Influence of fractality of fracture surfaces on stress and displacement fields at crack tips

In the classic theory of fracture mechanics, expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth surface or that a crack is a smooth crack. In fact, the surface of a crack formed during the fracture is usually very irregular. So the real asymptotic form of the stress and displacement fields at the crack tip is different from the classic one. Considering the irregularity of a real fracture surface or a real crack profile, the crack is taken as a fractal one, and then the real asymptotic form at the crack tip is developed by applying Griffith’s energy balance principle and fractal geometry. Through the developed asymptotic form, it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.

     

Influence of fractality of fracture surfaces on stress and displacement fields at crack tips

In the classic theory of fracture mechanics,expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth surface or that a crack is a smooth crack.In fact,the surface of a crack formed during the fracture is usually very irregular.So the real asymptotic form of the stress and displacement fields at the crack tip is different from the classic one.Considering the irregularity of a real fracture surfac...     

Crack tip higher order stress fields for functionally graded materials with generalized form of gradation

A generalized form of material gradation applicable to a more broad range of functionally graded materials (FGMs) was presented. With the material model, analytical expressions of crack tip higher order stress fields in a series form for opening mode and shear mode cracks under quasi-static loading were developed through the approach of asymptotic analysis. Then, a numerical experiment was conducted to verify the accuracy of the developed expressions for representing crack tip stress fields and their validity in full field data analysis by using them to extract the stress intensity factors from the results of a finite element analysis by local collocation and then comparing the estimations with the existing solution. The expressions show that nonhomogeneity parameters are embedded in the angular functions associated with higher terms in a recursive manner and at least the first three terms in the expansions must be considered to explicitly account for material nonhomogeneity effects on crack tip stress fields in the case of FGMs. The numerical experiment further confirms that the addition of the nonhomogeneity specific terms in the expressions not only improves estimates of stress intensity factor, but also gives consistent estimates as the distance away from the crack tip increases. Hence, the analytical expressions are suitable for the representation of crack tip stress fields and the analysis of full field data.     

受内压作用的管道表面斜裂纹尖端应力强度因子分析

裂纹是压力管道最危险的一种缺陷,是导致压力管道各种事故的主要原因。因此,依据断裂力学的相关概念,运用ANSYS有限元软件,建立了受内压作用的压力管道及其表面具有不同周向夹角的斜裂纹的三维模型,并对裂纹尖端的应力强度因子进行有限元计算及分析,得出了裂纹的应力强度因子随裂纹角度的变化而变化的规律。定量分析了裂纹尖端应力场的强弱,为压力管道表面斜裂纹的研究提供了一定的数据支持。     

混凝土预制缺口梁试件拉张破裂数值模拟

目的针对混凝土抗压不抗拉的特性,探讨混凝土预制缺口梁断裂过程中裂纹尖端应力分布及裂纹扩展规律．方法采用拉张破裂有限元软件,对预制缺口在梁的顶部和在底部不同位置的模型进行数值模拟,描述拉张破裂后形成的不连续面．结果得出了不同方案中预制梁受拉破裂的破坏形式．缺口到梁跨度中心线的距离越小,梁试件底部拉应力区域越小;缺口到梁跨度中心线的距离越大,梁试件底部的拉应力区域越大．结论由不同方案破坏形式可以看出,缺口梁受拉应力作用发生破裂,形成不连续面;随着破裂面的形成与发展,混凝土梁的结构形式发生相应改变,导致应力状态随之调整．缺口的位置直接影响梁结构的破裂方式,缺口到梁跨度中心线的距离在一定的范围内,缺口控制着梁破坏的形式,破裂沿缺口发展;超出范围以后,缺口的存在不影响梁的破坏形式,破裂的形成、发展形式与无缺口梁的破坏形式相同．     

静载下连杆裂解裂尖塑性区及其对裂解质量的影响

对静载条件下连杆裂解过程进行了数值分析,将连杆裂尖附近塑性区形状与理想状态进行了对比,定性给出了连杆断裂前裂纹区应力应变状态,并据此分析了不同位置的断裂状态。结果表明,连杆厚度方向不同的层面处于不同的平面应变与平面应力状态,裂尖塑性区大小也不同,启裂首先发生在塑性区较早达到变形极限的平面应变区。裂尖塑性区的差异造成启裂点散布、裂纹扩展不同步,扩展路径不同,极易造成裂纹分叉、交汇异常等问题,并引起撕裂、崩角、断裂面台阶、夹屑、外缘爆口等裂解缺陷,从而影响连杆裂解加工质量。     

扩展有限元法求解应力强度因子

在常规有限元单元形函数中加入模拟裂纹不连续位移场的跳跃函数,在裂纹尖端构造反映位移场奇异性的裂尖增强函数,采用相互作用积分法求得裂尖应力强度因子．算例结果表明,扩展有限元方法在分析断裂力学问题时具有计算精度高,对有限元网格依赖性小,操作简便等优点．     

Fracture characteristics of iron ore under uncoupled blast loading

A blasting experiment was conducted on iron ore samples by considering multiple coupling charge coefficients. The resulting internal fracture and damage characteristics were quantitatively analyzed via computerized tomography (CT), scanning, and three-dimensional (3D) model reconstruction. The results show that the iron ore primarily displayed radial and circumferential cracks along the blast hole under an explosive load. When the decoupling coefficient was small, the crack surface was dominated by transgranular fractures in the form of intracrystalline fractures. As the uncoupling coefficient increased, the crack surface exhibited transgranular and intergranular coupled fracture modes. Using fractal theory to analyze crack distribution characteristics, as the decoupled coefficient increased, the body fractal dimension tended to decrease, and the degree of damage gradually decreased. The degree of damage reached a turning point when the decoupling charge coefficient was approximately 1.33. A numerical simulation suggested that the explosion energy transmitted to the iron ore and the effective stress decrease sharply when the decoupling coefficient exceeds 1.33. In some optimal uncoupling coefficient range, excessive fragmentation of the ore body is prevented, thereby allowing full use of the explosive energy.     

Rock fracture under anti-plane shear (Mode III) loading

Anti-plane punch-through shear test and anti-plane four-point bending test are used to study the crack initiation and propagation under anti-plane shear (Mode III) loading. The tensile and shear stresses at the crack tip are calcualted by finite element method. The results show that under Mode III loading the maximum principal stress σ₁ at crack tip is smaller or a little larger than the maximum shear stress τ_max. Since the tensile strength of brittle rock is much lower than its shear strength, σ₁ is easy to reach its critical value before τ_max reaches its critical value and thus results in Mode I fracture. The fracture trajectory is helicoid and the normal direction of tangential plane with the fractured helicoid is along the predicted direction of the maximum principal stress at the notch tip. It is further proved that Mode I instead of Mode III fracture occurs in brittle rock under Mode III loading. The fracture mode depending on the fracture mechanism must be distinguished from the loading form. Foundation item: Project (50374073) supported by the National Natural Science Foundation of China; project (2002032256) supported by the Postdoctor Science Foundation of China     

幂软化材料动态裂纹尖端的弹塑性场

采用塑性动力学方程,对应变损伤材料平而应力动态裂纹尖端场进行了渐近分析。假定材料服从J_2流动理论,且损伤规律以幂律应变软化的规律给出,其结果表明:在裂纹尖端附近,应力和应变分别具有如下的奇异性:σ/(1n R/r)~(-n/n+1),∈～(1n R/r)~(1/n+1),并且通过数值计算给出了裂纹尖端附近的应力分布。而对于n=1情况下,即损伤规律服从反比例关系,本文对平面应变问题和Ⅲ型反平面剪切问题进行了研究。给出了动态弹塑性场的渐近解,揭示了场的渐近特性。     

一种确定聚碳酸酯裂纹尖塑性区边界的方法

从实验出发提出了一种确定聚碳酸酯裂纹尖塑性区边界的方法指出在圆偏振光场中聚碳酸酯裂纹尖等差线条纹密集区的边界就是塑性区的边界这种方法得到了Tresca屈服条件和平面应力—光律理论的支持在实用中这种方法比较直观测量方便     

受纯扭正交异性双材料的界面裂纹尖端场

通过构造特殊的挠度函数,利用复合材料断裂复变方法,对正交异性双材料在受纯扭曲载荷作用下的界面裂纹尖端进行了探讨。在特征方程组的判别式都小于零时,通过求解两个八元齐次线性方程组,推出了含两个实奇异指数的应力函数,并得到了界面裂纹尖端附近的弯矩、扭矩的计算公式。     

可压缩粘弹性材料Ⅰ型动态扩展裂纹尖端场

为了研究粘性效应作用下的动态扩展裂纹尖端渐近场,建立了可压缩粘弹性材料Ⅰ型动态扩展裂纹的力学模型,推导了可压缩材料Ⅰ型动态扩展裂纹的本构方程.在稳态蠕变阶段,弹性变形和粘性变形同时在裂纹尖端场中占主导地位,应力和应变具有相同的奇异量级.通过渐近分析求得了裂纹尖端应力、应变和位移分离变量形式的渐近解,并采用打靶法求得了裂纹尖端应力、应变和位移的数值结果,给出了应力、应变和位移随各种参数的变化曲线.数值计算表明,弹性可压缩变形对Ⅰ型裂纹尖端应力场影响甚微,而对应变场和位移场影响较大.裂纹尖端场主要受材料的蠕变指数n和马赫数M控制.当泊松比v=0.5时,可以退化为不可压缩粘弹性材料Ⅰ型动态扩展裂纹.     

Crack initiation ahead of piled—up of dislocations emitted from a mode Ⅱ blunt crack

In situ tensile tests in a transmission electron microscope (TEM) show that dislocations emitted from a mode II crack tip will form a inverse piled-up group after equilibrium or a double piled-up group when they meet a obstruction, e.g., grain boundary or second phase. A microcrack can initiates in front of the piled-up group of dislocations. Micromechanics analysis shows that dislocations emitted from a mode II blunt crack tip can form a inverse piled-up or double piled-up group, depending upon the applied stress intensity factor K_(lla), lattice friction stress τ_ f and the distance of the obstruction from the crack tip L. The maximum normal stress in front of the double piled-up group which is located at the direction of α = -64° increases with the increase in the stress intensity K_(lla) and the obstruction site L, and the decrease in the friction stress τ_f When it increases to equate the cohesive strength, a microcrack will initiate in front of the piled-up group.     

三点弯曲-剪切试样的应力强度因子

利用一种边界元法研究具有偏移边裂纹的三点弯曲-剪切试样.该边界元方法由Crouch与Starfield提出的常位移不连续单元和笔者最近提出的裂尖位移不连续单元构成.在该边界元方法实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其他边界.算例说明这种边界元法不论对无限大还是对有限大平面弹性复杂裂纹问题的应力强度因子的计算都是非常有效的.对具有偏移边裂纹的三点弯曲-剪切试样的应力强度因子进行了详细的研究,给出了数值结果.     

动载荷条件下水泥环损伤原因分析

为了避免射孔后在水泥石上形成一些微细的裂纹而导致井下作业(如压裂等)在这些裂纹尖端处形成应力集中,造成裂纹的扩展和延伸。对动载荷条件下水泥环损伤原因及程度进行了分析,提出了提高水泥环与套管、地层的胶结强度和水泥环抗冲击能力的措施。     

金属韧性启裂的微观模型

通过对金属韧性断裂的裂尖物理图象分析,提出了一种新的韧性启裂模型,在此基础上,结合钝化裂纹顶端的应力分布,导出了金属断裂韧性,拉伸性能以及伸张区宽度之间的关系,并得到了实验的验证。     

扩展裂纹尖端的弹—粘塑性场

弹性 -粘塑性模型对反平面剪切扩展裂纹尖端的应力应变场进行了分析 .文中给出了适当的位移模式 ,推导了渐近方程 ,并且给出了数值结果 .分析和计算表明对于低粘性情况应变场具有对数奇异性 .结果揭示了粘性对裂纹尖端场的作用     

焊接结构低周疲劳损伤分形演变模型

用宏观与微观相结合的方法研究焊接接头疲劳损伤演变规律。认为焊接接头中疲劳裂纹扩展路径在一定尺度范围内具有分形特征，用分形几何学方法建立裂纹扩展模型，将断裂力学的概念运用到损伤力学演化规律研究中，给出分形有效应力强度的表达式以及损伤演化率方程，推导出损伤演变方程，为从微观层次定量描述焊接结构疲劳断口特征及宏观疲劳断裂特性提供了一种新的有效方法。     

Mechanism on progressive failure of a faulted rock slope due to slip-weakening

Slip-weakening is one of the characteristics of geological materials under certain loadings. Non-uniform rock structure may exist in the vicinity of the slip surface for a rock slope. Some portion of the slip surface may be penetrated but the other not. For the latter case, the crack or the fault surface will undergo shear deformation before it becomes a successive surface under a certain loading. As the slipped portion advances, slip-weakening occurs over a distance behind the crack tip. In the weakening zone, the shear strength will decrease from its peak value to residual friction level. The stress will redistribute along the surface of crack and in the weakening zone. Thus the changed local stress concentration leads the crack to extend and the ratio of penetration of the slip surface to increase. From the view of large-scale for the whole slip surface, the shear strength will decrease due to the damage of interior rock structure, and the faulted rock behaves as a softening material. Such a kind of mechanism performs in a large number of practical landslides in the zones experienced strong earthquakes. It should be noted that the mechanism mentioned above is different from that of the breakage of structural clay, in which the geological material is regarded as a medium containing structural lumps and structural bands. In this paper, the softening behavior of a faulted rock should be regarded as a comprehensive result of the whole complicated process including slip-weakening, redistribution of stress, extension of crack tip, and the penetration of the slip surface. This process is accompanied by progressive failure and abrupt structural damage. The size of slip-weakening zone is related to the undergoing strain. Once the relative slide is initiated (local or integrated), the effect of slip-weakening will behave in a certain length behind the crack tip until the formation of the whole slip surface.