固体材料在高应变率条件下的TSHB实验技术*

本文介绍了分离式Hopkinson扭杆技术(TSHB),它克服了压杆技术的主要缺陷.具有测试精确,容易获得较大变形等特点.文中给出了在我们自制试验机上获得的部分工程材料的动态应力应变曲线.     

Fracture toughness investigations on UHPC by spalling tests

Ultra High Performance Concrete (UHPC) is defined as a new generation of concrete which shows improved performance and higher strength than traditional concrete. This allows to realize slender and much more durable structures and in this way significantly reduces the required resources. Despite its huge potential in construction, technical information about this new type of material is still limited. This contribution presents investigations on the dynamic mechanical behavior and properties of UHPC specimens by spalling experiments. Two different recipes were used to compare the properties. Due to the special specimen geometry (slender cylindrical) a flowable consistency was required to enable a sufficient degassing of the mixtures. For the test, a Split Hopkinson Pressure Bar (SHPB) has been modified and used. A high speed photograph system was focused on the fragmentation process during the test. On the basis of these experiments the dynamic E-moduli as well as the dynamic tensile strength of the UHPC specimens were determined. By observation of the specific crack patterns on each tested specimen and corresponding times, the dynamic fracture energy is calculated. Numerical simulations also were performed and compared to the experimental result. It is concluded that the dynamic tensile strength of the UHPC increases at higher strain rates. The results of the current study provide technical information about fracture and dynamic behavior of UHPC and the obtained values could be used for future computational models. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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 note on Bar Induction in Constructive Set Theory

Bar Induction occupies a central place in Brouwerian mathematics. This note is concerned with the strength of Bar Induction on the basis of Constructive Zermelo‐Fraenkel Set Theory, CZF. It is shown that CZF augmented by decidable Bar Induction proves the 1‐consistency of CZF. This answers a question of P. Aczel who used Bar Induction to give a proof of the Lusin Separation Theorem in the constructive set theory CZF. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical modeling of brittle fracture in porous CFC-materials

Both energy and stress criteria are necessary conditions for fracture but neither the one nor the other is sufficient. A combination of these criteria is proposed in [1]. This combined criterion is used for numerical simulation of crack propagation by the 4-point bending test in porous materials. Examples of such materials are carbon-carbon composites (CFC) [2, 3]. Micrographs of the cross-sections of these materials are used for FEM modeling of the crack propagation on the basis of the proposed criterion. Results of the numerical modeling are compared with experimental results. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

A computational framework of three dimensional configurational-force-driven crack propagation

A variational formulation of quasi-static brittle fracture is considered and a new finite-element-based computational framework is developed for propagation of cracks in three-dimensional bodies. We outline a consistent thermodynamical framework for crack propagation in elastic solids and show that the crack propagation direction associated with the classical Griffith criterion is identified by the material configurational force which maximizes the local dissipation at the crack front. The evolving crack discontinuity is realized by the doubling of critical nodes and triangular interface facets of the tetrahedral mesh. The crucial step for the success of the procedure is its embedding into an r-adaptive crack-facet reorientation procedure based on configurational-force-based indicators in conjunction with crack front constraints. We further propose a staggered algorithm which minimizes the stored energy at frozen crack state followed by the successive crack releases at frozen deformation. This constitutes a sequence of positive definite subproblems with successively decreasing overall stiffness, providing a very robust algorithmic setting in the postcritical range. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Assessment of asymmetric crack initiation in open-hole plates using a coupled stress and energy criterion

An application of the finite fracture mechanics concept to open-hole plates subject to combined tensile and bending loading is presented. In finite fracture mechanics, the simultaneous satisfaction of both, a stress and an energy criterion, is enforced as a condition for crack initiation. Efficient modeling and closed-form expressions for the dependence of the stress and energy quantities on governing structural and material parameters allow for a comprehensive numerical analysis of the onset of asymmetric crack patterns. The obtained failure load predictions are found to agree well with a cohesive zone model and experimental data from literature. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Probabilistic modeling and simulation of multiple surface crack propagation and coalescence

In the low cycle fatigue (LCF) regime, fatigue failure of metallic materials with high strength and less impurities generally dominates by multiple surface crack propagation and coalescence, in which its final failure shows a stochastic nature on crack initiation, propagation and coalescence under cyclic loadings. According to this, the competing failure modes of multiple surface cracks and interior cracks are studied through coupling numerical simulations with fracture mechanics methods. In particular, a probabilistic procedure for modeling multiple surface crack propagation and coalescence is established by incorporating Monte Carlo simulation with experimental evidences, including surface crack density and crack length distributions measured from LCF replica tests of 30NiCrMoV12 steel. In addition, it calculates the probability of coalescence of neighboring cracks with allowance for their interactions and local plastic deformation at the crack tips. Finally, it estimates the remaining usage lives of specimens from initial state to critical cracks by propagation and coalescence of dispersed cracks.     

Effect of biaxial orientation on the fracture kinetics of polymethyl methacrylate

Biaxially oriented PMM is shown to have important advantages as a structural material over unoriented PMM owing to a difference in fracture kinetics. Under identical conditions primary cracks appear later in the oriented PMM, their growth is impeded, and the rate of crack propagation in the avalanche stage of failure is much lower. This accounts for the greater resistance of biaxially oriented PMM to stress raisers and its higher fracture energy under biaxial loading.All-Union Scientific-Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 274–281, March–April, 1969.     

带复合型摩擦裂纹的圆盘动态断裂实验有限元分析

为验证考虑裂纹面接触和动态荷载时,中心裂纹巴西圆盘（CCBD）试件用于分离式Hopkinson压杆（SHPB）系统中测量脆性材料复合型动态断裂韧度的可行性,以及研究裂纹面接触对动态断裂韧度实验结果的影响.通过有限元法建立SHPB CCBD三维有限元模型,计算了不同加载条件下CCBD试件的动态应力强度因子（DSIF）.结果表明:在实验中,将考虑裂纹面接触的应力强度因子(SIF)准静态公式推广为动态公式,需要判定断裂时间是否达到应力平衡的时间条件;压剪复合型加载时,裂纹面接触导致裂纹面应力变化,会对Ⅱ型裂纹的DSIF产生显著影响,不考虑裂纹面接触的影响将会导致Ⅱ型DSIF的测试值偏大.     

应力波放大器二维数值分析

运用动态有限元方法,对应力波在锥形应力波放大器中传播特性进行了二维数值分析,对影响透射波放大系数和波形的几何因素、输入脉冲形状、脉冲升时等进行了讨论,可供应力波铆接器设计之参考.计算结果与在Hopkinson杆上实验测得值以及特征线计算值进行了比较,其与实验结果吻合程度是令人相当满意的,与一维特征线方法相比.其计算精度也得到较大改善,特别是在透射波峰值压力附近.     

Influence of particle size on the fracture toughness of a PP-based particulate composite

The main focus of this paper is a numerical investigation of the fracture behavior of a particulate composite (CaCO₃-PP). The composite is modeled as a three-phase continuum and simulated numerically on a microscale by using finite elements. The propagation of a microcrack in a matrix filled with rigid particles covered by an interphase is analyzed. The stress distribution is determined for a variety of particle sizes and material properties of the interphase. The final results, in agreement with experimental data, confirm that the microcrack behavior depends on particle sizes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 411-418, May-June, 2009.     

Modeling of fiber-reinforced PMMA at different scales

This paper deals with the modeling of fiber-reinforced PMMA. Focus is on the macroscopic mechanical response with emphasis on the fracture properties such as the ultimate strength and the fracture energy. In order to capture the macroscopic mechanical response of PMMA, a finite element formulation is presented. While the elastic response of the fibres and that of the surrounding matrix are modelled in standard manner, i.e., by standard bulk material models, the relevant failure modes such as cracking of the fibres are accounted for by means of the so-called Strong Discontinuity Approach (SDA). Since the fibres are relatively small, their fracture mechanical properties crucially depend on their geometry, i.e., they show a pronounced size effect. Based on numerical analyses of fibres with different geometries, the aforementioned size effect is naturally incorporated into the formulation [1]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Toughening effect of ferroelectric ceramics induced by domain switching and dislocations

The multi-scale analysis of fracture toughness of ferroelectric ceramics under complicate mechanical–electrical coupling effect is carried out in this paper. The generalized stress intensity factor (SIF) arising from spontaneous strains and polarization transformation in switching domain zones is accurately obtained by using an extended Eshelby theory. Taking BaTiO₃ ferroelectric ceramic for example, it is discovered that the crack propagation can be induced by domain switching arising from negative electrical field when the crack surface is parallel to the isotropic plane, and the obtained critical electric displacement intensity factor (EDIF) approximates closely to that obtained by the Green’s function method. Additionally, as pinning dislocations and slip dislocations can strongly influence properties of ferroelectric devices and induce the property degradation, it is necessary to investigate the dislocation toughening effects on fatigue and fracture mechanisms. The results show that the dislocation shielding and anti-shielding effects on mode II SIF, mode I SIF and EDIF are obviously different when a dislocation locates at a position near the crack tip. Through the calculation of the critical applied EDIF for crack propagation by using mechanical energy release rate (MERR) theory, it is discovered that the slip angles obviously influence fracture toughness, and the mode II SIF arising from dislocation has little influence on fracture toughness, however, the mode I SIF and EDIF arising from dislocation have great influences on fracture toughness.     

Investigation of the local behavior of different cohesive zone models

Cohesive interface elements are well suited for three-dimensional crack propagation analyses as long as the crack path is known. This is the case e.g. in delamination analyses of laminated composite structures or failure analyses of adhesively bonded joints. Actually, they are widely used in such applications for both brittle and ductile systems. As long as the strength and fracture toughness of the material are accurately captured it is generally accepted that the shape of the cohesive law has little to no influence on the mechanical behavior of the investigated structures. However, when having a look on the local behavior of different cohesive zone models, such as stress distribution in the fracture process zone, the results exhibit certain differences. These will be studied in the present contribution. Especially the local stress distribution will be investigated and the effect on the computational efficiency will be pointed out. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Configurational-Force-Driven Crack Propagation and Adaptive Mesh Refinement in Finite Inelasticity

We introduce a consistent variational framework for inelasticity at finite strains, yielding dual balances in physical and material space as the Euler equations. The formulation is employed for the simultaneous usage of configurational forces as both driving forces for crack propagation as well as h-adaptive mesh refinement. The theoretical basis builds upon a global balance of internal and external power, where the mechanical response is exclusively governed by two scalar functions, the free energy function and a dissipation potential. The resulting variational structure is exploited in the context of fracture mechanics and yields evolution equations for internal variables. In the discrete setting, we present a geometry model fully separated from the finite element mesh structure that represents structural changes of the material configuration due to crack propagation. Advanced meshing algorithms provide an optimal discretization at the crack tip. Local and global criteria are obtained via error estimators based on configurational forces being interpreted as indicators of an energetic misfit due to an insufficient discretization. The numerical handling is decomposed into a staggered algorithm scheme for the dual set of equilibrium equations in material and physical space and efficient mesh generation tools. Exemplary numerical examples are considered to illustrate the method and to underline the effects of inelastic material behaviour in the presented context. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crack propagation at bi-material interfaces

There is currently a gap in the understanding of how crack propagation by intergranular versus transgranular fracture varies with changes in material properties and grain size. Much of the prior work in this area has been in terms of LEFM and criterion based on toughness alone. More recent work has shown that a toughness-and-strength approach is required. In this study a strength-and-energy approach is applied to intergranular-versus-transgranular fracture through a cohesive-zone approach implemented in a finite element model. Results show that intergranular fracture becomes more likely, and has an increasing shear component, as grain toughness increases and grain stiffness and grain size decrease. These results can help guide material development. (© 2015 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.