下卧基岩饱和地基在移动荷载作用下的动力响应

基于Biot多孔弹性介质波动理论,在平面应变条件下研究了下卧基岩饱和地基在移动线荷载作用下的动力响应。通过引入势函数并利用Helmholtz原理,再经过Fourier变换和逆变换,获得了移动线荷载作用下饱和地基的位移、应力、孔隙水压力解答。最后通过快速逆傅里叶变化（IFFT）得到数值计算结果,详细分析了土颗粒的压缩性、孔隙水的压缩性、饱和土的剪切模量、孔隙率、渗透性、移动荷载速度和饱和土层厚度等参数对动力响应的影响     

Three-dimensional stress and displacement fields near an elliptical crack front

Local stress and deformation fields for an elliptical crack embedded in an infinite elastic body subjected to normal, shear and mixed loads are considered. Particular emphasis is placed on the direction of propagation of points along the crack border. A confocal curvilinear coordinate system related to a fundamental ellipsoid, and a local spherical coordinate system attached to the crack border are adopted. Using asymptotic analysis, this paper obtains the stress and displacement fields in a plane inclined to the 3D crack front. Results show that the present solutions are independent of the curvature of the ellipse, and different from those given by Sih (1991). Based on two different fracture criteria, crack growth analysis shows that a 3D crack would propagate in the direction of the normal plane along the crack front. As a result, the fracture initiation and propagation of a 3D flat crack can be analyzed in the plane normal to the crack front, and the local fields in the normal plane are the linear superposition of the plane strain mode-I, mode-II, and mode-III crack-tip fields.     

Estimates from atomic models of tension-shear coupling in dislocation nucleation from a crack tip

The normal stress distribution across a slip plane has the effect of reducing the critical loading required for dislocation emission from a crack tip. The reduction by normal stresses was found to be very significant for Si, based on properties estimated for it using density functional theory, to be large for Fe as modeled by the embedded atom method (EAM), and to be smaller in Al, Ni and ordered Ni₃Al, estimated using the EAM. The general dependence over a wide range on parameters characterizing the tension-shear coupling was also determined. In the context of a Peierls model for dislocation nucleation at a crack tip (J.R. Rice, J. Mech. Phys. Solids, 40 (1992) 239), our approach was to search for onset of the dislocation nucleation instability based on the numerical solution of the system of non-linear integral equations describing an incipient dislocation. The incipient dislocation consists of a distribution of sliding and opening displacements along a slip plane emanating from the crack tip; these displacements are related to the shear and tensile stresses across the slip plane by constitutive relations based on the atomic models mentioned. Results from the atomic models are used to parametrize constitutive relations involving a Frenkel sinusoidal dependence of shear stress on sliding displacement at any fixed opening displacement, and a Rose-Ferrante-Smith universal binding form of dependence of tensile stress on opening displacement at any fixed shear displacement. These relations then enter the system of integral equations, solved numerically, which describe the elasticity solution for a non-uniform distribution of sliding and opening along the slip plane. The results show that tension-shear coupling will often significantly reduce the loading for dislocation emission from the value estimated on the basis of an unstable stacking energy γ_us determined with neglect of such coupling, in a shear-only type analysis. For the EAM models of the metals considered, a simple and approximate method to account for the tension effects is to use a modified quantity γ_us^(u*), which is an unstable stacking energy for lattice planes which are constrained to a fixed opening Δ_θ^*, corresponding to that for vinishing normal stress at the unstable shear equilibrium position. Moreover, it is found that the normal stress effect can be described well in these cases by replacing the unstable stacking energy γ_us in the shear-only model by a tension softened γ_us(Ψ), which depends on the phase angle Ψ of the combined tension-shear loading along the slip plane according to the stress intensity factors of the elastic singular solution. The same simple procedures for accounting for tension effects on nucleation are less suitable for lattices with strong coupling such as Si.     

考虑应变梯度及刚度劣化的剪切带局部变形分析

基于梯度塑性理论,研究了应变软化阶段的刚度劣化对剪切带内部的局部应变及相对剪切位移的影响。剪切带被看作一维剪切问题,本构关系为线弹性及线性应变软化。考虑刚度劣化后,剪切带的弹性应变由弹性剪切模量、损伤变量及残余剪切模量确定。剪切带的非局部总应变由双线性的本构关系确定。将非局部总应变减去弹性应变,可得剪切带的非局部塑性应变。剪切带非局部塑性应变与流动应力及损伤变量等参数有关,此关系即为在经典弹塑性理论框架之内的考虑刚度劣化的屈服函数。将二阶应变梯度项引入该函数,可得剪切带内部的局部塑性剪切应变及局部总剪切应变的分布规律。对局部塑性剪切应变积分,得到了局部塑性剪切位移。结果表明:考虑了刚度劣化后,剪切带内部的弹性剪切应变及位移增加,而局部塑性剪切应变及位移降低。若不考虑刚度劣化,理论结果可蜕化为以前的结果。理论结果与岩石局部变形的观测结果在定性是一致的。     

考虑应变梯度效应的三点弯梁模型解析研究--第一部分:局部化带的传播

为分析应变软化和由此带来的应变局部化问题,将梯度塑性理论引入裂纹带模型。以拉应变局部化区域代替裂纹带,在三点弯梁裂纹带(具有一定尺寸的带宽由特征长度确定)内部存在着不均匀分布的拉应变,这与实验结果相符。对拉应变进行积分,得到了拉应变局部化区域的张拉位移的理论表达式,结果表明:该位移与拉应力成线性规律,拉应变局部化区域的宽度越大,弹性模量越小或降模量越小,则该位移越大。此外,采用应力平衡条件、应变软化的本构关系及平截面假定,还得到了拉应变局部化区域的扩展规律,结果表明:下降模量越大、三点弯梁高度越小及弹性模量越小,则在相同的拉应力的情况下,拉应变局部化区扩展的长度越小;抗拉强度对拉应变局部化区扩展长度的最大值没有影响。此外,还研究了梁中部横截面内中性轴到具有最大承载能力的点的距离的变化规律。     

Mixed-mode crack surface interference under cyclic shear loads

A previous modelling analysis predicted that crack surface interference under cyclic shear loads is a combination of cyclic shear attenuation and cyclic wedge-opening. In the present study, experimental evidence is provided on notched thin-walled tubular specimens to evaluate the modelling predictions. Tests were carried out with varied static tensions superimposed on fully reversed ( R _τ = −1) or pulsating ( R _τ = 0) cyclic shear loads. The crack surface interference was measured by near-tip strain gauge methods. Based on the single and dual strain gauge readings, the strains induced by the mode I and II interference are separately identified so that the cyclic wedge-opening behaviour was noted as a companion of the cyclic shear attenuation. The crack surface interference under cyclic shear loads is compared with the influence from varied static tensions and shear stress ratios. A comparison of the mode I crack surface interference is also made between the conditions with cyclic shear loads and cyclic tensile loads. Finally, the characteristics of crack surface displacements are discussed, and the experimental results of effective mode I and II stress intensity ranges are compared with the modelling predictions.     

单箱多室波形钢腹板组合箱梁的腹板剪应力分析

为研究单箱多室波形钢腹板组合箱梁的腹板受力特性,建立了单箱双室和单箱三室波形钢腹板组合梁的有限元模型,并与模型试验结果进行了对比验证。通过有限元分析得到了不同类型的横向对称和偏心荷载作用下各波形钢腹板剪应变的结果,并对单箱多室波形钢腹板组合箱梁各腹板剪应力分布的不均匀现象的特点和原因进行研究。结果表明:集中荷载和均布线荷载的横向作用位置不同时,单箱多室波形钢腹板组合箱梁各腹板的剪应力差异显著,对称荷载作用下的单个腹板实际剪应力与横截面所有腹板平均剪应力的比值可达2.0以上,偏心荷载作用下则超过4.5,设计计算时须考虑各腹板剪应力的不均匀分布;均布面荷载作用下各腹板的剪应力可近似按均匀分布计算。根据腹板剪应力特点,提出单箱多室波形钢腹板组合箱梁的钢腹板剪应力计算应包括弯曲剪应力、扭转剪应力以及局部畸变产生的剪应力。     

Crack tip fields in ductile crystals

Results on the asymptotic analysis of crack tip fields in elastic-plastic single crystals are presented and some preliminary results of finite element solutions for cracked solids of this type are summarized. In the cases studied, involving plane strain tensile and anti-plane shear cracks in ideally plastic f c c and b c c crystals, analyzed within conventional small displacement gradient assumptions, the asymptotic analyses reveal striking discontinuous fields at the crack tip.For the stationary crack the stress state is found to be locally uniform in each of a family of angular sectors at the crack tip, but to jump discontinuously at sector boundaries, which are also the surfaces of shear discontinuities in the displacement field. For the quasi-statically growing crack the stress state is fully continuous from one near-tip angular sector to the next, but now some of the sectors involve elastic unloading from, and reloading to, a yielded state, and shear discontinuities of the velocity field develop at sector boundaries. In an anti-plane case studied, inclusion of inertial terms for (dynamically) growing cracks restores a discontinuous stress field at the tip which moves through the material as an elastic-plastic shock wave. For high symmetry crack orientations relative to the crystal, the discontinuity surfaces are sometimes coincident with the active crystal slip planes, but as often lie perpendicular to the family of active slip planes so that the discontinuities correspond to a kinking mode of shear.The finite element studies so far attempted, simulating the ideally plastic material model in a small displacement gradient type program, appear to be consistent with the asymptotic analyses. Small scale yielding solutions confirm the expected discontinuities, within limits of mesh resolution, of displacement for a stationary crack and of velocity for quasi-static growth. Further, the discontinuities apparently extend well into the near-tip plastic zone. A finite element formulation suitable for arbitrary deformation has been used to solve for the plane strain tension of a Taylor-hardening crystal panel containing, a center crack with an initially rounded tip. This shows effects due to lattice rotation, which distinguishes the regular versus kinking shear modes of crack tip relaxation. and holds promise for exploring the mechanics of crack opening at the tip.     

A general method for solving dynamically accelerating multiple co-linear cracks

We present a general method for analyzing dynamically accelerating multiple co-linear cracks that can be applied to the contexts of plane strain or antiplane shear in an elastic material. The difficulty in solving such problems lies in the fact that the space-time regions containing known data evolve as the crack propagates in an a priori unknown manner. Using an analog to a Dirichlet-to-Neumann map, we can find complete knowledge of the stress and displacement along the fracture plane, facilitating the application of fracture criteria that require these values away from the crack tip. The method is demonstrated for a semi-infinite or finite mode III crack as well as for a pair of cracks in elastic material, using a stress intensity factor fracture criterion for simplicity.     

Application of the double slip plane crack model to temperature and strain rate sensitive BCC metals

The double slip plane crack model proposed by Weertman, Lin and Thomson (1982) has been applied to model the effect of temperature and strain rate on the stress intensity factor at a crack tip in temperature and strain rate sensitive materials. Increase in temperature or decrease in strain rate (as well as a decrease in slip plane spacing) are shown to increase the shielding of the crack tip by dislocation distributions on the slip planes. Furthermore, the effect of temperature on the fracture toughness, K_llc, at various strain rates was shown to exhibit the same sigmoidal shaped curve seen for K_lc data in typical alloy steels.     

红砂岩剪切储能与最大剪应变特征试验研究

为了明确干燥和饱水红砂岩剪切强度、剪切储能与剪应变特征,在岩石剪切试验系统进行了不同法向应力作用下干燥和饱水红砂岩剪切试验,详细分析了法向应力和饱水作用对红砂岩剪切强度、剪切应变能密度和剪应变的影响规律。结果表明：剪力-剪切位移曲线,干燥状态线性段明显,饱水状态屈服段明显,法向应力在10 MPa～20 MPa,剪切强度和剪切位移增加显著,法向应力在20 MPa～40 MPa切向位移变化很小;压剪应力状态下的粘聚力和内摩擦角明显低于三轴压缩应力状态下的粘聚力和内摩擦角,饱水使三轴应力路径下的粘聚力和内摩擦角都弱化,而压剪应力路径下只对内摩擦角弱化。法向应力小于20 MPa时,剪切强度劣化率随法向应力的增加线性增大,法向应力在20 MPa～40 MPa时,剪切强度劣化率在一定值上下波动。峰值剪切应变能密度与法向应力之间存在良好线性变化规律,随法向应力增大,饱水对峰值剪切应变能密度的影响增加。干燥和饱水红砂岩峰值剪切应变能密度分别趋于定值1.4579 MJ/m3和1.0033 MJ/m3,饱水使峰值剪切应变能密度的劣化率趋于31.18%。根据峰值剪应变随法向应力的变化规律,构建了干燥和饱水红...     

含双尺度界面复相陶瓷的细观界面滑移应力

基于复相陶瓷显微特征和双尺度界面特性,分析含双尺度界面复相陶瓷内的细观界面滑移应力。首先,基于复相陶瓷宏观、细观和纳观弹性性能,计算双尺度界面复相陶瓷产生弹性变形时的细观平均应力场。然后,在纳观界面位移和应力连续基础上,提出了界面应变模型,确定了纳观界面附近纤维和基体内的位移函数,考虑界面应变的突变值与界面模量间的比例关系,根据纳观界面特性和纤维分布形式,确定出弹性变形条件下外载传递到细观界面上的切应力。最后,基于压痕实验测得复相陶瓷细观界面滑移的屈服切应力,得到细观界面滑移应力的理论计算公式并进行了定量分析。结果表明,复相陶瓷内纳观界面弹性模量越小或泊松比越小时,细观界面越易滑移,复相陶瓷越易产生塑性变形。     

SHEAR FATIGUE CRACK GROWTH: A LITERATURE SURVEY

A fatigue crack is often initiated by a localized cyclic plastic deformation in a crystal where the active slip plane coincides with the plane of maximum shear stress. Once a crack is initiated, the crack will propagate on the maximum shear plane for a while and, in the majority of the cases, will eventually change to the plane of the applied tensile stress. The “shear” and “tensile” modes of fatigue crack propagation are termed stage I and stage II fatigue crack growth. They are also known as mode II and mode I fatigue crack growth. However, the mechanism of the tensile mode fatigue crack propagation is shear in nature. Considerable progress has been made recently in the understanding of mode II fatigue crack growth. This paper reviews the various test methods and related data analyses. The combined mode I and mode II elastic crack tip stress field is reviewed. The development and the design of the compact shear specimen are described and the results of fatigue crack growth tests using the compact shear specimens are reviewed. The fatigue crack growth tests and the results of inclined cracks in tensile panels, center cracks in plates under biaxial loading, cracked beam specimens with combined bending and shear loading, center cracked panels and the double edge cracked plates under cyclic shear loading are reviewed and analyzed in detail.     

Energy partitioning for a crack under remote shear and compression

The true nature and characteristics of crack growth mechanisms in geologic materials have not been adequately described and are poorly understood. The process by which deformation energy is converted to slipping and growing cracks under compressive stresses is complex and difficult to measure. A hybrid technique employing moiré interferometry as an experimental boundary condition to a finite element method (FEM) was employed for through-cracked polycarbonate plates under remote shear and compression. Cohesive end zone and dislocation slip models are used to approximate experimentally observed displacement characteristics. Shear-driven linear elastic fracture mechanics displacement predictions are shown to be inadequate for initial displacement progression. Moiré displacement fields of relative crack face slip reveal a near tip cohesive zone. The pre-slip moiré-FEM stress fields reveal that the maximum crack tip tensile stress occurs at approximately 45 degrees and further infers cohesive zone presence. A J integral formulation uses moiré displacement data and accounts for stored energy along the crack before and after shear driven crack face slip. These energy-partitioning results track the transfer of stored energy along the crack face to the crack tip until the entire crack is actively slipping. These laboratory-scale experiments capture basic mechanical behavior and simulate thousands of years of large-scale geologic feature displacement history in just a few hours.     

Shear lips on fatigue fractures in aluminium alloy sheet material

An analysis is made of shear lip width measurements and the transition of tensile mode fatigue cracks to shear mode fatigue cracks, as observed on fatigue crack surfaces of aluminium alloy sheet material. It could be shown that these phenomena were controlled by ΔK_eff, rather than K_max or ΔK. For crack growth in air the shear lip width was approximately proportional to (ΔK_eff)², but it was significantly larger than the estimated size of the reversed plastic zone. The initiation of shear lips, the transition from plane stress to plane strain along the crack front and the environmental effect on shear lips are briefly considered in the discussion.     

Triaxial compression deformation for artificial frozen clay with thermal gradient

In order to study the deformation characteristics of artificial frozen soil with thermal gradient, such as the stress-strain relationship, a series of triaxial compression tests for frozen clay had been conducted by K₀DCGF (K₀ consolidation, freezing with non-uniform temperature under loading) method and GFC (freezing with non-uniform temperature, isotropic consolidation) method at various consolidation pressures and thermal gradients. Stress-strain curves in K₀DCGF test present strain softening during shearing process and the elastic strain is approximately 0.001;but which present the strain hardening characteristics in GFC tests and the elastic strain is approximately 0.01. The elastic modulus and peak stress for frozen clay decrease as the thermal gradient increased at different consolidation pressure both in K₀DCGF test and GFC test. The peak stress and elastic modulus in K₀DCGF test are significant independent on the pressure melting and crushing phenomena occurring in GFC test. To describe the shear deformation characteristics for frozen clay with thermal gradient, the exponent and power equations considering the correction equation on thermal gradient and model parameters from frozen clay with uniform temperature are developed .The results indicated that the proposed equations can reproduce the shear deformation well both in K₀DCGF test and GFC test.     

On crack path evolution rules

The models of crack growth in mixed mode conditions are reviewed for the plane and three-dimensional (3D) states of stress. Both critical load value and crack path or surface growth are predicted by different criteria in terms of elastic singular stress states and T-stress component. Monotonic and cyclic loading induced crack growth is considered. The energy and critical plane criteria based on local or non-local measure of stress and strain are most useful in developing predictive crack growth simulation. The finite critical distance from the crack tip should be specified to provide averaged or local stress and strain states. The application of MK-criterion of crack growth expressed in terms of volumetric and deviatoric strain energies is presented for several specific cases of monotonic and cyclic loading. The concepts of smooth and rough crack surface are discussed with application to 3D crack surface growth.     

Crack tip displacements of microstructurally small surface cracks in single phase ductile polycrystals

A planar double slip crystal plasticity model is applied to the evaluation of crack tip opening (CTOD) and sliding (CTSD) displacements for microstructurally small stationary cracks under monotonic loading for a material with nominal stress-strain behavior that is representative of a relatively high strength helicopter rotor hub material. Two-dimensional plane strain finite element calculations are presented for CTSD and CTOD of microstructurally small transgranular surface cracks in a polycrystal subjected to monotonic loading. The effects of crack length relative to grain size, orientation distribution of nearest neighbor grains, stress state and stress level are considered for nominal stress levels below the macroscopic yield strength. The CTOD and CTSD are computed for stationary crystallographic surface cracks with various realizations of crystallographic orientations of surrounding grains. It is found that (i) the opening displacement is dominant for remote tension even for crystallographic cracks oriented along the maximum shear plane in the first surface grain, (ii) there is a strong dependence of the CTOD on the proximity to grain boundaries, but lesser dependence of the CTSD, and (iii) that the elastic solutions for CTOD and CTSD are valid below about 30% of the 0.2% offset-defined yield strength.     

初始应力线和原状土的修正Mohr-Coulomb准则

原状土与重塑土在力学性质方面存在显著差别的原因,本质上在于建立在初始应力状态之上的结构性。重塑土一般是各向同性的,故在三维应力空间中其屈服曲面以等倾线为轴线。原状土由于在形成过程中一直处于三向不等压状态,故理论上讲其屈服曲面不能再以等倾线为轴线而应以初始应力线为轴线。该文以某真三轴试验为例,首先研究了特定八面体应变对应的广义剪应力随加载角的变化特征。随后,基于广义塑性力学和原状土的初始应力状态,提出了初始应力线的概念,并研究了初始应力线与等倾线的关系。进一步给出了三个适用于原状土的修正Mohr-Coulomb屈服准则,即平移模式、缩移模式和旋转模式。其中平移模式、缩移模式的屈服迹线仍然位于π平面上,而旋转模式的屈服迹线位于与初始应力线垂直的χ平面上。前两种模式可以通过等p真三轴试验结果直接对原状土的结构性进行评估;最后一种模式可以通过σ₁+K₀σ₂+K₀σ₃=c真三轴试验或等p真三轴试验数据在χ平面上的映射对原状土的结构性和各向异性进行研究。文献资料的验证表明,旋转模式修正Mohr-Coulomb屈服准则更能反映原状土的结构性,且物理意义清晰明确。     

倾斜应力作用下垂直于功能梯度材料夹层的币型裂纹扩展问题

分析了功能梯度材料中币型裂纹扩展问题。该裂纹体受有与裂纹面成任意角度的张应力或压应力,裂纹垂直于无限域中功能梯度材料夹层。假定非均匀介质的功能梯度材料夹层与两个半无限域完全结合,其弹性模量沿厚度方向变化。利用已发表的裂纹应力强度因子数据和线弹性断裂力学的叠加原理,将应力强度因子耦合于最小应变能密度因子断裂判据,讨论了裂纹扩展的临界荷载;并讨论了荷载方向和材料性质对临界荷载的影响。