金属材料三维断裂韧度厚度效应的有限元模拟

随着金属材料大壁厚结构件在工程中的广泛应用,对其断裂韧度的厚度效应研究具有重要的科学意义和工程价值。本研究基于有限元和实验相结合的方法,对金属材料断裂韧度的厚度效应进行预测。首先,通过一组薄壁厚金属材料标准三点弯曲试验得到试样失效时的临界载荷值,并利用内聚力模型与基于虚拟裂纹闭合技术的裂纹扩展模拟方法得到裂纹扩展时的单元临界能量释放率。随后,以此临界能量释放率作为裂纹扩展的启裂准则门槛值,通过有限元计算得到不同试样厚度下裂纹启裂时的裂尖断裂参数随着厚度的变化规律。最后,为了验证有限元模拟结果的准确性,本研究进行了另外两组不同厚度下三点弯曲试样的断裂韧度试验,并将试验结果与有限元结果进行了对比,验证了有限元所模拟的断裂韧度厚度效应的准确性。本研究旨在,通过薄壁厚三点弯曲试样的实验结果结合有限元模拟工作,即可实现金属材料断裂韧度的整个厚度效应曲线,为任意厚度下金属材料断裂韧度预测提供一种可靠的研究方法,有益于缩减试验成本,为大壁厚工程结构件的失效预测提供依据。     

Crack buckling in soft gels under compression

Recent interest in designing soft gels with high fracture toughness has called for simple and robust methods to test fracture behavior. The conventional method of applying tension to a gel sample suffers from a difficulty of sample gripping. In this paper, we study a possible fracture mechanism of soft gels under uni-axial compression. We show that the surfaces of a pre-existing crack, oriented parallel to the loading axis, can buckle at a critical compressive stress. This buckling instability can open the crack surfaces and create highly concentrated stress fields near the crack tip, which can lead to crack growth. We show that the onset of crack buckling can be deduced by a dimensional argument com- bined with an analysis to determine the critical compression needed to induce surface instabilities of an elastic half space. The critical compression for buckling was verified for a neo-Hookean material model using finite element simulations.     

The characterization of telephone cord buckling of compressed thin films on substrates

The topology of the telephone cord buckling of compressed diamond-like carbon films (DLC) on glass substrates has been characterized with atomic force microscopy (AFM) and with the focused ion beam (FIB) imaging system. The profiles of the several buckles have been measured by AFM to establish the symmetry of each repeat unit, revealing similarity with a circular buckle pinned at its center. By making parallel cuts through the buckle in small, defined locations, straight-sided buckles have been created on the identical films, enabling the residual stress in the film to be determined from the profile.It has been shown that the telephone cord topology can be effectively modeled as a series of pinned circular buckles along its length, with an unpinned circular buckle at its front. The unit segment comprises a section of a full circular buckle, pinned to the substrate at its center. The model is validated by comparing radial profiles measured for the telephone cord with those calculated for the pinned buckle, upon using the residual stress in the film, determined as above. Once validated, the model has been used to determine the energy release rate and mode mixity, G(ψ).The results for G(ψ) indicate that the telephone cord configuration is preferred when the residual stress in the DLC is large, consistent with observations that straight-sided buckles are rarely observed, and, when they occur, are generally narrower than telephone cords. Telephone cords are observed in many systems, and can be regarded as the generic morphology. Nevertheless, they exist subject to a limited set of conditions, residing within the margin between complete adherence and complete delamination, provided that the interface has a mode II toughness low enough to ensure that the buckle crack does not kink into the substrate.     

A simple cohesive zone model that generates a mode-mixity dependent toughness

A simple, mode-mixity dependent toughness cohesive zone model (MDG_c CZM) is described. This phenomenological cohesive zone model has two elements. Mode I energy dissipation is defined by a traction–separation relationship that depends only on normal separation. Mode II (III) dissipation is generated by shear yielding and slip in the cohesive surface elements that lie in front of the region where mode I separation (softening) occurs. The nature of predictions made by analyses that use the MDG_c CZM is illustrated by considering the classic problem of an elastic layer loaded by rigid grips. This geometry, which models a thin adhesive bond with a long interfacial edge crack, is similar to that which has been used to measure the dependence of interfacial toughness on crack-tip mode-mixity. The calculated effective toughness vs. applied mode-mixity relationships all display a strong dependence on applied mode-mixity with the effective toughness increasing rapidly with the magnitude of the mode-mixity. The calculated relationships also show a pronounced asymmetry with respect to the applied mode-mixity. This dependence is similar to that observed experimentally, and calculated results for a glass/epoxy interface are in good agreement with published data that was generated using a test specimen of the same type as analyzed here.     

Asymptotic solutions for buckling delamination induced crack propagation in the thin film-compliant substrate system

In a thin film-substrate system in-plane compressive stress is commonly generated in the film due to thermal mismatch in operation or fabrication process. If the stress exceeds a critical value, part of the film may buckle out of plane along the defective interface. After buckling delamination, the interface crack at the ends may propagate. In the whole process, the compliance of the substrate compared with the film plays an important role. In this work, we study a circular film subject to compressive stress on an infinitely thick substrate. We study the effects of compliance of the substrate by modeling the system as a plate on an elastic foundation. The critical buckling condition is formulated. The asymptotic solutions of post-buckling deformation and the corresponding energy release rate of the interface crack are obtained with perturbation methods. The results show that the more compliant the substrate is, the easier for the film to buckle and easier for the interface crack to propagate after buckling.     

裂纹面摩擦接触引起的断裂韧性增长的研究

采用弹黏塑性的材料本构关系, 建立了压、剪混合型裂纹常速准静 态扩展的力学模型, 求得了裂纹面摩擦接触条件下裂纹尖端场的数值解, 并基于数 值结果讨论了扩展裂纹的摩擦效应. 计算和分析表明, 裂纹面的摩擦效应主要表现 在两个方面. 第一方面是摩擦会导致裂纹尖端区材料的断裂韧性增高, 并且裂纹面间的摩擦作用越强, 增韧效果越显著. 摩擦增韧的机制可以解释为裂纹 面间的摩擦作用导致裂纹尖端塑性区尺寸变大, 使裂纹尖端场的塑性变形能增加, 从而使得裂纹尖端区材料增韧. 摩擦生热并不是导致材料断裂韧性增长的根本机制. 第二方面是摩擦会导致``断裂延缓'. 利用裂纹面的摩擦来提高构件的承载能力和延长构件的服役寿命具有较大的工程实用价值.     

柱状电极屈曲或裂纹扩展的临界力学参数研究

柱形结构电极是近年来使用最为广泛的锂电池电极结构之一.本文以硅材料细长柱形电极为例,研究了充电电流大小、电极长径比、初始裂纹长度以及断裂韧性对于电极的屈曲现象和裂纹扩展现象发生时间的影响.计算结果表明,屈曲与裂纹扩展现象出现的先后顺序与充电电流大小无关;具有小的长径比,大的初始裂纹长度以及较小断裂韧性的电极,裂纹扩展比屈曲现象更早发生.对于硅材料,不同长径比的电极具有不同临界断裂韧性值,当材料的断裂韧性小于该临界值,在锂化过程中裂纹扩展会先于屈曲现象发生;该临界断裂韧性值随初始裂纹长度的增加而增加.本文的结论对于电极的结构设计以及材料选取具有一定指导意义.     

钢-混凝土组合梁负弯矩区畸变屈曲弯矩计算公式

侧向弯曲屈曲及侧向弯扭屈曲均为钢-混凝土组合梁负弯矩区钢梁的重要屈曲模式,而现有计算方法通常只考虑到侧向弯曲屈曲,未考虑到侧向弯扭屈曲,因此有一定局限性。本文在钢梁腹板对钢梁下翼缘的转动约束刚度及侧向约束刚度的计算公式上,结合弹性介质中薄壁杆件的屈曲理论推导了工形钢-混凝土组合梁负弯矩区的侧向弯曲屈曲弯矩及侧向弯扭屈曲弯矩计算公式。实例分析表明,现有计算方法均存在一定理论缺陷,本文计算方法更为合理;同时,本文计算式比现有文献中同类型计算式更为简洁,便于手算,实用性强并适于工程应用。     

Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models

Crack initiation and crack growth resistance in elastic plastic materials, dominated by crack-tip plasticity are analyzed with the crack modeled as a cohesive zone. Two different types (exponential and bilinear) of cohesive zone models (CZMs) have been used to represent the mechanical behavior of the cohesive zones. In this work, it is suggested that different forms of CZMs (e.g., exponential, bilinear) are the manifestations of different micromechanisms-based inelastic processes that participate in dissipating energy during the fracture process and each form is specific to each material system. It is postulated that the total energy release rate comprises the plastic dissipation rate in the bounding material and the separation energy rate within the fracture process zone, the latter is determined by CZMs. The total energy release rate then becomes a function of the material properties (e.g., yield strength, strain hardening exponent) and cohesive properties of the fracture process zone (e.g., cohesive strength and cohesive energy), and the form of cohesive zone model (CZM) that determines the rate of energy dissipation in the forward and wake regions of the crack. The effects of material parameters, cohesive zone parameters as well as the form/shape of CZMs in predicting the crack growth resistance and the size of plastic zone (SPZ) surrounding the crack tip are systematically examined. It is found that in addition to the cohesive strength and cohesive energy, the form (shape) of the traction–separation law of CZM plays a very critical role in determining the crack growth resistance (R-curve) of a given material. It is further observed that the shape of the CZM corresponds to inelastic processes active in the forward and wake regions of the crack, and has a profound influence on the R-curve and SPZ.     

A thermomechanical cohesive zone model for bridged delamination cracks

The coupled thermomechanical numerical analysis of composite laminates with bridged delamination cracks loaded by a temperature gradient is described. The numerical approach presented is based on the framework of a cohesive zone model. A traction-separation law is presented which accounts for breakdown of the micromechanisms responsible for load transfer across bridged delamination cracks. The load transfer behavior is coupled to heat conduction across the bridged delamination crack. The coupled crack-bridging model is implemented into a finite element framework as a thermomechanical cohesive zone model (CZM). The fundamental response of the thermomechanical CZM is described. Subsequently, bridged delamination cracks of fixed lengths are studied. Values of the crack tip energy release rate and of the crack heat flux are computed to characterize the loading of the structure. Specimen geometries are considered that lead to crack opening through bending deformation and buckling delamination. The influence of critical mechanical and thermal parameters of the bridging zone on the thermomechanical delamination behavior is discussed. Bridging fibers not only contribute to crack conductance, but by keeping the crack opening small they allow heat flux across the delamination crack to be sustained longer, and thereby contribute to reduced levels of thermal stresses. The micro-mechanism based cohesive zone model allows the assessment of the effectiveness of the individual mechanisms contributing to the thermomechanical crack bridging embedded into the structural analysis.     

数学网格和物理网格分离的有限单元法(II):粘聚裂纹扩展问题中的应用

强化有限单元法将物理网格与数学网格分离开来,可以方便地描述非连续变形;粘聚区域模型是模拟断裂过程区作用最简单有效的方法,且可以避免裂纹尖端的应力奇异性.本文以平面问题为例,将强化有限单元法与粘聚区域模型相结合,利用富集数学节点描述任意粘聚裂纹扩展过程中的非连续变形问题,提出了裂纹扩展过程中数学节点富集和数学单元定义的方法.本文还导出了与平面4～8节点平面等参单元对应的8～16节点粘聚裂纹单元列武.最后,通过三点弯梁的裂纹扩展过程模拟验证了本文提出的粘聚裂纹扩展模拟方法的有效性.     

数学网格和物理网格分离的有限单元法(I):基本理论

常规有限单元法在复杂边界问题的网格剖分、可移动边界和非连续变形问题的数值模拟等方面存在困难.本文将常规的有限单元分离为几何上相互独立的数学单元和物理单元,基于数学单元构造近似函数,引入位移模式关联法则以确定物理单元的位移模式,提出了在现有有限单元法框架内、基于数学网格和物理网格分离的强化有限单元法(FEM++).与常规有限单元法(SFEM)比较表明,强化有限单元法不仅很好地克服了常规有限单元法网格剖分上的困难,而且提供了一条更简便、更自然的分析移动边界问题和非连续变形问题的新途径.最后,通过数值算例验证了强化有限单元法的适用性和有效性.     

Crack tortuousity in the nacreous layer – Topological dependence and biomimetic design guideline

The nacreous layer in seashells is known for two phenomenal aspects: light-weightiness and superior fracture toughness. Of a multitude of toughening mechanisms, the highly meandering nature of the crack path through its staggered architecture has been reported to contribute approximately a third of its overall toughness. In the current article, we are trying to establish the scientific rationale associated with the influence of overlap length on the crack-tip driving force from a local perspective via development of a simplified analytical model. Characteristic overlap lengths computed showed reasonable agreement with the values reported in the nacreous layer and previously published experimental data. Biomimetic design guideline obtained from the current investigation would thereby lead to development of synthetic staggered architecture materials with improved stiffness, load-transfer and toughness.     

薄膜非线性撕裂三种弯曲模型的解答及讨论

针对薄膜非线性撕裂的弯曲模型,引入了3种表征薄膜撕裂过程的双参数准则.这3种表征分别为:(1)界面断裂韧度和分离应力; (2)界面断裂韧度和薄膜的裂尖转角; (3)界面断裂韧度和薄膜在裂尖的临界Mises等效应变.从3种双参数准则入手,分析并给出了针对上述各准则的薄膜非线性撕裂问题的解答.通过分析和比较,建立弯曲模型解答与严格平面应变弹塑性分析解答之间的关联.     

Crack propagation in wedged double cantilevered beam specimens

A closed form analytical solution of crack propagation in double cantilevered beam specimens opened at a constant rate has been found. Hamilton's principle for non-conservative systems was applied to describe the crack motion, under the assumption of a Bernoulli-Euler beam. The criterion of crack propagation is a critical bending moment at the crack tip. The calculations of beam motion take into account wave effects in the Bernoulli-Euler theory of elastic beams. The beam shape during the crack motion is found with a similarity transformation and expressed by Fresnel integrals. The boundary conditions satisfied are the fixed ones of zero bending moment and constant beam opening rate at the load end of the specimen and the moving ones of zero deflection and zero slope of the deflected beam at the tip of the moving crack. The fracture represents a moving critical bending moment. The analytical results show that the specific fracture surface energy is a unique function of the ratio of the crack length squared to the time subsequent to loading and this is computed from the recorded time-dependence of the crack length.     

Direct Extraction of Cohesive Fracture Properties from Digital Image Correlation: A Hybrid Inverse Technique

The accuracy of an adopted cohesive zone model (CZM) can affect the simulated fracture response significantly. The CZM has been usually obtained using global experimental response, e.g., load versus either crack opening displacement or load-line displacement. Apparently, deduction of a local material property from a global response does not provide full confidence of the adopted model. The difficulties are: (1) fundamentally, stress cannot be measured directly and the cohesive stress distribution is non-uniform; (2) accurate measurement of the full crack profile (crack opening displacement at every point) is experimentally difficult to obtain. An attractive feature of digital image correlation (DIC) is that it allows relatively accurate measurement of the whole displacement field on a flat surface. It has been utilized to measure the mode I traction-separation relation. A hybrid inverse method based on combined use of DIC and finite element method is used in this study to compute the cohesive properties of a ductile adhesive, Devcon Plastic Welder II, and a quasi-brittle plastic, G-10/FR4 Garolite. Fracture tests were conducted on single edge-notched beam specimens (SENB) under four-point bending. A full-field DIC algorithm was employed to compute the smooth and continuous displacement field, which is then used as input to a finite element model for inverse analysis through an optimization procedure. The unknown CZM is constructed using a flexible B-spline without any “a priori” assumption on the shape. The inversely computed CZMs for both materials yield consistent results. Finally, the computed CZMs are verified through fracture simulation, which shows good experimental agreement.     

Buckling-induced dislocation emission in thin films on substrates

Atomistic simulations of the evolution of a strained thin film on a substrate has been reported and the formation of dislocations has been observed in the film/substrate interface after the film has buckled. In the framework of the linear elasticity theory, an analytical model has been developed to explain the buckle effect on the formation of the dislocations. A stability diagram with respect to the buckling and dislocation emission phenomena is finally presented for the film as a function of the uniaxial strain and the Burgers vector.     

Bending effect of through-thickness reinforcement rods on mode I delamination toughness of DCB specimen. I. Linearly elastic and rigid-perfectly plastic models

The use of through-thickness reinforcement in the form of short rods has been proposed to improve the interlaminar properties of laminated composites in the recent years. Compared to a fibrous short rod, which is often referred to as z-fiber, a metallic rod, referred to as z-rod in this paper, has reasonably high capability to carry transverse loading, i.e., a z-rod can provide both axial and transverse bridging tractions to the delamination crack. Therefore, a new analytical model is proposed to study the bending effect of the z-rods on mode I delamination toughness of laminated composites. In this new model, both the axial pull-out and the transverse bending are considered simultaneously. New bending moment and displacement relationships for a single z-rod are established by modeling the z-rod embedded in a linearly elastic and rigid-perfectly plastic matrix using the classical beam theory. By using an approximate expression for mode I fracture toughness of double-cantilever-beam (DCB) specimen, a parametric analysis of DCB specimen reinforced by the z-rods is conducted. The present numerical results show that the bending effect should not be ignored when stiffer z-rods are employed to reinforce the laminated composites.     

Helical coil buckling mechanism for a stiff nanowire on an elastomeric substrate

When a stiff nanowire is deposited on a compliant soft substrate, it may buckle into a helical coil form when the system is compressed. Using theoretical and finite element method (FEM) analyses, the detailed three-dimensional coil buckling mechanism for a silicon nanowire (SiNW) on a polydimethylsiloxane (PDMS) substrate is studied. A continuum mechanics approach based on the minimization of the strain energy in the SiNW and elastomeric substrate is developed. Due to the helical buckling, the bending strain in SiNW is significantly reduced and the maximum local strain is almost uniformly distributed along SiNW. Based on the theoretical model, the energy landscape for different buckling modes of SiNW on PDMS substrate is given, which shows that both the in-plane and out-of-plane buckling modes have the local minimum potential energy, whereas the helical buckling model has the global minimum potential energy. Furthermore, the helical buckling spacing and amplitudes are deduced, taking into account the influences of the elastic properties and dimensions of SiNWs. These features are verified by systematic FEM simulations and parallel experiments. As the effective compressive strain in elastomeric substrate increases, the buckling profile evolves from a vertical ellipse to a lateral ellipse, and then approaches to a circle when the effective compressive strain is larger than 30%. The study may shed useful insights on the design and optimization of high-performance stretchable electronics and 3D complex nano-structures.     

An experimental investigation of T-beam stability under bending

This paper presents an experimental setup used to study the response and stability of T-beams subjected to pure bending. The setup consists of a four-point bending device instrumented to measure the moment and curvature in the beam. Special grips are used to attach the specimens to the bending device and enforce a no-twist condition at the ends of the beams. A special instrument is used to measure deformations induced by buckling along the axis of the beam. Results are presented for the cases of monotonic and cyclic bending of short beams that buckle in a local mode. The results indicate that the lateral deflection of the web of the beams develops a ripple relatively early in the bending process. Local buckles arise from localization of the amplitude of the ripple at a given point along the specimen.