弹塑性材料中孔洞成核、发展及应力场

采用Bermin的孔洞成核的局部应力准则以及Euler坐标系下大应变有限元方法,分析了平面应变条件下二相粒子与基体在三种不同的界面结合强度下的宏观材料的力学行为.     

A physical model for nucleation and early growth of voids in ductile materials under dynamic loading

Spall fracture and other rapid tensile failures in ductile materials are often dominated by the rapid growth of voids. Recent research on the mechanics of void growth clearly shows that void nucleation may be represented as a bifurcation phenomenon, wherein a void forms spontaneously followed by highly localized plastic flow around the new void. Although thermal, viscoplastic, and work hardening effects all play an essential role in the earliest stages of nucleation and growth, the flow becomes dominated by spherical radial inertia, which soon causes all voids to grow asymptotically at the same rate, regardless of differences in initial conditions or constitutive details, provided only that there is the same density of matrix material and the same excess loading history beyond the cavitation stress.These two facts, initiation by bifurcation at a cavitation stress, at which a void first appears, and rapid domination by inertia, are used to postulate a simple, but physically realistic, model for nucleation and early growth of voids in a ductile material under rapid tensile loading. A reasonable statistical distribution for the cavitation stress at various nucleation sites and a simple similarity solution for inertially dominated void growth permit a simple calculation of the initiation and early growth of porosity in the material.Parametric analyses are presented to show the effect that loading rate, peak loading stress, density of nucleation sites, physical properties of the material, etc. have on the applied pressure and distribution of void sizes when a critical porosity is reached.     

Onset of Cavitation in Compressible,Isotropic, Hyperelastic Solids

In this work, we derive a closed-form criterion for the onset of cavitation in compressible, isotropic, hyperelastic solids subjected to non-symmetric loading conditions. The criterion is based on the solution of a boundary value problem where a hyperelastic solid, which is infinite in extent and contains a single vacuous inhomogeneity, is subjected to uniform displacement boundary conditions. By making use of the “linear-comparison” variational procedure of Lopez-Pamies and Ponte Castañeda (J. Mech. Phys. Solids 54:807–830, 2006), we solve this problem approximately and generate variational estimates for the critical stretches applied on the boundary at which the cavity suddenly starts growing. The accuracy of the proposed analytical result is assessed by comparisons with exact solutions available from the literature for radially symmetric cavitation, as well as with finite element simulations. In addition, applications are presented for a variety of materials of practical and theoretical interest, including the harmonic, Blatz-Ko, and compressible Neo-Hookean materials.     

Investigation of the influence mechanisms of resin matrices on the strength of filamentary structures

The interrelationship between the burst strength of fiber-wound pressure vessels and resin properties has been investigated. Experimental results show that the effect of resin properties of the burst strength can be as large as 20–35 percent. Delamination occurring in the head region of a pressure vessel is identified as the main cause leading to the burst strength degradation, with help of the improved netting analysis. A special FORTRAN program is then developed to incorporate the spacial axisymmetric finite strain FEM approach, and the foregoing presupposition is further confirmed by numerical calculations. Interlaminar shear stresses are found to be the major cause in prompting the observed delaminations. It is argued then that the interlaminar shear strength (ILSS) of a composite should be considered as a fundamental parameter for vessel design and resin selection. Hydrostatic burst test results of glass fiber-wound pressure vessels correlate satisfactorily with this prediction. The best stress equilibrium coefficientK, being closely related to ILSS, is proposed as a proper criterion for resin matrix screening.     

树脂基体性能对纤维缠绕复合材料结构强度影响的研究

实验发现不同树脂基体配方对纤维缠绕复合材料压力容器的水压爆破强度有高达20～35%的影响。本文认为在容器前、后封头上观察到的分层现象是造成这种强度显著波动的主因,并用有限元分析进行了验证。计算结果表明层间剪切应力是引致分层的主要因素,进一步的实验发现基体的层间剪切强度(interlaminar shear strength,简称ILSS)与容器性能之间有很好的相关性。     

Dynamic void nucleation and growth in solids: A self-consistent statistical theory

We present a framework for a self-consistent theory of spall fracture in ductile materials, based on the dynamics of void nucleation and growth. The constitutive model for the material is divided into elastic and “plastic” parts, where the elastic part represents the volumetric response of a porous elastic material, and the “plastic” part is generated by a collection of representative volume elements (RVEs) of incompressible material. Each RVE is a thick-walled spherical shell, whose average porosity is the same as that of the surrounding porous continuum, thus simulating void interaction through the resulting lowered resistance to further void growth. All voids nucleate and grow according to the appropriate dynamics for a thick-walled sphere made of incompressible material. The macroscopic spherical stress in the material drives the response in all volume elements, which have a distribution of critical stresses for void nucleation, and the statistically weighted sum of the void volumes of all RVEs generates the global porosity. Thus, macroscopic pressure, porosity, and a distribution of growing microscopic voids are fully coupled dynamically. An example is given for a rate-independent, perfectly plastic material. The dynamics of void growth gives rise to a rate effect in the macroscopic material even though the parent material is rate independent.     

Analysis on high-temperature oxidation and growth stress of iron-based alloy using phase field method

High-temperature oxidation is an important property to evaluate thermal protection materials. However, since oxidation is a complex process involving microstructure evolution, its quantitative analysis has always been a challenge. In this work, a phase field method (PFM) based on the thermodynamics theory is developed to simulate the oxidation behavior and oxidation induced growth stress. It involves microstructure evolution and solves the problem of quantitatively computational analysis for the oxidation behavior and growth stress. Employing this method, the diffusion process, oxidation performance, and stress evolution are predicted for Fe-Cr-Al-Y alloys. The numerical results agree well with the experimental data. The linear relationship between the maximum growth stress and the environment oxygen concentration is found. PFM provides a powerful tool to investigate high-temperature oxidation in complex environments.     

Microvoid multistage nucleation model and its application in analysis of micro damage and fracture

In this paper, the microvoid multistage nucleation model [14,15] suggested by the authors of this paper has been studied on the micro ductile damage and fracture of metallic material under large elastic-plastic deformation.Using this model, the analyses of micro damage and fracture for various axisymmetric tensile specimens and for TPB and CCP cracked specimens have been carried out. And the results from these analyses on damage development and fracture are in good agreement with the experimental ones for axisymmetric specimens and reasonable for cracked specimens from the microscopic point of view.The project surported by National Science Foundations of China.     

Cohesive zone laws for fatigue crack growth: Numerical field projection of the micromechanical damage process in an elasto-plastic medium

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loading, but the model parameters are phenomenological and are not closely tied to the underlying micromechanics of the problem. In this paper, we will inversely extract the cohesive zone laws for fatigue crack growth in an elasto-plastic ductile solid using a field projection method (FPM), which projects the equivalent tractions and separations at the cohesive crack-tip from field information outside the process zone. In our small-scale yielding model, a single row of discrete voids is deployed directly ahead of a crack in an elasto-plastic medium subjected to cyclic mode I K-field loading. Damage accumulation under cyclic loading is captured by the growth of voids within the micro-voiding zone ahead of the crack, while the evolution of the cohesive zone law representing the micro-voiding zone is inversely extracted via the FPM. We show that the field-projected cohesive zone law captures the essential micromechanisms of fatigue crack growth in the ductile medium: from loading and unloading hysteresis caused by void growth and plastic hardening, to the softening damage locus associated with crack propagation via a void by void growth mechanism. The results demonstrate the effectiveness of the FPM in obtaining a micromechanics-based cohesive zone law in-place of phenomenological models, which opens the way for a unified treatment of fatigue crack problems.     

Anisotropic plastic stress field at a mixed-mode crack tip under plane and anti-plane strain

On condition that any perfectly plastic stress component at a crack tip is nothingbut the function ofθ.by making use of equilibrium equations,anisotropic plastic stress-strain-rate relations,compatibility equations and Hill anisotropic plastic yieldcondition,in the present paper,we derive the generally analytical expressions of theanisotropic plastic stress field at a mixed-mode crack tip under plane and anti-planestrain.Applying these generally analytical expressions to the mixed-mode cracks,wecan obtain the analytical expressions of anisotropic plastic stress fields at the tips ofmixed-modeⅠ-Ⅲ,Ⅱ-ⅢandⅠ-Ⅱ-Ⅲcracks.     

Temperature and pressure field visualizations in a porous medium dried in superheated steam

This work focuses on heat and mass transfers with phase change in porous media. The experimental analysis was carried out in an aerodynamic return-flow wind tunnel, with very small cylinders of cellular concrete. For the local analysis, the samples were fitted with thermocouples and pressure sensors. A method of temperature and pressure field visualization is developed to highlight the dynamics of transport phenomena. We show two specific phenomena: (1) liquid outflow generated by the overpressure and (2) vaporization of the water inside a two-phase zone that progressively pervades the sample.     

The non-isothermal rheological behaviour of molten polymers: Shear and elongational stress growth of polyisobutylene under heating

Summary Data of stress growth under both shear and elongational kinematics have been taken in presence of heating temperature ramps on a commerical polyisobutylene.The experimental results have been analysed on the basis of a generalized Maxwell model already proved to be very accurate in predicting the isothermal behaviour. A good agreement is observed between the theoretical predictions and the experimental results.Also the features usually observed in volume-temperature curves by effect of cooling acrossT _g are qualitatively reproduced by the model.With 6 figures     

Correlation of crack growth rate and stress ratio for fatigue damage containing very high cycle fatigue regime

A model is proposed to correlate the crack growth rate and stress ratio containing very high cycle fatigue regime. The model is verified by the experimental data in literature. Then a formula is derived for the effect of mean stress on fatigue strength, and it is used to estimate the fatigue strength of a bearing steel in very high cycle fatigue regime at different stress ratios. The estimated results are also compared with those by Goodman formula.     

Damage growth by debonding in a single fibre metal matrix composite: Elastoplasticity and strain energy density criterion

A displacement-based finite element-based numerical approach has been employed to study the damage growth in a unidirectional SiC/Al composite containing a pre-existing crack along the fibre/matrix interface. The composite is modeled as a two-material cylinder subjected to uniform displacement. A detailed analysis is made for the stress field in the vicinity of the debond crack tip. This approach incorporates an elastic-plastic analysis combined with a strain energy density criterion to predict debonded crack growth direction, extended stable growth and final termination. The influence of contact taking place between the debonded surfaces is also considered. It is shown that such surface contact leads to reduced stress and strain fields around the crack tip, while the extent of reduction is increased with debonding length. By combining the reduced stress field with the strain energy density criterion, a limiting value for the debonding extension can be calculated for the critical applied displacement that led to fibre fracture.     

组合超弹性材料中的空穴生成与增长

本文研究了一种组合不可压超弹性材料圆柱体中空穴的生成与增长问题，得到了这种材料受表面均布拉伸死荷载和轴向拉压共同作用下空穴生成问题的解析解，得到了不同组合情况下圆柱体中空穴生成时的临界载荷及分叉曲线，发现组合材料可以发生右分叉，也可以发生左分叉；给出了空穴生成后的应力分布，并讨论了所存在的应力间断和应力集中问题；通过能量比较分析了解的稳定性，讨论了发生右分叉或左分叉的条件，并分析了材料中预存微孔的增长情况。     

Boundary-layer corrections for stress and strain fields in randomly heterogeneous materials

Boundary-layer effects on the effective response of fibre-reinforced media are analysed. The distribution of the fibres is assumed random. A methodology is presented for obtaining non-local effective constitutive operators in the vicinity of a boundary. These relate ensemble averaged stress to ensemble averaged strain. Operators are also developed which re-construct the local fields from their ensemble averages. These require information on the local configuration of the medium. Complete information is likely not to be available, but averages of these operators conditional upon any given local information generate corresponding conditional averages of the fields. Explicit implementation is performed within the framework of an approximation of Hashin-Shtrikman type. Two types of geometry are considered in examples: a half-space and a crack in an infinite heterogeneous medium. These are representative, asymptotically, of the field in the vicinity of any smooth boundary, and in the vicinity of a crack tip, respectively. Results have been obtained for the case of anti-plane deformation, realized by the imposition of either Dirichlet or Neumann conditions on the boundary; those for the Neumann condition are presented and discussed explicitly. The stresses in both fibre and matrix adjacent to a crack tip are shown to differ substantially from the values that would be predicted by ordinary homogenization.     

The expression of stress and strain at the tip of notch in reissner plate

In this paper, the eigenequation of notch in Reissner plate is derived by the eigenfunction method. Eigenvalues of different notches with different angles are calculated by Muller iteration method.The expression of stress and strain at the tip of notch in Reissner plate is obtained.     

A combined first principles and analytical determination of the modulus of cohesion,surface energy,and the additional constants in the second strain gradient elasticity

Mindlin’s (1965) second strain gradient theory due to its competency in capturing the effects of edges, corners, and surfaces is of particular interest. Formulation in this framework, in addition to the usual Lamé constants, requires the knowledge of sixteen additional materials constants. To date, there are no successful experimental techniques for measuring these material parameters which reflect the discrete nature of matter. The present work gives an accurate remedy for the atomistic calculations of these parameters by utilizing the first principles density functional theory (DFT) for the calculations of the atomic force constants combined with an analytical formulation. It will be shown that writing the consistency conditions obtained from the equivalency between the atomistic crystal lattice dynamics of the bulk material and its counterpart in the second strain gradient elasticity is insufficient for the calculations of all the additional constants. As it will be discussed, there are two missing conditions which are then provided by consideration of the free standing film problem that bring the surface effect into account. As a consequence of surface effect consideration, the modulus of cohesion which is one of the important additional constants is calculated. Moreover, an analytical expression for the surface energy in terms of the modulus of cohesion, Lamé constants, materials characteristic lengths, and the film thickness is presented. If the film thickness is much bigger than the magnitude of the characteristic lengths of the material, then the surface energy would no longer depend on the film thickness.     

轴流泵参数化设计及应力与模态特征分析

以船用轴流式喷水推进泵为对象,探索了轴流泵参数化设计、水动力性能、静强度和结构声学特征分析的数值途径。轴流泵叶轮采用升力法设计,导叶采用流线法设计,叶片三维造型在NUMECA参数化设计平台中完成。轴流泵水动力性能校核由粘性CFD计算完成,CFD计算同时提取得到叶片分布式水动力载荷。叶片静强度校核由ANSYS有限元计算叶片应力和应变特征完成,应力分析时同时考虑水动力载荷、重力载荷和离心力载荷。叶片结构声学特征分析由NASTRAN有限元计算叶片模态振型和振型频率完成。计算结果表明,轴流泵扬程和功率满足设计指标,效率达87.13%;叶轮叶片形变相对于叶顶间隙来说为极小量,可忽略不计,叶片存在局部应力集中现象,最大应力小于许用应力,满足静强度要求;叶片前四阶振型特征与分析经验一致,且振型频率远离轴频、叶频及其谐频特征频率,能够避免共振产生。     

On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory： equilibrium, governing equation and static deflection

This paper has successfully addressed three critical but overlooked issues in nonlocal elastic stress field theory for nanobeams： （i） why does the presence of increasing nonlocal effects induce reduced nanostructural stiffness in many, but not consistently for all, cases of study, i.e., increasing static deflection, decreasing natural frequency and decreasing buckling load, although physical intuition according to the nonlocal elasticity field theory first established by Eringen tells otherwise？ （ii） the intriguing conclusion that nanoscale effects are missing in the solutions in many exemplary cases of study, e.g., bending deflection of a cantilever nanobeam with a point load at its tip; and （iii） the non-existence of additional higher-order boundary conditions for a higher-order governing differential equation. Applying the nonlocal elasticity field theory in nanomechanics and an exact variational principal approach, we derive the new equilibrium conditions, do- main governing differential equation and boundary conditions for bending of nanobeams. These equations and conditions involve essential higher-order differential terms which are opposite in sign with respect to the previously studies in the statics and dynamics of nonlocal nano-structures. The difference in higher-order terms results in reverse trends of nanoscale effects with respect to the conclusion of this paper. Effectively, this paper reports new equilibrium conditions, governing differential equation and boundary condi- tions and the true basic static responses for bending of nanobeams. It is also concluded that the widely accepted equilibrium conditions of nonlocal nanostructures are in fact not in equilibrium, but they can be made perfect should the nonlocal bending moment be replaced by an effective nonlocal bending moment. These conclusions are substantiated, in a general sense, by other approaches in nanostructural models such as strain gradient theory, modified couple stress models and experiments.