Mode I crack growth resistance of metallic foams

A Dugdale-type cohesive zone model is used to predict the mode I crack growth resistance (R-curve) of metallic foams, with the fracture process characterized by an idealized traction-separation law that relates the crack surface traction to crack opening displacement. A quadratic yield function, involving the von Mises effective stress and mean stress, is used to account for the plastic compressibility of metallic foams. Finite element calculations are performed for the crack growth resistance under small scale yielding and small scale bridging in plane strain, with K-field boundary conditions. The following effects upon the fracture process are quantified: material hardening, bridging strength, T-stress (the non-singular stress acting parallel to the crack plane), and the shape of yield surface. To study the failure behaviour and notch sensitivity of metallic foams in the presence of large scale yielding, a study is made for panels embedded with either a centre-crack or an open hole and subjected to tensile stressing. For the centre-cracked panel, a transition crack size is predicted for which the fracture response switches from net section yielding to elastic-brittle fracture. Likewise, for a panel containing a centre-hole, a transition hole diameter exists for which the fracture response switches from net section yielding to a local maximum stress criterion at the edge of the hole.

Crack Tip Field and J-Integral with Strain Gradient Effect

The mode I plane strain crack tip field with strain gradient effects is presented in this paper based on a simplified strain gradient theory within the framework proposed by Acharya and Bassani. The theory retains the essential structure of the incremental version of the conventional J_2 deformation theory No higher-order stress is introduced and no extra boundary value conditions beyond the conventional ones are required. The strain gradient effects are considered in the constitutive relation only through the instantaneous tangent modulus. The strain gradient measures are included into the tangent modulus as internal parameters. Therefore the boundary value problem is the same as that in the conventional theory Two typical crack Problems are studied: (a) the crack tip field under the small scale yielding condition induced by a linear elastic mode-I K-field and (b) the complete field for a compact tension specimen. The calculated results clearly show that the stress level near the crack tip with strain gradient effects is considerable higher than that in the classical theory The singularity of the strain field near the crack tip is nearly equal to the square-root singularity and the singularity of the stress field is slightly greater than it. Consequently, the J-integral is no longer path independent and increases monotonically as the radius of the calculated circular contour decreases.

Mode I and Mode II Crack Tip Asymptotic Fields with Strain Gradient Effects

The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

Crack problems of piezoelectric materials

This paper presents an analysis of crack problems in homogeneous piezoelectrics or on the interfaces between two dissimilar piezoelectric materials based on the continuity of normal electric displacement and electric potential across the crack faces. The explicit analytic solutions are obtained for a single crack in piezoelectrics or on the interfaces of piezoelectric bimaterials. A class of boundary problems involving many cracks is also solved. For homogeneous materials it is found that the normal electric displacement D-2 induced by the crack is constant along the crack faces which depends only on the applied remote stress field. Within the crack slit, the electric fields induced by the crack are also constant and not affected by the applied electric field. For the bimaterials with real H, the normal electric displacement D-2 is constant along the crack faces and electric field E-2 has the singularity ahead of the crack tip and a jump across the interface.

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.