A micro-mechanism based analysis for size-dependent indentation hardness

A micro-scale analytical model for predicting size-dependent microhardness is presented. The indentation size effect is explained by dissipation energy associated with the contact surfaces. Micro-mechanics mechanism of this energy dissipation is studied via a plastic deformation analysis of micro-scale asperities on the contact surface under indentation. The analysis shows that the microhardness depends not only on the properties of the bulk material under test, but also the properties of the contact surface, such as the plastic behavior of the micro-asperities on contact surfaces. The dependence of microhardness on the roughness parameters of the contact surfaces is also revealed from the analysis.     

Nano-sized aluminum oxide reinforced commercial casting A356 alloy matrix: Evaluation of hardness,wear resistance and compressive strength focusing on particle distribution in aluminum matrix

Achieving a uniform distribution of reinforcement within the matrix is a challenge which impacts directly on the properties and quality of the composite material. In the present study a fabrication and evaluation approach was used focusing on particle distribution in metal matrix. Al and Cu powders were separately milled with nano-Al₂O₃ particles and incorporated into A356 alloy via vortex method to produce cylindrical A356/nano-Al₂O₃ composites. The stirring was carried out in various durations. The variations of density, hardness, compressive strength, and wear resistance were measured throughout the cylindrical samples. The evaluation of mechanical properties and microstructural studies showed that an increase in stirring time led to a more uniform dispersion of particles in the matrix and also led to a decrease in mechanical properties due to an increase in porosity content of the composites compared with those of the samples stirred for shorter durations. Moreover, milling process affected particle distribution. Nanoparticles more uniformly dispersed in the Al₂O₃–Cu reinforced samples compared with that of the samples reinforced with Al₂O₃–Al or pure alumina powders.     

The relationship between indentation hardness of organic solids and their molecular structure

A model has been developed relating the indentation hardness of organic molecular solids to their cohesive energy density, the length of the Burgers vector, the weakest plane from the crystal structure and crystal structural parameters. Whilst the described model is pragmatic, calculated indentation values for a variety of materials based on the weakest plane using specific Burgers vectors agree well with those from literature data.     

On the strength of discontinuous silicon carbide reinforced aluminum composites

The incorporation of dSiC into aluminum matrices results in substantial improvements in yield strength relative to the matrix material, but little change in the proportional limit. The Orowan strengthening mechanism was shown to be insufficient to account for the increase in yield strength of the composite. An increased dislocation density of the matrix due to a difference in the thermal expansion of the SiC and the matrix does predict an increase in composite strength, but is unable to explain why the proportional limit of the composite remains similar to that of the matrix or why the strength of the SiCw/6061Al is anisotropic. The conventional shear lag theory predicts yield strength values that are less than those observed. This is particularly so for the SiCp/Al composites, where the yield strength of the composite is predicted to be equal to that of the matrix independent of SiC volume fraction. If, however, the shear lag theory is modified to take into account the tensile transfer of load, the predicted composite strength is of sufficient magnitude to explain the strengthening effect of both the SiC whisker and platelet material. In addition, the modified shear lag theory can be used to rationalize why the proportional limit of the composite is similar to that of the matrix.     

Multi-scale characterization of particle clustering in discontinuously reinforced composites

The applicability of a quantitative characterization scheme for cluster detection in particle reinforced composites is discussed. The method considers the pattern from the perspective of individual particles, so that even in a pattern that globally conforms to a random distribution, micro-scale heterogeneities can be detected. The detected clusters are visualized by kernel surfaces. Results indicate that the presented methodology is an effective discriminator of clusters and can successfully be used for quantitative characterization of particle clustering in discontinuously reinforced composites.     

A computational approach to the investigation of impact damage evolution in discontinuously reinforced fiber composites

 A micromechanical damage constitutive model for discontinuous fiber-reinforced composites is developed to perform impact simulation. Progressive interfacial fiber debonding and a crack-weakened model are considered in accordance with a statistical function to describe the varying probability of damage. Emanating from a constitutive damage model for aligned fiber-reinforced composites, a micromechanical damage constitutive model for randomly oriented, discontinuous fiber-reinforced composites is developed. The constitutive damage model is then implemented into a finite element program DYNA3D to simulate the dynamic behavior and the progressive damage of composites. Finally, numerical simulations for a biaxial loading test and a four-point bend impact test of composite specimens are performed to validate the computational model and investigate impact damage evolution in discontinuous fiber-reinforced composite structures. Furthermore, in order to address the influence of Weibull parameter S _o on the damage evolution in composites, parametric analysis is carried out. Received 29 April 2000     

Thickness dependence of the indentation hardness of glass plates

The load required to produce fracture in glass plates by pressing steel balls onto both upper and lower surfaces of the plate has been recorded experimentally as a function of the thickness of the plate and the diameter of the indenter. It is observed that for a sufficiently large indenter the fracture load decreases rapidly as the thickness of the plate decreases. The variation of the fracture load with plate thickness is shown to be a consequence of the fact that the value of the maximum tensile stress at the boundary of the contact area is larger in a thin plate than in a thick plate, for the same indentation pressure. A method of calculation is described for determining the maximum tensile stress in an elastic plate subjected to arbitrary symmetrical spherical indentations.

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Zusammenfassung Die erforderliche Kraft, um Bruch in Glasplatten durch das Drücken Stahlbälle auf die Ober- and Unterfläche der Platte zu bewirken, ist durch Experiment als eine Funktion der Plattendicke and des Durchmessers des Balles eingetragen worden. Es wird bemerkt, daß bei einem genügend großen Ball, wenn die Plattendicke sich vermindert, die Bruchkraft sich schnell vermindert. Die Abweichung der Bruchkraft mit der Plattendicke zeigt sich als Folge der Tatsache, daß der Wert der Maximalzugspannung um den Rand des Berührungsraums größer bei einer diinnen Platte ist, als bei einer dicken Platte unter demselben Druck des Eindrucks. Eine Berechnungsmethode wird beschrieben, um die Maximalzugspannung einer elastischen Platte zu bestimmen, die unumschränkten symmetrischen sphärischen Eindrücken unterzogen wurden.

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Résumé Le poids nécessaire a produire de la cassure dans des plaques de verres en imposant des billes d'acier aux surfaces en dessus de et en dessous de la plaque a été expérimentalement rapporté comme une fonction de l'épaisseur de la plaque et du diamètre de la bille. On note que pour une bille assez grande, le poids de cassure amoindrit rapidement comme l'épaisseur de la plaque amoindrit. La variation du poids de cassure avec l'épaisseur de plaque est montrée d'etre conséquence du fait que la valeur de la tension de traction maximale a l'extérieure de la surface de contact est plus grande dans une plaque mince que daps une plaque épaisse chez la même pression d'échancrure. Une manière a calculer est décrite pour determiner la tension de traction maximale dans une plaque élastique soumise aux échancrures symétriques sphériques arbitraires.

     

Modeling the hardness and yield strength evolutions of aluminum alloy with rod/needle-shaped precipitates

For heat-treatable aluminum alloy containing rod/needle-shaped precipitates, a strengthening model for aging hardening behavior has been developed to describe the variations of dimension and volume fraction of the precipitates, and the yield strength and hardness with aging time. The model incorporates both the strengthening mechanisms of dislocation cutting the precipitates at underaged stage and bypassing the precipitates at overaged stage. It has been shown that the model predictions broadly agree with the experimental data for Al–Mg–Si alloys at varied aging time and aging temperatures. Thus, the model can be used to predict the variation of yield strength and hardness with aging time and aging temperature.     

Hertzian analysis of the self-consistency and reliability of the indentation hardness measurements on superhard nanocomposite coatings

The measurement of elastic properties of superhard nanocomposite coatings can be subject to a number of possible errors, such as indentation size effects (indenter tip blunting, non-representative small volume of the material to be tested upon nanoindentation and a too small stress under the indenter which does not reach the yield stress of that material if a too low load is used), the composite effect of the system of superhard coating on a softer substrate, high compressive or tensile stress in the coatings, drifts and/or stiffness of the indenter etc. We shall present a systematic study of these possible artefacts on superhard coatings using a large range of applied loads on a number of super- and ultrahard samples. The hardness values obtained from the indentation measurements are compared with the Vickers hardness calculated from the projected area of the plastic deformation. The data will be also compared with finite element method computer modeling in order to obtain a deeper insight into the complex problems. It will be shown that reliable results can be obtained if sufficiently thick coatings are used which allows one to obtain load independent values of hardness measured at sufficiently large indentation depths. Hertzian analysis of the non-linear elastic response upon unloading provides analytical solutions that can be used in order to check if the hardness values measured on the super- and ultrahard coatings are self-consistent. In particular, it is possible to estimate the maximum tensile stress that the coatings survive without failure. This stress occurs at the periphery of the contact between the coating and the indenter and, in the case of ultrahard coatings, it can reach values in the range of tens of GPa. The results show a very good agreement with the theoretical predictions based on the Universal Binding Energy Relation.     

原位自生非连续增强钛基复合材料的研究现状与展望

从基体和增强相选取、制备方法、微观结构、界面、氧化特性及力学性能方面综述了目前原位自生非连续增强钛基复合材料的发展状况, 结合本文作者的课题研究重点介绍了反应热压法(RHP) 制备钛复合材料的工艺以及所制备复合材料显微组织和力学性能。提出了当前研究中存在的问题和今后潜在的发展方向。      

Fracture and fatigue of discontinuously reinforced copper/tungsten composites

The strength, toughness and resistance to cyclic crack propagation of composites consisting of copper reinforced with short tungsten wires of various lengths have been studied and the results compared with the behaviour of continuously reinforced composites manufactured by the same method, i.e. by vacuum hot-pressing. It has been found that whereas the resistance to fatigue crack growth of continuously reinforced composites is very similar to that of continuous Al/stainless steel composites reported elsewhere, the addition of short fibres completely changes the mode of fracture, and no direct comparisons are possible. In effect, short fibres inhibit single crack growth by causing plastic flow to be distributed rather than localized, and although these composites are much less strong than continuous fibre composites, they nevertheless have much greater fatigue resistance. The fracture toughness of the composites is thought to be derived simply from the separate contributions of matrix and fibre plastic flow and, in composites containing fibres near to the critical length, from the very substantial work of fibre pull-out.     

Relationship between the stored energy and indentation hardness of copper after compression test: models and measurements

Utilizing the differential scanning calorimetry (DSC) and Vickers hardness tests, the relationship between the stored energy and indentation hardness of copper after compression test is achieved experimentally. Three dislocation models are utilized to develop the relationships between the stored energy and hardness for justifying the experimental relationship. The relationships show that the stored energy is increased by increasing the hardness, non-linearly. By comparing the models’ results with the experimental data, the validity of each model at different ranges of hardness is determined.     

Hot workability and processing maps of aluminium based discontinuously reinforced composites

Abstract

Hot deformation behaviour under tensile conditions of Al6061/20%Al₂O₃ , Al2618/20%Al₂O₃, and Al2618/20%SiC particle reinforced composites and of an unreinforced 6061 aluminium alloy was investigated in the temperature range 350–500°C and in the strain rate range 10^–3-10^–1s^–1. Processing maps were generated from the obtained data and the domains of optimal hot workability were identified for the different materials. Microstructural analyses on deformed specimens allowed it to be stated that dynamic recovery was the main restoration mechanism for the composites investigated. The concurrent evaluation of ductility and flow stress data also suggested that differences in reinforcement properties can play a significant role on property definition.     

Relationship of hardness to load on the indentor and hardness with a fixed diagonal of the indentation

For high-hardness materials, particularly for ceramics, the relationship of hardness to load is revealed very strongly. An equation is proposed for conversion of Vickers hardness from one load to another: $$HV = HV_1 \left( {\frac{P}{{P_1 }}} \right)^{1 - 2/n}$$ where HV and HV₁ are the hardness with loads on the indentor of P and P₁ respectively. The parameter n is determined from the equation P = const dⁿ, where d is the indentation diagonal. The parameter n may also be determined on the basis of a normalized curve of the value of HV/E (E is Young's modulus). The physical nature of the relationship of hardness to load is discussed and the hardness \(HV_{d_f }\) is introduced with a fixed indentation diagonal d_f (and not with a fixed load) calculated using the equation $$HV_{d_f } = HV\left( {\frac{d}{{d_f }}} \right)^{2 - n}$$ . The introduction of \(HV_{d_f }\) makes it possible to unify measurement of microhardness for different materials at different temperatures. Curves are given simplifying conversion of hardness from one load to another and determination of the hardness \(HV_{d_f }\) .     

Study of the correlation between hardness and structure of nitrogen-implanted titanium surfaces

Several spectroscopies analysing the composition and chemical nature of thin films (Rutherford backscattering spectrometry, nuclear reaction analysis, secondary ion mass spectroscopy, X-ray photoelectron spectroscopy) were combined with a specially designed technique of X-ray diffraction at grazing incidence on bulk samples, in order to characterize Ti_1–x N _x films of nearly homogeneous composition obtained by ion implantation at several energies. Differences in the nature of the phases observed, with respect to previous TEM studies on thin foils, are discussed in terms of radiation-enhanced diffusion and of thermal dissipation of the ion-beam power. The distribution of nitrogen atoms, defects and phases as a function of the nitrogen concentration are also correlated with changes in depth profiles of hardness measured by a submicroscopic indentation test.     

Bearing strength of commingled boron/glass fiber reinforced aluminum laminates

The bearing properties of recently developed hybrid fiber/metal laminates, or COmmingled Boron/glass fiber Reinforced Aluminum laminates (COBRA), are investigated in this study. The bolt-type bearing tests on GLass REinforced aluminum laminates (GLARE), non-commingled hybrid boron/glass/aluminum fiber/metal laminates (HFML) and COBRA were carried out as a function of e/D ratio, metal volume fraction, fiber volume fraction, and fiber orientation. Experimental results show that with the same joint geometry and metal volume fraction, the commingling of boron fibers improves the bearing strength of fiber/metal laminates. Observations show the boron/glass fiber prepreg, transverse to the loading direction, results in a bearing mechanism that effectively increases the bearing strength. The bearing strength of COBRA with longitudinal fibers is lower than that with transverse fibers due to the fact that shearout failure takes place before maximum bearing strength is reached. The experimental results show that, with only either transverse fiber orientation or longitudinal fiber orientation, COBRA with 18% boron fiber volume fraction possesses a higher bearing strength when compared to HFML with 6% boron fiber volume fraction. In addition to the properties in COBRA with parallel-plies commingled prepreg, the bearing properties of various COBRA with [0°/90°] and [0°/90°/90°/0°] cross-ply commingled prepregs are also discussed.     

Statistical analysis for strength and spatial distribution of reinforcement in SiC particulate reinforced aluminum alloy composites fabricated by die-casting

Statistical analysis for strength and spatial distribution of reinforcement in die-cast SiC_p/Al alloy composites was performed in order to predict the reliability of composites. Microstructural analysis was also done to determine the critical features of the composites. Die-casting was carried out using the preheated die at the casting temperature range of 620–750°C. It was found that the SiC pacticulates were homogeneously dispersed in die-cast Al matrix alloy, resulting from the refinement of dendritic cell size due to rapid cooling rate. The tensile strength of die-cast SiC_p/Al alloy composites was higher than that of die-cast Al matrix alloy. Also, the tensile strength was slightly increased with increasing SiC particulate volume fraction at the casting temperature range of 650–700°C. It was concluded that the die-cast temperatures of 750 and 700°C are optimum condition for the distribution of SiC particulates in consequence of good fluidity of melt for 10 and 20 vol.% SiC_p/Al alloy composites, respectively. However, the strength scattering of composites was increased with increasing SiC particulate volume fraction. For the statistical evaluation of strength, the maximum Weibull modulus of die-cast SiC_p/Al alloy composites, which was obtained at the cast temperature of 700°C, was 29.6 in Al matrix alloy, 22.2 in 10 vol.% SiC_p and 14.2 in 20 vol.% SiC_p, respectively.