The roles of toughness and cohesive strength on crack deflection at interfaces

In order to design composites and laminated materials, it is necessary to understand the issues that govern crack deflection and crack penetration at interfaces. Historically, models of crack deflection have been developed using either a strength-based or an energy-based fracture criterion. However, in general, crack propagation depends on both strength and toughness. Therefore, in this paper, crack deflection has been studied using a cohesive-zone model which incorporates both strength and toughness parameters simultaneously. Under appropriate limiting conditions, this model reproduces earlier results that were based on either strength or energy considerations alone. However, the general model reveals a number of interesting results. Of particular note is the apparent absence of any lower bound for the ratio of the substrate to interface toughness to guarantee crack penetration. It appears that, no matter how tough an interface is, crack deflection can always be induced if the strength of the interface is low enough compared to the strength of the substrate. This may be of significance for biological applications where brittle organic matrices can be bonded by relatively tough organic layers. Conversely, it appears that there is a lower bound for the ratio of the substrate strength to interfacial strength, below which penetration is guaranteed no matter how brittle the interface. Finally, it is noted that the effect of modulus mismatch on crack deflection is very sensitive to the mixed-mode failure criterion for the interface, particularly if the cracked layer is much stiffer than the substrate.     

Nanoparticle debonding strength: A comprehensive study on interfacial effects

The most appealing feature of nanofilled polymers is the perspective of obtaining surprisingly high mechanical properties at low nanofiller volume fractions. The knowledge of nanostructure–property relationships is however essential for the design of these materials.In the present work, a model for the critical hydrostatic tension related to nanoparticle debonding is presented. The model accounts for some important issues inherently related to the nanoscale with particular reference to surface elastic stresses on the nanoparticle periphery and the emergence of a zone of altered chemistry surrounding the nanoparticle. The analytical solution suggests that the range of nanoparticle radii where interfacial effects do affect the solution is limited to the nanometer scale. In more details, considering the interphase and surface elastic properties used in the analysis, it has been found that for stiff particles with radius between 10 nm and 100 nm (silica, alumina and other metal oxide nanoparticles) the prominent role is played by the interphase elastic properties. Surface elastic constants were found to have, instead, only a negligible effect.     

适用于自洽强度方法的冲击加载-再加载实验技术

针对自洽强度方法存在的冲击加载-再加载的难题,提出了一种采用较高硬度材料为支撑制作组合飞片的简便方法。利用该方法获得了铝、锡和锆基金属玻璃较理想的冲击加载-再加载粒子速度剖面,验证了该方法的有效性。由本文获得的冲击加载-再加载粒子速度剖面,并根据自洽方法,计算得到了铝、锡和锆基金属玻璃再加载过程剪应力变化数据。进一步分析表明,在本文涉及的压力范围内,仅由冲击加载-卸载实验得到的铝、锡和锆基金属玻璃屈服强度将比实际结果降低20%~50%。因此,在采用自洽方法计算高压强度时,冲击加载-再加载数据不可或缺。     

A relationship between effective work of adhesion and peel force for thin hyperelastic films undergoing large deformation

A method to determine the effective work of adhesion for hyperelastic thin films undergoing large deformations is presented. Starting from energy balance equation a relationship between work of adhesion, the peel force, the peel angle, and the stretch is derived. Based on this relation a procedure to compute the energy of adhesion from peel tests is proposed. To this end the peel force as well as the engineering stress vs. engineering strain diagram for thin film is required. The derived relationship shows that the non-linearity of the stress-stain relation must be taken into account in computing the effective work of adhesion from the peel force. The processing of experimental data within the standard linear elasticity approach would lead to an overestimation of effective work of adhesion. The error would increase with a decrease of the peel angle.     

A simple method for compressible multiphase mixtures and interfaces

We develop a Godunov‐type scheme for a non‐conservative, unconditional hyperbolic multiphase model. It involves a set of seven partial differential equations and has the ability to solve interface problems between pure materials as well as compressible multiphase mixtures with two velocities and non‐equilibrium thermodynamics (two pressures, two temperatures, two densities, etc.).Its numerical resolution poses several difficulties. The model possesses a large number of acoustic and convective waves (seven waves) and it is not easy to upwind all these waves accurately and simply. Also, the system is non‐conservative, and the numerical approximations of the corresponding terms need to be provided. In this paper, we focus on a method, based on a characteristic decomposition which solves these problems in a simple way and with good accuracy. The robustness, accuracy and versatility of the method is clearly demonstrated on several test problems with exact solutions. Copyright © 2003 John Wiley & Sons, Ltd.     

一种投影浸入边界法的快速直接求解方法

根据投影浸入边界法分步投影求解的特点,同时针对压力泊松方程离散后的大型稀疏线性方程组是非奇异非对称的特点,结合开源函数库UMFPACK,在传递线性方程组的系数矩阵和右端向量时,采用函数库Eigen将系数矩阵的数据结构改写优化,大大降低了存储空间,实现对高维大型稀疏线性方程组的快速求解,同时求解保持良好的稳定性。本文首先利用一具有解析解的数值算例验证了求解泊松方程数值方法的准确性和网格依赖性,进而利用VC++编写投影浸入边界法的数值计算程序,以单圆柱绕流为基准数值算例,通过与其他文献和实验结果的对比,验证了投影浸入边界法数值计算结果的可靠性,并进一步分析了不同雷诺数下圆柱绕流的流场结构特征和尾涡结构的动态演化过程。     

结构强度可靠性分析的模糊随机边界元法

利用模糊随机变量和模糊概率特征建立模糊随机边界元代数方程，对方程作λ水平截集，得到随机区间方程，将该方程中的系数矩阵，结点位移列阵和荷载列车在初始随机向量的均值处展开，利用区间数分解和小参数摄动理论导出求解应力统计特征、结构破坏概率指标和可靠度的计算公式，并给出算例。     

结构系统静强度与断裂的综合可靠性分析

基于疲劳载荷作用下裂纹扩展的随机性,建立了结构系统综合考虑静强度和断裂的可靠性分析方法,该方法给出了元件静强度失效时所对应的当量寿命,并建立了元件综合失效判别准则,分析了元件静强度失效和断裂失效之间的相关性.算例表明,随使用年限的增加,元件静强度失效和断裂失效之间的相关性也在增加;在不同的使用年限内,结构系统主要失效路径是不同的,并且在结构系统主要失效路径中既有元件静强度失效又有元件断裂失效;若只考虑静强度或断裂的结构可靠性分析,分析结果偏于危险.     

A moving discontinuous Galerkin finite element method for flows with interfaces

A moving discontinuous Galerkin finite element method with interface condition enforcement is formulated for flows with discontinuous interfaces. The underlying weak formulation enforces the interface condition separately from the conservation law, so that the residual only vanishes upon satisfaction of both. In this formulation, the discrete grid geometry is treated as a variable, so that, in contrast to the standard discontinuous Galerkin method, this method has both the means to detect interfaces, via interface condition enforcement, and to satisfy, via grid movement, the conservation law and its associated interface condition. The method therefore directly fits interfaces, including shocks, preserving a high-order representation up to the interface without requiring shock capturing or an upwind numerical flux to achieve stability. It can be generalized to flows with a priori unknown interfaces with nontrivial topology and curved interface geometry as well as to an arbitrary number of spatial dimensions. Unsteady flows are represented in a manner similar to steady flows using a space-time formulation. In addition to computing flows with interfaces, the method can represent point singularities in a flow field by degenerating cuboid elements. In general, the method works in conjunction with standard local grid operations, including edge collapse, to ensure that degenerate cells are removed. Test cases are presented for up to three-dimensional flows that provide an initial assessment of the stability and accuracy of the method.     

A reconstructed discontinuous Galerkin method for multi-material hydrodynamics with sharp interfaces

Discontinuous Galerkin (DG) methods have been well established for single-material hydrodynamics. However, consistent DG discretizations for non-equilibrium multi-material (more than two materials) hydrodynamics have not been extensively studied. In this work, a novel reconstructed DG (rDG) method for the single-velocity multi-material system is presented. The multi-material system being considered assumes stiff velocity relaxation, but does not assume pressure and temperature equilibrium between the multiple materials. A second-order DG(P₁) method and a third-order least-squares based rDG(P₁P₂) are used to discretize this system in space, and a third-order total variation diminishing (TVD) Runge-Kutta method is used to integrate in time. A well-balanced DG discretization of the non-conservative system is presented and is verified by numerical test problems. Furthermore, a consistent interface treatment is implemented, which ensures strict conservation of material masses and total energy. Numerical tests indicate that the DG and rDG methods are, indeed, the second- and third-order accurate. Comparisons with the second-order finite volume method show that the DG and rDG methods are able to capture the interfaces more sharply. The DG and rDG methods are also more accurate in the single-material regions of the flow. This work focuses on the general multidimensional rDG formulation of the non-equilibrium multi-material system and a study of properties of the method via one-dimensional numerical experiments. The results from this research will be the foundation for a multidimensional high-order rDG method for multi-material hydrodynamics.     

提高飞机着陆气动性能的一种新方法探索研究

提出了一种新型气动技术,其主要原理是:将机翼上表面的一部分翼面设计为活动翼面,当飞机进入降落阶段、迎角较大时,适当抬高该活动翼面,从而在该活动翼面后形成一个台阶,通过台阶中产生的稳定驻涡来控制机翼上表面的流动;与此同时,打开安装在机翼上的Gurney襟翼,可达到同时提高机翼升力和失速迎角的目的。将该技术在DLR-F4上应用,数值模拟结果表明:机翼的最大升力系数提高了17.37%;失速迎角从11°提高到13°,提高了18.18%。本文为提高飞机的着落性能探索出一种具有发展潜力的方法。     

A simple technique for determining yield strength of thin films

A technique to measure the yield strength of thin films has been developed which combines experimental observations of deflection and plastic deformation with finite element predictions of stress. This technique relies on integrated circuit technology to build bridge and cross beam test structures with a range of dimensions. Each structure is deflected in increments of 1 μm until the structure no longer elastically recovers upon release. In tandem with experimentally verified numerical predictions of force and stress, the yield strength of the thin film can be bounded between the highest elastic stress result and the lowest plastic stress result. For our test material of copper, this method provides a yield strength between 2.80 and 3.09 GPa, a value significantly larger than that for bulk copper, but consistent with thin film theory.     

A novel method for residual strength prediction for sheets with multiple site damage: Methodology and experimental validation

A unified method for solving the strip yield model for collinear cracks in finite and infinite sheet is proposed. The method is based on the weight function of a single crack. Two collinear cracks in finite and infinite sheets are used to apply and verify this method. The plastic zone size, crack opening displacement and stress distribution along the ligament between cracks obtained by using the present method are extensively compared with existing available results and finite element solutions, and very good agreements are observed. Combined with the Crack Tip Opening Angle (CTOA) criterion, the unified method is used to predict the crack growth behavior and residual strength for 2024-T3 aluminum alloy sheet with Multiple Site Damage (MSD). Thirty-two sheets with four types of MSD are designed and tested to verify this method. It is shown that the present method is able to predict various crack growth behaviors observed in experiment. The predicted residual strengths are within 9% of the corresponding test results. Compared to the elastic–plastic finite element method, the present method is much more efficient.     

混凝土类材料动态拉伸强度的微观力学模型

基于水泥砂浆试样动态劈裂拉伸实验,研究了不同加载速率下水泥砂浆材料动态劈裂时的裂纹发 生和扩展规律,提出一个微观力学模型。结果表明,微裂纹惯性是混凝土类材料动态拉伸实验中测量到的动 态拉伸强度随应变率的增加而提高的一种微观机制。     

A height–flux method for simulating free surface flows and interfaces

A new technique for the numerical simulation of the free surface flows is developed. This technique is based on the finite element method with penalty formulation, and a flux method for surface advection. The advection part which is completely independent of the momentum solver is based on subdividing the fluid domain into small subvolumes along one of the co-ordinate axis. The subvolumes are then used to find the height function which will later describe the free surface. The free surface of the fluid in each subvolume is approximated by a line segment and its slope is calculated using the volume of the fluid in the two neighbouring subvolumes. Later, the unidirectional volume flux from one subvolume to its neighbouring one is calculated using the conservation laws, and the new surface line segments are reconstructed. This technique, referred to as the Height–Flux Method (HFM) is implemented to simulate the temporal instability of a capillary jet. The results of the numerical simulation well predict the experimental data. It is also shown that the HFM is computationally more efficient than the techniques which use a kinematic boundary condition for the surface advection.     

A relaxation method for the energy and morphology of grain boundaries and interfaces

The energy density of crystal interfaces exhibits a characteristic “cusp” structure that renders it non-convex. Furthermore, crystal interfaces are often observed to be faceted, i.e., to be composed of flat facets in alternating directions. In this work, we forge a connection between these two observations by positing that the faceted morphology of crystal interfaces results from energy minimization. Specifically, we posit that the lack of convexity of the interfacial energy density drives the development of finely faceted microstructures and accounts for their geometry and morphology. We formulate the problem as a generalized minimal surface problem couched in a geometric measure-theoretical framework. We then show that the effective, or relaxed, interfacial energy density, with all possible interfacial morphologies accounted for, corresponds to the convexification of the bare or unrelaxed interfacial energy density, and that the requisite convexification can be attained by means of a faceting construction. We validate the approach by means of comparisons with experiment and atomistic simulations including symmetric and asymmetric tilt boundaries in face-centered cubic (FCC) and body-centered cubic (BCC) crystals. By comparison with simulated and experimental data, we show that this simple model of interfacial energy combined with a general microstructure construction based on convexification is able to replicate complex interfacial morphologies, including thermally induced morphological transitions.     

A novel robust design method for improving stability of optimized structures

It is known that structural optimization may lead to designs of structures having low stability and sometimes even kinematically unstable designs. This paper presents a robust design method for improving the stability of optimized structures. A new approach is proposed, in which certain perturbation loads are introduced and the corresponding compliance is added to the objective function as a penalization. The stability of the optimized structures can thus be improved substantially by considering structural responses to the original and the introduced loads. Numerical examples show the simplicity and effectiveness of the proposed method.     

双屈服面法测量金属材料动高压屈服强度的若干改进

在J.R.Asay等提出的双屈服面法（简称AC方法）测量动态屈服强度的基础上,对实验设计和数据处理做了部分改进。在实验设计方面,在满足实验物理设计的前提下,将 AC方法的卸载实验装置(双层飞片和双台阶样品)简化为单飞片和单台阶样品,以简化波系作用,并减少了声速测量不确定度的引入因素。在数据处理方面,发现由Lagrange声速和工程应变关系曲线外推求预冲击态的体积声速容易引入较大的不确定度,而通过Lagrange声速和粒子速度关系曲线可以更清晰地得到塑性卸载起始点,使图解法和积分法得到的屈服强度值趋于一致。利用改进后的AC方法,得到了低温退火后LY12铝在20.0 GPa预冲击压力下的屈服强度为0.6 GPa。     

A hybrid model for computationally efficient fatigue fracture simulations at microelectronic assembly interfaces

Modern microelectronic assemblies are heterogeneous, layered structures joined by interconnects made of solder alloys with low homologous temperatures. The solder interconnections join devices to circuit boards and they fail by thermal fatigue fracture at their interfaces either to the device or to the circuit board. Predicting the fatigue fracture of the solder interconnections is a challenge due to the fact that they undergo large inelastic deformations during temperature cycling tests. In this paper we develop a hybrid approach inspired by cohesive zone fracture mechanics and the Disturbed State Concept to predict the crack trajectory and fatigue life of a solder interconnection subjected to both isothermal temperature cycling and anisothermal temperature cycling conditions (representing the two common accelerated test conditions for microelectronic products). A hybrid computational approach is used in which a first order approximation of the disturbance is used to estimate incremental cycles to criticality and thereby propagate the crack. The modeled crack fronts and the fatigue lives are validated through a comparison to results from the two types of accelerated tests. Overall, the model is shown to predict the fatigue life of the critical interconnection in the assembly to within 20% of the experimentally determined life. More importantly, the predicted crack trajectory is demonstrated to agree very well with the experimentally observed trajectory. Strikingly, the microscopically observed microstructural changes during crack propagation from that corresponding to creep fatigue to that of shear overload were found to be excellently correlated with the rate of change of the disturbance calculated in the model.