混凝土梁三点弯曲断裂模式转变的近场动力学模拟

混凝土结构的宏观损伤开裂与其非均质微观结构紧密相关。底部带切口的混凝土梁在进行三点弯曲破坏时,随着切口的位置由梁中向梁边转移,裂纹由从切口处萌生并生长转变为从梁的中部萌生。本文采用半均质化近场动力学（IH-PD）模型和全均质化近场动力学（FH-PD）模型,分别对混凝土梁三点弯断裂问题进行模拟研究。IH-PD模型根据混凝土中骨料体积分数随机生成不同键的组合方式,将微观尺度的非均质性引入模型,无需详细描绘骨料形状和分布即可考虑混凝土非均质性。本文将IH-PD与FH-PD模型得到的断裂模式随切口位置的变化关系,与实验结果对比,分析微观结构对混凝土梁开裂的影响;基于非均质材料特征尺寸与IH-PD模型网格参数的相关性,模拟骨料大小对混凝土梁断裂模式的影响;另外,通过在IH-PD模型中设置预损伤的方式引入随机分布的孔隙,探讨孔隙率对混凝土断裂模式的影响。     

冲击波-破片群联合作用下舰船复合材料结构近场动力学损伤模拟

采用一种新兴的无网格法——近场动力学理论,模拟复合材料结构在冲击波-破片群联合作用下的损伤情况。根据复合材料结构承受的载荷特性,分析冲击波-破片群联合作用下层合板及加筋板结构的损伤模式,考虑载荷作用次序等因素对于联合作用毁伤能力的影响规律。结果表明:联合作用对复合材料结构的损伤程度主要与冲击波强度、破片群侵彻能力、作用次序有关,主要损伤模式为分层失效、基体损伤、剪切损伤以及结构大变形;对于层合板而言,在冲击波先作用的工况下,结构损伤程度更高,损伤范围更大;对于加筋板而言,由于加筋板的筋条能显著降低冲击波作用,进而降低冲击波对破片群侵彻能力的增强效应,最终影响联合作用的毁伤能力,因而在破片群先作用的工况下反而损伤更严重。     

破片群作用下复合材料层合板近场动力学损伤模拟

采用一种新兴的无网格法——近场动力学理论,模拟复合材料结构在破片群载荷作用下的损伤情况。根据复合材料结构受到载荷的特性,总结破片群冲击作用下复合材料结构损伤特性,分析其破坏过程,研究破片群增强效应,并对破片速度、破片数量、破片群间距对侵彻能力增强效应的影响进行分析。结果表明:层合板结构在高速破片群侵彻作用下损伤模式多样,与破片数量、速度、间距相关;破片数量的增加,对破片群侵彻能力增强效应明显;破片间距与破片群侵彻能力增强效应负相关,破片间距减小,破片群损伤效应提高;破片速度直接决定穿透时间,破片速度的提高使得穿透时间缩短,应力波的叠加效应不足以影响破片群的侵彻能力。     

Experimental study on crack curving propagation in bending beams under impulsive load

Dynamic fracture behaviour of crack curving in bent beams has been investigated. In order to understand the propagation mechanism of such cracks under impact, an experimental method is used that combines dynamic photoelasticity with dynamic caustics to study the interaction of the flexural waves and the crack. From the state change of the transient stresses in polymer specimen, the curving fracture in the impulsively loaded beams is analyzed. The dynamic responses of crack tips are evaluated by the stress intensity factors for the cracks running in varying curvature paths under bending stress wave. The project supported by the National Natural Science Foundation of China and the Scientific Commission of Yunnan Province of China     

Adaptive coupling between damage mechanics and peridynamics: A route for objective simulation of material degradation up to complete failure

The objective (mesh-independent) simulation of evolving discontinuities, such as cracks, remains a challenge. Current techniques are highly complex or involve intractable computational costs, making simulations up to complete failure difficult. We propose a framework as a new route toward solving this problem that adaptively couples local-continuum damage mechanics with peridynamics to objectively simulate all the steps that lead to material failure: damage nucleation, crack formation and propagation. Local-continuum damage mechanics successfully describes the degradation related to dispersed microdefects before the formation of a macrocrack. However, when damage localizes, it suffers spurious mesh dependency, making the simulation of macrocracks challenging. On the other hand, the peridynamic theory is promising for the simulation of fractures, as it naturally allows discontinuities in the displacement field. Here, we present a hybrid local-continuum damage/peridynamic model. Local-continuum damage mechanics is used to describe “volume” damage before localization. Once localization is detected at a point, the remaining part of the energy is dissipated through an adaptive peridynamic model capable of the transition to a “surface” degradation, typically a crack. We believe that this framework, which actually mimics the real physical process of crack formation, is the first bridge between continuum damage theories and peridynamics. Two-dimensional numerical examples are used to illustrate that an objective simulation of material failure can be achieved by this method.     

混凝土复合型裂纹扩展的非局部近场动力学建模分析

基于非局部近场动力学理论,构建了修正的能反映混凝土宏观拉压异性和断裂特征的近场动力学本构模型,开发了相应的离散、加载和时间积分算法,实现典型混凝土构件中复合型裂纹扩展过程模拟。在物质点对尺度上定义局部损伤并考虑物质点对的相对转动,通过求解时空微-积分方程实现裂纹的自然萌生与扩展,避免裂尖不连续带来的求解奇异性、网格依赖性和网格重构以及常规近场动力学本构模型的泊松比限制。通过含单边和双边初始裂纹四点剪切混凝土梁裂纹扩展破坏全过程模拟,得到破坏形态、破坏荷载以及完整的荷载-裂纹开口滑移曲线,并与试验和其他数值模拟结果对比,验证了模型的精确性和算法的稳定性。     

基于Cosserat近场动力学的纤维混凝土破坏模拟

本文基于Cosserat近场动力学发展了一种纤维混凝土的近场动力学模型,对纤维混凝土的破坏现象进行研究。该模型考察了物质点独立的转动自由度和物质点间的力偶作用,而且有表征微结构尺寸的内禀长度,相比于传统的近场动力学模型,更适合描述纤维混凝土这类胶结颗粒材料的力学行为。本文采用完全离散的方式对纤维进行建模,引入了纤维拔出实验中拔出位移和切应力的关系,并且采用组构张量描述纤维的局部分布。数值算例部分模拟了单纤维拔出实验、带预制裂纹的平板拉伸实验和三点弯曲梁实验。数值结果和已有的数值模型以及实验进行了对比,验证了所提出模型的正确性。此外,本文还调查了微结构对纤维混凝土破坏的影响,数值结果显示Cosserat剪切模量和内禀长度会影响裂纹的局部分布,但是不会改变裂纹的主方向。     

Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions

The effect of constraint on brittle fracture of solids under predominantly elastic deformation and mode I loading conditions is studied. Using different cracked specimen geometry, the variation of constraint is achieved in this work. Fracture tests of polymethyl methacrylate were performed using single edge notch, compact tension and double cantilever beam specimens to cover a bread range of constraint. The test data demonstrate that the apparent fracture toughness of the material varies with the specimen geometry or the constraint level. Theory is developed using the critical stress (strain) as the fracture criterion to show that this variation can be interpreted using the critical stress intensity factorK _Cand a second parameterT orA ₃,whereT andA ₃are the amplitudes of the second and the third term in the Williams series solution, respectively. The implication of this constraint effect to the ASTM fracture toughness value, crack tip opening displacement fracture criterion and energy release rateG _Cis discussed. Using the same critical stress (strain) as the fracture criterion, the theory further predicts crack curving or instability under mode I loading conditions. Experimental data are presented and compared with the theory.     

近场动力学在断裂力学领域的研究进展

近场动力学采用非局部积分计算节点内力, 利用统一数学框架描述空间连续与非连续, 避免了非连续区局部空间导数引起的应力奇异, 数值上具有无网格属性, 可自然模拟材料结构的断裂问题. 本文概述了近场动力学的弹性本构力模型, 系统介绍了近场动力学临界伸长率、临界能量密度以及材料强度相关的键失效准则. 详细介绍了近场动力学在断裂力学领域的研究进展, 包括断裂参数能量释放率与应力强度因子的求解、J积分、混合型裂纹、弹塑性断裂、黏聚力模型、动态断裂、材料界面断裂以及疲劳裂纹扩展等. 最后讨论了断裂问题近场动力学研究的发展方向.      

Dynamic fracture of concrete – compact tension specimen

The behavior of concrete structures is strongly influenced by the loading rate. Compared to quasi-static loading concrete loaded by impact loading acts in a different way. First, there is a strain-rate influence on strength, stiffness, and ductility, and, second, there are inertia forces activated. Both influences are clearly demonstrated in experiments. Moreover, for concrete structures, which exhibit damage and fracture phenomena, the failure mode and cracking pattern depend on loading rate. In general, there is a tendency that with the increase of loading rate the failure mode changes from mode-I to mixed mode. Furthermore, theoretical and experimental investigations indicate that after the crack reaches critical speed of propagation there is crack branching. The present paper focuses on 3D finite-element study of the crack propagation of the concrete compact tension specimen. The rate sensitive microplane model is used as a constitutive law for concrete. The strain-rate influence is captured by the activation energy theory. Inertia forces are implicitly accounted for through dynamic finite element analysis. The results of the study show that the fracture of the specimen strongly depends on the loading rate. For relatively low loading rates there is a single crack due to the mode-I fracture. However, with the increase of loading rate crack branching is observed. Up to certain threshold (critical) loading rate the maximal crack velocity increases with increase of loading rate, however, for higher loading rates maximal velocity of the crack propagation becomes independent of the loading rate. The critical crack velocity at the onset of crack branching is found to be approximately 500 m/s.     

Dynamic Brittle Fracture as a Small Horizon Limit of Peridynamics

We consider the nonlocal formulation of continuum mechanics described by peridynamics. We provide a link between peridynamic evolution and brittle fracture evolution for a broad class of peridynamic potentials associated with unstable peridynamic constitutive laws. Distinguished limits of peridynamic evolutions are identified that correspond to vanishing peridynamic horizon. The limit evolution has both bounded linear elastic energy and Griffith surface energy. The limit evolution corresponds to the simultaneous evolution of elastic displacement and fracture. For points in spacetime not on the crack set the displacement field evolves according to the linear elastic wave equation. The wave equation provides the dynamic coupling between elastic waves and the evolving fracture path inside the media. The elastic moduli, wave speed and energy release rate for the evolution are explicitly determined by moments of the peridynamic influence function and the peridynamic potential energy.     

含预制裂纹L形梁柱试件动态断裂过程

针对含预制裂纹L形梁柱试件,为研究预制裂纹动态扩展的力学特征及其对梁柱试件破坏模式的影响,采用数字动态焦散线实验系统,对距节点核心区不同距离l处含有预制裂纹的试件进行落锤冲击实验,得到预制裂纹的扩展轨迹、速度、动态应力强度因子的变化规律。结果表明,l值增大,扩展裂纹在梁下边缘的贯通点与预制裂纹的夹角逐渐增大,曲裂程度变大。裂纹扩展速度随着l的增大振荡性增强,裂纹扩展平均速度逐渐降低。l值为2 mm时,裂尖表现为Ⅰ型断裂,l值增大,裂尖受到剪应力作用增强,Ⅰ型动态应力强度因子减小,Ⅱ型动态应力强度因子增大,断裂逐渐转变为Ⅰ-Ⅱ复合型。     

冲击作用下含预制裂纹梁柱试件的动态断裂

利用焦散线实验系统,进行了冲击加载下含预制裂纹梁柱试件的断裂实验,研究了梁柱试件的梁柱节点、梁上和柱端裂纹的扩展轨迹、扩展速度和应力强度因子的变化规律。实验结果表明:受冲击后,试件首先在梁柱节点处开裂,并在裂纹扩展过程中发生明显的曲裂运动,证明梁柱节点处最容易受到破坏。预制裂纹条数越多,梁柱节点处开裂越晚,说明裂纹条数少,能量可以在裂纹尖端积聚得更集中、更快。含柱端预制裂纹的试件,2条裂纹的开裂相隔时间要长于含梁上预制裂纹的试件;同时,试件的第2条裂纹优先在梁上裂纹处开裂,说明固端支座比简支梁断裂需要更多的能量。随着预制裂纹的增多,梁上裂纹在扩展过程中的曲裂现象减弱, 由于部分能量在柱端裂纹处积聚,用于推动梁上裂纹扩展的能量相应地减少。并且由于柱端裂纹的存在,梁上裂纹受到的拉应力分量减小,导致裂纹尖端受到弯矩变小,影响了裂纹的曲裂运动。     

Flexural model for a notched beam: Direct and inverse problems

Matching conditions simulating a transverse notch in a beam are proposed. These conditions are used to determine the location and size of the notch. The notch is identified from beam deflections at several points in the static case and from the first eigenfrequencies of the beam in the dynamic case. Dependences of the first eigenfrequencies on the characteristic parameters of the problem are obtained. The effect of the relative error of frequency measurements on the relative error of calculation of the notch parameters is studied. It is shown that the use of the first eigenfrequencies of flexural vibrations of the beam with respect to different axis provides a more accurate identification than the use of eigenfrequencies of flexural vibrations relative to one axis. Since local defects such as hollows, local corrosion, and an open crack can be simulated by a notch, the results can also be used to identify these defects.     

编织复合材料的冲击损伤与断裂行为研究

本文利用冲击加载实验装置对含V型裂纹碳纤维编织复合材料梁的冲击损伤与断裂行为进行了实验研究,记录了冲击载荷的时间历程,梁的动态位移变化以及裂纹尖端损伤的动态应变演化历史,确定了裂纹尖端的应变能密度分布。并利用扫描电镜对其断裂表面进行了微观分析。     

动载作用下复合型裂纹扩展的近场动力学模拟

构建改进的非局部近场动力学模型和粒子系统动力加载算法,开展复合型裂纹动力扩展过程模拟。在常规近场动力学微极模型中引入能反映非局部长程力尺寸效应的核函数修正项,以提高计算精度和收敛稳定性。通过模拟动载作用下含复合型裂纹混凝土三点弯梁的裂纹扩展与破坏过程并与试验结果对比,验证了本文模型和算法的可靠性。在此基础上,通过分组模拟分析了动载作用下,初始裂纹的位置、长度和方向对含复合型裂纹三点弯梁破坏模式、起裂时间与承载能力的影响规律。     

加载角度对层理页岩裂纹扩展影响的实验研究

采用分离式霍普金森压杆（SHPB）系统对页岩进行冲击实验,研究层理角度对页岩动态断裂过程的影响,在裂尖设置裂纹扩展计,借助高速摄影和数字图像相关（DIC）技术对页岩中心切槽半圆盘弯曲（NSCB）试件断裂的全过程进行研究,得到了不同加载角度下页岩的动态起裂韧度、裂纹扩展速度、断裂过程中应变场和水平位移场的变化规律。实验发现:不同加载角度下,页岩的动态起裂韧度具有显著的各向异性,加载角度与动态起裂韧度呈正相关;加载角度对试样的裂纹扩展速度具有显著影响,与裂纹扩展速度呈负相关;当冲击速度较低时,切槽方向是裂纹扩展的优势方向,而当冲击速度较高时,试样会产生沿层理弱面的次生裂纹,次生裂纹对试样的断裂具有显著影响。     

含初始裂纹巴西圆盘劈裂问题的非局部近 场动力学建模

巴西圆盘劈裂是弹性力学及岩石力学与工程中的经典问题。在非局部键型近场动力 学理论的基础上,引入物质点对的转动自由度构建双参数微观弹脆性近场动力学本构力模型 以突破常规模型的应用范围限制,并考虑岩石混凝土类材料的宏观拉压异性和断裂特征。引 入动态松弛、粒子系统力边界条件和系统平衡弛豫等算法,实现了含不同倾角中心裂纹巴西 圆盘受压劈裂破坏全过程的近场动力学数值模拟,裂纹扩展路径及破坏形式均与试验结果高 度吻合,为裂纹扩展和断裂破坏问题的数值模拟提供了新的选择。     

STUDY ON NONLINEAR CONSTITUTIVE RELATIONSHIP AND FRACTURE BEHAVIOR OF STITCHED C/SiC COMPOSITES$^{\bf 1)}$

C/SiC复合材料具有高比强度、高比模量和优良的热稳定性能等一系列优点, 广泛应用于航空航天领域中. 裂纹扩展进而引起的脆性断裂是其主要失效形式之一, 因而材料的断裂性能分析对材料的结构设计和应用有重要的指导意义. 本文开展了缝合式C/SiC复合材料简单力学试验和断裂试验, 研究了材料在不同载荷下的力学响应及断裂特征. 基于缝合式C/SiC复合材料简单力学试验, 建立了材料宏观非线性损伤本构方程, 并模拟了缝合式C/SiC复合材料单边切口梁和双悬臂梁的断裂行为. 本构方程采用简单函数描述了材料在复杂应力状态下的非线性应力-应变曲线, 并考虑了反向加载过程中造成的裂纹闭合. 基于商业有限元软件ABAQUS, 通过编写UMAT子程序实现非线性损伤本构方程, 采用单个单元验证了建立的本构方程的有效性. 在此基础上, 采用线弹性损伤本构和非线性损伤本构分别模拟了缝合式C/SiC复合材料单边切口梁和双悬臂梁的断裂行为. 采用非线性损伤本构方程模拟的力-位移曲线结果与试验结果更为吻合, 非线性损伤本构预测的失效载荷与试验失效载荷更为接近, 验证了所建立的非线性损伤本构方程的准确性, 为C/SiC复合材料断裂行为的研究提供了借鉴, 为缝合式C/SiC复合材料结构的设计和应用提供了理论基础.     

沥青混合料三点弯曲断裂的扩展有限元模拟

利用随机骨料生成和投放算法建立沥青混合料两相异质模型,借助ABAQUS软件开展了分别在跨中、偏中20mm和40mm不同位置包含预切口的沥青混合料三点弯曲试件断裂行为的扩展有限元模拟,分析了预切口位置对裂纹扩展路径、载荷位移曲线等的影响规律,并与实验结果进行了比较。结果表明,预切口偏离跨中越远,裂纹扩展方向偏离预切口延长线的角度越大,试件的峰值载荷越大,对试件承载能力的削弱越弱。实验和数值模拟结果在定性上的一致性表明,利用扩展有限元方法模拟沥青混合料断裂行为是可行的。