154 resultados para ELASTIC-MODULUS
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The positive temperature coefficient (PTC) and negative temperature coefficient (NTC) effect of carbon black (CB) filled low density polyethylene (LDPE) composites was studied using electrical resistivity spectra, DSC, tensile mechanical analysis (TMA) and small-angle X-ray scattering (SAXS) techniques. The three LDPEs used have a similar crystallinity and different melting index (MI). The experimental results indicate that the CB has no significant effect on the crystallinity and the long spacing of crystalline domains of LDPE. Based upon the TMA and dynamic elastic modulus spectra, it can be concluded that the PTC effect is related to the thermal expansion of the polymer matrix, and the NTC effect is caused by a decrease of the elastic modulus of the polymer at high temperatures. The NTC effect can be reduced by enhancing either the elastic modulus or the interaction between carbon black and matrix. (C) 1997 Elsevier Science Ltd.
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The effect of processing conditions on the electrical and dynamic behavior of carbon black (CB) filled ethylene/ethylacrylate copolymer (EEA) composites was investigated. The compounds were prepared by two methods, solution blending and mechanical mixing. Compared with the solution counterpart, the mechanical composites have a strong positive temperature coefficient (PTC) effect and a high dynamic elastic modulus, which results from the good dispersion state of carbon black in EEA, i.e. the strong interaction between carbon black and EEA. It can be concluded that the strong interaction between polymer and carbon black is essential for composites to have a high PTC intensity, good electrical reproducibility and high dynamic elastic modulus. Copyright (C) 1996 Published by Elsevier Science Ltd.
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An equation has been derived for the equilibrium swelling of sequential interpenetrating polymer networks (IPNs), which exhibit a single glass transition temperature and the two components are considered to be compatible. The properties of the equilibrium swelling and elastic modulus of sequential poly(vinyl acetate)/poly(methyl acrylate) IPNs have been discussed according to the derived equation and the Siegfried-Thomas-Sperling formula of the elastic modulus for homo IPNs. In both fully swollen and bulk states, there was favourable evidence for added physical crosslinks in poly(vinyl acetate)/poly(methyl acrylate) IPNs. The Binder-Frisch theory is also discussed.
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Blends with a liquid-crystal polymers (LCP) as one component show, in general, very interesting properties. Reduction of shear visocity and improvement of mechanical properties are very remarkable. High melting temperatures and high costs of the LCP limit the use of these blends. A new class of thermotropic LCPs with flexible spaces, with relatively low melting temperatures, can overcome the first problem. In this work, rheological and mechanical properties of blends of polypropylene with low contents of this LCP are presented. Torque during extrusion and viscosity decrease with LCP content. Elastic modulus is remarkably increased when the LCP phase is oriented.
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Attenuations of different types of gas hydrate cementation in fluid-saturated porous solids are discussed. The factors affecting estimation of gas hydrate and free gas saturation are analyzed. It is suggested that porosity of sediment, the P wave velocity model and methods of calculating elastic modulus are key factors in the estimation of gas hydrate and free gas saturations. Attenuation of gas hydrate-bearing sediment is closely related with the cementation types of gas hydrate. Negative anomalies of quality factors indicate that gas hydrate deposits away from grain as part of fluid. Positive anomalies of the quality factors indicate that gas hydrate contacts with solid and changes the elastic modulus of matrix. Low frequency velocity and high frequency velocity models are used to estimate gas hydrate and free gas saturation in the Blake Ridge area according to the well log data of the hole 995 in ODP leg 164. The gas hydrate saturation obtained by low frequency velocity is 10% similar to 20% of the pore space and free gas saturation is 0.5% similar to 1% of the pore space. The gas hydrate saturation obtained by high frequency velocity is 5% similar to 10% of the pore space and free gas saturation is 1% similar to 2% of the pore space.
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The two major issues in mining industry are work safety and protection of ground environment when carrying on underground mining activities. Cut-and-fill mining method is increasingly applied in China owing to its advantages of controlling ground pressure and protecting the ground environment effectively. However, some cut-and-fill mines such as Jinchuan nickel mine which has big ore body, broken rock mass and high geostress have unique characteristics on the law of ground pressure and rock mass movement that distinguish from other mining methods. There are still many problems unknown and it is necessary for the further analysis. In this dissertation, vast field survey, geology trenching and relative data analysis are carried out. The distribution of ground fissures and the correlation of the fissures with the location of underground ore body is presented. Using of monitoring data by three-dimension fissure meter and GPS in Jinchuan Deposit Ⅱ, the rule of the surface deformation and the reason of ground fissures generation are analyzed. It is shown that the stress redistribution in surrounding rocks resulting from mining, the existence of the void space underground and the influence of on-going mining activities are three main reasons for the occurrence of ground fissures. Based on actual section planes of No.1 ore body, a large-scale 3D model is established. By this model, the complete process of excavation and filling is simulated and the law of rock mass movement and stability caused by Cut-and-fill Mining is studied. According to simulation results, it is concluded that the deformation of ground surface is still going on developing; the region of subsidence on the ground surface is similar with a circle; the area on the hanging wall side is larger than one on the lower wall side; the contour plots show the centre of subsidence lay on the hanging wall side and the position is near the ore body boundary of 1150m and 1250m where ore body is the thickest. Along strike-line of Jinchuan Deposit Ⅱ, the deformation at the middle of filling body is larger than that in the two sides. Because of the irregular ore body, stress concentrates at the boundary of ore body. With the process of excavation and filling, the high stress release and the stress focus disappear on the hanging wall side. The cut-and-fill mechanism is studied based on monitoring data and numerical simulation. The functions of filling body are discussed. In this dissertation, it is concluded that the stress of filling body is just 2MPa, but the stress of surrounding rock mass is 20MPa. We study the surface movement influenced by the elastic modulus of backfill. The minimal value of the elastic modulus of backfill which can guarantee the safety production of cut-and-fill mine is obtained. Finally, based on the real survey results of the horizontal ore layer and numerical simulation, it is indicated that the horizontal ore layer has destroyed. Key words: cut-and-filling mining, 3D numerical simulation, field monitoring, rock mass movement, cut-and-filling mechanism, the elastic modulus of backfill, the horizontal ore layer
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Using the popular CERCHAR testing to measure the abrasiveness of rock which is CERCHAR abrasiveness index(CAI). The digital imagine processing program IPP is used to quantify the rock texture such as the grain size, the shape of grain and the index of grain homogeneity. And the rock mechanical testing machine are used to measure the strength, hardness and elastic modulus. Basic on these three experiments, this paper finds the relationship between the CAI and physical and mechanical properties of rock. They are both the mesostructure and macroscopical properties of rock. According to the theory of tribology and wear, this paper finds the disc cutter wear mechanism during the machine and rock interaction process. The detail research results are as follows: (1) The size and form of the mineral grains constituting the rocks affect the abrasiveness of the rock. The rock abrasiveness CAI is a function of the product of the texture coefficient(TC) multiplying equivalent quarts content(Q%). (2) There is no obvious relationship between the rock abrasiveness CAI and the single macroscopical property of rock such as hardness, unconfined compressive strength, tensile strength and elastic modulus. But when taking the texture coefficient(TC) and the mineral composition in consideration, it shows that the rock abrasiveness CAI is relative to the combination of the rock mechanical property, the texture coefficient(TC) and the mineral composition. That is to say various factors which are from the mesostructure feature to the macroscopical property of rock control the rock abrasiveness. (3) The disc cutter penetrating into rock is a machine/rock interaction process. During this interaction, the wear of disc cutter is mainly coming from the abrasive of abrasiveness matters. First, the surface of the cutter ring is hunched, and then the material of the cutter ring is being wiped off during the iterative interaction. Second, the hard mineral in the rock and the muck will microcosmic cutting the surface material of cutter ring. (4) The disc cutters consumption is determined by the machine parameters and the geology condition. The machine parameters include the thrust and the revolution rate of the cutterhead. The geology condition include two aspects: the macroscopical properties which are the strength and/or hardness of rock, the presence of discontinuities in rock mass, the hardness, sharp, edge and size of the muck and so on. And the mesostructure features which are the hard mineral composition, the sharp and size of the grain of the rock.
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As we all know, rock-like materials will absolutely show very different mechanical properties under the compressive stress and tensile stress respectively. Similarly, under the dynamic compressive stress or dynamic tensile stress, the characteristics of the dynamics showed by the rock-like materials also have great differences from the mechanical behavior under static force. Studying their similarities and differences in rock mechanics theory and practical engineering will be of great significance. Generally, there are compression modulus of elasticity and tensile modulus of elasticity corresponding to compressive stress state and the tensile stress state in the rock. Both the two kinds of elastic modulus play an extremely important role in calculation of engineering mechanics. Their reliability directly affects the accuracy and reliability of the calculation results of internal stress field and displacement field of engineering rock mass. At present, it is easy to obtain the compression modulus of elasticity in laboratory; but it is very difficult to determine the tensile modulus of elasticity with direct tensile test due to that direct tensile test is difficult to perform in laboratory in general. In order to solve this problem, this thesis invents and develops several indirect test methods to determine the static or dynamic tensile modulus of elasticity of rock-type materials with high reliability and good interoperability. For the static tensile modulus of elasticity, the analytical stress field solution has been given out for the Brazilian disc under the radial and linear concentration load with Airy stress function method. At the same time, the stress field has been modeled for the Brazilian disc test by using the finite element software of ANSYS and ADINA. The analytical stress field solution is verified to be right by comparatively researching the analytical stress field solution and the numerical stress field solution. Based on the analytical stress field solution, this thesis proposes that a strain gauge is pasted at the Brazilian disc center along the direction perpendicular to the applied force to indirectly determine the static tensile modulus of elasticity, and related measurement theory also has been developed. The method proposed here has good feasibility and high accuracy verified by the experimental results. For the dynamic tensile modulus of elasticity, two measuring methods and theories are invented here. The first one is that the Split Hopkinson Pressure Bar is used to attract the Brazilian disc to generate the dynamic load, make the dynamic tensile stress is formed at the Brazilian disc center; and also a strain gauge is pasted at the Brazilian disc center to record the deformation. The second is that, in the Hopkinson effect phenomenon, the reflection tensile stress wave is formed when the shock wave propagates to the free end of cylindrical rock bar and reflect, which can make the rock bar is under dynamic tensile stress state; and some strain gauges are pasted at the appropriate place on the rock bar to record the strain coursed by the tensile or compressive stress wave. At last, the dynamic tensile modulus of elasticity can be determined by the recorded strain and the dynamic tensile stress which can be determined by related theories developed in this thesis.
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Rock mass is widely recognized as a kind of geologic body which consists of rock blocks and discontinuities. The deformation and failure of rock mass is not only determined by rock block,but also by discontinuity which is virtually more important. Mutual cutting and combination of discontinuities controlled mechanical property of rock mass. The complex cutting of discontinuities determine the intense anisotropy on mechanical property of rock mass,especially under the effect of ground stress. Engineering practice has show that the brittle failure of hard rock always occurs when its working stress is far lower than the yield strength and compressive strength,the failure always directly related to the fracture propagation of discontinuities. Fracture propagation of discontinuities is the virtue of hard rock’s failure. We can research the rock mass discontinuous mechanical properties precisely by the methods of statistical analysis of discontinuities and Fracture Mechanics. According to Superposition Principle in Fracture Mechanics,A Problem or C Problem could be chosen to research. Problem A mainly calculates the crack-tip stress field and displacement field on internal discontinuities by numerical method. Problem C calculate the crack-tip stress field and displacement field under the assumption of that the mainly rock mass stress field has been known. So the Problem C avoid the complex mutual interference of stress fields of discontinuities,which is called crack system problem in Fracture Mechanics. To solve Problem C, field test on stress field in the rock mass is needed. The linear Superposition of discontinuities strain energies are Scientific and Rational. The difference of Fracture Mechanics between rock mass and other materials can mostly expression as:other materials Fracture Mechanics mostly face the problem A,and can’t avoid multi-crack puzzle, while the Rock mass Fracture Mechanics answer to the Problem C. Problem C can avoid multi-discontinuities mutual interference puzzle via the ground stress test. On the basis of Problem C, Fracture Mechanics could be used conveniently in rock mass. The rock mass statistics fracture constitutive relations, which introduced in this article, are based on the Problem C and the Discontinuity Strain Energy linear superposition. This constitutive relation has several merits: first, it is physical constitutive relation rather than empirical; second, it is very fit to describe the rock mass anisotropy properties; third, it elaborates the exogenous factors such as ground stress. The rock mass statistics fracture constitutive relation is the available approach to answer to the physical, anisotropic and ground stress impacted rock mass problems. This article stand on the foundation of predecessor’s statistics fractures constitutive relation, and improved the discontinuity distributive function. This article had derived the limitation of negative exponential distribution in the course of regression analysis, and advocated to using the two parameter negative exponential distribution for instead. In order to solve the problems of two-dimension stability on engineering key cross-sectional view in rock mass, this article derived the rock mass planar flexibility tensor, and established rock mass two-dimension penetrate statistics fracture constitutive relation on the basis of penetrate fracture mechanics. Based on the crack tip plasticity research production of penetrate fracture, for example the Irwin plasticity equifinality crack, this article established the way to deal with the discontinuity stress singularity and plastic yielding problem at discontinuity tip. The research on deformation parameters is always the high light region of rock mass mechanics field. After the dam foundation excavation of XiaoWan hydroelectric power station, dam foundation rock mass upgrowthed a great deal of unload cracks, rock mass mechanical property gotten intricacy and strong anisotropy. The dam foundation rock mass mostly upgrowthed three group discontinuities: the decantation discontinuity, the steep pitch discontinuity, and the schistosity plane. Most of the discontinuities have got partial unload looseness. In accordance with ground stress field data, the dam foundation stress field greatly non-uniform, which felled under the great impaction of tectonic stress field, self-weight stress field, excavation geometric boundary condition, and excavation, unload. The discontinuity complexity and stress field heterogeneity, created the rock mass mechanical property of dam foundation intricacy and levity. The research on the rock mass mechanics, if not take every respected influencing factor into consideration as best as we can, major errors likely to be created. This article calculated the rock mass elastic modulus that after Xiao Wan hydroelectric power station dam foundation gutter excavation finished. The calculation region covered possession monolith of Xiao Wan concrete double-curvature arch dam. Different monolith were adopted the penetrate fracture statistics constitutive relation or bury fracture statistics constitutive relation selectively. Statistics fracture constitutive relation is fit for the intensity anisotropy and heterogeneity rock mass of Xiao Wan hydroelectric power station dam foundation. This article had contrastive analysis the statistics fracture constitutive relation result with the inclined plane load test actual measurement elastic modulus and RMR method estimated elastic modulus, and find that the three methods elastic modulus have got greatly comparability. So, the statistics fracture constitutive relations are qualified for trust. Generally speaking,this article had finished following works based on predecessors job: “Argumentation the C Problems of superposition principle in Fracture Mechanics, establish two-dimension penetrate statistics fracture constitutive relation of rock mass, argue the negative exponential distribution limitation and improve it, improve of the three-dimension berry statistics fracture constitutive relation of rock mass, discontinuity-tip plastic zone isoeffect calculation, calculate the rock mass elastic modulus on two-dimension cross-sectional view”. The whole research clue of this article inherited from the “statistics rock mass mechanics” of Wu Faquan(1992).
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The research on mechanical effects of water-rock and soil interaction on deformation and failure of rocks and soils involves three aspects of mechanics, physics and chemistry. It is the cross between geochemistry and rock mechanics and soil mechanics. To sum up, the mechanical effects of water-rock and soil interaction is related to many complex processes. Research in this respect has been being an important forward field and has broad prospects. In connection with the mechanism of the effects of the chemical action of water-rock on deformation and failure of rocks and soils, the research significance, the present state, the developments in this research domain are summarized. Author prospects the future of this research. The research of the subject should be possessed of important position in studying engineering geology and will lead directly to a new understand on geological hazard and control research. In order to investigation the macroscopic mechanics effects of chemical kinetics of water-rock interaction on the deformation and failure, calcic rock, red sandstone and grey granite reacting chemically with different aqueous solution at atmospheric temperature and atmospheric pressure are uniaxially compressed. The quantitative results concerning the changes of uniaxially compressive strength and elastic modulus under different conditions are obtained. It is found that the mechanical effects of water on rock is closely related to the chemical action of water-rock or the chemical damage in rock, and the intensity of chemical damage is direct ratio to the intensity of chemical action in water-rock system. It is also found that the hydrochemical action on rock is time-dependent through the test. The mechanism of permeation and hydrochemical action resulting in failure of loaded rock mass or propagation of fractures in rocks would be a key question in rock fracture mechanics. In this paper, the fracture mechanical effects of chemical action of water-rock and their time- and chemical environment-dependent behavior in grey granite, green granite, grey sandstone and red sandstone are analyzed by testing K_(IC) and COD of rock under different conditions. It is found that: ①the fracture mechanical effect of chemical action of water-rock is outstanding and time-dependent, and high differences exist in the influence of different aqueous solution, different rocks, different immersion ways and different velocity of cycle flow on the fracture mechanical effects in rock. ②the mechanical effects of water-rock interaction on propagation of fractures is consistent with the mechanical effects on the peak strength of rock. ③the intensity of the mechanical fracture effects increases as the intensity of chemical action of water-rock increases. ④iron and calcium ion bearing mineral or cement in rock are some key ion or chemical composition, and especially iron ion-bearing mineral resulting in chemical action of water-rock to be provided with both positive and negative mechanical effects on rock. Through the above two tests, we suggest that primary factors influencing chemical damage in rock consist of the chemical property of rock and aqueous solution, the structure or homogeneity of rocks, the flow velocity of aqueous solution passing through rock, and cause of formation or evolution of rock. The paper explores the mechanism on the mechanical effects of water-rock interaction on rock by using the theory of chemistry and rock fracture mechanics with chemical damage proposed by author, the modeling method and the energy point of view. In this paper, the concept of absorbed suction between soil grains caused by capillary response is given and expounded, and the relation and basic distinction among this absorbed suction, surface tension and capillary pressure of the soil are analyzed and established. The law of absorbed suction change and the primary factors affecting it are approached. We hold that the structure suction are changeable along with the change of the saturation state in unsaturated soils. In view of this, the concept of intrinsic structure suction and variable structure suction are given and expounded, and this paper points out: What we should study is variable structure suction when studying the effective stress. By IIIy κHH's theory of structure strength of soils, the computer method for variable structure suction is analyzed, the measure method for variable structure suction is discussed, and it reach the conclusions: ①Besides saturation state, variable structure suction is affected by grain composition and packing patter of grains. ②The internal relations are present between structure parameter N in computing structure suction and structure parameter D in computing absorbed suction. We think that some problems exit in available principle of effective stress and shear strength theory for unsaturated soil. Based on the variable structure suction and absorbed suction, the classification of saturation in soil and a principle of narrow sense effective stress are proposed for unsaturated soils. Based on generalized suction, the generalized effective stress formula and a principle of generalized effective stress are proposed for unsaturated soils. The experience parameter χ in Bishop's effective stress formula is defined, and the principal factors influencing effective stress or χ. The primary factor affecting the effective stress in unsaturated soils, and the principle classifying unsaturated soils and its mechanics methods analyzing unsaturated soils are discussed, and this paper points out: The theory on studying unsaturated soil mechanics should adopt the micromechanics method, then raise it to macromechanics and to applying. Researching the mechanical effects of chemical action of water-soil on soil is of great importance to geoenvironmental hazard control. The texture of soil and the fabric of soil mass are set forth. The tests on physical and mechanical property are performed to investigate the mechanism of the positive and negative mechanical effects of different chemical property of aqueous solution. The test results make clear that the plastic limit, liquid limit and plasticity index are changed, and there exists both positive and negative effects on specimens in this test. Based on analyzing the mechanism of the mechanical effects of water-soil interaction on soil, author thinks that hydrochemical actions being provided with mechanical effects on soil comprise three kinds of dissolution, sedimentation or crystallization. The significance of these tests lie in which it is recognized for us that we may improve, adjust and control the quality of soils, and may achieve the goal geological hazard control and prevention.The present and the significance of the research on environmental effects of water-rock and soil interaction. Various living example on geoenvironmental hazard in this field are enumerated. Following above thinking, we have approached such ideals that: ①changing the intensity and distribution of source and sink in groundwater flow system can be used to control the water-rock and soil interaction. ②the chemical action of water-rock and soil can be used to ameliorate the physical and mechanical property of rocks and soils. Lastly, the research thinking and the research methods on mechanical effects and environmental effects of water-rock and soil interaction are put forward and detailed.
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The scholars in the world have been trying to find an effective analytic algorithm of multiple hole problems usually meet in engineering designs. Though some studies on circular or elliptic holes had been achieved under specific conditions, no efforts were made to any multiple hole problems that is most significant for engineering designs. The author has made further studies on any multiple hole problems, using complex variable function method and Schwarz alternating method. After solving a series of technological difficulties, the author obtains an effective analytic algorithm, and acquires stress field and displacement field with high accuracy, which can be conducted for arbitrary many iterations according to practical accuracy requirements. In addition, th solution of stress and displacement fields, even for multiple holes of complex shapes and smaller distances. Further, the author made preliminary studies on viscoelastic displacement solution for any double holes. In terms of the obtained displacement solution of any multiple holes, this paper studies displacement back-analysis for the excavations of two tunnels, and find that the back-analysis method is accurate. Additionally, the author presents the mathematical prove of inversion uniqueness for ground stresses, elastic modulus and Poisson ratio. The author believes that the accurate analytic algorithm provided in this paper will presents an effective way to stress and displacement analysis for any multiple hole problems, optimal arrangement of multiple holes, hole shape optimization of multiple holes, etc..
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In order to realize fast development of the national economy in a healthy way and coordinate progress with whole society, the country has implemented the strategy of development of the western region. An important action of finishing this strategic task is to accelerate the highway construction in the western region, join the western region and places along the coast, the river, the border with goods and materials, technology, and personnel interchanges, and then drive development of the local economy.The western region was influenced by the Himalaya Tectonization in Cenozoic, and the crust rose and became the plateau. In the course of rising, rivers cut down sharply to form a lot of high mountains and gorges.Because of topography and geomorphology, bridges in the traffic construction in the alpine gorge area are needed. Rivers have characteristics of large flow, fast velocity and high and steep river valley, so building a pier in the river is not only very difficult, but also making the cost increase. At the same time, the impact that the pier is corroded and the bridge base that is drawn to be empty by flow are apt to cause destruction of the pier. For those reasons, suspending bridge and cable-stay bridge are usually adopted with the single and large span. For the large span bridge, the pier foundation could receive ten thousand and more vertical strength, bending moment and near kiloton horizontal thrust.Because bank slope in the alpine gorge district is cut deeply and unsettled big, natural stability is worse under endogenic and exogenic force. When bank slope bears heavy vertical strength, bending moment and horizontal thrust facing the river, it will inevitably make the balance state of rock and soil mass change, bridge bank slope deform, and even destroyed. So the key problem at the time of the large span's bridge construction in the alpine gorge area is how to make it stable.So based on the spot investigation, the Engineering Geology Analysis Method is very important to grasp the bank slope stability. It can provide the bank slope stability macroscopic ally and qualitatively, and reference to the indoor calculation. The Engineering Geology Analysis Method is that by way of analyzing and investigating terms of bank slope instability, stability development trend, the ancient rock slide and devolution in the site, stability comprehensive evaluation primarily, current and future stability of bank slope is gotten, realizing the intention to serving the concrete engineering.After the Engineering Geology Analysis Method is applied to project instances of BeiPan River Bridge and BaLin River Bridge, results are accord with bank slope actual conditions, which proves sites are suited to building bridges from site stability.we often meet bank slope stability issues in the traffic construction in the alpine gorge areao Before the evaluation of the bank slope stability, the engineering geological condition is investigated first. After that, the next exploration target and geology measures are decided. So, the Engineering Geology Analysis Method that the investigation of the engineering geological condition is the main content is quite important in practice. The other evaluations of the bank slope stability are based on it. Because foundation receives very heavy load, for the big span's bridge in the alpine gorge area, a long pile of the large diameter (D^0.8m) is usually selected. In order to reflect rock mass's deformation properties under rock-socketed pile function, the author has used the FLAG30 software for rock and soil mass and done many numerical simulations. By them, the author launches the further investigation on deformation properties of bank slope under different slope angle, pile length, diameter, elastic modulus, load, bank slope's structure, etc. Some conclusion meaningful to the design and produce are obtained.
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Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.
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We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic–plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a “hold” period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and “hold-at-the-maximum-indenter-displacement” for determining the instantaneous modulus using spherical indenters.
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Size-dependent elastic properties of Ni nanofilms are investigated by molecular dynamics ( MD) simulations with embedded atom method (EAM). The surface effects are considered by calculating the surface relaxation, surface energy, and surface stress. The Young's modulus and yield stress are obtained as functions of thickness and crystallographic orientation. It is shown that the surface relaxation has important effects on the the elastic properties at nanoscale. When the surface relaxation is outward, the Young's modulus decreases with the film thickness decreasing, and vice versa. The results also show that the yield stresses of the films increase with the films becoming thinner. With the thickness of the nanofilms decreasing, the surface effects on the elastic properties become dominant.