半无穷大裂纹端部粘聚力分析

准脆性材料裂纹端部断裂过程区粘聚力是导致非线性断裂特性的重要原因,根据准脆性材料的断裂特性,对存在粘聚力分布的半无穷大裂纹力学分析模型,由变形叠加原理得到以该粘聚应力分布为未知函数的积分方程,通过对积分方程的分析推证,得到了该分布函数解的数学结构和级数型表达式;提出了由实际裂纹张开位移,确定裂纹端部粘聚力分布函数的两种方法:其一由连续的裂纹张开位移通过积分变换求解未知函数级数展开项的系数,其二是由离散的裂纹张开位移数据通过最小二乘法确定该函数;推导出了相应方法求解未知量的代数方程,并且给出了适当的算例和讨论。     

Damage and fracture behavior in dynamic tension tests: Modelling and numerical simulations

The continuum damage model is based on a general thermodynamic framework for the modeling of rate and temperature dependent behavior of anisotropically damaged elastic-plastic materials subjected to fast deformation. The introduction of damaged and fictitious undamaged configurations allows the definition of damage tensors and the corresponding free energy functions lead to material laws affected by damage and temperature. The damage condition and the corresponding damage rule strongly depend on stress triaxiality. Furthermore, the rate and temperature dependence is reflected in a multiplicative decomposition of the plastic hardening and damage softening functions. The macro crack behavior is characterized by a triaxiality dependent fracture criterion. The continuum damage model is implemented into LS-DYNA as user defined material model. Corresponding numerical simulations of unnotched and notched tension tests with high strain rates demonstrate the plastic and damage processes during the deformation leading to final fracture numerically predicted by an element erosion technique. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于裂纹尖端二阶弹性解的断裂过程区尺度

基于Westergaard应力函数裂纹尖端二阶弹性解,推导了裂纹尖端微裂区的轮廓线和特征尺寸的解析表达式;采用幂函数模型描述的拉应变软化模型,确定了在最大拉应力强度理论和最大拉应变强度理论下断裂过程区（FPZ）临界值的解析表达式;将基于Westergaard应力函数一阶弹性解及二阶弹性解、Muskhelishvili应力函数和Duan-Nakagawa模型确定的FPZ临界值进行了比较．结果表明裂纹尖端微裂区和FPZ临界值随着Poisson比的减小而增加并逐渐趋近于应用最大拉应力强度理论确定的结果;二阶弹性解确定的裂纹尖端微裂区和FPZ临界值大于一阶弹性解的值;FPZ临界值随着拉应变软化指数的增加而增加;二阶弹性解确定的FPZ临界值的精度远高于一阶弹性解确定的值.     

幂律非线性粘弹性材料中的裂纹扩展*

对蠕变不可压幂律非线性粘弹性材料中裂纹的蠕变扩展进行了分析,为描述银纹带中的力学行为,假设在裂纹尖端邻域中断裂过程区中分布着阻抗裂纹张开的粘聚应力б_f,.通过对均匀应力参考状态平凡解的摄动,将非线性粘弹性问题化成线性问题处理.对于幂指数.n≌1的弱非线性情况得到了应力与位移表达式.提出断裂过程区局域能量判据,导出了裂纹孕育时间t*与蠕变扩展率a的预测公式.     

Interlaminar Crack Propagation Analysis of ENF Specimens Based on the Cohesive Zone Model北大核心CSCD

Based on the classical laminated plate theory and the cohesive zone model, a theoretical model for general delamination cracked laminates was established for crack propagation of pure mode Ⅱ ENF specimens. Compared with the conventional beam theory, the proposed model fully considered the softening process of the cohesive zone and introduced the nonlinear behavior of ENF specimens before failure. The predicted failure load is smaller than that under the beam theory and closer to the experimental data in literatures. Compared with the beam theory with only fracture toughness considered, the proposed model can simultaneously analyze the influences of the interface strength, the fracture toughness and the initial interface stiffness on the load-displacement curves in ENF tests. The results show that, the interface strength mainly affects the mechanical behavior of specimens before failure, but has no influence on crack propagation. The fracture toughness is the main parameter affecting crack propagation, and the initial interface stiffness only affects the linear elastic loading stage. The cohesive zone length increases with the fracture toughness and decreases with the interface strength. The effect of the interface strength on the cohesive zone length is more obvious than that of the fracture toughness. When the adhesive zone tip reaches the half length of the specimen, the adhesive zone length will decrease to a certain extent. Copyright ©2022 Applied Mathematics and Mechanics. All rights reserved.     

A Phase Field Model for Three-Dimensional Dynamic Fracture and its Efficient Numerical Implementation

The numerical modeling of dynamic failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies and demands the formulation of additional branching criteria. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. We focus on the extension of a recently developed phase field model for fracture from the quasi-static setting towards the dynamic setting. It is obtained by taking into account inertial terms and associated dynamic integrators. The introduction of a history field, containing a maximum fracture-driving energy, provides a very transparent representation of the balance equation that governs the diffusive crack topology. In particular, it allows for the construction of an extremely robust operator split technique. In a subsequent step, the proposed model is extended to three dimensional problems. The dynamic treatment opens the door to the analysis of complex fracture phenomena like multiple crack branching and crack arrest. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crack growth modeling via 3D automatic adaptive mesh refinement based on modified-SPR technique

In this paper, the three-dimensional automatic adaptive mesh refinement is presented in modeling the crack propagation based on the modified superconvergent patch recovery technique. The technique is developed for the mixed mode fracture analysis of different fracture specimens. The stress intensity factors are calculated at the crack tip region and the crack propagation is determined by applying a proper crack growth criterion. An automatic adaptive mesh refinement is employed on the basis of modified superconvergent patch recovery (MSPR) technique to simulate the crack growth by applying the asymptotic crack tip solution and using the collapsed quarter-point singular tetrahedral elements at the crack tip region. A-posteriori error estimator is used based on the Zienkiewicz–Zhu method to estimate the error of fracture parameters and predict the crack path pattern. Finally, the efficiency and accuracy of proposed computational algorithm is demonstrated by several numerical examples.     

Fracture analysis of a high-strength concrete and a high-strength steel-fiber-reinforced concrete

This paper addresses the use of R-curves to study the fracture behavior of high-strength concrete and steel-fiber-reinforced concrete subjected to crack ing in a three-point bending configuration. The R-curves are modeled through an effective approach based on the equations of linear-elastic fracture mechanics (LEFM), which relates the applied load to the fundamental displacements of notched-through beams loaded monotonically. It is initially shown that, for quasi-brittle materials, the R-curves responses can be evaluated in a quasi-analytical way, using the load-crack mouth opening, the load-load line displacement, or exclusively the displacement responses obtained experimentally. Afterward, the methodology is used to obtain the fracture responses of high-strength and fiber-reinforced concretes, up to the final stages of rupture. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 701–710, September–October, 2007.     

Variational Phase Field Modeling of Fracture Caused by Fluid Transport in Poroelastic Solids

The numerical modeling of failure mechanisms due to fracture based on sharp crack discontinuities is extremely demanding and suffers in situations with complex crack topologies. This drawback can be overcome by recently developed diffusive crack modeling concepts, which are based on the introduction of a crack phase field. Such an approach is conceptually in line with gradient-extended continuum damage models which include internal length scales. In this paper, we extend our recently outlined mechanical framework [1–3] towards the phase field modeling of fracture in the coupled problem of fluid transport in deforming porous media. Here, extremely complex crack patterns may occur due to drying or hydraulic induced fracture, the so called fracking. We develop new variational potentials for Biot-type fluid transport in porous media at finite deformations coupled with phase field fracture. It is shown, that this complex coupled multi-field problem is related to an intrinsic mixed variational principle for the evolution problem. This principle determines the rates of deformation, fracture phase field and fluid content along with the fluid potential. We develop a robust computational implementation of the coupled problem based on the potentials mentioned above and demonstrate its performance by the numerical simulation of complex fracture patterns. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Implementation of a cohesive zone model for the investigation of the dynamic behavior of a rotating shaft with a transverse crack

The influence of a transverse crack on the vibration of a rotating shaft has been at the focus of attention of many researchers. The knowledge of the dynamic behavior of cracked shaft has helped in predicting the presence of a crack in a rotor. Here, the changing stiffness of the cracked shaft is investigated based on a cohesive zone model. This model is developed for mode-I plane strain and accounts for triaxiality of the stress state explicitly by using basic elastic-plastic constitutive relations. Then, the proposed numerical solution is compared to the switching crack model, which is based on linear elastic fracture mechanics. The cohesive zone model is implemented in finite element techniques to predict and to analyse the dynamic behavior of cracked rotor system. Timoshenko beam theory is used to model the discrete shaft under the effect of gravity, unbalance force and gyroscopic effect. The analysis includes the cohesive function for describing the breathing crack and the reduction of the second moment of area of the element at the location of the crack. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

关于McClintock和Irwin修正

在准脆断情形中,裂纹尖端存在一个微小塑性区.这一塑性区虽然微小.但其影响又不能忽略,因此需要对原有的线弹性渐近场进行校正.F.A.McClintock和G.R.Irwin[1]于1965年提出了一个修正理论,并被广泛引用至今.本文指出这一修正结果是错误的,并给出了正确的修正结果.     

Phase-Field Modeling of Hydraulic Fracture

Hydraulically driven fracture has gained more and more research activity in the last few years, especially due to the growing interest of the petroleum industry. Key challenge for a powerful simulation of this scenario is an effective modeling and numerical implementation of the behavior of the solid skeleton and the fluid phase, the mechanical coupling between the two phases as well as the incorporation of the fracture process. Existing models for hydraulic fracturing can be found for example in [1], where the crack path is predetermined, or in [2] who use a phase field fracture model in an elastic framework, however without incorporating the fluid flow. In this work we propose a new compact model structure for the Biot-type fluid transport in porous media at finite strains based on only two constitutive functions, that is the free energy function ψ and a dissipation potential ϕ that includes the incorporation of an additional Poiseuille-type fluid flow in cracks. This formulation is coupled to a phase field approach for fracture and is fully variational in nature, as shown in [3]. In contrast to formulations with a sharp-crack discontinuity, the proposed regularized approach has the main advantage of a straight-forward modeling of complex crack patterns including branching. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A fracture angle based three-dimensional damage model for unidirectional fibre-reinforced plastics

Since the failure analysis of fibre-reinforced plastics is not limited to the first-ply failure, it is mandatory to use adequate damage models to simulate the failure process. The paper describes a damage model for three-dimensional stress states, which uses the crack orientation of the inter-fibre fracture (IFF). The fracture angle describes the crack orientation and can be obtained by using Puck's IFF criterion. The fracture angle enables the possibility to take the causal stress situation for the IFF into account. This means that each Young's or shear modulus has its own damage function, which depends on the stress state and the fracture angle. Therefore, the stress-strain extrapolation method of Schürmann and Weber for two dimensional stress states was advanced and modified for the three-dimensional stress space. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The phase-field model with an auto-calibrated degradation function based on general softening laws for cohesive fracture

Phase-field models have become popular to simulate cohesive failure problems because of their capability of predicting crack initiation and propagation without additional criteria. In this paper, a new phase-field damage model coupled with general softening laws for cohesive fracture is proposed based on the unified phase-field theory. The commonly used quadratic geometric function in the classical phase-field model is implemented in the proposed model. The modified degradation function related to the failure strength and length scale is used to obtain the length scale insensitive model. Based on the analytical solution of a 1-D case, general softening laws in cohesive zone models can be considered. Parameters in the degradation function can be calibrated according to different softening curves and material properties. Numerical examples show that the results obtained by the proposed model have a good agreement with experimental results and the length scale has a negligible influence on the load-displacement curves in most cases, which cannot be observed in classical phase-field model.     

Analysis of concrete fracture using a novel cohesive crack method

Numerical analysis of fracture in concrete is studied with a simplified discrete crack method. The discrete crack method is a meshless method in which the crack is modeled by discrete cohesive crack segments passing through the nodes. The cohesive crack segments govern the non-linear response of concrete in tension softening and introduce anisotropy in the material model. The advantage of the presented discrete crack method over other discrete crack method is its simplicity and applicability to many cracks. In contrast to most other discrete crack methods, no representation of the crack surface is needed. On the other hand, the accuracy of discrete crack methods is maintained. This is demonstrated through several examples.     

Simulation of crack growth using cohesive crack method

We present an effective cohesive discrete crack method in the context of the Reproducing Kernel Particle Method (RKPM) in order to study fracture of concrete structures. The discrete crack approach is based on the visibility method and a simple node splitting scheme. We also present an effective implementation of the visibility method and an iteration free algorithm by including the cohesive force term directly into the stiffness equations. The crack is represented by straight-line segments and the cohesive zone model is employed to model the post-localization behavior of concrete. The method is applied to several examples involving mode I and mixed-mode fracture. These results are compared to experimental data and show good agreement.     

Role of the supermolecular structure of PMM in the morphology of fracture and features introduced by the type of loading

The spherulitic supermolecular structure of PMM, expressed in the fracture surface, determines the fracture pattern and kinetics. The effect of the type of loading on the morphology of the fracture surface is described. Banding of the fracture surface is attributed to periodic energy pulses leading to quasi-brittle fracture at the moving crack front and selective local crack development at the band edges.Riga Lenin Komsomol Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 776–782, September–October, 1968.     

双I—型裂纹断裂动力学问题的非局部理论解

研究了非局部理论双中I－型裂纹弹性波散射的力学问题,并利用富里叶变换使本问题的求解转换为三重积分方程的求解,进而采用新方法和利用一维非局部积分核代替二维非局部积分核来确定裂纹尖端的应力状态,这种方法就是Schmidt方法,所得结是比艾林根研究断裂静力学问题的结果准确和更加合理,克服了艾林根研究断裂静力学问题时遇到的数学困难,与经典弹性解相比,裂纹尖端不再出现物理意义下不合理的应力奇异性,并能够解释宏观裂纹与微观裂纹的力学问题。     

考虑磁通流动效应的超导薄膜基底结构界面断裂行为研究北大核心CSCD

超导薄膜是一种采用化学涂层制备而成的多层薄膜结构,作为性能优越的导电功能结构材料,其载流能力与结构完整性直接相关.在超导薄膜制备过程中,超导层与金属基底之间的界面裂纹很难避免.因此,在载流运行过程中,由于外磁场的存在,这类界面裂纹的强度问题成为关键.为此,该文针对超导薄膜结构,以磁通量子穿透薄膜理论和线弹性断裂理论为基础,建立了研究超导层与基底界面裂纹强度问题的解析模型.深入分析了外加磁场作用下界面裂纹强度问题,得到了超导磁通流动对裂纹尖端应力场和能量释放率的影响.结果表明:磁通流动速度越大,界面裂纹尖端处应力越大且能量释放率越大,这将导致界面更容易发生裂纹破坏.该文所得结果有助于分析相关的界面裂纹问题.