蠕变条件下梯度材料球罐应力应变行为研究

探究内外压载荷下梯度材料球罐与相关时间行为之间的解析公式，在这一基础上，对蠕变梯度分布与弹性梯度分布对于球罐蠕变应力应变造成的影响进行分析；根据计算出来的结果显示，弹性参量的梯度变化，只会影响蠕变初始阶段中存在的应力，当蠕变应力处于一个稳定状态之后，蠕变参量的梯度分布状况是球罐应力水平的唯一决定因素；对于蠕变应变分布而言，它与材料的蠕变梯度变化以及弹性梯度变化存在着紧密的联系。本文主要针对梯度材料球罐应力在蠕变条件下的应力应变进行深入的分析，探讨梯度材料球罐蠕变应力应变值的降低，以此对梯度材料球罐结构进行优化，保证梯度材料球罐结构设计的合理性，同时，为其提供相应的理论依据。     

TiC-Ni系功能梯度材料的断裂力学有限元分析

根据实验结果给出了功能梯度材料热物性参数的估计模型,用有限元素法研究了含有垂直于梯度方向裂纹的功能梯度材料,分别考虑了机械载荷、均匀热载荷以及非均匀热载荷作用下,梯度分布指数对裂纹尖端应力强度因子、应变能密度以及裂纹扩展角的影响。      

红外热像技术测量Ⅰ型裂纹应力强度因子的研究

目前工程中出现的裂纹形态主要是I型,大多数工程构件中裂纹的应力强度因子难以直接接触测量,建模计算也因受力条件复杂而耗时和困难。红外热像技术以非接触式测量方法为研究材料和结构的断裂问题提供新的实验手段。通过研究在不同频率循环拉伸条件下304不锈钢试件的热-力响应,得到材料体积应变与温度变化的定量关系,进而对紧凑拉伸试件进行循环加载,同步测量裂纹尖端的温度场,获得I型材料裂尖附近应力强度因子。实验结果表明:在近绝热条件下,材料热弹性区的温度变化与体积应变成定量线性关系;不同荷载条件下实测裂纹尖端附近应力强度因子与理论值对比,误差均在2%以内,说明利用红外热像实验方法测量工程实际中循环荷载情况下的应力强度因子是可行并且可靠的。     

倾斜应力作用下垂直于功能梯度材料夹层的币型裂纹扩展问题

分析了功能梯度材料中币型裂纹扩展问题。该裂纹体受有与裂纹面成任意角度的张应力或压应力,裂纹垂直于无限域中功能梯度材料夹层。假定非均匀介质的功能梯度材料夹层与两个半无限域完全结合,其弹性模量沿厚度方向变化。利用已发表的裂纹应力强度因子数据和线弹性断裂力学的叠加原理,将应力强度因子耦合于最小应变能密度因子断裂判据,讨论了裂纹扩展的临界荷载;并讨论了荷载方向和材料性质对临界荷载的影响。     

含倾斜裂纹三点弯动态断裂试验研究

为研究冲击荷载下巷道围岩不同角度径向裂纹的破坏机制,采用落锤冲击加载平台和数字激光动态焦散线实验系统,以有机玻璃为试验材料,设计冲击荷载下半圆孔上不同角度裂纹的三点弯动态断裂试验,记录预制裂纹的角度α的改变对裂纹动态力学行为的影响,通过分析动态应力强度因子和裂纹扩展轨迹的分形维数对实验现象进行归纳总结。研究发现:①预制裂纹角度对裂纹尖端应变能的积累和释放的快慢有较大影响,随着角度的增大,起裂时间变短,起裂更容易,裂纹尖端应变能积累的更快;②裂纹尖端应变能释放的快慢在α=45°两侧表现出不同的规律;③不同角度裂纹的Ⅰ型动态应力强度因子随时间的变化规律具有相似性,但最大值却具有差异性;④不同角度裂纹的扩展轨迹满足一定的分形规律。     

承受双向等拉应力的平面应变I型裂纹线弹性断裂的I1准则与K准则一致性分析

采用线弹性有限元方法计算了承受双向等拉应力的平面应变I型裂纹的应力场,分析了裂纹尖端各应力分量间的关系,拟合了各非零应力分量关于裂纹半长度a和裂纹尖端最小网格尺寸l₁的函数,分析了应力第一不变量I₁与应力场强度因子K_I的相关性。结果表明,裂纹尖端各非零应力分量间存在稳定的比例关系;各非零应力分量值和加载应力的比值与裂纹半长度a的1/2次幂呈正比例关系、与裂纹尖端最小网格尺寸l₁的1/2次幂呈反比例关系;相同最小网格尺寸条件下,裂纹尖端的应力第一不变量与应力场强度因子的比值l₁/K_I为与加载应力和裂纹长度无关的常数,证明了承受双向等拉应力的平面应变I型裂纹线弹性断裂的I₁准则与K准则具有一致性。     

梯度涂层材料中裂纹问题的非均匀元分析

本文采用非均匀等参有限元的方法研究了薄膜梯度涂层/均匀基材中的界面裂纹问题,并与双材料界面裂纹情况进行了对比计算。研究表明:在均匀基材上采用梯度涂层,与双材料相比可以有效地降低裂尖场应力强度因子;同时还分析了涂层厚度与梯度参数对界面应力强度因子的影响。结果表明:当薄膜厚度大于或等于裂纹长度时,应力强度因子(KI、KII)对其尺度的变化显得不敏感;对梯度参数的影响而言,当材料性能曲线的幂指数m大于1时,裂尖场的应力强度因子KII相对KI很小且基本不随m变化,因此裂尖场与均匀材料情况类似;当m小于1时,应力强度因子KII随m减小而急剧增大,裂尖场由KI及KII控制,断裂趋于混合型。     

高温下的金属基复合材料双剪切试样应力应变有限元分析

对金属基复合材料双剪切试样的应力应变分布进行蠕变有限元计算分析,得到受剪区的应力应变随时间的分布规律。通过典型取向试样分析,表明受剪区的应力应变与纤维随机分布平面和加载方向夹角θ之间存在很大的相关性:随角度θ的减小,其蠕变应力分布越均匀;当角度θ=45°时,其稳态蠕变率γ·最大。双剪切试样能得到较均匀的剪应力区域,适合研究材料纯剪应力状态下的蠕变行为。     

组份成分分布规律对功能梯度防护装甲动态响应的影响

利用数值模拟方法研究了在冲击载荷作用下组份成分对称分布的功能梯度板的动态响应。梯度板材料为陶瓷颗粒增强的铝基复合材料(MMC) 。增强相体积分数随厚度服从指数定律连续分布, 在对称分布条件下增强相体积分数分别在梯度板的前后表面达到最大值。结果显示, 在这种功能梯度装甲板中, 应力波的传播非常复杂, 弹性和粘塑性波耦合在一起, 反射拉伸波和卸载波的大小依赖于组份成分沿厚度的分布; 等效塑性应变的幅值、动能、弹性应变能及耗散能随时间的变化规律与功能梯度材料组份成分沿厚度的变化密切相关。这些因素对强冲击载荷作用下功能梯度板的优化设计非常重要。      

非均匀复合材料中反平面裂纹的动态断裂力学研究

对于非均匀复合材料中多个裂纹的动态断裂力学问题, 提出了一种分析方法, 假设复合材料为正交各向异性并含有多个垂直于厚度方向的裂纹, 材料参数沿厚度方向为变化的, 沿该方向将复合材料划分为许多单层, 假设单层材料参数为常数, 应用柔度矩阵/刚度矩阵方法及Fourier变换法, 在L aplace 域内推导出了控制问题的奇异积分方程组, 并用虚位移原理求解, 给出了应力强度因子及能量释放率的表达式, 然后利用Laplace 数值反演, 得出了裂纹尖端的动态应力强度因子和能量释放率。作为算例, 研究了带有两个裂纹的功能梯度结构, 分析了材料参数的优化对降低应力强度因子的意义。      

A treatment of interfacial cracks in the presence of friction

Frictional sliding on interface crack surfaces results in weak crack tip stress singularity and zero strain energy release rate. A fracture criterion based on finite extension strain energy release rate, is proposed to capture the intrinsic fracture toughness. The finite extension strain energy release rate is shown to represent the magnitude of the singular stress field. Numerical simulations of a center crack in a bimaterial infinite medium under remote shear as well as fiber pull-out and push-out in composite materials are presented to illustrate the frictional effect in both small and large scale contacts near the crack tip.     

Steady-state crack growth in rubber-like solids

The fracture toughness of rubber-like materials depends on several factors. First there is the surface energy required to create new crack surface at the crack tip. Second, a significant amount of energy is dissipated through viscoelastic processes in the bulk material around the crack tip. Third, if the crack propagates very rapidly, inertia effects will come into play and contribute to the fracture toughness. In the present study, a computational framework for studying high-speed crack growth in rubber-like solids under conditions of steady-state is proposed. Effects of inertia, viscoelasticity and finite strains are included. The main purpose of the study is to study the contribution of viscoelastic dissipation to the total work of fracture required to propagate a crack in a rubber-like solid. The model was fully able to predict experimental results in terms of the local surface energy at the crack tip and the total energy release rate at different crack speeds. In addition, the predicted distributions of stress and dissipation around the propagating crack tip are presented.     

梯度复合材料裂纹扩展路径和起裂载荷的有限元分析

为了模拟功能梯度材料(FGM)在工程应用中可能会出现的断裂问题并计算相应的开裂载荷,通过编写用户自定义UEL子程序将梯度扩展单元嵌入到ABAQUS软件中模拟功能梯度材料的物理场,并编写交互能量积分后处理子程序计算裂纹尖端的混合模式应力强度因子(SIF),采用最大周向应力准则编写子程序计算裂纹的偏转角,并模拟了裂纹扩展路径,计算了裂纹的起裂载荷。讨论了材料梯度参数对裂纹扩展路径以及起裂载荷的影响规律。通过与均匀材料的对比,验证了功能梯度材料断裂性能的优越性。研究表明:外载平行于梯度方向时,垂直梯度方向的初始裂纹朝着等效弹性模量小的方向扩展,且偏转角在梯度指数线性时出现峰值,并随着组分弹性模量比的增加而变大;当外载和初始裂纹均平行于梯度方向时,材料等效弹性模量和断裂韧性的增加或者梯度指数的减小都导致起裂载荷变大。     

Theoretical analysis of Hertzian contact fracture: Ring crack

The axisymmetric fracture behavior of brittle materials under an applied indentation force is investigated by considering the pile-up of Somigliana ring dislocations. For such a mixed-mode crack problem, the stress intensity factors (SIFs) and strain energy release rate are obtained by solving a system of Cauchy singular integral equations. The Auerbach range is extensively studied during the formation of a shallow ring crack. The Auerbach constant is also determined from the exact solutions, enabling the prediction of surface energy from Hertzian indentation tests. The obtained results can be used to extract the fracture parameters of brittle materials by using the indentation technique.     

Evaluation of crack tip stress and strain fields under nonproportional loading in a viscoelastic material

The crack tip strain and stress fields in a viscoelastic material under nonproportional loading conditions are evaluated. In order to evaluate the strain field, the crack tip displacement field is measured by using the digital image correlation (DIC) technique. This displacement field is then approximated by using the theoretically obtained crack tip displacement field in viscoelastic materials. The result shows that the approximation method can smoothly reconstruct the experimentally obtained displacement field. From the approximated displacement field, the crack tip strain field can be precisely obtained by using the differential form of the theoretical displacement. On the other hand, the crack tip stress field is analyzed by using the stress function. This suggests that the strain and stress fields can be independently evaluated. In addition, different time dependencies between stress and strain fields near the crack tip are observed. Based on this experiment, we can discuss the several criteria for the crack propagation directions in viscoelastic materials.     

Fracture investigation of U‐notch made of tungsten–copper functionally graded materials by means of strain energy density

The averaged strain energy density over a well‐defined control volume was employed to assess the fracture of U‐notched specimens made of tungsten–copper functionally graded materials under prevalent mode II loading. The boundary of control volume was evaluated by using a numerical method. Power law function was employed to describe the mechanical properties (elasticity modulus, Poisson's ratio, fracture toughness and ultimate tensile stress) through the specimen width. The effect of notch tip radius and notch depth on notch stress intensity factors and mode mixity parameter χ were assessed. In addition, a comparison based on fracture load between functionally graded and homogeneous W–Cu was made. Furthermore, in this research, it was shown that the mean value of the strain energy density over the control volume can be accurately determined using coarse meshes for functionally graded materials.     

Toughening due to domain switching in single crystal ferroelectric materials

In this paper Mode I steady state crack growth in single crystal ferroelectric materials is investigated. Specifically, the fracture toughness enhancement due to domain switching near a steadily growing crack tip is analyzed. For this purpose, an incremental phenomenological constitutive law for single crystal ferroelectric materials is implemented within a finite element model to calculate the stress and remanent strain fields around the crack tip. Also, the ratio of the far field applied energy release rate to the crack tip energy release rate, i.e. the toughening, is calculated. The numerical computations are carried out for single crystal ferroelectric materials of tetragonal or rhombohedral structure with different switching hardening and irreversible remanent strain levels. Toughening levels for crack growth along different crystallographic directions and planes are obtained and compared. Results from numerical computations for the toughening anisotropy for both tetragonal and rhombohedral crystals are presented and discussed.     

Viscoelastic Creep Crack Growth: A Review of Fracture Mechanical Analyses

The study of time dependent crack growth in polymers using a fracture mechanics approach has been reviewed. The time dependence of crack growth in polymers is seen to be the result of the viscoelastic deformation in the process zone, which causes the supply of energy to drive the crack to occur over time rather than instantaneously, as it does in metals. Additional time dependence in the crack growth process can be due to process zone behavior, where both the flow stress and the critical crack tip opening displacement may be dependent on the crack growth rate. Instability leading to slip-stick crack growth has been seen to be the consequence of a decrease in the critical energy release rate with increasing crack growth rate due to adiabatic heating causing are duction in the process zone flow stress, a decrease in the crack tip opening displacement due to a ductile to brittle transition at higher crack growth rates, or an increase in the rate of fracture work due to more rapid viscoelastic deformation. Finally, various techniques to experimentally characterize the crack growth rate as a function of stress intensity have been critiqued. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fracture response of fibre-reinforced materials with macro/microcrack damage using the Boundary Element Technique

The Boundary Element Method (BEM) incorporating the Embedded Cell Approach (ECA) has been used to analyse the effects of constituent material properties, fibre spatial distribution and microcrack damage on the localised behaviour of transversely fractured, unidirectional fibre-reinforced composites. Three specific composites, i.e., glass fibre reinforced polyester, carbon fibre reinforced epoxy and a glass-carbon hybrid, are considered. The geometrical structures examined were perfectly periodic, uniformly spaced fibre arrangements in square and hexagonal embedded cells. In addition, numerical simulations were also conducted using embedded cells containing randomly distributed fibres. The models involve both elastic fibres and matrix, with the interfaces between the different phases being fully bonded. The results indicate that the constituent material properties (two phase composite) and spatial distribution have a significant effect on the localised stress distributions around the primary crack tip. However, the strain energy release rate associated with crack propagation is predominantly influenced by the material composition. The three-phase hybrid composite exhibited an apparent intermediate fracture toughness value, compared to the all-glass and all-carbon models. Furthermore, the strain energy release rate for the macrocrack lowers as it enters a zone of localised damage (microcracking). The presence of microcracks relaxes the stress field, which can result in a significant reduction in the energetics of the primary crack.     

A solution method for finding dynamic stress intensity factors for arbitrarily oriented cracks in transversely isotropic materials

The transient elastodynamic response of a transversely isotropic material containing a semi-infinite crack under uniform impact loading on the faces is examined. The crack lies in a principle plane of the material, but the crack front does not coincide with a principle direction. Rather, the crack front is at an angle to a principle direction and thus the problem becomes more three-dimensional in nature. Three loading modes are considered, i.e., opening, in-plane shear and anti-plane shear. The solutions for the stress intensity factor history around the crack tip are found. Laplace and Fourier transforms together with the Wiener-Hopf technique are employed to solve the equations of motion directly. The asymptotic expression of stress near the crack tip leads to a closed-form solution for the dynamic stress intensity factor for each loading mode. It is found that the stress intensity factors are proportional to the square root of time as expected. Results given here converge to known solutions in transversely isotropic materials with a crack oriented along a principle direction and isotropic materials as special cases. The results of this analysis are used to find approximate strain energy release rates for dynamically loaded penny shaped cracks.