Stress intensity factor histories of a steadily propagating crack under 3-D combined mode traction

Elastodynamic stress intensity factor histories of an unbounded solid containing a semi-infinite plane crack that propagates at a constant velocity under 3-D time-independent combined mode loading are considered. The fundamental solution, which is the response of point loading, is obtained. Then, stress intensity factor histories of a general loading system are written out in terms of superposition integrals. The methods used here are the Laplace transform methods in conjunction with the Wiener-Hopf technique.

A New Finite Element Method for Strain Gradient Theories and Applications to Fracture Analyses

A new compatible finite element method for strain gradient theories is presented. In the new finite element method, pure displacement derivatives are taken as the fundamental variables. The new numerical method is successfully used to analyze the simple strain gradient problems – the fundamental fracture problems. Through comparing the numerical solutions with the existed exact solutions, the effectiveness of the new finite element method is tested and confirmed. Additionally, an application of the Zienkiewicz–Taylor C1 finite element method to the strain gradient problem is discussed. By using the new finite element method, plane-strain mode I and mode II crack tip fields are calculated based on a constitutive law which is a simple generalization of the conventional J2 deformation plasticity theory to include strain gradient effects. Three new constitutive parameters enter to characterize the scale over which strain gradient effects become important. During the analysis the general compressible version of Fleck–Hutchinson strain gradient plasticity is adopted. Crack tip solutions, the traction distributions along the plane ahead of the crack tip are calculated. The solutions display the considerable elevation of traction within the zone near the crack tip.

Interactions of Penny-Shaped Cracks in Three-Dimensional Solids

The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is developed in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.

Analysis of two-dimensional finite solids with microcracks

A general method is presented for solving the plane elasticity problem of finite plates with multiple microcracks. The method directly accounts for the interactions between different microcracks and the effect of outer boundary of a finite plate. Analysis is based on a superposition scheme and series expansions of the complex potentials. By using the traction-free conditions on each crack surface and resultant forces relations along outer boundary, a set of governing equations is formulated. The governing equations are solved numerically on the basis of a boundary collocation procedure. The effective Young's moduli for randomly oriented cracks and parallel cracks are evaluated for rectangular plates with microcracks. The numerical results are compared with those from various micromechanics models and experimental data. These results show that the present method provides a direct and efficient approach to deal with finite solids containing multiple microcracks.

Toughness Of Ni/Al2O3 Interfaces As Dependent On Micron-Scale Plasticity And Atomistic-Scale Separation

Ceramic/metal interfaces were studied that fail by atomistic separation accompanied by plastic dissipation in the metal. The macroscopic toughness of the specific Ni alloy/Al2O3 interface considered is typically on the order of ten times the atomistic work of separation in mode I and even higher if combinations of mode I and mode II act on the interface. Inputs to the computational model of interface toughness are: (i) strain gradient plasticity applied to the Ni alloy with a length parameter determined by an indentation test, and (ii) a potential characterizing mixed mode separation of the interface fit to atomistic results. The roles of the several length parameters in the strain gradient plasticity are determined for indentation and crack growth. One of the parameters is shown to be of dominant importance, thus establishing that indentation can be used to measure the relevant length parameter. Recent results for separation of Ni/Al2O3 interfaces computed by atomistic methods are reviewed, including a set of results computed for mixed mode separation. An approximate potential fit to these results is characterized by the work of separation, the peak separation stress for normal separation and the traction-displacement relation in pure shearing of the interface. With these inputs, the model for steady-state crack growth is used to compute the toughness of the interface under mode I and under the full range of mode mix. The effect of interface strength and the work of separation on macroscopic toughness is computed. Fundamental implications for plasticity-enhanced toughness emerge.

Elastodynamic stress-intensity factors for a semiinfinite crack under 3-d combined mode loading

The dynamic stress intensity factor histories for a half plane crack in an otherwise unbounded elastic body are analyzed. The crack is subjected to a traction distribution consisting of two pairs of suddenly-applied shear point loads, at a distance L away from the crack tip. The exact expression for the combined mode stress intensity factors as the function of time and position along the crack edge is obtained. The method of solution is based on the direct application of integral transforms together with the Wiener-Hopf technique and the Cagniard-de Hoop method, which were previously believed to be inappropriate. Some features of solutions are discussed and the results are displayed in several figures.

Crack extension and kinking in laminates and bicrystals

Singular fields at the tip of an interface crack in anisotropic solids are reviewed with emphasis on establishing a framework to quantify fracture resistance under mixed mode conditions. The concepts of mode mixity and surface toughness are unified by using generalized interface traction components. The similarity between the anisotropic theory and existing isotropic theory is shown. Explicit formulae are given for misoriented orthotropic bimaterials with potential applications envisioned including composite laminates and semiconductor crystals. Competition between crack extension along the interface and kinking into the substrate is investigated using a boundary layer formulation. Several case studies reveal the role of anisotropy. An explicit complex variable representation for orthotropic materials and a solution to a dislocation interacting with a crack are presented in two self-contained Appendices.

A unified law of motion of lithospheric plates and the driving mechanism

From observed data on lithospheric plates, a unified empirical law for plate motion,valid for continental as well as oceanic plates, is obtained in the following form: The speedof plate motion U depends linearly on a geometric parameter T_d, ratio of the sum of effectiveridge length and trench arc length to the sum of area of continental part of plate and total areaof cold sinking slab. Based on this unified law, a simple mechanical analysis shows that, themain driving forces for lithospheric plates come from push along the mid-ocean ridge andpull by the cold sinking slab, while the main drag forces consist of the viscous traction beneaththe continental part of plate and over both faces of the sinking slab. Moreover, the specific-push along ridge and pull by slab are found to be of equal magnitude.

Stabilizing to disruptive transition of focal adhesion response to mechanical forces

Strong mechanical forces can, obviously, disrupt cell-cell and cell-matrix adhesions, e.g., cyclic uniaxial stretch induces instability of cell adhesion, which then causes the reorientation of cells away from the stretching direction. However, recent experiments also demonstrated the existence of force dependent adhesion growth (rather than dissociation). To provide a quantitative explanation for the two seemingly contradictory phenomena, a microscopic model that includes both integrin-integrin interaction and integrin-ligand interaction is developed at molecular level by treating the focal adhesion as an adhesion cluster. The integrin clustering dynamics and integrin-ligand binding dynamics are then simulated within one unified theoretical frame with Monte Carlo simulation. We find that the focal adhesion will grow when the traction force is higher than a relative small threshold value, and the growth is dominated by the reduction of local chemical potential energy by the traction force. In contrast, the focal adhesion will rupture when the traction force exceeds a second threshold value, and the rupture is dominated by the breaking of integrin-ligand bonds. Consistent with the experiments, these results suggest a force map for various responses of cell adhesion to different scales of mechanical force. PMID: 20542514

First principles based predictions of the toughness of a metal/oxide interface

We describe a first-principles-based strategy to predict the macroscopic toughness of a gamma-Ni(Al)/alpha-Al2O3 interface. Density functional theory calculations are used to ascertain energy changes upon displacing the two materials adjacent to the interface, with relaxation conducted over all atoms located within adjoining rows. Traction/displacernent curves are obtained from derivatives of the energy. Calculations are performed in mode I (opening), mode II (shear) and at a phase angle of 45 degrees. The shear calculations are conducted for displacements along < 110 > and < 112 > of the Ni lattice. A generalized interface potential function is used to characterize the results. Initial fitting to both the shear and normal stress results is required to calibrate the unknowns. Thereafter, consistency is established by using the potential to predict other traction quantities. The potential is incorporated as a traction/displacement function within a cohesive zone model and used to predict the steady-state toughness of the interface. For this purpose, the plasticity of the Ni alloy must be known, including the plasticity length scale. Measurements obtained for a gamma-Ni superalloy are used and the toughness predicted over the full range of mode mixity. Additional results for a range of alloys are used to demonstrate the influences of yield strength and length scale.

First principles based predictions of the toughness of a metal/oxide interface

We describe a first-principles-based strategy to predict the macroscopic toughness of a gamma-Ni(Al)/alpha-Al2O3 interface. Density functional theory calculations are used to ascertain energy changes upon displacing the two materials adjacent to the interface, with relaxation conducted over all atoms located within adjoining rows. Traction/displacernent curves are obtained from derivatives of the energy. Calculations are performed in mode I (opening), mode II (shear) and at a phase angle of 45 degrees. The shear calculations are conducted for displacements along < 110 > and < 112 > of the Ni lattice. A generalized interface potential function is used to characterize the results. Initial fitting to both the shear and normal stress results is required to calibrate the unknowns. Thereafter, consistency is established by using the potential to predict other traction quantities. The potential is incorporated as a traction/displacement function within a cohesive zone model and used to predict the steady-state toughness of the interface. For this purpose, the plasticity of the Ni alloy must be known, including the plasticity length scale. Measurements obtained for a gamma-Ni superalloy are used and the toughness predicted over the full range of mode mixity. Additional results for a range of alloys are used to demonstrate the influences of yield strength and length scale.

全地形移动机器人建模与控制研究综述

本文主要针对复杂地形给移动机器人机动性和安全性所带来的相关问题,从机器人建模、轮—地接触模型、车轮滑移、牵引力控制及稳定性控制等方面,对全地形移动机器人建模与控制的相关研究进行了全面综述,并分析了国内外研究现状,特别是近年来所取得的最新成果.最后,指出了目前存在的问题及将来可能的发展趋势.

基于滑转率的六轮纵列式月球车驱动控制研究

基于车轮滑转率和车轮地面力学,研究了月球车在松软月面行驶时的车轮过度下陷问题.将月球车车轮下陷和车轮—土壤作用力表达为车轮滑转率的函数,结合车辆地面力学理论并考虑纵列式车轮多通过性土壤参数的修正,建立了月球车的动力学模型.判断车轮是否发生过度下陷的标准为土壤所提供给驱动轮的土壤推力能否克服土壤对车轮的阻力.利用建立的动力学模型,计算出能够保证车轮不会过度下陷的期望滑转率.考虑到月球车动力学系统的非线性和不确定性,设计了以车轮滑转率为状态变量的滑模驱动控制器.仿真结果表明,采用该控制器可以较快地跟踪期望滑转率,避免车轮的过度滑转下陷,保证月球车能够在软质路面上正常行驶.

滑转率对月球车车轮驱动力学特性的影响分析

应用车辆地面力学理论研究滑转率对月球车车轮挂钩牵引力、驱动效率以及功率消耗的影响。建立刚性车轮与松软月壤交互作用的动力学模型。通过实例对月球车车轮驱动动力学特性进行仿真分析。研究结果表明,车轮的挂钩牵引力、驱动效率以及驱动能耗均受到车轮滑转率的制约。存在一个最优的滑转率区间,在此区间内车轮可获得较大的挂钩牵引力、较高的驱动效率以及较低的驱动能耗。求取轮、地相对速度,对月球车车轮的地面摩擦力功率进行了估算。

地幔对流理论及其在解释地球物理观测的应用

With the improving of mantle convection theory, the developing of computing method and increasing of the measurement data, we can numerically simulate more clearly about the effects on some geophysical observed phenomenons such as the global heat flow and global lithospheric stress field in the Earth's surface caused by mantle convection, which is the primary mechanism for the transport of heat from the Earth's deep interior to its surface and the underlying force mechanism of dynamics in the Earth.Chapter 1 reviews the historical background and present research state of mantle convection theory.In Chapter 2, the basic conception of thermal convection and the basic theory about mantle flow.The effects on generation and distribution of global lithospheric stres s field induced by mantle flow are the subject of Chapter 3. Mantle convection causes normal stress and tangential stresses at the bottom of the lithosphere, and then the sublithospheric stress field induces the lithospheric deformation as sixrface force and results in the stress field within the lithosphere. The simulation shows that the agreement between predictions and observations is good in most regions. Most of subduction zones and continental collisions are under compressive. While ocean ridges, such as the east Pacific ridge, the Atlantic ridge and the east African rift valley, are under tensile. And most of the hotspots preferentially occur in regions where calculated stress is tensile. The calculated directions of the most compressive principal horizontal stress are largely in accord with that of the observation except for some regions such as the NW-Pacifie subduction zone and Qinghai-Tibet Plateau, in which the directions of the most compressive principal horizontal stress are different. It shows that the mantel flow plays an important role in causing or affecting the large-scale stress field within the lithosphere.The global heat flow simulation based on a kinematic model of mantle convection is given in Chapter 4. Mantle convection velocities are calculated based on the internal loading theory at first, the velocity field is used as the input to solve the thermal problem. Results show that calculated depth derivatives of the near surface temperature are closely correlated to the observed surface heat flow pattern. Higher heat flow values around midocean ridge systems can be reproduced very well. The predicted average temperature as a function of function of depth reveals that there are two thermal boundary layers, one is close to the surface and another is close to the core-mantle boundary, the rest of the mantle is nearly isothermal. Although, in most of the mantle, advection dominates the heat transfer, the conductive heat transfer is still locally important in the boundary layers and plays an important role for the surface heat flow pattern. The existence of surface plates is responsible for the long wavelength surface heat flow pattern.In Chapter 5, the effects on present-day crustal movement in the China Mainland resulted from the mantle convection are introduced. Using a dynamic method, we present a quantitative model for the present-day crustal movement in China. We consider not only the effect of the India-Eurasia collision, the gravitational potential energy difference of the Tibet Plateau, but also the contribution of the shear traction on the bottom of the lithosphere induced by the global mantle convection. The comparison between our results and the velocity field obtained from the GPS observation shows that our model satisfactorily reproduces the general picture of crustal deformation in China. Numerical modeling results reveal that the stress field on the base of the lithosphere induced by the mantle flow is probably a considerable factor that causes the movement and deformation of the lithosphere in continental China with its eflfcet focuing on the Eastern China A numerical research on the small-scale convection with variable viscosity in the upper mantle is introduced in Chapter 6. Based on a two-dimensional model, small-scale convection in the mantle-lithosphere system with variable viscosity is researched by using of finite element method. Variation of viscosity in exponential form with temperature is considered in this paper The results show that if viscosity is strongly temperature-dependent, the upper part of the system does not take a share in the convection and a stagnant lid, which is identified as lithosphere, is formed on the top of system because of low temperature and high viscosity. The calculated surface heat flow, topography and gravity anomaly are associated well with the convection pattern, namely, the regions with high heat flow and uplift correspond to the upwelling flow, and vice versa.In Chapter 7, we give a brief of future research subject: The inversion of lateral density heterogeneity in the mantle by minimizing the viscous dissipation.