The near crack tip fields of stress and damage for concrete

The crack tip fields of stress, strain and damage for concrete under both antiplane shear and plane strain conditions are investigated based on the damage model proposed by Mazars and Lemaitre [2]. The structures of near tip fields obtained are similar to those for an elastic-perfectly-plastic material. It has been found that damage boundaries can not be determined by the near-tip analysis due to the discontinuities of stresses on the damage boundaries induced by the damage model used in the present paper.The Project is Supported by National Natural Science Fundation of China.     

自适应分析在确定裂纹尖端塑性区中的应用

在分析裂纹扩展及材料强度时对塑性区的估算是很重要的,本文提出采用自适应有限元分析来确定裂纹尖端塑性区的方法,计算结果表明这种方法通过网格自动加密能够有效地跟踪出弹塑性的交界面。     

A viscoplastic model combined smedamage and smeared crack for softening of concrete

A viscoplastic model accounting for developing damage in concrete is proposed by assuming the rate of damage to be dependent on viscous strain and stress rates. The damage is measured by a scalar parameter affecting both the yield stress and the material viscosity. For a post-critical range of deformation, the localized mode occurs for which additional constitutive equations are specified. The model is applied to simulate uniaxial strain rate controlled and creep response for the concrete.     

Field structure at mode III dynamically propagating crack tip in elastic-viscoplastic materials

An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.     

Model of the fracture process zone at the tip of a crack reaching the nonsmooth interface between elastic media

The paper is concerned with the fracture process zone at the tip of a crack at the nonsmooth interface between isotropic elastic media. A plane symmetric problem is formulated. The zone is modeled by lines of discontinuity of the normal displacement at the interface. The exact solution of the elastic problem is found by the Wiener-Hopf method Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 13–22, October 2008.     

The crack tip zone shielding effect for ductile particle reinforced brittle materials

The crack tip zone shielding effect for the ductile particle reinforced brittle materials is analyzed by using a micromechanics constitutive theory. The theory is developed here to determine the elastoplastic constitutive behavior of the composite. The elastoplastic particles, with isotropic or kinematical hardening, are uniformly dispersed in the brittle elastic matrix. The method proposed is based on the Mori-Tanaka's concept of average stress in the composite. The macroscopic yielding condition and the incremental stress strain relation of the composite during plastic deformation are explicity given in terms of the macroscopioc applied stress and the microstructural parameters of the composite such as the volume fraction and yield stress of ductile particles, elastic constants of the two phases, etc. Finally, the contribution of the plastic deformation in the particles near a crack tip to the toughening of the composite is evaluated. The project supported by National Natural Science Foundation of China     

On the direction of development of a thin fracture process zone at the tip of an interfacial crack between dissimilar media

The Wiener-Hopf method is used to study, under the conditions of plane strain, the direction of development of a thin fracture process zone at the tip of an interfacial crack in a piecewise homogeneous isotropic elastoplastic body. The zone is modeled by a straight line of tangential displacement discontinuity that emerges from the crack tip at an angle to the interface. The dependences of the zone length and the angle on the load and other parameters of the problem are investigated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 14–23, February 2006.     

A statistical theory of fatigue crack growth at damage cumulation

Summary A statistical theory of the fatigue crack growth at damage cumulation is proposed. The theory gives the average of fatigue crack length at any time t, and deduces the evolution of failure probability with time varying. Furthermore, the variance and relative error of fatigue crack length at any time t are acquired. The Paris equation for the average of the crack length at any time t is derived from the statistical theory. Therefore, the prediction of the probability distribution of the crack length can be given for any time t. Actual applications of the theory are given, which conform to the experiments. Accepted for publication 17 June 1996     

The crack tip fields of orthotropic composite plate under bending

1MechhacalModelThefractUreproblemwhichisthesameasthatinpaper[I]isfurtherdiscussedinthispaper.TheanalysisoffractUrebehavioursnearcracktipforinfinitelinearelasticorthotropiccompositeplatewithacentralthroughcrackoflengthZaiscarriedout.ThegeometryandloadingcondihonsareshowninFig.1.Tosolvesuchaproblem,weneedtosolvethepanaldifferentialequationwiththefollowingboundaryconditions:wherewisdeflectionofcoddleplane;M.andM,arebendingmoment,Ma.istwistingmoment,andstiffnessmatrixFromthetheoryofplateL'],w…     

The near tip fields and temperature distribution around a crack in a body of hardening material containing small damage

In this paper, the following conclusions are reached: The influence of damage on the stress and strain feilds can be neglected in an asymptotic sense for the solutions of damage field in a plastic solid containing small damage. The formulation of the problem is simplified with an uncoupled approach. Based on experimental results of plastic damage, most of the damage in the material are considered as small damage with the critacal damage variable ω _c ≪1. Using this approach, closed form expressions of the near tip damage fields for mode III, mode I and the temperature distribution induced by plastic dissipation in a hardening material containing damage are deduced. We point out that the temperature distribution in the process zone is strongly dependent on the damage of materials even for the small damage case. The results of the predicted value of the temperature rise near the tip region ignoring the damage effect is appreciably higher than the observed data. The main reason of this discrepancy is the presence of damage dissipation and the fact that its influence on the calculation of plastic dissipation have not been appropriately taken account of. The calculation is improved by taking into account the damage effect on the temperature rise, then theT _max value is in better accord with the experimental value. The project supported by the National Natural Science Foundation of China.     

混凝土率型内时损伤本构模型

混凝土是一种典型的率敏感材料,为了更好地描述混凝土结构在动力、冲击荷载作用下的强度和变形特征,本文结合内时理论和损伤理论建立了一种考虑混凝土率效应的内时损伤本构模型。该模型的特点:将混凝土材料的受力软化效应分解为密实状态的塑性效应和由微裂缝扩展引起的刚度退化效应。前者由内时理论来描述,这使该模型摆脱了一般弹塑性模型中屈服面的概念,从而更符合混凝土的变形特性,并且简化了非线性计算过程;后者由损伤理论来描述,根据混凝土的动力试验结果建立了增量型的损伤演变方程,从而使该模型能够较好地反映混凝土的动力特性。最后,应用本文建议的模型对一钢筋混凝土简支梁进行了非线性分析,结果表明:当结构承受快速荷载作用时,应变率对结构的受力性能影响较大,在进行结构分析时必须予以考虑。     

Stress field near interface crack tip of double dissimilar orthotropic composite materials

In this paper, double dissimilar orthotropic composite materials interfacial crack is studied by constructing new stress functions and employing the method of composite material complex. When the characteristic equations＇ discriminants △1 〉 0 and △2 〉0, the theoretical formula of the stress field and the displacement field near the mode I interface crack tip are derived, indicating that there is no oscillation and interembedding between the interfaces of the crack.     

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.     

Computer simulation of creep damage at crack tip in short fibre composites

Creep damage at crack tip in short fibre composites has been simulated by using the finite element method (FEM). The well-known Schapery non-linear viscoelastic constitutive relationship was used to characterize time-dependent behaviour of the material. A modified recurrence equation was adopted to accelerate the iteration. Kachanov-Rabotnov's damage evolution law was employed. The growth of the damage zone with time around the crack tip was calculated and the results were shown with the so-called “digit photo”, which was produced by the printer. The project supported by the National Natural Science Foundation of China and the LNM of Institute of Mechanics, CAS     

Stress-strain field near crack tip and calculation of critical stress of crack propagation in a pure bending beam of rectangular section with one-sided mode i crack

This paper studies the stress-strain field near crack tip in a pure bending beam of rectangular section with one-sided mode I crack by the analytic method of Ref. [1], then it gives the stress and strain components at the crack tip when the crack propagates and further it obtains the formulas of calculating the elastic deformed area width, the deformed intensity area width and the equation groups of calculating the critical stress of crack propagation, last the equation group of calculating critical stress of crack propagation is verified by calculating instance. The maximum error is 0.18%. First Received May 7, 1994.     

Moving line crack accompanied with damage zone subject to remote tensile loading

In the 1920s, a closed-form solution of the moving Griffith crack was first obtained by Yoffe. Based on Yoffe's solution, the Dugdale model for the moving crack case gives a good result. However, the Dugdale model fails when the crack speed is closed to the Rayleigh wave speed because of the discontinuity occurred in the crack opening displacement (COD). The problem is solved in this paper by introducing a restraining stress zone ahead of the crack tip and two velocity functions. The restraining stresses are linearly distributed and related to the velocity of the moving crack. An analytical solution of the problem is obtained by use of the superposition principle and a complex function method. The final result of the COD is continuous while the crack moves at a Rayleigh wave speed. The characteristics of the strain energy density (SED) and numerical results are discussed, and conclusions are given.     

混凝土冻融损伤本构模型研究

基于各向同性连续损伤力学理论,以损伤条件下的弹性模量和泊松比为变量,基于Ottosen理论模型建立了混凝土冻融损伤破坏准则,并以Ottosen本构理论模型为基础,利用建立的冻融损伤破坏准则构建了混凝土冻融损伤本构模型,并编制了本构模型有限元程序,经过试验验证模型计算结果较为准确,为有限元计算和冻融作用后混凝土结构模拟应...     

Mode I crack tip field with strain gradient effects

A plane strain mode I crack tip field with strain gradient effects is investigated. A new strain gradient theory is used. An elastic-power law hardening strain gradient material is considered and two hardening laws, i. e. a separation law and an integration law are used respectively. As for the material with the separation law hardening, the angular distributions of stresses are consistent with the HRR field, which differs from the stress results^[19]; the angular distributions of couple stresses are the same as the couple stress results^[19]. For the material with the integration law hardening, the stress field and the couple stress field can not exist simultaneously, which is the same as the conclusion^[19], but for the stress dominated field, the angular distributions of stresses are consistent with the HRR field; for the couple stress dominated field, the angular distributions of couple stresses are consistent with those in Ref. [19]. However, the increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only, while the crack tip field of mode I is dominated by the tension gradient, which will be shown in another paper. Supported by the National Science Foundation of China (No. 19704100), Science Foundation of Chinese Academy of Sciences (Project KJ951-1-20), CAS K. C. Wong Post-doctoral Research Award Fund and the Post Doctoral Science Fund of China.     

冻土破坏过程的微裂纹损伤区的计算分析

对冻土破坏过程进行了试验研究,冻土破坏的过程是微裂纹损伤与临界串接的演化过程,确认了冻土微裂纹损伤区的存在,并分别用莫尔准则和最大拉应力准则建立了微裂纹损伤区计算模式。将微裂纹损伤区按缺陷处理并简化为当量裂纹,进行了裂纹尺寸的定量计算,结果表明其尺寸与冻土中初始裂纹尺寸相当,将计算结果与观测结果相比较,误差不超过10％。     

混凝土损伤与试件尺寸效应

本文在运用概率方法确定了混凝土材料的初始损伤门槛值εＤ的前提下采用已有内时损伤本构模型，利用有限元方法对单边切口混凝土梁在三点弯曲荷载和四点剪切荷载作用下的力学行为进行了分析，计算了所有试件 的极限荷载Ｐｍａｘ，运用计算结果对混凝土断裂力学参数的尺寸效应规律进行了分析，并与已有试验结果进行了比较，其结果表明本文的数值分析怀华权及其它方法的分析结果吻合较好。