Fracture parameters of a penny-shaped crack at the interface of a piezoelectric bi-material system

A penny-shaped crack at the interface of a piezoelectric bi-material system is considered. Analytical general solutions based on Hankel integral transforms are used to formulate the mixed-boundary value problem corresponding to an interfacial crack and the problem is reduced to a system of singular integral equations. The integral equations are further reduced to two systems of algebraic equations with the aid of Jacobi polynomials and Chebyshev polynomials. Thereafter, the exact expressions for the stress intensity factors and the electric displacement intensity factor at the tip of a crack are obtained. Selected numerical results are presented for various bi-material systems to portray the significant features of crack tip fracture parameters and their dependence on material properties, poling orientation and electric loading.     

Analysis of multiple interfacial cracks in an orthotropic bi-material subjected to anti-plane shear loading

The present work concerns with the elasto-static problem of double interfacial cracks located between two dissimilar orthotropic plates. The dimensions of the bi-material composite, are assumed to be finite. The crack faces are subjected to anti-plane shear traction. Finite Fourier transforms are applied to reduce the problem to a triple series equations, and then to a system of singular integral equations with Cauchy type singularity. That are solved numerically using Gauss-Chebyshev integration formulae. The stress intensity factors, are determined in a closed form expressions. The obtained results agreed with the previous analytical ones. Further, a parametric study is introduced to investigate the effects of the geometric and elastic characteristics of the composite on the values of the stress intensity factors.     

Numerical simulation of crack deflection and penetration at an interface in a bi-material under dynamic loading by time-domain boundary element method

The hybrid time-domain boundary element method (BEM), together with the multi-region technique, is applied to simulate the dynamic process of crack deflection/ penetration at an interface in a bi-material. The whole bi-material is divided into two regions along the interface. The traditional displacement boundary integral equations (BIEs) are employed with respect to the exterior boundaries; meanwhile, the non-hypersingular traction BIEs are used with respect to the part of the crack in the matrix. Crack propagation along the interface is numerically modelled by releasing the nodes in the front of the moving crack tip and crack propagation in the matrix is modeled by adding new elements of constant length to the moving crack tip. The dynamic behaviours of the crack deflection/penetration at an interface, propagation in the matrix or along the interface and kinking out off the interface, are controlled by criteria developed from the quasi-static ones. The numerical results of the crack growth trajectory for different inclined interface and bonded strength are computed and compared with the corresponding experimental results. Agreement between numerical and experimental results implies that the present time-domain BEM can provide a simulation for the dynamic propagation and deflection of a crack in a bi-material.     

Cohesive zone modeling of interface fracture in elastic bi-materials

Some basic issues regarding the cohesive zone modeling of interface fracture between two dissimilar elastic materials are studied. The dependence of the cohesive energy density on the phase angle is first discussed under small scale cohesive zone conditions. It is then shown that in general the stress singularities in tension and shear cannot be simultaneously removed at the cohesive zone tip if a single cohesive zone length is adopted for both tensile and shear fracture modes. Finally, the energy dissipation at the tip of a prescribed cohesive zone is examined using a bilinear cohesive zone model under the uncoupled tension/shear conditions.     

Dynamic analysis of interfacial crack problems in anisotropic bi-materials by a time-domain BEM

A time-domain boundary element method (BEM) together with the sub-domain technique is applied to study dynamic interfacial crack problems in two-dimensional (2D), piecewise homogeneous, anisotropic and linear elastic bi-materials. The bi-material system is divided into two homogeneous sub-domains along the interface and the traditional displacement boundary integral equations (BIEs) are applied on the boundary of each sub-domain. The present time-domain BEM uses a quadrature formula for the temporal discretization to approximate the convolution integrals and a collocation method for the spatial discretization. Quadratic quarter-point elements are implemented at the tips of the interface cracks. A displacement extrapolation technique is used to determine the complex dynamic stress intensity factors (SIFs). Numerical examples for computing the complex dynamic SIFs are presented and discussed to demonstrate the accuracy and the efficiency of the present time-domain BEM.     

Meso-structural study of concrete fracture using interface elements. I: numerical model and tensile behavior

A recently developed FE-based mesostructural model for the mechanical behavior of heterogeneous quasi-brittle materials is used systematically to analyze concrete specimens in 2D. The numerical model is based on the use of zero-thickness interface elements equipped with a normal-shear traction-separation constitutive law representing non-linear fracture, which may be considered a mixed-mode generalization of Hillerborg’s “Fictitious Crack Model.” Specimens with 4 × 4 and 6 × 6 arrays of aggregates are discretized into finite elements. Interface elements are inserted along the main lines in the mesh, representing potential crack lines. The calculations presented in this paper consist of uniaxial tension loading, and the continuum elements themselves are assumed to behave as linear elastic. In this way, the influence of various aspects of the heterogeneous geometry and interface parameters on the overall specimen response has been investigated. These aspects are aggregate volume fraction, type of arrangement and geometry, interface layout, and values of the crack model parameters chosen for both the aggregate-aggregate and matrix-aggregate interfaces. The results show a good qualitative agreement with experimental observations and illustrate the capabilities of the model. In the companion second part of the paper, the model is used to represent other loading states such as uniaxial compression, Brazilian test, or biaxial loading.     

爆炸层状金属复合板的层裂问题研究

本文以冲击波的相互作用和反射规律,从理论上阐明了爆炸复合板产生层裂的原因,为确保爆炸焊接质量并对合理爆炸工艺的选择,作了有益的探讨。     

Quasi-static and dynamic fracture behavior of composite sandwich beams with a viscoelastic interface crack

Fracture analysis of sandwich beams with a viscoelastic interface crack under quasi-static and dynamic loading has been studied. Firstly, a three-parameter standard solid material model was employed to describe the viscoelasticity of the adhesive layer. And a novel interfacial fracture analysis model called three material media model was established, in which an interface crack was inserted in the viscoelastic layer. Secondly, a finite element procedure based on Rice J-integral and Kishimoto J-integral theories was used to analyze quasi-static and dynamic interface fracture behavior of the sandwich beam, respectively. Finally, the influence of viscoelastic adhesive layer on the quasi-static J-integral was discussed. In addition, comparison of quasi-static Rice J-integral with Kishimoto J-integral under various loading rates was carried out. The numerical results show that the oscillating characteristic of dynamic J-integral is more evident with shorter loading rise time.     

Study on crack propagation behavior in a quenched glass plate

Crack pattern transition and crack propagation behavior in a quenched glass plate are investigated. Theoretical analysis indicates that the distance between the crack tip and the cold front is closely related to the crack pattern transition. This theoretical result is examined experimentally using instantaneous phase-stepping photoelasticity. As expected theoretically, when the crack tip remains close enough to the cold front, crack propagation remains straight. When this distance reaches a given value, the crack oscillates. These experimental results are in good agreement with the theory of crack pattern transition. Therefore, present theoretical analysis is valid in predicting the instability of crack propagation. The crack tip stress field is also examined by the present experimental method. In particular, in the oscillating regime, the mode-I stress intensity factor frequently becomes larger than the fracture toughness, and the mode-II stress intensity factor has a nonzero value during propagation. For the former result, some reasons are discussed, but the cause of this problem is still unknown. However, the latter result can be explained by the theoretical analysis of an infinitesimal kinked edge crack just after crack initiation.     

Fracture behavior of nano-layered coatings under tension

The fracture of brittle/ductile multilayers composed of equal thicknesses of Si and Ag layers evaporated on a thick substrate is studied with the aid of a four-point bending apparatus. The system variables include individual layer thickness (2.5 to 30 nm), total film thickness (0.5 to 3.5 μm) and substrate material (polycarbonate, aluminum alloy and hard steel). The fracture is characterized by transverse cracks that proliferate with load. The crack initiation strain ε_i is virtually independent of total film thickness and substrate material while increasing with decreasing layer thickness h, to a good approximation as ε_i ~ 1/h^1/2. At higher strains, film debonding and buckling are evident.The fracture conditions are determined with the aid of a 2D finite element analysis incorporating the inelastic response of the interlayer. A fracture scenario consisting of tunnel cracking in the brittle layers followed by cracking in the interlayers is shown to be capable of predicting the observed increase in crack initiation strain with decreasing layer thickness. To realize this benefit the interlayer must be compliant and tough to force tunnel cracking in the brittle layers. The explicit relation for the crack initiation strain obtained from the analysis can be used to assess fracture toughness and improve damage tolerance in nanoscale layered structures.     

Coupled horizontal and rocking vibrations of a rigid circular plate on a transversely isotropic bi-material interface

This paper investigates the coupled rocking and horizontal vibratory response of a rigid circular plate embedded in viscoelastic, transversely isotropic, three-dimensional unbounded media. The boundary-value problem corresponding to the case of distributed horizontal and rocking ring loads at a bi-material interface is solved to obtain the required influence functions for the solution of the present problem. The case of an embedded rigid plate is formulated in terms of a discretized integral equation, which couples the rigid body displacements of the plate with the tractions acting over its contact surface through a set of displacement influence functions. The system of resulting discretized integral equations is solved numerically. The solution results in the tractions over each disc element. This paper carefully takes into account the coupling of the rocking and horizontal responses of the plates that is typical of non-homogeneous interfaces, i.e., their horizontal displacements due to rocking moments and their rotations due to horizontal loads. The dynamic direct and cross compliances of the embedded plate are shown for different governing parameters such as frequency of excitation and bi-material configuration. The present results are useful to the study of dynamic response of deeply buried foundations and anchors in non-homogeneous soils.     

板状构件粘结强度的非线性超声导波检测

相较于铆接、螺接、焊接等连接方式,板状粘结构件具有质量轻、应力分布均匀等特点,广泛运用于航空航天、车辆制造等工业领域。板状粘结构件在服役过程中出现的粘结强度退化、弱粘结等会影响其服役可靠性及安全性,因此对粘结强度进行检测十分必要。非线性超声导波对材料微观结构特征变化比较敏感,可用于粘结构件的粘结强度检测。采用非线性超声导波对铝合金-环氧树脂-铝合金板状构件进行检测,通过不同的固化工艺制备粘结结构件模拟不同粘结强度,检测结构件中传播的非线性超声导波,计算超声非线性参量,获得超声非线性参量在不同固化工艺下的变化趋势。通过拉伸实验测得粘结强度,进而构建超声非线性参量与粘结强度的关系。实验结果显示,粘结强度越大,超声导波的非线性参量越小。该研究表明,非线性超声导波可有效检测板状构件的粘结强度,为工业检测板状结构粘结强度提供了有效方法。     

Analysis of three-dimensional interface cracks using enriched finite elements

Many important interface crack problems are inherently three-dimensional in nature, e.g., debonding of laminated structures at corners and holes. In an effort to accurately analyze three-dimensional interface fracture problems, an efficient computational technique was developed that utilizes enriched crack tip elements containing the correct interface crack tip asymptotic behavior. In the enriched element formulation, the stress intensity factors K _I, K _II, and K _III are treated as additional degrees of freedom and are obtained directly during the finite element solution phase. In this study, the results that should be of greatest interest are obtained for semi-circular surface and quarter-circular corner cracks. Solutions are generated for uniform remote tension and uniform thermal loading, over a wide range of bimaterial combinations. Of particular interest are the free surface effects, and the influence of Dundurs’ material parameters on the strain energy release rate magnitudes and corresponding phase angles.     

Indentation-induced subsurface tunneling cracks as a means for evaluating fracture toughness of brittle coatings

When a plate glued to a compliant substrate is subject to indentation, cracks may initiate from its subsurface due to flexure. Upon increasing the load, the damage develops into a set of tunnel radial cracks which propagate stably under a diminishing stress field. This phenomenon is utilized here to extract fracture toughness K _C for brittle materials in the form of thin plates or films. Experiments show that the SIF at the tip of the subsurface radial cracks is well approximated as K ~ P/c ^3/2, where P is the indentation load and c the mean length of the crack fragments. Using a transparent substrate, c can be easily determined after unloading, from which K _C is found. This simple and economic concept is applied to a wide variety of thin ceramic coatings, yielding toughness data consistent with literature values. Because the tip of the tunneling cracks are well removed from the contact site, the method circumvents certain complications encountered in common top-surface radial cracking techniques such as the effect of plastic deformation, residual stresses and crack extension after unloading. Although the present tests are limited to coating thicknesses >150 μm, it is believed that thinner coatings may be studied as well provided that the indenter radius is kept sufficiently small to insure that subsurface radial cracking dominates over all other failure modes.     

Mixed mode fracture criterion of interface crack between dissimilar materials

This study presents an application of fracture mechanics to the interface crack between dissimilar materials. In this study, a concept of the stress intensity factors of an interface crack is discussed, and various types of specimens are tested experimentally for investigating the mixed mode fracture toughness criterion of an interface crack. The fracture toughness based on the stress intensity factors of an interface crack is decided by the fracture test and the boundary element analysis using the contour integral method. The mixed mode fracture toughness criterion is successfully characterized by the stress intensity factors of an interface crack.     

Application of meso- and fracture mechanics to material affected by a network of thermal fatigue cracks

Within the concept of physical mesomechanics of materials and fracture mechanics the peculiarities of deformation and failure of heat resistant 25Cr1Mo1V steel with a network of thermal fatigue cracks are investigated. The basic regularities and typical characteristic stages of deformation process in specimens of 25CrMo1V steel damaged volumetrically by a network of cracks under localization of plastic strain are found and described numerically.     

A model on twinning-induced crack kinking out of a metal-ceramics interface

A continuum model is proposed to study the effects of deformation twinning on interface crack kinking in metal/ceramics layered materials. At the final stage of material failure, plastic work hardening exhausts and lattice rotation becomes main mechanism after competing with dislocation gliding. The crack-tip plasticity is established in terms of the second gradient of microrotation due to the coupling effect of the twins. The formed twinning structures not only shield the crack tip, but inhibit further dislocation emission by increasing the near-tip stress levels. A Dislocation-Free Zone (DFZ) can exist in the immediate vicinity of the tip. The model is based on the equivalence of the stresses derived from twin-based crack-tip plasticity, macroscopic plasticity and elasticity on the boundary. The two-parameter characterization of near-tip stress fields is used for the outer plastic zone to account for constraint effects. Crack kinking out of the interface follows the direction of the maximum flow stress from the crack-tip plasticity. The DFZ size and the crack-tip shielding ratio, as well as the kink angle, are obtained for various values of low hardening exponents and crack-tip constraints.     

Modeling of frosting behavior on a cold plate

This paper proposes a mathematical model to predict the frost properties and heat and mass transfer within the frost layer formed on a cold plate. Laminar flow equations for moist air and empirical correlations for local frost properties are employed to predict the frost layer growth. Correlations for local frost density and effective thermal conductivity of the frost layer, derived from various experimental data, are expressed as a function of the various frosting parameters: the Reynolds number, frost surface temperature, absolute humidity and temperature of the moist air, cooling plate temperature, and frost density. The numerical results are compared with experimental data to validate the proposed model, and those agree well with the experimental data within a maximum error of 10%. Heat and mass transfer coefficients obtained from the numerical analyses are also presented. The results show that the model for the frost growth using the correlation of the heat transfer coefficient without considering the air flow has a limitation in its application.     

金属薄板中导波的模态识别和波速测定

按照Lamb波理论,板内导波由多阶对称波和反对称波组成。当波长远大于板厚时,利用经典平板理论对Lamb方程进行简化,此时板内主要有零阶对称波S0和反对称波A0两种模态。认识薄板内声波模态,不仅有助于分析声源性质,提取有效信号,而且可以提高声发射检测中时差定位的准确性。利用PAC公司的Fieldcal标准信号发生器和Nielsen Hsu断铅法作为信号源在0.7 mm薄钢板上进行声波传播实验。通过比较实测波速和理论波速甄别板内的声波模态。实验发现对称波S0实测波速和理论波速比较吻合,而反对称波A0的波速由于频散而较难精确测量。综合两种模态波的波速情况,声发射检测中利用对称波速度进行声源定位计算更加接近薄壁结构声波的传播状况。     

离合器波形片轴向非线性特性分析与优化

建立了用于计算波形片轴向非线性特性的有限元模型,并对模型精细化以提高仿真曲线与试验曲线的吻合程度。分析了波形片各结构参数对其轴向非线性特性的灵敏度,选取了除厚度外的三个主要结构参数作为波形片轴向非线性特性优化的参数。基于正交试验获得主要结构参数的设计空间,采用响应面法构建系统的代理模型,利用遗传算法求解代理模型,获得主要结构参数取值的最优组合。通过实例验证了波形片结构参数优化设计方法的正确性。