800℃保温3h控温冷却后,试样组织均匀性显著改善,低温抗拉强度提高约30%。多次热循环处理后,试样各温度下的拉伸性能均有所下降,这与高温氧化、脱碳有关。试样经30次热处理后,碳的质量分数降至1.55%,致使珠光体转变难以完成。同时,在石墨片周围形成硅、锰、铁等氧化物的疏松带,二次渗碳体和晶粒粗化也均是试样抗拉强度下降的重要原因。     

Measurement of green strength of warm pressed Distaloy PM compacts: influence of specimen geometry and test method

Abstract

It is important that the green strength properties of powder compacts be accurately determined if advanced manufacturing techniques, such as green machining, are to be exploited successfully. In this study, the green strength of Distaloy AE Densmix, a powder mix designed for such applications, was measured using several test methods. Fracture statistics were correlated with compact density and test method employed, and the Weibull modulus calculated for each case. It was found that Weibull analysis accurately predicted the green strength dependence on the test configuration utilised.     

Aspects of fracture in particulate reinforced metal matrix composites

The tensile deformation and fracture behaviour of the aluminium alloy 6061 reinforced with SiC has been investigated. In the T4 temper plastic deformation occurs throughout the gauge length and the extent of SiC particle cracking increases with increasing strain. In the T6 temper strain becomes localised and particle cracking is more concentrated close to the fracture. The elastic modulus decreases with increasing particle damage and this allows a damage parameter to be identified. The fraction of SiC particles which fracture is less than 5%, and over most of the strain range the damage controlling the tensile ductility can be recovered, indicating that other factors, in addition to particle cracking are important in influencing tensile ductility. It is suggested that macroscopic fracture is initiated by the SiC particle clusters that are present in these composites as a result of the processing. The matrix within the clusters is subjected to high levels of triaxial stress due to elastic misfit and the constraints exerted on the matrix by the surrounding particles. Final fracture is then produced by crack propagation through the matrix between the clusters.     

Probabilistic Nonlocal Theory for Quasibrittle Fracture Initiation and Size Effect.?I: Theory

The nonlocal generalization of Weibull theory previously developed for structures that are either notched or fail only after the formation of a large crack is extended to predict the probability of failure of unnotched structures that reach the maximum load before a large crack forms, as is typical of the test of modulus of rupture (flexural strength). The probability of material failure at a material point is assumed to be a power function (characterized by the Weibull modulus and scaling parameter) of the average stress in the neighborhood of that point, the size of which is the material characteristic length. This indirectly imposes a spatial correlation. The model describes the deterministic size effect, which is caused by stress redistribution due to strain softening in the boundary layer of cracking with the associated energy release. As a basic check of soundness, it is proposed that for quasibrittle structures much larger than the fracture process zone or the characteristic length of material, the probabilistic model of failure must asymptotically reduce to Weibull theory with the weakest link model. The present theory satisfies this condition, but the classical stochastic finite-element models do not, which renders the use of these models for calculating loads of very small failure probabilities dubious. Numerical applications and comparisons to test results are left for Part II.     

Analytic Solution for Axial Point Load Strength Test on Solid Circular Cylinders

This paper presents a new analytic solution for the stresses within an elastic solid finite cylinder subjected to the axial point load strength test (PLST). The “displacement potential approach” is used to uncouple the equations of equilibrium; then the contact stresses on the end surfaces induced by the point load indentors are expanded in terms of a Fourier-Bessel expansion to yield the unknown constants of the appropriate form of the displacement potential. Our solution shows that a zone of higher tensile stress is developed in the vicinity of the applied point loads, compared with the roughly uniform tensile stress in the central portion of the line between the two point loads. This peak tensile stress within the cylinder decreases with increasing Poisson's ratio and the size of the loading area, and it increases with increasing Young's modulus. The tensile stress distributions along the axis of symmetry in a cylinder under the axial PLST are remarkably similar to that observed in a sphere under the diametral PLST. Our solution also demonstrates both size and shape effects on the point load strength index (PLSI) that we observed in our experiments. In particular, for a fixed length-to-diameter ratio, the larger the specimen, the smaller the PLSI, whereas for a fixed diameter, the longer the specimen the smaller the PLSI.     

Damage initiation in metal matrix composites

The process of damage by particle cracking has been followed in a composite of A356 Al containing 20% by volume SiC. The probability of particle cracking is influenced by both particle size and aspect ratio and the results indicate that the relative importance of these factors depends on the Weibull modulus of the SiC particles. A simple model is developed to describe the process of load transfer and crack initiation in the particles. This initial model does not take into account particle interactions and the role of clustering but does provide an initial fragment to describe the damage initiation process.     

考虑岩石交界面方向效应的巴西劈裂试验研究

为了研究硬岩与软岩交界面方向对其破坏形式的影响,对含岩石-水泥砂浆(代替软岩)交界面的组合试样进行了多组加载角度的巴西劈裂试验,获得了不同交界面方向的组合试样的\     

金山金矿矿岩力学特征试验研究

通过对金山金矿矿岩的抗拉强度、抗压强度、抗剪强度、泊松比、弹性模量、内摩擦角以及内聚力的室内试验,分析了金山金矿矿岩力学特征,提出了矿体、上下盘围岩各向同性特征差,呈现出较强的各向异性特征。在实际工程应用中,应按各向异性矿岩来处理。     

The psychological profile using the Minnesota Multiphasic Personality Inventory and the value of this test in the evaluation of post-traumatic stress disorder in combat participants

Previous theoretical studies of the mechanical properties of tissues such as skin, bone and tendon, have used approaches based on composite materials and have tended to neglect the contribution of individual microscopic components. In this paper, we examine the relationship between the fine structure of a collagen fibril and its relative tensile strength. Collagen is a fibrous protein which provides associated tissues with the majority of their tensile strength. It is present in the form of elongated structures termed fibrils which are created by the self-assembly of rod-like collagen molecules in an entropy-driven process termed fibrillogenesis. Mutations that alter the primary structure of the collagen molecule, interfere with this assembly process and can lead to the potentially fatal brittle bone disease, osteogenesis imperfecta. Here we investigate the mechanical properties of a range of computer-generated aggregates. The aggregates, created by the diffusion limited aggregation of rods, were subjected to a simple tensile test based on local rules of damage accumulation. In the test, core samples are "extracted' from the aggregates, and the network of particles involved in the transmission of stress resolved. Increasing stress applied to the core leads to the removal of individual rods from this network; the tensile strength is determined from the force necessary to form a discontinuous network. Using this approach, we have shown that collagen fibril morphology is critical in determining its tensile strength. We suggest a possible mechanism to account for the increasing severity of osteogenesis imperfecta associated with the distance of mutation from the N-terminal of the collagen molecule.     

Effect of pitting corrosion in NaCl solutions on the statistics of fracture of beryllium

The effect of pitting corrosion, occurring in NaCl solutions, on the bending behavior of commercial beryllium was studied. Three concentrations of NaCl solutions (0.01, 0.1, and 1 M) were used in the experiments. Bend specimens were exposed to these solutions for a total of 168 hours. Weibull statistics were used to analyze the experimental bend-strength data and were applied to the failure strength, displacement to failure, and yield strength. Samples exposed to the 1 M NaCl solution exhibited a high Weibull modulus, with a higher retained mean failure strength and displacement to failure. On the other hand, the samples exposed to the 0.01 and 0.1 M NaCl solution exhibited significantly lower mechanical property values and Weibull moduli, accompanied by a larger scatter in the failure strength and displacement to failure. The engineering yield strength of the samples did not change significantly with exposure to the NaCl solutions, although there was an increase in the scatter of the values. These effects on the mechanical properties were attributed to a decreasing propensity for the formation of localized deep pits and an increasing propensity for uniform shallow pitting with increasing NaCl concentrations. Scanning electron microscopy (SEM) was primarily used for quantifying these corrosion pitting effects. In addition, atomic-force microscopy (AFM) and potentiodynamic polarization experiments were also conducted to provide supportive evidence for the differences in the pitting behavior of the beryllium with different NaCl concentrations.     

Microstructure and mechanical properties of copper alloyed austempered grey cast iron

Austempered grey cast iron (AGI) has emerged as a major engineering material in recent years because of its attractive mechanical properties. The main aim of this investigation is to assess the mechanical properties of copper alloyed AGI. Alloyed grey cast iron specimens are subjected to austempering heat treatment at six different temperatures for four different time periods. The resulting microstructures have been evaluated and characterised by means of light microscope and scanning electron microscope and X-Ray diffraction analysis. The microstructural features of AGI such as austenite content and its carbon content have been also found to influence the hardness, tensile properties and elongation. Both duration of the austempering time and the austempering temperature affect the mechanical properties of AGI. The hardness, tensile strength and ductility initially increase, and thereafter it decreases on longer periods of austempering. On the other hand hardness, tensile strength decreases as increasing austempering temperature, while ductility increases. The best combination of hardness 380BHN and strength 332?MPa; observed at 927°C of austenitising and 260°C of austempering temperature for 60?min.     

Guidelines for Two-Parameter Weibull Analysis for Flaw-Containing Materials

Two-parameter Weibull statistics used in the analysis of mechanical data from flaw-containing materials, such as ceramics and castings, are reviewed. Guidelines to estimate Weibull parameters with the linear regression technique are provided. Moreover goodness-of-fit tests for Weibull fits and calculating confidence intervals for the estimated Weibull modulus are discussed. Methods of estimating lower bounds as well as a new hypothesis test for comparing two estimated Weibull moduli are explained. The use of these guidelines is demonstrated by using data from the literature.     

退火时间对Zr- 4合金管材性能影响

采用高温拉伸试验、均匀腐蚀试验、金相显微组织观察试验和第二相粒子统计的方法研究了Zr- 4合金管材在不同退火时间后的高温拉伸性能、均匀腐蚀性能、金相组织及第二相粒子的变化规律。结果表明,退火时间在3.5~5.5 h变化时,Zr- 4合金管材的高温抗拉强度、屈服强度和伸长率的变化曲线趋势基本波动不大,均匀腐蚀结果略有降低,Zr- 4管材内中外层的晶粒度均为11级,无异常晶粒长大组织,第二相粒子尺寸范围逐渐增大。     

The Effect of Holding Liquid Aluminum Alloys on Oxide Film Content

Melts of commercially pure liquid aluminum, and an Al-7Si-0.3Mg alloy, were cast into molds designed to produce entrainment of oxide film defects. The melts were held for periods of up to 20 minutes to investigate whether changes in the oxide film defects in the melt could occur, once sufficient time had elapsed for consumption of their internal atmosphere. The alloys were characterized by the determination of their Weibull modulus, examination of fracture surfaces under scanning electron microscopy (SEM), and determination of their porosity characteristics. The Weibull moduli of the ultimate tensile strength (UTS) values of the Al-7Si-0.3Mg alloy were reduced initially by holding in the liquid state for 10 minutes, but then the values increased after holding for 20 minutes. This high Weibull modulus was found despite oxide films being observed on the fracture surfaces. In the case of the commercial purity Al, the UTS Weibull moduli increased only slightly with holding for 20 minutes. The results suggested that holding of Al alloys in the liquid state influenced the scatter of mechanical properties by influencing the porosity content of the castings, which was related to their oxide film content. Some evidence for healing of a double oxide film defect with time was also found in the commercial purity Al alloy.     

Hydroxyapatite-polyethylene composites for bone substitution: effects of ceramic particle size and morphology

Synthetic hydroxyapatite particles of two median sizes and different morphologies have been used to manufacture hydroxyapatite reinforced high density polyethylene composites (HAPEX) for medical applications. The effects of hydroxyapatite particle size on properties of the resultant composites were investigated using various techniques. It was found that composites with smaller hydroxyapatite particles had higher torsional modulus, tensile modulus and tensile strength, but lower strain to failure. Examination of fracture surfaces revealed that only a mechanical bond existed between the filler and the matrix. It was shown that dynamic mechanical analysis is useful in studying the viscoelastic behaviour of the composite.     

Estimating Subgrade Reaction Modulus for Transversely Isotropic Rock Medium

Most of the rock medium possesses intrinsic grain orientation or preferred bedding and joint directions, thus requiring the use of at least transverse isotropy to describe its elastic behavior. This paper presents a series of charts, based on extensive finite element parametric studies along with nonlinear regression analysis of FE simulation results, for estimating the subgrade reaction modulus (or initial tangent to the p-y curve) using five elastic constants of a transversely isotropic rock mass. The proper characterization of subgrade reaction modulus is critical for accurate prediction of the elastic lateral deflection of a rock socketed drilled shaft under the applied lateral loads. The sensitivity of the response of a laterally loaded drilled shaft to the degree of anisotropy and orientation of the plane of anisotropy (bedding plane direction of the rock medium) was demonstrated in this paper for an actual lateral load testing case in Ohio. It is highly recommended to use five elastic constants to estimate subgrade reaction modulus of rock medium exhibiting high degree of cross anisotropy.