动态裂纹扩展中的分形效应

假设裂纹顶端沿着分形轨迹运动，建立了裂纹扩展的分形弯折（ｋｉｎｋｉｎｇ）模型来描述裂纹的动态扩展。根据这个模型，我们推导了分形裂纹扩展对劝态应力强度和裂纹速度的影响．动态应力强度因子与表观应力强度因子之比Ｋ（ｌ（ｔ），Ｖ）／Ｋ（Ｌ（ｔ），Ｏ）是表观裂纹速度Ｖ＿Ｏ，材料微结构参数（ｄ／Δａ），分维Ｄ和裂纹扩展路径的弯折角θ的函数。本文研究结果表明：在分形裂纹扩展中，表观（或量测）的裂纹速度Ｖ＿Ｏ很难接近Ｒａｙｌｅｉｇｈ波速Ｃ＿ｒ．动态断裂实验中Ｖ＿Ｏ明显低于Ｃ＿ｒ的原因可能是分形裂纹扩展效应所致。材料的微结构，裂纹扩展路径的分维和弯折角均很强地影响动态应力强度因子和裂纹扩展速度。     

增韧环氧树脂的动态裂纹扩展研究

本文主要进行了环氧及增韧环氧树脂的断裂韧性及裂纹快速扩展的试验研究。试验过程中采用了ＧＬＣ－１型高速裂纹扩展测试仪来测试裂纹的扩展速度,得到在裂纹扩展过程中裂纹扩展速度曲线。本文结合不同的计算公式及有限元分析方法,讨论了各个确定断裂韧性公式的准确程度,发现传统的静态断裂韧性的分析方法所得到的结果偏大,有一定的危险性,建议使用试验与数值计算相结合的方法;同时还发现增韧不仅可以提高材料的静态和动态断裂性能,而且在裂纹扩展过程中可以起到减缓裂纹扩展的作用     

脆性材料的分形统计强度理论

基于脆性材料中裂纹尺度的分形分面和最弱环原理的假设，导出了裂纹尺频分布的分形维数Ｄ与经典统计强度理论中Ｗｅｉｂｕｌｌ模量ｍ之间的关系，揭示了ｍ的几何实质，并且同时考虑裂纹的尺度分布和方位分布及裂纹扩展路径的不规则性对统计强度的影响，从理论上推导了复杂应力状态下脆性材料统计强度σ的一般表达式。     

冲击载荷作用下黑砂岩动态断裂参数的分形修正

基于分形理论研究了偏折裂纹扩展路径对动载荷作用下黑砂岩的动态断裂力学参数的测试误差影响作用,采用传统的分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）实验装置对修正侧开单裂纹半孔板（improved single cleavage semi-circle specimen, ISCSC）试样进行动态冲击实验,随后采用裂纹扩展计进行裂纹起裂时间与裂纹扩展速度等动态断裂力学参数测试,采用分形理论对测试的裂纹扩展速度与动态应力强度因子进行修正,利用实验-数值法对黑砂岩的动态断裂韧度进行计算。研究结果表明,ISCSC构型构件能够有效应用于岩石材料动态裂纹扩展行为的研究,并发生了止裂现象,经分形修正的裂纹扩展速度与动态断裂韧度更接近实际裂纹动态扩展情况,修正前后得到黑砂岩材料的裂纹扩展速度误差为33.51%,动态断裂韧度最大误差为7.68%,说明利用分形理论对动态断裂韧度等动态断裂参数计算更合理。     

基于数字散斑相关法的紧凑拉伸试样断裂韧性实验研究

本文采用数字散斑相关方法对2A12T4铝合金紧凑拉伸试样的断裂韧性进行了实验研究。应用数字散斑相关方法计算了实验过程中试样的应变场、应力场以及位移场。针对实验所得的结果以及紧凑拉伸试样的裂纹特征,采用了矩形积分路径。选择沿裂纹方向和垂直裂纹方向的J积分路径,并且推导出各方向上J积分的数值计算公式。根据推导得到的公式选择不同的积分路径进行J积分的计算,得到了断裂韧性J0积分路径的合理选择范围,同时验证了J积分的路径守恒性。然后根据所得的路径选择标准,选择合理的积分路径,计算出2A12T4铝合金断裂韧性J0的值。将所得结果与国标计算的J0值对比,误差为1.22%,说明了此种方法的正确性。从而为数字散斑相关方法在紧凑拉伸试样断裂韧性的测试研究中提供参考。     

冻融循环作用下沥青混凝土分形断裂特性研究

沥青混凝土作为一种主要的路面材料，暴露于外部寒冷环境下冻融损伤是不可避免的。通过对经历不同冻融循环次数的沥青混凝土试件进行CT扫描，采用数字图像处理技术对CT灰度图像进行处理分析，可获得其内部冻融损伤情况。基于分形理论量化表征了冻融循环作用下内部裂纹扩展的几何特征。沥青混凝土经过冻融循环后的断裂韧性被认为是决定其力学性能损伤程度的关键指标，建立了考虑分形特征的临界裂纹应力、应力强度因子和断裂韧性方程。研究发现：平均分形维数反映了冻融循环过程中的波动特征；断裂韧性由裂纹几何参数决定；弹性模量、临界开裂应力及断裂韧性等力学参数随冻融循环次数的增加而逐渐减弱。     

预制AIN—SiCw材料微裂纹的静态爆破法

本文采用静态爆破法对 AIN—SiC_w 材料进行了预制裂纹实验,研究了静态爆破剂预制微裂纹的基本方法与裂纹扩展的控制问题。研究表明:静态爆破预制AIN-SiC_w 这类脆性材料的微裂纹是一种较好的实验方法。     

岩石材料动态破坏的近场动力学方法数值模拟

裂纹的聚集、扩展、分叉是岩石等脆性材料破坏失效的关键因素，本文在验证了近场动力学方法在研究岩石类材料裂纹动态扩展方面的有效性之后，采用近场动力学方法分别对冲击载荷作用下含有双裂纹岩石材料和单轴压缩作用下含单斜裂纹的岩石材料进行数值模拟．结果表明，对于双垂直裂纹，其裂纹扩展路径大致与预制裂纹成70°夹角；对于单裂纹，裂纹的扩展路径随裂纹倾角的变化而变化，最终导致构件的整体破坏．数值模拟结果表明近场动力学方法可以很好地模拟岩石等脆性材料的裂纹扩展直至破坏的过程，反映裂纹扩展的物理机理；其作为一种新的基于非局部理论的数值方法，在地下岩体工程方面及页岩气的开采方面会有很好的发展前景．     

高温疲劳表面短裂纹的分形研究

对2.25Cr-1Mo合金钢进行了高温疲劳实验，采用中断试验与复膜技术相结合的方法观测了试样表面疲劳短裂纹萌生，扩展及合体的演化过程，并用数据格子方法研究了含裂纹表面的分形特征。结果表明：疲劳短裂纹的萌生扩展行为具有分形特征，可以用分形理论加以描述；分形维数随着疲劳过程的继续而稳定地成比例增加；分形维数可以作为把握材料总体损伤状态的参数，可作为寿命评价的依据。     

多裂纹扩展分析的边界元方法

采用边界元数值模拟和即时等效材料常数计算相结合的办法，只需模拟一个裂纹的扩展情况便可预测裂纹体的整体响应。针对准脆性材料的特点，采用粘性裂纹模型模拟裂纹开裂行为；采用二次裂纹扩展量作为增量控制变量，避免了软化及失稳分析中用力或位移作控制变量时遇到的困难。针对二交裂纹扩展路径未知情况，给出了预测和修正裂纹开裂界面的迭代技术，分析计算了含多个规则分布裂纹石膏板受压时的响应，并与实验结果进行了比较。结果表明该文方法的可行性与有效性。     

Effects of fractal crack

Experimental results indicate that propagation paths of cracks in geomaterials are often irregular, producing rough fracture surfaces which are fractal. In this paper, crack tip motion along a fractal crack trace is discussed. A fractal kinking model of the crack extension path is established to describe irregular crack growth. The length, velocity and kinking effects of the fractal crack are analysed. A formula is derived to describe the effects of fractal crack propagation on the dynamic stress intensity factor and on crack velocity. Finally, expressions of stress and displacement fields near the fractal crack tip are given.     

Fractal geometry concerned with stable and dynamic fracture mechanics

Fractal modeling of the rugged crack geometry is considered for the stable and dynamic fracture mechanics characterizing the morphology of a fracture surface and the influence of its growth. It is shown that the fractal dimension has a strong influence on the rising of the R-curve in brittle materials. For the unstable Griffith–Mott’s approach or dynamical crack growth the fractal dimension has a strong influence on the velocity limit of the crack growth. It is also shown that the limit of crack velocity lowers with increasing surface ruggedness (higher fractal dimension D = 2 − H) explaining the intangibility of the Rayleigh wave velocity by the cracks.     

Dynamic fracture instabilities in brittle crystals generated by thermal phonon emission: Experiments and atomistic calculations

Dynamic cleavage fracture experiments of brittle single crystal silicon revealed several length scales of surface and path instabilities: macroscale path selection, mesoscale crack deflection, and nanoscale surface ridges. These phenomena cannot be predicted or explained by any of the continuum mechanics based equations of motion of dynamic cracks, as presumably critical energy dissipation mechanisms are not fully accounted for in the theories. Experimentally measured maximum crack speed, always lower than the theoretical limit, is another phenomenon that is as yet not well understood.We suggest that these phenomena depend on velocity dependent and anisotropic material property that resists crack propagation. The basic approach is that the bond breaking mechanisms during dynamic crack propagation vibrate the atoms at the crack front to generate thermal phonon emission, or heat, which provides additional energy dissipation mechanisms. This energy dissipation mechanism is a material property that resists crack propagation. To evaluate this property, we combined the continuum based elastodynamic Freund equation of motion with molecular dynamics atomistic computer “experiments”.We analyzed the above experimental dynamic fracture instabilities in silicon with the obtained velocity dependent and anisotropic material property and show its importance in cleavage of brittle crystals.     

Relationship Between the Crack Velocity,Fractal Dimension,and Dynamic Fracture Toughness of a Material

This paper presents the results of experimental studies of the crack propagation velocity and the dynamic fracture toughness of St. 45 steel and D16T Duralumin using a modified Kolsky method with a split Hopkinson bar. The results of microfractographic analysis of samples are given, and the fractal dimension is determined. The critical stress intensity factors are calculated using the obtained fractal dimension values.     

Dynamic instabilities in {1 1 1} silicon

The phenomena occurring during rapid crack propagation in brittle single crystals was studied by cleaving strip-like silicon specimens along the {1 1 1} low-energy cleavage plane under bending. The experiments reveal phenomena associated with rapid crack propagation in brittle single crystals not previously reported, and new crack path instabilities in particular. In contrast to amorphous materials, the observed instabilities are generated at relatively low velocity, while at high velocity the crack path remains stable. The experiments demonstrate that crack velocity in single crystals can attain the theoretical limit. No evidence for mirror, mist, and hackle instabilities, typical in amorphous materials, was found. The important role played by the atomistic symmetry of the crystals on controlling and generating the surface instabilities is explained; the importance of the velocity and orientation-dependent cleavage energy is discussed. The surface instabilities are generated to satisfy minimum energy dissipation considerations. These findings necessitate a new approach to the fundamentals of dynamic crack propagation in brittle single crystals.     

STATISTICALLY FRACTAL STRENGTH THEORY FOR BRITTLE MATERIALS

Based on the hypothesis of the fractal distribution of crack sizes in brittle materials andthe weakest link principle,the relationship between the fractal dimension of the size-frequency distri-bution of cracks and the Weibull Modulus is derived,which reveals the geometrical nature of theWeibull Modulus.The influences of the size distribution and the orientation distribution of cracks aswell as the irregularity of the crack propagation on the strength are all taken into account.Finally,ageneral expression for the statistical strength of brittle materials in complex tensile stress state is ob-tained.     

Brittle fracture dynamics with arbitrary paths I. Kinking of a dynamic crack in general antiplane loading

We present a new method for determining the elasto-dynamic stress fields associated with the propagation of anti-plane kinked or branched cracks. Our approach allows the exact calculation of the corresponding dynamic stress intensity factors. The latter are very important quantities in dynamic brittle fracture mechanics, since they determine the crack path and eventual branching instabilities. As a first illustration, we consider a semi-infinite anti-plane straight crack, initially propagating at a given time-dependent velocity, that changes instantaneously both its direction and its speed of propagation. We will give the explicit dependence of the stress intensity factor just after kinking as a function of the stress intensity factor just before kinking, the kinking angle and the instantaneous velocity of the crack tip.     

Geometric Characteristics of Fracture‐Associated Space and Crack Propagation in a Material

It is shown that fracture can be treated as a process occurring in the Finsler space. The use of the Finsler space allows one to construct a delaminated manifold whose characteristics are related to the defect structure of the medium. A method of determining the fractal dimension of fracture is developed using the concept of crack propagation along geodesics.     

EXPERIMENTAL AND THEORETICAL INVESTIGATIONS ON THE VELOCITY OSCILLATIONS OF DYNAMIC CRACK PROPAGATING IN BRITTLE MATERIAL TENSION

设计了一种精确测量裂纹在预拉伸带板中的传播速度的实验装置, 系统研究了裂纹在受不同预加载荷作用的不同尺寸的有机玻璃 板中的传播行为.实验结果表明:在一个细长、上下表面固定的带板中, 裂纹速度分为加速和稳定2个阶段.在稳定速度阶段, 裂纹平均速度v₀ 是预加载荷在板中储存的弹性能Wh的增函数.由于此时裂纹处于自相似传播阶段, 可以认为材料的动态断裂能G_c是裂纹传播速度v₀的增函数, 即材料存在"速度增韧性".当裂纹传播速度达到一定阈值, 裂纹的传播速度出现明显的振荡现象, 裂纹的振荡周期与断裂面出现的周期性沟槽的尺度一致.在更高的预加能量下, 裂纹传播路径出现弯曲、微分岔以及宏观分岔现象.建立了一个描述裂纹在带板中的直线传播行为的动力学模型, 并用这个模型模拟裂纹在传播过程中的速度振荡现象.