T. C. Wang

Analysis of strip electric saturation model of crack problem in piezoelectric materials

This paper presents a fully anisotropic analysis of strip electric saturation model proposed by Gao et al. (1997) (Gao, H.J., Zhang, T.Y., Tong, P., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids, 45, 491-510) for piezoelectric materials. The relationship between the size of the strip saturation zone ahead of a crack tip and the applied electric displacement field is established. It is revealed that the critical fracture stresses for a crack perpendicular to the poling axis is linearly decreased with the increase of the positive applied electric field and increases linearly with the increase of the negative applied electric field. For a crack parallel to the poring axis, the failure stress is not effected by the parallel applied electric field. In order to analyse the existed experimental results, the stress fields ahead of the tip of an elliptic notch in an infinite piezoelectric solid are calculated. The critical maximum stress criterion is adopted for determining the fracture stresses under different remote electric displacement fields. The present analysis indicates that the crack initiation and propagation from the tip of a sharp elliptic notch could be aided or impeded by an electric displacement field depending on the field direction. The fracture stress predicted by the present analysis is consistent with the experimental data given by Park and Sun (1995) (Park, S., Sun, C.T., 1995. Fracture criteria for piezoelectric materials. J. Am. Ceram. Soc 78, 1475-1480).

Magnetization and Raman scattering studies of (Co,Mn) codoped ZnO nanoparticles

Single-phase (Co,Mn) codoped ZnO nanoparticles were synthesized by an autocombustion method. Hysteresis loop was observed at 300 K for the sample Zn0.98Co0.01Mn0.01O with a low coercivity (40±5 Oe). Temperature dependence of magnetization rules out the possibility of superparamagnetism or spin-glass behavior. Raman scattering studies manifested that there might exist a defect annihilation arising from the (Co,Mn) codoped into ZnO host lattice. As the ferromagnetism of diluted magnetic semiconductors is closely related to the dopant-defect hybridization, the ferromagnetic ordering was significantly enhanced in the sample Zn0.98Co0.01Mn0.01O by the (Co,Mn) codoping, in comparison to the Zn0.99Co0.01O and Zn0.99Mn0.01O fabricated by the same method.

Size Effects in the Particle-Reinforced Metal-Matrix Composites

SummaryMany experimental observations have shown the influences of particle size on the mechanical propertics of the particle-reinforced metal-matrix composite. However, the conventional theory cannot explain the phenomena because no length scale parameters are included in the conventional theory. In the present paper, the strain gradient theory proposed by Chen and Wang [32] is used, and a systematic research of the particle size effect in the particle-reinforced metal-matrix composite is carried out. Many composite factors, such as the particle size, the particle aspect ratio, the Youngs modulus ratio of the particle to the matrix material, particle volume fraction and the strain hardening exponent of the matrix material, are investigated in detail. Two kinds of particle shapes, spheroidal particle and cylindrical particle, are considered to check the strength dependence of the particle shapes. Calculation to the special materials used by Ling [9] has been done, and the calculation results are consistent with the experimental results in Ling [9]. The material length scale parameter is predicted.

Fracture mechanics 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 an infinite piezoelectric or on the interface of piezoelectric bimaterials. For homogeneous materials it is found that the normal electric displacement D2, induced by the crack, is constant along the crack faces which depends only on the remote applied stress fields. Within the crack slit, the perturbed electric fields induced by the crack are also constant and not affected by the applied electric displacement fields. For bimaterials, generally speaking, an interface crack exhibits oscillatory behavior and the normal electric displacement D2 is a complex function along the crack faces. However, for bimaterials, having certain symmetry, in which an interface crack displays no oscillatory behavior, it is observed that the normal electric displacement D2 is also constant along the crack faces and the electric field E2 has the singularity ahead of the crack tip and has a jump across the interface. Energy release rates are established for homogeneous materials and bimaterials having certain symmetry. Both the crack front parallel to the poling axis and perpendicular to the poling axis are discussed. It is revealed that the energy release rates are always positive for stable materials and the applied electric displacements have no contribution to the energy release rates.

Kinking of an interface crack between two dissimilar anisotropic elastic solids

A detailed analysis of kinking of an interface crack between two dissimilar anisotropic elastic solids is presented in this paper. The branched crack is considered as a distributed dislocation. A set of the singular integral equations for the distribution function of the dislocation density is developed. Explicit formulas of the stress intensity factors and the energy release rates for the branched crack are given for orthotropic bimaterials and misoriented orthotropic bicrystals. The role of the stress parallel to the interface, sigma0 is taken into account in these formulas. The interface crack can advance either by continued extension along the interface or by kinking out of the interface into one of the adjoining materials. This competition depends on the ratio of the energy release rates for interface cracking and for kinking out of the interface and the ratio of interface toughness to substrate toughness. Throughout the paper, the influences of the inplane stress sigma0 on the stress intensity factors and the energy release rates for the branched crack, which can significantly alter the conditions for interface cracking, are emphasized.

Dislocation nucleation and emission from crack tip

The problems of dislocation nucleation and emission from a crack tip are analysed based on Peierls model. The concept adopted here is essentially the same as that proposed by Rice. A slight modification is introduced here to identify the pure linear elastic response of material. A set of new governing equations is developed, which is different from that used by Beltz and Rice. The stress field and the dislocation density field can be expressed as the first and second Chebyshev polynomial series respectively. Then the opening and slip displacements can be expanded as the trigonometric series. The Newton-Raphson Method is used to solve a set of nonlinear algebraic equations. The new governing equations allow us to extend the analyses to the case of dislocation emission. The calculation results for pure shearing, pure tension and combined tension and shear loading are given in detail.

A crack perpendicular to the bimaterial interface in finite solid

The dislocation simulation method is used in this paper to derive the basic equations for a crack perpendicular to the bimaterial interface in a finite solid. The complete solutions to the problem, including the T stress and the stress intensity factors are obtained. The stress field characteristics are investigated in detail. It is found that when the crack is within a weaker material, the stress intensity factor is smaller than that in a homogeneous material and it decreases when the distance between the crack tip and interface decreases. When the crack is within a stiffer material, the stress intensity factor is larger than that in a homogeneous material and it increases when the distance between the crack tip and interface decreases. In both cases, the stress intensity factor will increase when the ratio of the size of a sample to the crack length decreases. A comparison of stress intensity factors between a finite problem and an infinite problem has been given also. The stress distribution ahead of the crack tip, which is near the interface, is shown in details and the T stress effect is considered.

Brittle and ductile fracture at the atomistic crack tip in copper crystals

Abstract A study of hydrogen enhanced thermal fatigue cracking was carried out for a gamma-based Ti-48Al-2Cr alloy by cycling between room temperature and 750 or 900 °C. The results showed that hydrogen can severely attack the gamma alloy, with resulting lifetimes as low as three cycles, while no failures were observed in helium for test durations of over 4000 cycles. The severity of hydrogen attack strongly depends on the upper limit of the temperature cycled and the cleanliness of the hydrogen. Specifically, the large scatter of life times at 750 °C (ranging from 36 to more than 3000 cycles) have resulted from the competition between surface oxidation and hydrogen attack. The results suggest that an understanding of the combined actions of thermal cycling and hydrogen degradation is needed for assessing materials for high temperature applications in hydrogen.

Interface crack problems with strain gradient effects

In this paper, the strain gradient theory proposed by Chen and Wang (2001a, 2002b) is used to analyze an interface crack tip field at micron scales. Numerical results show that at a distance much larger than the dislocation spacing the classical continuum plasticity is applicable; but the stress level with the strain gradient effect is significantly higher than that in classical plasticity immediately ahead of the crack tip. The singularity of stresses in the strain gradient theory is higher than that in HRR field and it slightly exceeds or equals to the square root singularity and has no relation with the material hardening exponents. Several kinds of interface crack fields are calculated and compared. The interface crack tip field between an elastic-plastic material and a rigid substrate is different from that between two elastic-plastic solids. This study provides explanations for the crack growth in materials by decohesion at the atomic scale.

SIMULATION OF NUCLEATION AND EMISSION OF DISLOCATIONS BY MOLECULAR-DYNAMICS METHOD

The nucleation and emission of dislocations from the crack tip under mode II loading are analyzed by the molecular‐dynamics method in which the Finnis–Sinclair potential has been used. A suitable atom lattice configuration is employed to allow one to fully analyze the nucleation, emission, dissociation, and pileup of the dislocations. The calculated results show that although the pure mode II loading is applied, the crack tip generally exhibits a combined mode. The stress distributions before the dislocation emission are in agreement with the elasticity solution, but are not after the emission. The critical stress intensity factor corresponding to the dislocation nucleation KIIe is dependent on the loading rate KII. The separations of a pair of partial dislocations and the full dislocations are also dependent on the loading rate. When the first partial dislocation is blocked, a pileup of dislocations can be set up. It is also found that the dislocation can move at subsonic wave speed (less than the shear...