Dynamic crack kinking from a PMMA/Homalite interface

The behavior of a pre-existing, dynamically loaded, interfacial crack kinking away from the interface separating two materials was experimentally investigated under dynamic loading conditions. Dynamic fracture experiments were performed on pre-cracked bimaterial panels of PMMA bonded with Homalite-100 impact loaded using a high-speed gas gun. By varying the location of impact, a large range of mixed mode loading at the crack tip was produced. Information about the stress state surrounding the crack tip was obtained through use of the lateral shearing interferometer of coherent gradient sensing in conjunction with high-speed photography. The high-speed interferogram corresponding, to the time of crack initiation was analyzed in each case to find the preinitiation mode mixity at the crack tip. Measurement of both the local initiation mode mixity and the crack kink angle allows for possible extension of existing quasi-static interface crack kinking criteria, such as maximum opening stress or maximum energy release rate, to the case of dynamic loading. It was found that for bimaterial systems with small material property mismatch, such as the PMMA/Homalite system, the maximum opening stress criterion accurately predicts the relation between crack tip mode mixity and resulting kink angle for small initial crack kinking speeds.     

瓷修复体界面断裂行为的模拟实验研究

本文利用云纹干涉法和云纹干涉－－有限元混合法，对瓷修复体的模拟双材料模型界面断裂问题进行了实验研究。用云纹干涉和数字错位云纹干涉法测量带边裂纹的双材料四点简支梁在剪切作用下界面表面的剪应变分布及界面两侧局部表面的位移场，实验表明，由于界面两两侧材料力学性质不同，表现出界面剪切断裂问题的非称性和裂尖附近复合型断裂的特点；用云纹干涉法和有限元法相结合的混合法对粘接界面角点应力奇异性进行研究，并对角点附近应力应变场作了分析，得到了应力奇异指数与边界楔角，载荷的关系，证明了用界面应力强度因子Kf来描述界面端部区域应力分布的公式，并得到了双材料界面端部区域的应力应变分布情况。本文的实验结果为进一步研究口腔金瓷修复体界面的优化设计提供了基础，同时也说明云纹干涉法对于双材料界面断裂行为的研究是有效的。     

基于GMTS准则的岩石复合型断裂机理研究

使用国际岩石力学协会规定的半圆盘岩石试件,加工不同倾角的直裂纹试样,通过三点弯曲加载试验得到不同I-II复合比断裂的断裂韧性和初始断裂角．传统裂纹扩展准则忽视了常数项即T应力及更高阶项的影响,导致该扩展准则的理论预测结果存在较大缺陷,本文通过考虑常数项,建立广义最大周向应力准则(GMTS)．在此基础上,分别采用传统的裂纹扩展准则和考虑T应力的裂纹扩展准则预测不同复合比裂纹的断裂韧性和初始扩展角,然后对比理论预测结果和实验结果．分析可得：常数项即T应力对断裂的临界应力强度因子和初始断裂角的影响是不可忽略的,且II型断裂占比较大时影响更大,广义最大周向应力准则预测值与实验测试结果之间的误差最小．     

Stress intensity factors for interface crack in finite size specimen using a generalized variational approach

A generalized variational approach together with eigenfunction expansion is applied to determine the stress intensity factors for interface crack in finite size specimen. Application is also made of the complex potentials such that a complex stress intensity factor with components corresponding to the Mode I and II stress intensity factors can be identified with one of the leading coefficients in the eigenfunction expansion. Obtained are the numerical values of the stress intensity factors for an interface edge crack in a bimaterial rectangular specimen. The outside boundary is subjected to uniform stress normal and parallel to the crack. Solutions are also obtained for the same crack aand specimen geoinetry is subjected to a pair of equal and opposite concentrated forces along the open end away from the edge crack. The third example pertains to the case of three-point bending where the centre concentrated load is directed along the interface dividing the two materials. Numerical results are obtained for four different combinations of the bimaterial specimen with an interface edge crack.     

A Nano-Cantilever Method for Crack Initiation at the Free Edge of the Cu/Si Interface in Nanoscale Components

Straight and Bent nano-cantilever specimens are respectively proposed to investigate the single-mode and mixed-mode crack initiation at the Cu/Si interface edge in nanoscale components. With a minute loading apparatus, all nanoscale samples are in situ loaded and observed. Numerical analysis is employed to acquire the critical interfacial stress distributions during crack initiation. The stress concentration regions near the edge of Cu/Si interface in all specimens are within the scale of 100 nm, and the critical normal and shear stresses have a circular relation in nanoscale components, which represents the fracture criterion of the interface in nanoscale components.     

Empirical assessment of ductile fracture initiation in steel bars with notch and three-point bend specimen with edge crack

Proposed is a parameter defined to characterize the onset of macrocrack initiation in notched steel bars and cracked three-point bend specimens. It accounts for stress triaxiality and damage by plasticity reflected via the effective plastic strain. Results are obtained for notched round bars made of 20#, A3, DE36I and DE36II steel by assuming that the stress triaxiality increases with increasing effective plastic strain; they are compared with the results by letting the stress triaxiality to be constant. Use are made of experimental data on the necking of tensile bars. The parameter corresponding to the onset of ductile fracture were found to be nearly constant. Since the local effective plastic stress can be related to the crack tip opening (COD) distance, the same procedure can be applied to evaluate fracture initiation in three-point bend specimens with an edge crack. It is found that the COD in AS1204-350 and AS1405-180 structural steels decreased with increasing stress triaxiality.     

垂直于界面V型缺口尖端的应力奇异性及其应用

基于双材料垂直于界面V型缺口理论,给出了单一材料和双材料裂纹问题、V型缺口问题应力强度因子的统一定义,得到了应力外推法计算双材料K_I的公式,数值算例验证了本文方法的有效性.以双材料单向拉伸和三点弯曲模型为对象,深入研究了双材料中弹性模量、泊松比、缺口深度、缺口张角对缺口尖端奇异应力场的影响,获得了一定范围内各种参数变化对缺口尖端奇异应力场的影响规律,为异体材料形成的V型缺口在应力断料中的应用提供了必要的参考依据.     

Crack propagation in glass coatings under expanding spherical contact

The growth of transverse cracks under expanding spherical contact in a model system consisted of soda-lime glass bonded to a polycarbonate substrate is observed in situ from below or from the polished edge of the bilayer. Abrasion or chemical etching is employed on the coating surfaces to control the initial fracture. In the limit case of monoliths, the crack mouth becomes fully engulfed by the expanding contact, which results in a much steeper crack angle compared to the classical Hertzian cone case. As the coating thickness is reduced, flexure stresses are set in the coating which drive the cone crack to well away from the contact circle and initiate semi-elliptical-like radial cracks at the subsurface, right under the contact. Common to all three fracture modes is an initial unstable propagation phase following by a stable growth, with detrimental failure associated with severe damage to the top surface and/or delamination at the coating/substrate interface taking place at loads several times the fracture initiation loads.LEFM in conjunction with a large-strain FEM contact code is used to study the post-initiation fracture, with the crack path controlled by the principal stress trajectory or zero-mode II S.I.F. The analysis exposes the leading geometric and material parameters in each fracture mode, which may be useful in the design of bilayer structures for optimal mechanical performance. The well-known Auerbach law governing the initial fracture of monoliths is found to apply also to the bilayer crack systems within a certain range of the problem parameters. The numerical prediction for the crack profiles and the fracture envelopes generally collaborate well with the tests.     

平行于异材界面的三维椭圆平片裂纹分析

讨论了拉伸载荷作用下平行于两相材料界面的椭圆平片裂纹问题．首先,使用有限部积分概念和两相材料界面完全接合时的点力基本解导出了一组以裂纹表面位移差为未知函数的超奇异积分方程组．该组方程表明,此时三种裂纹模型同时存在;其次,在数值求解该组方程的过程中,未知函数裂纹表面位移差被近似为位移差的基本密度函数与多项式之积．基本密度函数反映了裂纹前沿应力奇性性态;最后,以拉伸载荷为例,讨论了椭圆平片裂纹与界面的距离、裂纹形状比和不同材料组合对应力强度因子的影响,并以图表形式给出。     

Delamination fracture analysis in the GII–GIII plane using prestressed transparent composite beams

In this paper, the mixed-mode II/III version of the prestressed end-notched flexure fracture specimen is developed, which combines the well-known end-notched flexure and the modified split-cantilever beam specimens using a special rig. The new beam-like specimen is able to provide any combination of the mode-II and mode-III strain energy release rates. The mode-III part of the strain energy release rate is fixed by using the special rig, which loads the specimen in the plane of the delamination. The mode-II part of the strain energy release rate is provided by the external load using a three-point bending fixture. A simple closed-form solution using beam theory is developed for the strain energy release rates of the new configuration. The applicability and the limitations of the novel fracture mechanical test are demonstrated using unidirectional E-glass/polyester composite specimens. If only crack propagation onset is involved then the mixed-mode II/III prestressed end-notched flexure specimen can be used to obtain the fracture criterion of transparent composite materials in a relatively simple way.     

Singular stress fields of angle-ply and monoclinic bimaterial wedges

The characteristic equations for the order of stress singularity of anisotropic bimaterial wedges subjected to traction boundary conditions are investigated. For an angle-ply bimaterial wedge, both fully bonded and frictional interfaces are considered, whereas for a monoclinic bimaterial wedge, a frictional interface is considered. Here, the Stroh formalism and the separation of variables technique are used. In general, the order of stress singularity can be real or complex, but for the special geometry of a crack along the frictional interface of a monoclinic composite, it is always real. Explicit characteristic equations for the order of singularity are presented for an aligned orthotropic composite with a frictional interface. Numerical results are given for an angle-ply bimaterial wedge and a monoclinic bimaterial wedge consisting of a graphite/epoxy fiber-reinforced composite.     

Compliance rate change of tapered double cantilever beam specimen with hybrid interface bonds

This paper presents a combined numerical and experimental study of compliance rate change of Tapered Double Cantilever Beam (TDCB) specimens for Mode-I fracture of hybrid interface bonds. The easily machinable TDCB specimen, which is designed to achieve a constant rate of compliance change with respect to crack length, is developed for Mode-I fracture tests of hybrid material bonded interfaces, such as wood bonded to fiber-reinforced plastic (FRP) composite. The linearity of compliance crack-length relationship of the specimen is verified by both Rayleigh–Ritz method and finite element analysis. An experimental compliance calibration program for specimens with wood–wood and FRP–FRP bonded interfaces is carried out, and a constant rate change of compliance with respect to crack length is obtained for a specific range of crack length. Fracture tests are further performed using TDCB specimens for wood–wood and wood–FRP bonded interfaces to determine the critical loads for crack initiation and crack arrest, and using the constant compliance rate change of the specimens determined by experiment or analysis, the respective critical strain energy release rates, or fracture energies, are obtained. This study indicates that the constant compliance rate change obtained from experiment or finite element analysis for linear-slope TDCB specimens can be used with confidence for fracture studies of hybrid material interface bonds.     

Boundary Integral Analysis of the Symmetric Dynamic Problem for an Infinite Bimaterial Solid with an Embedded Crack

The symmetric frequency domain problem for two ideally bonded elastic half-spaces with a perpendicular plane crack is considered. It is reduced to the boundary integral equation (BIE) with integration over the limited crack region. The contact conditions on the bimaterial interface are satisfied identically in the initial stage of obtaining the equation. After boundary element solution of the equation, the stress concentration in the vicinity of a penny-shaped crack under time-harmonic loading of constant amplitude is studied. The mode I stress intensity factors as functions of angular coordinate of a crack front point and wave number for various relations between the material parameters are computed. The crack depth relative to the bimaterial interface is determined, when the effect of the material dissimilarity on the crack can be neglected.     

Magneto-electro-elastic antiplane analysis of a bimaterial BaTiO3–CoFe2O4 composite wedge with an interface crack

The antiplane analysis is made for a bimaterial BaTiO₃–CoFe₂O₄ composite wedge containing an interface crack. The coupled magneto-electro-elastic field is induced by the piezoelectric/piezomagnetic BaTiO₃–CoFe₂O₄ composite materials. For the crack problems, the intensity factors of stress, strain, electric displacement, electric field, magnetic induction and magnetic field at crack tips are derived analytically. Also, the energy density criterion is applied to predict the fracture behavior of the interface crack. The numerical results also show that the energy release rate for a crack in a single wedge is negative.     

Fracture in metal powder compaction

This paper presents a preliminary assessment and qualitative analysis on fracture criterion and crack growth in metal powder compact during the cold compaction process. Based on the fracture criterion of granular materials in compression, a displacement based finite element model has been developed to analyse fracture initiation and crack growth in metal powder compact. Approximate estimation of fracture toughness variation with relative density is established in order to provide the fracture parameter as compaction proceed. A single crack initiated from the boundary of a multi-level component made of iron powder is considered in this work. The finite element simulation of the crack propagation indicates that shear crack grows during the compaction process and propagates in the direction of higher shear stress and higher relative density. This also implies that the crack grows in the direction where the compaction pressure is much higher, which is in line with the conclusion made by previous researchers on shear crack growth in materials under compression. In agreement with reported work by previous researchers, high stress concentration and high density gradient at the inner corner in multi-level component results in fracture of the component during preparation.     

双材料中平片裂纹问题的超奇异积分方程解法

利用三维断裂力学的超奇异积分方程方法,对双材料空间中重直于界面的平片裂纹Ⅰ型问题进行了研究。首先根据双材料空间的弹性力学基本解,使用边界积分方程方法,在有限部积分的意义下导出了以裂纹面位罗间断为未知函数的超奇异积分方程,并为其建立了数值法。在此基础上,讨论了用裂纹面位移问题计算应力强度因子的方法。最后用此计算了几个典型的Ⅰ型下片裂纹问题的应力强度因子,其数值结果令人满意。     

Green's function of a point dislocation for the bending of a composite infinite plate with an elliptical hole at interface

Summary  The problem of a hole at bimaterial interface is of practical importance in providing a good understanding of the debonding phenomenon and for determining factors that affect the mechanical properties of composite elements of structures. The problem of a point dislocation in bending bonded dissimilar semi-infinite plates with an elliptical hole at interface is tackled in this paper. Based on the method of analytic continuation and the rational mapping function technique, the problem of obtaining the stress functions in the upper and lower plates is decoupled, and reduced to two Riemann–Hilbert problems. The closed-form solution is obtained. The stress distributions at the bimaterial interface, as well as the debonding at both vertices of the elliptical hole are studied. The stress intensities of debonding are depicted for various parameters. Received 16 March 2000; accepted for publication 12 July 2000     

Analysis of tapered ENF specimen and characterization of bonded interface fracture under Mode-II loading

An engineering approach for evaluating the shear-mode (Mode-II) fracture toughness of wood–wood and wood-composite bonded interfaces is presented. A tapered beam on elastic foundation model is developed to analyze and design a linear tapered end-notched flexure (TENF) specimen for fracture tests of bonded interfaces. The elastic foundation model is verified numerically by finite element analysis and experimentally by compliance calibration tests, which demonstrate that the present model can accurately predict the compliance and compliance rate-change of the specimen, and with proper design, an approximate constant rate of compliance change with respect to crack length can be achieved. The proposed TENF specimen can be used for Mode-II fracture toughness evaluations with reasonable confidence in the linearity of compliance crack-length relationship. The fracture of wood–wood and wood-composite bonded interfaces under Mode-II loading is experimentally evaluated using the proposed TENF specimen, and the corresponding values of critical strain energy release rate are obtained. The modeling technique and testing method presented can be efficiently used for characterization of Mode-II fracture of bonded bimaterial interfaces.     

Hertzian fracture at unloading

Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally. Initiation of cone cracks has been observed and failure loads together with contact and fracture radii determined at monotonically increasing load but also during unloading phases. Contact of dissimilar elastic solids under decreasing load may cause crack inception triggered by finite interface friction and accordingly the coefficient of friction was determined by two different methods. In order to make relevant predictions of experimental findings, a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. It was found that at continued loading it is possible to specify in advance how the contact domain divides into invariant regions of stick and slip. The maximum tensile stress was found to occur at the free surface just outside the contact contour, the relative distance depending on the different elastic compliance properties and the coefficient of friction. In contrast, at unloading invariance properties are lost and stick/slip regions proved to be severely history dependant and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. Predictions of loads to cause crack initiation during full cycles were made based on a critical stress fracture criterion and proved to be favourable as compared to the experimental results.