A review of dynamic fracture mechanics in China

This paper summarizes the recent development of dynamic fracture in China. The review covers analytical and numerical results on elastodynamic crack fields in 3D and layered media; experimental and theoretical research on dynamic mechanical properties of rocks and advanced materials; transient effects on ideally plastic crack-tip fields when the inertia forces are not negligible.

3-dimensional transient wave response in a cracked elastic solid

The three-dimensional transient wave response problem is presented for an infinite elastic medium weakened by a plane crack of infinite length and finite width. Tractions are applied suddenly to the crack, which simulates the case of impact loading. The integral transforms are utilized to reduce the problem to a standard Fredholm integral equation in the Laplace transform variable and sequentially invert the Laplace transforms of the stress components by numerical inversion method. The dynamic mode I stress intensity factors at the crack tip are obtained and some numerical results are presented in graphical form.

Singular behaviour near the tip of a sharp V-notch in a power law hardening material

This paper presents an asymptotic analysis of the near-tip stress and strain fields of a sharp V-notch in a power law hardening material. First, the asymptotic solutions of the HRR type are obtained for the plane stress problem under symmetric loading. It is found that the angular distribution function of the radial stress sigma(r) presents rapid variation with the polar angle if the notch angle beta is smaller than a critical notch angle; otherwise, there is no such phenomena. Secondly, the asymptotic solutions are developed for antisymmetric loading in the cases of plane strain and plane stress. The accurate calculation results and the detailed comparisons are given as well. All results show that the singular exponent s is changeable for various combinations of loading condition and plane problem.

Local stresses and strains in axially cracked cylindrical shells

A perturbation solution is obtained for the local stress-strain fields in an axially cracked cylindrical shell. The tenth-order differential equations are used that take into account the transverse shear deformation. The perturbation of a curvature parameter, λ, is employed, where . The stress intensity factors for finite size cylindrical shells subjected to bending and internal pressure are evaluated. Sufficient accuracy can be obtained without using fine mesh sizes in regions near the crack tip. Also analyzed are the influence of cylinder diameter and shearing stiffness on bulging.

Study on cracked plates, shells and 3 dimensional bodies

This paper presents a summary of the authors' recent work in following areas: (1) The stress-strain fields at crack tip in Reissner's plate. (2) The calculations of the stress intensity factors in finite size plates. (3) The stress-strain fields at crack tip in Reissner's shell. (4) The calculations of the stress intensity factors and bulging coefficients in finite size spherical shells. (5) The stress-strain fields along crack tip in three dimensional body with surface crack. (6) The calculation of stress intensity factors in a plate with surface crack.

Study on cracked spherical shells

The local-global anatysis method is systematically extended to the fracture analysis of spherical shells. On the basis of the shallow shell theory, which takes into account transverse shear deformations, governing equations for cracked spherical shells expressed in displacement and stress functions f, F and φ are proposed, and then a general solution including Modes, Ⅰ, Ⅱ, Ⅲ for stress-strain fields at crack tip in a spherical shell is obtained, which plays the same role as Williams's expansion in plane elasticity. The numerical results for finite-size spherical shells under different boundary conditions have been obtained. Furthermore, the bulging factors are analyzed with regard to shearing stiffness and an approximate formula is given.

Elastic-plastic finite element analyses of short cracks

Stress and strain distributions and crack opening displacement characteristics of short cracks have been studied in single edge notch bend and centre cracked panel specimens using elastic–plastic finite element analyses incorporating both a non strain hardening and a power law hardening behaviour. J contour integral solutions to describe stress strain conditions at crack tips for short cracks differ from those for long cracks. The analyses show that (i) short cracks can propagate at stress levels lower than those required for long cracks and (ii) a two-parameter description of crack tip fields is necessary for crack propagation.

黏弹性材料界面裂纹应力场奇性分析

研究两半无限大黏弹性体间Griffith界面裂纹在简谐载荷作用下裂纹尖端动应力场的奇异特性。通过引入裂纹张开位移和裂纹位错密度函数，相应的混合边值问题归结为一组耦合的奇异积分方程。渐近分析表明裂尖动应力场的奇异特征完全包含在奇异积分方程的基本解中。通过对基本解的深入分析发现黏弹性材料界面裂纹尖动应力场具有与材料参数和外载荷频率相关的振荡奇异特性。以标准线性固体黏弹材料为例讨论了材料参数和载荷频率对奇性指数和振荡指数的影响。

机械载荷作用下单边裂纹载流薄板的应力场

采用坐标变换的方式,将单边裂纹载流薄板通电瞬间由温度产生的应力场表达式中的各应力分量分离,并用极坐标进行表示.给出了Ⅰ型穿透裂纹尖端附近的应力场的表达式.最后将温度产生的应力场与单向拉伸载荷作用产生的应力场相叠加,推导出用极坐标表示的机械载荷作用下单边裂纹载流薄板的应力场的表达式,并给出算例.

含环向裂纹厚壁圆筒电磁止裂的应力场分析

以具有轴对称性质、端部带有半埋藏环形裂纹的厚壁圆筒为研究对象，通过对长厚壁圆筒内外环面均匀通入超强脉冲电流进行电磁热止裂。采用复变函数方法求解了脉冲放电瞬间裂纹尖端的温度场和热应力场。在一定的超强脉冲电流作用下，由于环形裂纹尖端的电流绕流热集中效应，裂尖温升超过了金属熔点，使裂尖处金属熔化在内部形成堆焊，钝化了裂尖，并且在裂纹前缘形成了热压应力，阻止了裂纹的扩展。在此基础上还讨论了在电载荷和机械载荷共同作用下裂纹前缘的应力场。

A Finite Element Analysis of a Crack Penetrating or Deflecting into an Interface in a Thin Laminate

The crack tip driving force of a crack growing from a pre-crack that is perpendicular to and terminating at an interface between two materials is investigated using a linear fracture mechanics theory. The analysis is performed both for a crack penetrating the interface, growing straight ahead, and for a crack deflecting into the interface. The results from finite element calculations are compared with asymptotic solutions for infinitesimally small crack extensions. The solution is found to be accurate even for fairly large amounts of crack growth. Further, by comparing the crack tip driving force of the deflected crack with that of the penetrating crack, it is shown how to control the path of the crack by choosing the adhesion of the interface relative to the material toughness.

Discontinuous growth mechanisms of mode II crack under high-speed impact conditions

A recoverable plate impact testing technology has been used for studying the growth mechanisms of mode II crack. The results show that interactions of microcracks ahead of a crack tip cause the crack growth unsteadily. Failure mode transitions of materials were observed. Based on the observations, a discontinuous crack growth model was established. Analysis shows that the shear crack grows unsteady as the growth speed is between the Rayleigh wave speed c(R) and the shear wave speed c(s); however, when the growth speed approaches root 2c(s), the crack grows steadily. The transient microcrack growth makes the main crack speed to jump from subsonic to intersonic and the steady growth of all the sub-cracks leads the main crack to grow stably at an intersonic speed.

Molecular dynamics studies of brittle fracture of SiO2

By applying for molecular dynamics (MD) simulation and Griffith fracture criterion, the brittle behavior of crack extension of mode I type is investigated. The critical stress intensity factor (SIF)K-Ic(MD) of crack extension is calculated, and the evolution of atoms near crack tip is observed. It is found that K-Ic(MD) is in good agreement with the Griffith ftacture criterion K-Ic(Griffith).

A Mechanical Model For The Quantification Of The Effect Of Laser Quenching On Ctod In Steels

The technology of laser quenching is widely used to improve the surface properties of steels in surface engineering. Generally, laser quenching of steels can lead to two important results. One is the generation of residual stress in the surface layer. In general, the residual stress varies from the surface to the interior along the quenched track depth direction, and the residual stress variation is termed as residual stress gradient effect in this work. The other is the change of mechanical properties of the surface layer, such as the increases of the micro-hardness, resulting from the changes of the microstructure of the surface layer. In this work, a mechanical model of a laser-quenched specimen with a crack in the middle of the quenched layer is developed to quantify the effect of residual stress gradient and the average micro-hardness over the crack length on crack tip opening displacement (CTOD). It is assumed that the crack in the middle of the quenched layer is created after laser quenching, and the crack can be a pre-crack or a defect due to some reasons, such as a void, cavity or a micro-crack. Based on the elastic-plastic fracture mechanics theory and using the relationship between the micro-hardness and yield strength, a concise analytical solution, which can be used to quantify the effect of residual stress gradient and the average micro-hardness over the crack length resulting from laser quenching on CTOD, is obtained. The concise analytical solution obtained in this work, cannot only be used as a means to predict the crack driving force in terms of the CTOD, but also serve as a baseline for further experimental investigation of the effect after laser-quenching treatment on fracture toughness in terms of the critical CTOD of a specimen, accounting for the laser-quenching effect. A numerical example presented in this work shows that the CTOD of the quenched can be significantly decreased in comparison with that of the unquenched. (C) 2008 Elsevier B.V. All rights reserved.

Biaxial stress dependence of the electrostimulated near-band-gap spectrum of GaN epitaxial film grown on (0001) sapphire substrate

The biaxial piezospectroscopic coefficient (i.e., the rate of spectral shift with stress) of the electrostimulated near-band-gap luminescence of gallium nitride (GaN) was determined as Pi=-25.8 +/- 0.2 meV/GPa. A controlled biaxial stress field was applied on a hexagonal GaN film, epitaxially grown on (0001) sapphire using a ball-on-ring biaxial bending jig, and the spectral shift of the electrostimulated near-band-gap was measured in situ in the scanning electron microscope. This calibration method can be useful to overcome the lack of a bulk crystal of relatively large size for more conventional uniaxial bending calibrations, which has so far hampered the precise determination of the piezospectroscopic coefficient of GaN. The main source of error involved with the present calibration method is represented by the selection of appropriate values for the elastic stiffness constants of both film and substrate. The ball-on-ring calibration method can be generally applied to directly determine the biaxial-stress dependence of selected cathodoluminescence bands of epilayer/substrate materials without requiring separation of the film from the substrate. (c) 2006 American Institute of Physics.