Indentation of a hard film on a soft substrate: Strain gradient hardening effects

The strain gradient work hardening is important in micro-indentation of bulk metals and thin metallic films, though the indentation of thin films may display very different behavior from that of bulk metals. We use the conventional theory of mechanism-based strain gradient plasticity (CMSG) to study the indentation of a hard tungsten film on soft aluminum substrate, and find good agreement with experiments. The effect of friction stress (intrinsic lattice resistance), which is important in body-center-cubic tungsten, is accounted for. We also extend CMSG to a finite deformation theory since the indentation depth in experiments can be as large as the film thickness. Contrary to indentation of bulk metals or soft metallic films on hard substrate, the micro-indentation hardness of a hard tungsten film on soft aluminum substrate decreases monotonically with the increasing depth of indentation, and it never approaches a constant (macroscopic hardness). It is also shown that the strain gradient effect in the soft aluminum substrate is insignificant, but that in the hard tungsten thin film is important in shallow indentation. The strain gradient effect in tungsten, however, disappears rapidly as the indentation depth increases because the intrinsic material length in tungsten is rather small.     

The Effect of Heterogeneity on the Onset of Double-Diffusive Convection Induced by Internal Heating in a Porous Medium: A Layered Model

In this paper we have investigated the effects of both weak and strong heterogeneity on the onset of double-diffusive convection which is induced by combined effects of internal heating and solutal gradient. To make analytical progress, we considered a composite porous medium consisting of two horizontal layers. We investigated the effects of heterogeneities in permeability, thermal conductivity, volumetric heat source strength, and porosity. The solutal diffusivity, which becomes effective when a vertical salinity gradient is imposed, is affected by variation of porosity. We found that the effect of solutal diffusivity is stabilizing when the porosity increases upwards.     

Oil Recovery by Low Salinity Water Injection into a Reservoir: A New Study of Tertiary Oil Recovery Mechanism

Low salinity water injections for oil recovery have shown seemingly promising results in the case of clay-bearing sandstones saturated with asphaltic crude oil. Reported data showed that low salinity water injection could provide up to 20% pore volume (PV) of additional oil recovery for core samples and up to 25% PV for reservoirs in near wellbore regions, compared with brine injection at the same Darcy velocity. The question remains as to whether this additional recovery is also attainable in reservoirs. The answer requires a thorough understanding of oil recovery mechanism of low salinity water injections. Numerous hypotheses have been proposed to explain the increased oil recovery using low salinity water, including migration of detached mixed-wet clay particles with absorbed residual oil drops, wettability alteration toward increased water-wetness, and emulsion formation. However, many later reports showed that a higher oil recovery associated with low salinity water injection at the common laboratory flow velocity was neither necessarily accompanied by migration of clay particles, nor necessarily accompanied by emulsion. Moreover, increased water-wetness has been shown to cause the reduction of oil recovery. The present study is based on both experimental and theoretical analyses. Our study reveals that the increased oil recovery is only related to the reduction of water permeability due to physical plugging of the porous network by swelling clay aggregates or migrating clay particles and crystals. At a fixed apparent flow velocity, the value of negative pressure gradient along the flow path increases as the water permeability decreases. Some oil drops and blobs can be mobilized under the increased negative pressure gradient and contribute to the additional oil recovery. Based on the revealed mechanism, we conclude that low salinity water injection cannot be superior to brine injection in any clay-bearing sandstone reservoir at the maximum permitted injection pressure. Through our study of low salinity water injection, the theory of tertiary oil recovery has been notably improved.     

Wettability Alteration Mechanism for Oil Recovery from Fractured Carbonate Rocks

Oil can be recovered from fractured, initially oil-wet carbonate reservoirs by wettability alteration with dilute surfactant and electrolyte solutions. The aim of this work is to study the effect of salinity, surfactant concentration, electrolyte concentration, and temperature on the wettability alteration and identify underlying mechanisms. Contact angles, phase behavior, and interfacial tensions were measured with two oils (a model oil and a field oil) at temperatures up to 90°C. There exists an optimal surfactant concentration for varying salinity and an optimal salinity for varying surfactant concentration at which the wettability alteration on an oil-aged calcite plate is the maximum for anionic surfactants studied. As the salinity increases, the extent of maximum wettability alteration decreases; also the surfactant concentration needed for the maximum wettability alteration decreases. IFT and contact angle were found to have the same optimal salinity for a given concentration of anionic surfactants studied. As the ethoxylation increases in anionic surfactants, the extent of wettability alteration on calcite plates increases. Wettability of oil-aged calcite plates can be altered by divalent ions at a high temperature (90°C and above). Sulfate ions alter wettability to a greater extent in the presence of magnesium and calcium ions than in the absence. A high concentration of calcium ions can alter wettability alone. Magnesium ions alone do not change calcite plate wettability. Wettability alteration increases the oil recovery rate from initially oil-wet Texas Cordova Cream limestone cores by imbibition.     

Effect of inclined gradients on thermohaline convection in porous medium

Onset of convection in a thermohaline fluid staturating a porous medium subjected to inclined temperature as well as salinity gradients of finite magnitude is analysed using Galerkin technique. Due to unequal horizontal gradients of heat and salt the basic state fluid density varies horizontally also. It is found that (i) when the horizontal temperature gradient is greater than salinity gradient the system becomes unstable and stationary convection is possible in the stable quadrant, (ii) when the horizontal salinity gradient is greater than temperature gradient the stable region extends to the basically unstable quadrant, (iii) in the case of compensating horizontal gradients also the region of stationary convection gets extended to the stable quadrant when horizontal gradient increases, (iv) if only one of the horizontal gradients (heat or salt) is present the point where stationary convection changes over to oscillatory pattern is shifted to the region conductive to stationary convection; the effect of salinity gradient being more than that of temperature gradient.Mit Hilfe der Galerkin-Methode wird das Einsetzen der Konvektion in einem, ein poröses Medium tränkenden Thermohaline-Fluid unter dem gleichzeitigen Einfluß von veränderlichen Temperatur- und Salzkonzentrationsgradienten endlicher Höhe untersucht. Wegen der ungleichen Horizontalgradienten von Temperatur und Konzentration ändert sich auch die Gesamtfluiddichte in Horizontalrichtung. Es zeigt sich: (1) Ist der horizontale Temperaturgradient größer als der Konzentrationsgradient, so wird das System instabil und im stabilen Quadranten ist stationäre Konvektion möglich. (2) Im umgekehrten Fall erstreckt sich das stabile Gebiet bis zum grundsätzlich instabilen Quadranten. (3) Kompensieren sich die Horizontalgradienten, so erstreckt sich auch das Gebiet stationärer Konvektion bis zum stabilen Quadranten, falls der Horizontalgradient zunimmt. (4) Ist nur einer der beiden Horizontalgradienten vorhanden, so verschiebt sich der Punkt, wo stationäre Konvektion in die oszillatorische Mode übergeht, vom Gebiet reiner Wärmeleitung in das stationärer Konvektion. Der Einfluß des Konzentrationsgradienten überwiegt dabei den des Temperaturgradienten.C. Parthiban thanks University Grants Commission for awarding a fellowship.     

考虑压头曲率半径和应变梯度的微压痕分析

在压头尖端曲率半径取100nm的前提下，采用Chen和Wang的应变梯度理论，对微压痕实验进行了系统的数值分析. 首先通过拟合载荷-位移实验曲线的后半段来确定材料的屈服应力和幂硬化指数值,然后用有限元方法数值模拟压痕实验，并将计算得到的整段载荷-位移曲线及硬度-位移曲线和实验结果进行了比较. 结果表明应变梯度理论所预测的计算结果和实验结果很好地符合,包括压痕深度在亚微米和微米范围内的整段曲线.     

The influence of confinement on the bearing capacity of strip footingsEffet du confinement sur la capacité portante d'une fondation superficielle

The bearing capacity for a strip footing acting on a soil foundation with rigid boundaries at a finite distance is investigated within the framework of the Yield design theory both for a purely cohesive soil and for a frictional soil. It is shown that the analysis can be performed simply by referring to already existing results concerning the bearing capacity of a strip footing on a soil layer with limited thickness. Each bearing capacity factor in Terzaghi formula is increased by a factor that increases when the distance of the rigid boundary to the edge of the footing decreases. The bearing capacity is proved to be the more sensitive to this confining effect as the friction angle of the soil increases. From a physical point of view this theoretical analysis would show that, when effective, confinement reduces the depth of the soil layer involved in the collapse mechanism. To cite this article: J. Salençon, C. R. Mecanique 330 (2002) 319–326.     

45~#钢/GCr15钢摩擦副的滚动磨损特性研究

通过对液压式试验台夹具进行改造 ,研制了往复滚动试验装置 ,以实现对运动位移和表面摩擦力的精确控制 .利用该装置考察了表面摩擦力变化对 45 #钢 / GCr15钢摩擦副滚动磨损特性的影响 .结果表明 :随着表面摩擦力的增加 ,钢的滚动磨损明显加剧 ,磨损机制亦发生变化 .     

Small scale,grain size and substrate effects in nano-indentation experiment of film–substrate systems

The mechanical properties of film–substrate systems have been investigated through nano-indentation experiments in our former paper (Chen, S.H., Liu, L., Wang, T.C., 2005. Investigation of the mechanical properties of thin films by nano-indentation, considering the effects of thickness and different coating–substrate combinations. Surf. Coat. Technol., 191, 25–32), in which Al–Glass with three different film thicknesses are adopted and it is found that the relation between the hardness H and normalized indentation depth h/t, where t denotes the film thickness, exhibits three different regimes: (i) the hardness decreases obviously with increasing indentation depth; (ii) then, the hardness keeps an almost constant value in the range of 0.1–0.7 of the normalized indentation depth h/t; (iii) after that, the hardness increases with increasing indentation depth. In this paper, the indentation image is further investigated and finite element method is used to analyze the nano-indentation phenomena with both classical plasticity and strain gradient plasticity theories. Not only the case with an ideal sharp indenter tip but also that with a round one is considered in both theories. Finally, we find that the classical plasticity theory can not predict the experimental results, even considering the indenter tip curvature. However, the strain gradient plasticity theory can describe the experimental data very well not only at a shallow indentation depth but also at a deep depth. Strain gradient and substrate effects are proved to coexist in film–substrate nano-indentation experiments.     

条形荷载下梯度非均匀非饱和土的动力响应分析

基于多孔介质混合物理论, 建立了梯度非均匀非饱和土地基模型, 研究了条形荷载作用下梯度非均匀非饱和土地基的动力响应问题. 通过傅里叶积分变换和Helmholtz矢量分解原理, 获得频域内非饱和土地基动力响应问题的通解, 结合回传射线矩阵法和边界条件, 求解获得了非均匀非饱和土层中位移、应力以及孔隙压力的计算列式. 假设沿深度方向梯度非均匀非饱和土的物理力学性质按幂函数连续变化, 通过数值傅里叶逆变换得到了非均匀非饱和土地基中的应力、位移以及孔隙压力等物理量的数值解, 分析讨论了土体非均匀性对非饱和土介质动力响应的影响规律. 结果表明: 土体非均匀性显著改变了非饱和土中竖向位移、正应力和孔隙压力在其深度方向上的振动模态, 其中孔隙气压在其深度方向的振动频率随着梯度因子的增加而不断增大, 波峰值不断靠近地表处附近; 竖向位移随着梯度因子的增大不断减小; 正应力和孔隙水压随着梯度因子的增大先增大后减小, 并且土体非均匀程度越高, 正应力与孔隙水压的幅值越大.      

Analysis of spherical indentation of materials with plastically graded surface layer

In the present work, a comprehensive parametric study for establishing contact mechanics of instrumented normal spherical indentation on homogeneous materials and materials with plastically graded surface layer (PGSL) was undertaken by dimensional analysis and finite element modeling. The spherical indentation response for homogeneous materials can be described only by two dimensionless parameters: strain hardening exponent and a unified parameter that can describe effects of both the normalized yield strength and the normalized indentation depth. The influences of these two parameters were investigated for a wide range of engineering materials, and the results may be used as an estimate of loading response and pile-up/sink-in behavior when the material properties are known. In the materials with PGSL, a linear gradient in yield strength, and no variation in elastic modulus and strain hardening exponent were explored. The indentation response of the materials with PGSL can be described only by three dimensionless parameters: the normalized indentation depth, the dimensionless strength gradient parameter, and the normalized PGSL thickness. The effects of these three parameters were studied systematically. The normalized pile-up/sink-in parameter is found to be an increasing function of the strength gradient parameter. The normalized pile-up/sink-in parameter increases (decreases) with increasing PGSL thickness for a fixed positive (negative) gradient case at large indentation depth. The results also indicate that the materials with positive PGSL can bear more loads and have significantly more resistance to contact crack formation.     

土体剖面温度物理模型试验研究

利用自主开发的土体温度物理模型试验系统,研究了土体剖面温度随时间的变化规律,通过改变土体表面的覆盖层属性,对比分析了裸土和混凝土板覆盖下土体剖面的热传递特点。结果表明:在恒定热源作用下,土体剖面温度迅速上升到一定值之后逐渐趋于稳定,初始升温速率随深度的增加而呈指数递减,最终平衡温度随深度的增加而显著衰减; 温度在土体剖面上的传递存在明显的滞后效应; 混凝土板覆盖下土体的初始升温速率和最终平衡温度较裸土高; 土体剖面热通量反映了土体中热量的传递特征,其变化规律与上下土层间的温度差变化规律一致。     

Buoyancy Effects on Upward Brine Displacement Caused by CO2 Injection

Upward displacement of brine from deep reservoirs driven by pressure increases resulting from CO₂ injection for geologic carbon sequestration may occur through improperly sealed abandoned wells, through permeable faults, or through permeable channels between pinch-outs of shale formations. The concern about upward brine flow is that, upon intrusion into aquifers containing groundwater resources, the brine may degrade groundwater. Because both salinity and temperature increase with depth in sedimentary basins, upward displacement of brine involves lifting fluid that is saline but also warm into shallower regions that contain fresher, cooler water. We have carried out dynamic simulations using TOUGH2/EOS7 of upward displacement of warm, salty water into cooler, fresher aquifers in a highly idealized two-dimensional model consisting of a vertical conduit (representing a well or permeable fault) connecting a deep and a shallow reservoir. Our simulations show that for small pressure increases and/or high-salinity-gradient cases, brine is pushed up the conduit to a new static steady-state equilibrium. On the other hand, if the pressure rise is large enough that brine is pushed up the conduit and into the overlying upper aquifer, flow may be sustained if the dense brine is allowed to spread laterally. In this scenario, dense brine only contacts the lower-most region of the upper aquifer. In a hypothetical case in which strong cooling of the dense brine occurs in the upper reservoir, the brine becomes sufficiently dense that it flows back down into the deeper reservoir from where it came. The brine then heats again in the lower aquifer and moves back up the conduit to repeat the cycle. Parameter studies delineate steady-state (static) and oscillatory solutions and reveal the character and period of oscillatory solutions. Such oscillatory solutions are mostly a curiosity rather than an expected natural phenomenon because in nature the geothermal gradient prevents the cooling in the upper aquifer that occurs in the model. The expected effect of upward brine displacement is either establishment of a new hydrostatic equilibrium or sustained upward flux into the bottom-most region of the upper aquifer.     

A novel model for analysis of multilayer graphene sheets taking into account the interlayer shear effect

In this study, a multiplate shear model is developed for dynamic analysis of multilayer graphene sheets with arbitrary shapes considering the interlayer shear effect. By utilizing the model, then some free-vibration analysis is presented. According to the experimental results, the weak interlayer van der Waals interaction cannot maintain the integrity of carbon atoms in adjacent layers. Therefore, it is required that the interlayer shear effect is accounted to study multilayer graphene mechanical behavior. The governing differential equation of motion is derived for the multilayer graphene sheets utilizing a variational approach based on the Kirchhoff plate model. The essential and natural boundary conditions are also obtained at both the smooth periphery parts of the multilayer graphene sheets and the possible sharp corners. By considering cantilever and simply supported multilayer rectangular graphene sheets as two case studies, the results for the free-vibration analysis are presented based on the developed model, and these results are compared with those of molecular dynamics simulations as some sort of verification. These results show that when the layers number increases, the natural frequency also increases up to a specific number, and afterward the influence of layers number on the natural frequency significantly decreases. Moreover, the natural frequency decreases with increase in the sheet aspect ratio up to a specific value, then the changes in the aspect ratio have no considerable effect in the natural frequency.     

Nonlinear vibration analysis of micro-plates based on strain gradient elasticity theory

In this study, non-linear free vibration of micro-plates based on strain gradient elasticity theory is investigated. A general form of Mindlin’s first-strain gradient elasticity theory is employed to obtain a general Kirchhoff micro-plate formulation. The von Karman strain tensor is used to capture the geometric non-linearity. The governing equations of motion and boundary conditions are obtained in a variational framework. The Homotopy analysis method is employed to obtain an accurate analytical expression for the non-linear natural frequency of vibration. For some specific values of the gradient-based material parameters, the general plate formulation can be reduced to those based on some special forms of strain gradient elasticity theory. Accordingly, three different micro-plate formulations are introduced, which are based on three special strain gradient elasticity theories. It is found that both geometric non-linearity and size effect increase the natural frequency of vibration. In a micro-plate having a thickness comparable with the material length scale parameter, the strain gradient effect on increasing the non-linear natural frequency is higher than that of the geometric non-linearity. By increasing the plate thickness, the strain gradient effect decreases or even diminishes. In this case, geometric non-linearity plays the main role on increasing the natural frequency of vibration. In addition, it is shown that for micro-plates with some specific thickness to length scale parameter ratios, both geometric non-linearity and size effect have significant role on increasing the frequency of non-linear vibration.     

Laminar film condensation from downward flowing superheated vapors onto a non-isothermal sphere

 A model is developed for the study of mixed convection film condensation from downward flowing superheated vapors onto a sphere with variable wall temperature. The model combined natural convection dominated and forced convection dominated film condensation, including effects of superheated vapor, pressure gradient and wall temperature variation can be solved numerically by the fourth-order Runge–Kutta technique. By the present numerical approach, the mean heat transfer is evaluated up to the critical angle of the condensate layer, φ_c. In general, the result of mean heat transfer shows that, as A, the wall-temperature amplitude, increases, the value of with inclusion of P, the pressure gradient effect, goes down slightly, however, the value of with the pressure gradient effect ignored will remain almost uniform. Further, for P=2.0, the mean heat transfer coefficient increases significantly, by 8.6–23.9%, depending on A, as the superheat parameter, S p, increases within a practical range. Received on 7 September 2000     

A NUMERICAL STUDY OF INDENTATION WITH SMALL SPHERICAL INDENTERS

The finite element method for the conventional theory of mechanism-based strain gradient plasticity is used to study the indentation size effect. For small indenters （e.g., radii on the order of 10μm）, the maximum allowable geometrically necessary dislocation （GND） density is introduced to cap the GND density such that the latter does not become unrealistically high. The numerical results agree well with the indentation hardness data of iridium. The GND density is much larger than the density of statistically stored dislocations （SSD） underneath the indenter, but this trend reverses away from the indenter. As the indentation depth （or equivalently, contact radius） increases, the GND density decreases but the SSD density increases.     

混凝土靶侵爆条件下破坏深度的模型实验研究

为研究混凝土靶侵彻后空腔对爆炸效应的影响,开展了450～700 m/s速度下混凝土靶体侵彻与爆炸模型实验。基于10组实验结果,结合量纲分析等方法,研究了侵彻结果对爆坑深度的影响。结果表明,可采用无量纲冲击系数表征侵彻深度、开坑体积以及侵彻损伤值等侵彻效应,不考虑装药长径比的影响,侵彻后爆炸带来的破坏深度增加量h_e主要受无量纲冲击系数I_p与爆炸系数I_e的影响。利用实验数据获得了长径比为5时h_e的影响规律:(1) I_p较小时,侵彻深度较小,I_e的变化对爆炸弹坑深度h_e变化影响较小;(2) 随着I_p的增加,h_e不断增加,但增加幅度逐渐变小,I_e对h_e的影响不断变大;(3)随着I_p增加到一定程度,h_e趋于常数,I_e对h_e的影响趋于稳定。     

水面舰船尾流电导率信号分布规律的研究

在舰船尾流区与非尾流区之间存在显著的速度差和盐度(或密度)差,利用电导率探头可获得对应于这些差别的尾流电导率信号。在水槽中形成了与海洋环境类似的盐度分层流场,由双螺旋桨自航水面船模产生尾流,分别在盐度分层流场和非分层均匀流场中测量了尾流电导率信号的横向分布,并对盐度分层流场中水面舰船尾流的纵向速度分布进行了数值计算。结果表明:在盐度分层流场和非分层均匀流场中水面舰船尾流的电导率信号沿其横向近似呈高斯分布;尾流速度对其电导率信号的影响比盐度梯度的影响大得多;尾流的无量纲纵向速度亏损的数值计算结果与尾流的相对电导率信号横向分布的实测结果具有很好的一致性。     

Wake-boundary layer interaction subject to convex and concave curvatures and adverse pressure gradient

Measurements of mean velocity and turbulent quantities have been carried out when the wake of a symmetrical airfoil interacts with the boundary layer on the (i) walls of a straight duct/diffuser and (ii) convex and concave walls of a curved duct/diffuser. The effects of adverse pressure gradient and of curvatures on the interaction are studied separately and in combination. Six cases are considered, viz. with (i) neither pressure gradient nor curvature, (ii) adverse pressure gradient and no curvature, (iii) and (iv) convex curvature with zero and adverse pressure gradients, respectively, (v) and (vi) concave curvature with zero and adverse pressure gradients, respectively. For the flows with curvature, the curvature parameter δ/R is 0.023, and for the flows with adverse pressure gradient, the Clauser pressure gradient parameter β is 0.62. The individual influences of adverse pressure gradient and convex and concave curvatures on the boundary layer are similar to those observed by earlier investigations. It is further observed that the combined effect of concave/convex curvature and the adverse pressure gradient causes higher turbulence intensities than the sum of the individual effects. The effect of curvature is to make the wake asymmetric, and in combination with adverse pressure gradient the asymmetry increases. It is observed that the adverse pressure gradient causes faster wake–boundary-layer interaction. Comparing measurements in a straight duct, a curved duct, a curved diffuser and a straight diffuser, it is seen that the convex curvature reduces the boundary layer thickness. The asymmetry in wake development compensates for this effect and the wake–boundary-layer interaction on a convex surface is almost the same as that on a straight surface. In the case of interaction with the boundary layer on a concave surface, the curvature increases the boundary layer thickness and causes enhanced turbulence intensities. However, the asymmetry in wake is such that the extent of wake is lower towards the boundary layer side. As a result, the wake–boundary-layer interaction on concave surface is almost the same as on a straight surface. The interaction is faster in the presence of adverse pressure gradient. Received: 16 June 2000 / Accepted: 17 May 2001