Mode I crack tip field with strain gradient effects

A plane strain mode I crack tip field with strain gradient effects is investigated. A new strain gradient theory is used. An elastic-power law hardening strain gradient material is considered and two hardening laws, i.e. a separation law and an integration Law are used respectively. As for the material with the separation law hardening, the angular distributions of stresses are consistent with the HRR field, which differs from the stress results([19]); the angular distributions of couple stresses are the same as the couple stress results([19]). For the material with the integration law hardening, the stress field and the couple stress field can not exist simultaneously, which is the same as the conclusion([19]), but for the stress dominated field, the angular distributions of stresses are consistent with the HRR field; for the couple stress dominated field, the angular distributions of couple stresses are consistent with those in Ref. [19]. However, the increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only, while the crack tip field of mode I is dominated by the tension gradient, which will be shown in another paper.

Closed form solutions of T-stress in plane elasticity crack problems

The T-stress is considered as an important parameter in linear elastic fracture mechanics. In this paper, several closed form solutions of T-stress in plane elasticity crack problems in an infinite plate are investigated using the complex potential theory. In the line crack case, if the applied loading is the remote stress or the concentrated forces, the T-stress can be derived from the basic field. Here, the basic field is defined as the field caused by the applied loading in the infinite plate without the crack. For the circular are crack, the T-stress can be abstracted from a known solution. For the cusp crack problems, the T-stress can be separated from the obtained stress solution for which the conformal mapping technique is used.

Singularity of Stress Field Around Interface Crack Between Viscoelastic Bodies

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裂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.

Some advances in study of crack identification problems

In the present paper, the crack identification problems are investigated. This kind of problems belong to the scope of inverse problems and are usually ill-posed on their solutions. The paper includes two parts: (1) Based on the dynamic BIEM and the optimization method and using the measured dynamic information on outer boundary, the identification of crack in a finite domain is investigated and a method for choosing the high sensitive frequency region is proposed successfully to improve the precision. (2) Based on 3-D static BIEM and hypersingular integral equation theory, the penny crack identification in a finite body is reduced to an optimization problem. The investigation gives us some initial understanding on the 3-D inverse problems.

A probabilistic model for fatigue crack propagation analysis

A simple probabilistic model for predicting crack growth behavior under random loading is presented. In the model, the parameters c and m in the Paris-Erdogan Equation are taken as random variables, and their stochastic characteristic values are obtained through fatigue crack propagation tests on an offshore structural steel under constant amplitude loading. Furthermore, by using the Monte Carlo simulation technique, the fatigue crack propagation life to reach a given crack length is predicted. The tests are conducted to verify the applicability of the theoretical prediction of the fatigue crack propagation.

Finite Boundary Effects in Problem of a Crack Perpendicular to and Terminating at a Bimaterial Interface

In this paper, the problem of a crack perpendicular to and terminating at an interface in bimaterial structure with finite boundaries is investigated. The dislocation simulation method and boundary collocation approach are used to derive and solve the basic equations. Two kinds of loading form are considered when the crack lies in a softer or a stiffer material, one is an ideal loading and the other one fits to the practical experiment loading. Complete solutions of the stress field including the T stress are obtained as well as the stress intensity factors. Influences of T stress on the stress field ahead of the crack tip are studied. Finite boundary effects on the stress intensity factors are emphasized. Comparisons with the problem presented by Chen et al. (Int. J. Solids and Structure, 2003, 40, 2731-2755) are discussed also.

Stress state in front of a crack perpendicular to bimaterial interface

Using a dislocation simulation approach, the basic equation for a crack perpendicular to a bimaterial interface is formulated in this paper. A novel expansion method is proposed for solving the problem. The complete solution for the problem, including the T stress ahead of the crack tip and the stress intensity factors are presented. The stress field characteristics are analyzed in detail. It is found that ahead of the crack tip and near the interface the normal stress, perpendicular to the crack plane, sigma(x), is characterized by the K fields and the normal stress sigma(y) is dominated by the K field plus T stress in the region of 0 < r/b < 0.4 for b/a(0) less than or equal to 0.1, where b is the distance from the crack tip to the interface.

Fractography and Crack Initiation of Very-High-Cycle Fatigue for a High Carbon Low Alloy Steel

Very-High-Cycle Fatigue (VHCF) is the phenomenon of fatigue damage and failure of metallic materials or structures subjected to 108 cycles of fatigue loading and beyond. This paper attempts to investigate the VHCF behavior and mechanism of a high strength low alloy steel (main composition: C-1% and Cr-1.5%; quenched at 1108K and tempered at 453K). The fractography of fatigue failure was observed by optical microscopy and scanning electron microscopy. The observations reveal that, for the number of cycles to fatigue failure between 106 and 4108 cycles, fatigue cracks almost initiated in the interior of specimen and originated at non-metallic inclusions. An “optical dark area” (ODA) around initiation site is observed when fatigue initiation from interior. ODA size increases with the decrease of fatigue stress, and becomes more roundness. Fracture mechanics analysis gives the stress intensity factor of ODA, which is nearly equivalent to the corresponding fatigue threshold of the test material. The results indicate that the fatigue life of specimens with crack origin at the interior of specimen is longer than that with crack origin at specimen surface. The experimental results and the fatigue mechanism were further analyzed in terms of fracture mechanics and fracture physics, suggesting that the primary propagation of fatigue crack within the fish-eye local region is the main characteristics of VHCF.

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.

Instability Of Crack Propagation In Brittle Bulk Metallic Glass

The instability of the crack tip in brittle Mg-based bulk metallic glass (BMG) is studied. The formation of various fractographic surfaces of the BMG is associated with the instability of the fluid meniscus, which is due to viscous fluid matter being present on the fracture process zone. Depending on the values of the wavelength of the initial perturbation of the fluid meniscus and the local stress intensity factor, different fracture surface profiles, i.e. a dimple-like structure, a periodic corrugation pattern and a pure mirror zone are formed. The fractographic evolution is significantly affected by the applied stress. A decreased fracture Surface roughness is observed under a low applied stress. An increased fracture surface roughness, which has frequently been reported by other researchers, is also observed in the present studies under a high applied stress. Unique fractographic features are attributed to the non-linear hyperelastic stiffening for less softening) mechanism. (C) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Investigation Of Mode Ii Crack Growth Following A Very High Speed Impact

A recoverable plate impact testing technology has been developed for studying fracture mechanisms of mode II crack. With this technology, a single duration stress pulse with submicrosecond duration and high loading rates, up to 10(8) MPam(1/2)s(-1), can be produced. Dynamic failure tests of Hard-C 60# steel were carried out under asymmetrical impacting conditions with short stress-pulse loading. Experimental results show that the nucleation and growth of several microcracks ahead of the crack tip, and the interactions between them, induce unsteady crack growth. Failure mode transitions during crack growth, both from mode I crack to mode II and from brittle to ductile fracture, were observed. Based on experimental observations, a discontinuous crack growth model was established. Analysis of the crack growth mechanisms using our model shows that the shear crack extension is unsteady when the extending speed is between the Rayleigh wave speed c(R) and the shear wave speed c(S). However, when the crack advancing speed is beyond c(S), the crack grows at a steady intersonic speed approaching root 2c(S). It also shows that the transient mechanisms, such as nucleation, growth, interaction and coalescence among microcracks, make the main crack speed jump from subsonic to intersonic and the steady growth of all the subcracks causes the main crack to grow at a stable intersonic speed.

Dynamic mode I perturbation solution for a moving crack unsteadily

Rice et al. (Jounal of Mechanics and Physics of Solids 42, 813-843) analyze the propagation of a planar crack with a nominally straight front in a model elastic solid with a single displacement component. Using the form of Willis er al. (Journal of the Mechanics and Physics of Solids 43, 319-341), of dynamic mode I weight functions for a moving crack, we address that problem solved by Rice ei al. in the 3D context of elastodynamic theory. Oscillatory crack tip motion results from constructive-destructive interference of stress intensity waves. Those waves, including system of the dilatational, shear and Rayleigh waves, interact on each other and with moving edge of crack, can lead to continuing fluctuations of the crack front and propagation velocity. (C) 1997 Elsevier Science Ltd.

Crack propagation in the power-law nonlinear viscoelastic material

An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented. The creep incompressilility assumption is used. To simulate fracture behavior of craze region, it is assumed that in the fracture process zone near the crack tip, the cohesive stress sigma(f) acts upon the crack surfaces and resists crack opening. Through a perturbation method, i. e., by superposing the Mode-I applied force onto a referential uniform stress state, which has a trivial solution and gives no effect on the solution of the original problem, the nonlinear viscoelastic problem is reduced to linear problem. For weak nonlinear materials, for which the power-law index n similar or equal to 1, the expressions of stress and crack surface displacement are derived. Then, the fracture process zone local energy criterion is proposed and based on which the formulas of cracking incubation time t

Asymptotic analysis of plane-strain mode I steady-state crack growth in transformation toughening ceramics (II)

Based on a constitutive law which includes the shear components of transformation plasticity, the asymptotic solutions to near-tip fields of plane-strain mode I steadity propagating cracks in transformed ceramics are obtained for the case of linear isotropic hardening. The stress singularity, the distributions of stresses and velocities at the crack tip are determined for various material parameters. The factors influencing the near-tip fields are discussed in detail.