Analytical representation of the non-square-root singular stress field at a finite angle sharp notch

The stress field near the tip of a finite angle sharp notch is singular. However, unlike a crack, the order of the singularity at the notch tip is less than one-half. Under tensile loading, such a singularity is characterized by a generalized stress intensity factor which is analogous to the mode I stress intensity factor used in fracture mechanics, but which has order less than one-half. By using a cohesive zone model for a notional crack emanating from the notch tip, we relate the critical value of the generalized stress intensity factor to the fracture toughness. The results show that this relation depends not only on the notch angle, but also on the maximum stress of the cohesive zone model. As expected the dependence on that maximum stress vanishes as the notch angle approaches zero. The results of this analysis compare very well with a numerical (finite element) analysis in the literature. For mixed-mode loading the limits of applicability of using a mode I failure criterion are explored.     

压应力场中爆生裂纹分布与扩展特征实验分析

采用动静组合加载实验装置和数字激光焦散线实验系统,进行了0、3、6、9 MPa等4种压应力场中PMMA试件的爆破致裂实验,分析了沿静态主应力方向扩展的裂纹运动学和力学行为。实验结果表明:首先,静态竖向载荷在预制炮孔周围产生应力集中,在炮孔壁上下端部处出现最大拉应力;随后,在动态爆炸载荷的叠加作用下,裂纹优先在炮孔壁上最大拉应力位置处起裂,并沿最大主应力方向扩展;裂纹扩展过程中,静态竖向载荷越大,裂纹扩展速度越大,且裂纹尖端应力强度因子值越大。     

Fictitious Notch Rounding approach of pointed V-notch under in-plane shear

The Fictitious Notch Rounding approach (FNR) is applied here for the first time to V-shaped notches under in-plane shear loading. The fictitious radius is evaluated for different opening angles as a function of the Microstructural Characteristic Length (MCL), the actual radius and the failure hypothesis. A multiaxiality factor is introduced and found to be very sensitive to the opening angle. Under mode II loading, the problem is more complex than under mode I and mode III, mainly because the maximum elastic stress is outside the notch bisector line. The main problem is the choice of the expected crack initiation angle, which defines the direction where the relevant stress has to be integrated. This integration carried out over the MCL gives the effective stress value for the pointed V-notch. To this end, two different criteria are used, the Maximum Tangential Stress (MTS) criterion and the Minimum Strain Energy Density criterion (MSED). A large number of finite element analyses have been carried out to determine the multiaxiality factor. This factor has been evaluated by comparing the theoretical stress concentration factor (SCF) obtained from fictitiously rounded notches to the effective stress concentration factor obtained by integrating the relevant stress over the Microstructural Characteristic Length.     

Photoelastic validation of a theoretical solution for an edge cracked disk

In this paper, the theoretical solution developed by Vaughan and Wu for the stress analysis of a circular disk with a radial edge crack extending to its center is validated by photoelasticity. The photoelastic results include the fullfield isochromatics as well as measurements of the maximum shear stress at a number of test points. Additionally, the experimental stress intensity factor is extracted from the photoelastic data by Irwin's two-parameter method. Good agreement is observed when the theoretical stress field and stress intensity factor are compared with the experimental results. It is concluded that the Vaughan-Wu solution can be confidently applied in fracture mechanics analyses. The application of such a solution to the stress analysis of two-dimensional bodies with complex geometries subjected to complex loading is also noted.     

高应变率下断裂韧性实验的数值模拟

采用有限元软件ANSYS/LS-DYNA程序对静态和冲击荷载作用下的含裂纹半圆弯曲(SCB)实验进行了数值模拟。根据静态实验的模拟结果,提出了适合复合型加载的Ⅰ型应力强度因子拟合公式,采用该公式计算应力强度因子的最大误差不超过10%。动态实验的模拟结果表明:对于纯Ⅰ型加载的SCB实验,动态应力强度因子随着试样半径、支座间距以及相对裂纹长度的变化呈现规律性变化;当试样半径小于60mm、相对支座间距为1.2、相对裂纹长度在0.1~0.4范围内时,惯性效应的影响较小,采用静态拟合公式计算裂尖的动态应力强度因子的误差约10%;对于复合型加载的SCB实验,当相对裂纹长度为0.2~0.4、裂纹倾角在10°~40°范围内时,采用静态拟合公式计算裂尖的动态应力强度因子的误差小于10%。     

SH波作用下界面任意形状孔洞附近的动应力集中

采用Green函数和复变函数法求解了平面SH波在界面任意形状孔洞上的散射问题.首先,取含有任意形状凹陷的弹性半空间,在其水平表面上任意一点承受时间谐和的反平面线源荷载作用时的位移场作为Green函数.然后,按契合方式构造出界面任意形状孔洞对SH波的散射模型,利用所得Green函数按界面位移连续条件建立求解问题的定解积分方程组,求解界面孔附近的动应力集中系数. 最后,给出了界面上椭圆孔和方孔边缘动应力集中系数的数值结果,并讨论了不同介质参数和孔洞形状对孔附近动应力集中系数的影响.     

Shape optimization of the hole in an orthotropic plate

The exploration in this work is how to minimize the stress concentration around the edge of the hole in an orthotropic plate. The study first presents the analytical solution of the stress distribution around arbitrary holes using the complex variable method and then carries out the shape optimization using the mixed penalty function method. In the optimization process, optimal holes and stress distributions under the different factors are investigated, i.e., the loading, the Young’s modulus, and the fiber direction. Finally, we come to the conclusion that in the biaxial compressive load state, the shape and the stress are mainly affected by the loading, followed by the fiber direction and the Young’s modulus. In the pure shear condition, all three factors determine the optimum results.     

Pre-kinking of a moving crack in a magnetoelectroelastic material under in-plane loading

A constant moving crack in a magnetoelectroelastic material under in-plane mechanical, electric and magnetic loading is studied for impermeable crack surface boundary conditions. Fourier transform is employed to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. Steady-state asymptotic fields near the crack tip are obtained in closed form and the corresponding field intensity factors are expressed explicitly. The crack speed influences the singular field distribution around the crack tip and the effects of electric and magnetic loading on the crack tip fields are discussed. The crack kinking phenomena is investigated using the maximum hoop stress intensity factor criterion. The magnitude of the maximum hoop stress intensity factor tends to increase as the crack speed increases.     

Stress concentration due to an array or hemispherical cavities at the surface of an elastic half-space

The paper investigates the perturbation in an otherwise uniform stress field in an elastic half-space due to a doubly-periodic array of small hemispherical holes at the free surface. The solution is obtained using three potential functions of double Fourier series form in Galerkin's strain potential solution, the coefficients of which are determined using the collocation method. The unperturbed field is taken to be one of uniform plane stress parallel to the free surface. Two special cases are studied—uniform tension and uniform shear stress. Numerical results for these cases can be generalized by superposition to give solutions for a general state of biaxial plane stress. It is found that, for both tension and shear, the maximum stress concentration occurs at the bottom of the holes. The stress concentration factor increases with the ratio of hole spacing to radius, approaching the known solution for a single hemispherical hole at large ratios.     

Influence of reinforcement arrangement on the local reinforcement stresses in composite materials

The state of stress in and around reinforcements governs a number of physical processes in composite (multi-phase) materials, including the initiation of damage by either reinforcement cracking or interfacial decohesion. The stresses in the reinforcements have been observed to depend on the spatial distribution of the reinforcements, although the exact correlation is unclear. The present work determines the reinforcement stress for different reinforcement arrangements, ranging from a linear array of three uniformly spaced particles, to random and clustered microstructures. The stress calculations for elastic matrices were undertaken using a computationally efficient iterative technique. The technique was validated by comparing the results to finite element models, and the range of validity was determined. For the three-particle arrangements, the maximum reinforcement stress was observed when the particles were close to each other along the line of loading (a vertical arrangement). On the other hand, when the particle arrangement made a large angle with the loading direction, the reinforcement stress was low. Similar observations were recorded for the random and clustered arrangements where the location of the maximum reinforcement stress coincided with a vertical arrangement. The present work also develops a scheme for determining ‘representative volume elements’ for composite micromechanical models, based on the length scales of stress field interactions. These observations can be used to rationalize damage evolution mechanisms in commercial composites, and aid the development of physically based failure models for such materials.     

Detection of stress concentration regions in cyclic loading by the heat monitoring method

We present a method for determining stress concentration regions in structures under multiply repeated cyclic loads. To determine the stress concentration regions, we propose to stabilize the structure temperature characteristics before the cyclic loading and then, in the process of cyclic loading, measure the structure temperature field by thermal imaging equipment with subsequent analysis and processing of the obtained thermograms. The stress concentrations regions in the structures correspond to anomalous regions of thermograms, where the temperature excess is more than 0.3° C, and hence the stress concentration regions are clearly seen in the thermograms.     

SH波作用下地表软覆盖层中圆形夹杂的动应力分析

利用复变函数法和波函数展开法, 对地表软覆盖层中浅埋圆形夹杂在稳态SH波作用下的动应力集中问题进行研究并给出了解析解。根据SH波散射时的衰减特性, 采用了大圆弧假定的方法, 将半空间覆盖层直线边界问题转化为曲面边界问题。通过算例分析了SH波垂直入射时, 不同入射波波数和圆夹杂与半空间的波数比对圆形夹杂周边动应力集中因子的分布和动应力集中因子最大值变化的影响。算例表明, 圆形夹杂越“软”, 其波数越大, 夹杂周边的动应力集中因子越大; 入射波波数约0.35时, 夹杂周边的最大动应力集中因子达到最大值。

     

Theoretical analysis and digital photoelastic measurement of circular disks subjected to partially distributed compressions

The disk in diametral compression has been quoted most frequently on developing conventional/digital photoelasticity to illustrate new theories and experimental techniques for several decades. Theoretically, the compression as a concentrated force is more conducive to analysis, but it is impossible to achieve such loading condition experimentally. The distributed compression on a finite area at rim is relatively closer to actual testing and it is complicated to seek an analytical solution. In this paper, we extend the work of Hondros to derive the full-field stress distribution of disk subjected to diametral distributed compression in an explicit functional form. The principal stress difference and principal stress orientation related to isochromatic and isoclinic fringes, respectively, are also expressed in a simple closed form. The maximum shear stress for the whole disk and the validity of using isochromatic fringes to interpret the maximum shear stress are discussed in detail. The isoclinic fringes are compared with theory, and the fringe multiplication isochromatic is compared with simulated image. All of the comparisons are in good agreement with respect to full field.     

I-II复合型裂缝断裂角的分层剪滞模型与分析

采用修正的剪滞理论建立了岩石、混凝土等准脆性材料的I-II复合型裂缝在单向拉伸荷载作用下的计算模型,得到了与实验相吻合且优于传统S判据的断裂角。通过对远场应力、斜裂缝区应力以及子层位移的合理简化,得到了求解剪滞分析模型的边界条件,进而得到了含斜裂缝的各子层位移分布函数。引入最大应力集中因子,对I-II复合型裂缝前缘应力场进行简化;基于斜裂缝沿最大应力集中因子方向扩展,得到裂缝的断裂角。根据斜裂缝的应力分布,设置不同的子层分区,得到了更为细化的位移分布模式。通过对计算数据的分析,针对单向拉伸荷载作用下的I-II复合型裂缝,建立了按应力场分区设置子层的分层剪滞模型,得到更为精确的斜裂缝断裂角。     

A variational model for stress analysis in cracked laminates with arbitrary symmetric lay-up under general in-plane loading

The present research work presents a variational approach for stress analysis in a general symmetric laminate, having a uniform distribution of ply cracks in a single orientation, subject to general in-plane loading. Using the principle of minimum complementary energy, an optimal admissible stress field is derived that satisfies equilibrium, boundary and traction continuity conditions. Natural boundary conditions have been derived from the variational principle to overcome the limitations of the existing methodology on the analysis of general symmetric laminates. Thus, a systematic way to formulate boundary value problem for general symmetric laminates containing many cracked and un-cracked plies has been derived, and appropriate mathematical tools can then be employed to solve them. The obtained results are in excellent agreement with the available results in the literature. In the field of matrix cracks analysis for symmetric laminates, the present formulation is the most complete variational model developed so far.     

爆炸载荷下板条边界斜裂纹的动态扩展行为

为了研究爆炸应力波作用下板条边界斜裂纹的动态扩展行为,首先分析了爆炸应力波在含边界斜裂纹板条中的传播,其次采用动态焦散线实验方法,进行了爆炸载荷下板条边界斜裂纹扩展规律的实验研究.研究结果表明,爆炸应力波作用下,板条试件边界斜裂纹的扩展过程中,裂纹扩展速度、扩展加速度和裂尖动态应力强度因子随时间波动变化,扩展速度最大值...     

具有界面相的球形粒子在无限大基体中的应力集中分析

研究了无限大基体内具有界面相的球形粒子在轴对称载荷作用下的应力场,并与线弹簧界面模型的情形进行了比较,对粒子/界面相以及界面相/基体两个界面的应力集中系数以及粒子内部的应力集中系数进行了分析研究了应力三轴度、界面相厚度以及三相的模量对应力集中系数的影响结果表明,对给定的模量和界面相厚度值,存在一个临界应力三轴度值若应力三轴度小于此临界值,则界面相/基体界面的应力集中系数大于粒子/界面相界面的应力集中系数;否则,前者会小于后者所做的应力分析可以为颗粒增强复合材料的强韧化设计提供一定参考.     

Note on arc crack experiencing slip

Under certain loading conditions a crack surface may undergo partial sliding (slip). Such slip may be triggered by non-uniformity of frictional characteristics along the crack surface, variability of applied stresses or curvilinearity of a crack path. In the present work we study the influence of a curvilinear shape of a crack on slip evolution. The analysis is carried out for the case of a two-dimensional circular arc crack. Initiation and propagation of a slip zone is investigated based on the criterion that the shear stress intensity factor vanishes at endpoints of the slip zone. Two case scenarios are studied: first, when slip is attributed to the non-uniform distribution of a coefficient of friction and, second, when slip is initiated by the far field compressive loads. The curvilinear effects are estimated by comparing the obtained solutions with the ones for a straight crack. Analytical expressions for the stress intensity factors (SIFs) derived in this work may also present certain interest of their own.     

THREE-DIMENSIONAL ANALYSIS OF A MAGNETOELECTROELASTIC HALF-SPACE UNDER AXISYMMETRIC TEMPERATURE LOADING 1)

考虑力-电-磁-热等多场耦合作用, 基于线性理论给出了磁-电-弹性半空间在表面轴对称温度载荷作用下的热-磁-电-弹性分析, 并得到了问题的解析解. 利用Hankel 积分变换法求解了磁-电-弹性材料中的热传导及控制方程, 讨论了在磁-电-弹性半空间在边界表面上作用局部热载荷时的混合边值问题, 利用积分变换和积分方程技术, 通过在边界表面上施加应力自由及磁-电开路条件, 推导得到了磁-电-弹性半空间中位移、电势及磁势的积分形式的表达式. 获得了磁-电-弹性半空间中温度场的解析表达式并且给出了应力, 电位移和磁通量的解析解. 数值计算结果表明温度载荷对磁-电-弹性场的分布有显著影响. 当温度载荷作用的圆域半径增大时, 最大正应力发生的位置会远离半无限大体的边界; 反之当温度载荷作用的圆域半径减小时, 最大应力发生的位置会靠近半无限大体的边界. 电场和磁场在温度载荷作用的圆域内在边界表面附近有明显的强化, 而磁-电-弹性场强化区域的强化程度跟温度载荷的大小和作用区域大小相关. 本研究的相关结果对智能材料和结构在热载荷作用下的设计和制造具有指导意义.